QUESTION 9 Solve for R: R - 2 = W

Answers

Answer 1

Answer:

Step-by-step explanation:

R-2=W

R-2(+2)=W+2

R=W+2

Key concept:

x+(−x)=0

If we have a+x=b, adding the opposite of a to both side we have:

a+x+(−a)=b+(−a)⟺x=b−a

Answer 2

The formula is:

R = W + 2

Work/explanation:

Rearrange the formula for R.

All we should do is add 2 to each side :

R - 2 = W

R = W + 2

Hence, this is the right answer.


Related Questions

Question 2 Multiple Choice Worth 5 points)
(Reflections MC)
Triangle DEF has vertices at D(-3, 5), E(-10, 4), and F(-11, 8). Triangle D'EF is the image of triangle DEF after a reflection. Determine the line of reflection if E' is located at (10, 4)
Oy=-4
Ox-10
Oy-axis
Ox-axis



please help me i need this asap

Answers

The correct answer is "Oy-axis" as it represents the line of reflection for triangle DEF to triangle D'EF.

To determine the line of reflection that maps triangle DEF to triangle D'EF, we can examine the coordinates of the corresponding vertices.

Given that E' is located at (10, 4) and the corresponding vertex E in triangle DEF is at (-10, 4), we can observe that the x-coordinate of E' is the negation of the x-coordinate of E.

This suggests that the line of reflection is the y-axis. A reflection across the y-axis results in a transformation where the x-coordinate of each point is negated while the y-coordinate remains the same.

Since "Oy-axis" indicates the line of reflection from triangle DEF to triangle D'EF, it is the appropriate response.

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what number should go in box a on this number line?

Answers

Answer:

1/4 I think

You haven't said which number line, so please provide some context.

Please help!!
If z1=3+3i and z2=7(cos(5pi/9)+isin(5pi/9)) then z1z2=?

Answers

z1 = 3 + 3i and z2 = 7(cos(5π/9) + i sin(5π/9)). z1z2, we first need to convert z2 into Rectangular form using the trigonometric form of complex numbers.z1z2 = 42 √2 cos(13π/36) + i 42 √2 sin(13π/36).Thus, the answer is z1z2 = 42 √2 cos(13π/36) + i 42 √2 sin(13π/36).

Given that, z1 = 3 + 3i and z2 = 7(cos(5π/9) + i sin(5π/9)).To find z1z2, we first need to convert z2 into rectangular form using the trigonometric form of complex numbers.

As we know, cosθ = Re^(iθ), where Re is the real part and i is the imaginary part.

Therefore, cos(5π/9) = Re^(i5π/9) = Re^(iπ/9) * Re^(i2π/3) = cos(π/9) + i sin(π/9) * (-1/2 + i √3/2) = (7/2) cos(π/9) - (7/2) sin(π/9) i √3 and sinθ = Im^(iθ),

where Im is the imaginary part and i is the imaginary unit.

Therefore, sin(5π/9) = Im^(i5π/9) = Im^(iπ/9) * Im^(i2π/3) = sin(π/9) + i cos(π/9) * (-1/2 + i √3/2) = (7/2) sin(π/9) + (7/2) cos(π/9) i √3So, z2 = 7(cos(5π/9) + i sin(5π/9)) = 7[(7/2) cos(π/9) - (7/2) sin(π/9) i √3 + (7/2) sin(π/9) + (7/2) cos(π/9) i √3]= 7(2 cos(π/9) + i 2 sin(π/9))= 14 cos(π/9) + i 14 sin(π/9)Now, z1z2= (3 + 3i)(14 cos(π/9) + i 14 sin(π/9))= 42 cos(π/9) + i 42 sin(π/9) + 42i cos(π/9) - 42 sin(π/9)= 42(cos(π/9) + i sin(π/9)) (1 + i)= 42(cos(π/9) + i sin(π/9)) √2 cis(π/4)= 42 √2 cos(π/9 + π/4) + i 42 √2 sin(π/9 + π/4)

Therefore, z1z2 = 42 √2 cos(13π/36) + i 42 √2 sin(13π/36).Thus, the answer is z1z2 = 42 √2 cos(13π/36) + i 42 √2 sin(13π/36).

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Answer:

[tex]21\sqrt{2} (cos\frac{29\pi }{36} +i sin\frac{29\pi }{36} )[/tex]

Step-by-step explanation:

Convert z1 to trig form, multiply the modulus and add the angles together with a common denominator of 36

is 7 1/5 x 49 7/5 equivalent to 49

Answers

First change the mixed numbers into improper fractions

7 1/5 becomes. 36/5
49 7/5 becomes. 252/5

Now multiply. 36/5. x. 252/5 = 9072/25

9072/25 becomes. 362.88 so

No it is not equivalent to 49

Jane bought 6 boxes of beads. She used 14 of it to make face mask holders and also gave 12 of the boxes to her sister. How many boxes of beads were left?

Answers

Jane has 6 - 14 - 12 = -20 boxes of beads left.

Jane initially had 6 boxes of beads.

She used 14 of those boxes to make face mask holders and gave 12 boxes to her sister.

To find out how many boxes of beads she has left, we need to subtract the boxes used and given away from the initial number.

First, let's calculate the total number of boxes used and given away:

Total boxes used and given away = Boxes used for face mask holders + Boxes given to sister

Total boxes used and given away = 14 + 12

Total boxes used and given away = 26

Next, we can subtract the total boxes used and given away from the initial number of boxes Jane had:

Boxes left = Initial number of boxes - Total boxes used and given away

Boxes left = 6 - 26

Boxes left = -20

The result is -20, which implies that Jane has a deficit of 20 boxes of beads.

This means she doesn't have any boxes of beads left; she has a shortage of 20 boxes based on the activities she performed.

It's important to note that having a negative value indicates that Jane doesn't have enough boxes to fulfill her activities.

If the result were positive, it would represent the number of boxes remaining.

However, in this case, Jane has used and given away more boxes than she initially had, resulting in a negative value.

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QUESTION 5: CALCULATIONS. a) b) c) 4.516 x 215 486,71 (29,774 +4,5) - 8 451 + 15​

Answers

a) 4.516 multiplied by 215 equals 971.54.

b) (29.774 + 4.5) minus 8,451 equals -8,416.726.

c) 486.71 minus (29.774 + 4.5) plus 8,451 plus 15 equals 8,903.451.

a) To calculate 4.516 multiplied by 215, we multiply the two numbers:

4.516 x 215 = 971.54

Therefore, the result is 971.54.

b) To evaluate the expression (29.774 + 4.5) - 8,451, we perform the addition and then the subtraction:

29.774 + 4.5 = 34.274

34.274 - 8,451 = -8,416.726

Therefore, the result is -8,416.726.

c) To calculate 486.71 minus (29.774 + 4.5) plus 8,451 plus 15, we first perform the addition within parentheses, then the subtraction, and finally the addition:

(29.774 + 4.5) = 34.274

486.71 - 34.274 = 452.436

452.436 + 8,451 = 8,903.436

8,903.436 + 15 = 8,903.451

Therefore, the result is 8,903.451.

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Which graph best represents the solution to the following pair of equations?

y = 4x + 2
y = x + 5

A graph is plotted with values ranging from negative 10 to 10 on both x axis and y axis at increments of 1. Two lines having equations y is equal to 4 times x plus 2 and y is equal to x plus 5 are plotted. These 2 lines intersect at the ordered pair 1, 6.
A graph is plotted with values ranging from negative 10 to 10 on both x axis and y axis at increments of 1. Two lines having equations y is equal to 4 times x plus 2 and y is equal to x plus 5 are plotted. These 2 lines intersect at the ordered pair 2, negative7.
A graph is plotted with values ranging from negative 10 to 10 on both x axis and y axis at increments of 1. Two lines having equations y is equal to 4 times x plus 2 and y is equal to x plus 5 are plotted. These 2 lines intersect at the ordered pair negative 1, negative 6.
A graph is plotted with values ranging from negative 10 to 10 on both x axis and y axis at increments of 1. Two lines having equations y is equal to 4 times x plus 2 and y is equal to x plus 5 are plotted. These 2 lines intersect at the ordered pair negative 2, 7.

Answers

The given pair of equations is y = 4x + 2 and y = x + 5, and we are to determine which of the given graphs represents their solution. The first equation is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Comparing this with the given equation, we see that its slope is 4 and y-intercept is 2.

The second equation is also in slope-intercept form, y = mx + b. Comparing it with the given equation, we see that its slope is 1 and y-intercept is 5.Since we have two lines, we need to find their point of intersection. Substituting y = 4x + 2 into y = x + 5, we have4x + 2 = x + 5Simplifying the equation, we get3x = 3, which gives x = 1.

Substituting this value of x into either of the equations, say y = 4x + 2, we have y = 4(1) + 2 = 6. Hence, the point of intersection is (1, 6). Now, let's examine the given graphs and see which one has (1, 6) as a point of intersection:

Graph 1: The line y = 4x + 2 passes through (0, 2) and has a slope of 4, which means it will be steeper than the line y = x + 5. The line y = x + 5 passes through (0, 5) and has a slope of 1, which means it will be flatter than the line y = 4x + 2. Hence, these two lines cannot intersect at (1, 6). Graph 1 is not the solution.

Graph 2: The line y = 4x + 2 passes through (-1, -2) and has a slope of 4, which means it will be steeper than the line y = x + 5. The line y = x + 5 passes through (0, 5) and has a slope of 1, which means it will be flatter than the line y = 4x + 2. Hence, these two lines cannot intersect at (1, 6). Graph 2 is not the solution.

Graph 3: The line y = 4x + 2 passes through (-1, -2) and has a slope of 4, which means it will be steeper than the line y = x + 5. The line y = x + 5 passes through (0, 5) and has a slope of 1, which means it will be flatter than the line y = 4x + 2.

Hence, these two lines cannot intersect at (1, 6). Graph 3 is not the solution.Graph 4: The line y = 4x + 2 passes through (0, 2) and has a slope of 4, which means it will be steeper than the line y = x + 5. The line y = x + 5 passes through (0, 5) and has a slope of 1, which means it will be flatter than the line y = 4x + 2. Hence, these two lines cannot intersect at (1, 6). Graph 4 is not the solution.

Therefore, none of the given graphs represents the solution to the pair of equations.

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You need to arrange 9 of your favorite books along a small shelf. How many different ways can you arrange the​ books, assuming that the order of the books makes a difference to​ you?

Answers

Answer:

362880

Step-by-step explanation:

There are 9 ways to place the first book

There are 8 ways to place the second book given the first book

...

There is 1 way to place the ninth book given the eighth.

This can be represented by 9! (9 factorial), which is 9*8*7*6*5*4*3*2*1 = 362880.

The question reads The graph of y=f(x) is shown below (dashed curve). Manipulate the green draggable points to obtain the graph of y=f(-x+5)-4 (solid curve). Someone help me please!!!

Answers

To obtain the graph of y = f(-x+5)-4 from y = f(x), shift the graph 5 units to the right, reflect it across the y-axis, and shift it 4 units downward.

To obtain the graph of y = f(-x+5)-4 from the graph of y = f(x), follow these steps:

1. Locate the point (5, -4) on the dashed curve. This is the new vertex of the transformed function.

2. Observe the distance between the original vertex of the function and the x-axis. Let's call this distance "a".

3. Measure the horizontal distance between the new vertex (5, -4) and the original vertex of the function. Let's call this distance "b".

4. Shift the entire dashed curve "b" units to the right. This can be done by moving all the points on the graph horizontally "b" units to the right.

5. Reflect the shifted dashed curve about the y-axis. This can be done by changing the signs of the x-coordinates of all the points on the graph.

6. Finally, shift the reflected curve "a" units downward. This can be achieved by moving all the points on the graph vertically "a" units downward.

By following these steps, you will be able to obtain the graph of y = f(-x+5)-4 (solid curve) using the graph of y = f(x) (dashed curve).

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A popular restaurant has 48 tables. On each table are 3 different types of salsa. In one day, all of the tables are used for 9 different sets of customers. Which expression can be used to estimate how many containers of salsa are needed for all the tables in one day?

A 50 × 9
B 16 × 3 × 9
C 50 × 3 × 10
D 40 × 5 × 5

Answers

The expression to estimate the number of containers of salsa needed is: 48 × 3 × 9. none of the option is correct.

To estimate how many containers of salsa are needed for all the tables in one day, we need to consider the total number of tables and the number of salsa containers required for each table.

Given that there are 48 tables and each table has 3 different types of salsa, we can estimate the total number of containers needed by multiplying the number of tables by the number of salsa types.

However, we also need to account for the fact that there are 9 different sets of customers throughout the day. Each set of customers will use all the tables, so we need to multiply the estimated number of containers by the number of sets of customers to get an accurate estimation for the day.

Let's analyze the options provided:

A) 50 × 9: This option assumes there are 50 tables, which is incorrect based on the given information.

B) 16 × 3 × 9: This option assumes there are 16 tables, which is incorrect based on the given information.

C) 50 × 3 × 10: This option assumes there are 50 tables and 10 different sets of customers. Although the number of tables is incorrect, this option accounts for the number of salsa types and the number of sets of customers. However, it does not accurately represent the given scenario.

D) 40 × 5 × 5: This option assumes there are 40 tables and 5 different sets of customers. It also considers the number of salsa types. However, it does not accurately represent the given scenario as the number of tables is incorrect.

None of the options provided accurately represent the given scenario. The correct expression to estimate the number of containers of salsa needed for all the tables in one day would be:48 × 3 × 9

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PLEASE ANSWER AND FILL IN THE BOX if needed

Answers

The true statement in the augmented matrix is that  (d) the system is inconsistent

How to determine the solution to the system

From the question, we have the following parameters that can be used in our computation:

The augmented matrix

In the augmented matrix, we have the number of rows and columns to be

Rows = 4 and Columns = 5

This means that

There are 4 equations in the system and there are 5 variables

The general rule is that

The number of equations must be at least the number of variables

Hence, there is no solution in the system

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Find the volume of the region bounded above by the paraboloid z=x^{2} +y^{2} and below by the triangle enclosed by the lines y=x, x=0 and x+y=6 in the​ xy-plane.\\
what is the volume under the paraboloid

Answers

The volume of the region bounded by the paraboloid and the triangle is 96 cubic units.

To find the volume of the region bounded by the paraboloid and the triangle, we can set up a double integral in the xy-plane. The paraboloid is represented by the equation z = x^2 + y^2, which forms a circular surface that extends infinitely in the positive z-direction. The triangle is defined by the lines y = x, x = 0, and x + y = 6 in the xy-plane.

To set up the integral, we need to determine the limits of integration for x and y. From the equations of the triangle, we can see that x ranges from 0 to 6, and y ranges from x to 6 - x. This means that for each value of x, y will vary within the corresponding range.

The volume can be calculated by integrating the function z = x^2 + y^2 over the given region. This gives us the double integral:

V = ∫∫[x^2 + y^2] dA,

where dA represents the differential area element in the xy-plane.

Integrating over the limits of integration for x and y, the volume can be expressed as:

V = ∫[0 to 6] ∫[x to 6 - x] (x^2 + y^2) dy dx.

To evaluate this double integral, we need to perform the integration step by step. First, we integrate with respect to y, treating x as a constant:

V = ∫[0 to 6] [xy + (y^3)/3] evaluated from y=x to y=6-x dx.

Simplifying the expression inside the square brackets, we have:

V = ∫[0 to 6] [x(6-x) + ((6-x)^3)/3 - x(x) - (x^3)/3] dx.

Combining like terms, we get:

V = ∫[0 to 6] [(6x - x^2) + (216 - 36x + 3x^2 - x^3)/3 - x^2 - (x^3)/3] dx.

Simplifying further, we have:

V = ∫[0 to 6] [(216 - 36x + 3x^2 - x^3)/3] dx.

Now, we integrate with respect to x:

V = [(72x - 18x^2 + x^3/3) / 3] evaluated from x=0 to x=6.

Substituting the limits of integration, we get:

V = [(72(6) - 18(6^2) + (6^3)/3) / 3] - [(72(0) - 18(0^2) + (0^3)/3) / 3].

Simplifying the expression, we find:

V = [(432 - 216 + 72) / 3] - [0 / 3].

V = 288 / 3.

V = 96.

Therefore, the volume of the region bounded by the paraboloid and the triangle is 96 cubic units.

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can some1 help. 20 points.

Answers

The transformation involves a vertical shift downward by 2 units, a vertical stretching by a factor of 1/9, and no horizontal shift or scaling.

Suppose an investment of $6000 at r% per annum compounded annually is worth
$16000 in 10 years.

(a) Find the value of r.
(b) Find the time taken for the investment to be worth at least $40, 000.

Answers

(a) The annual interest rate is approximately 14.79%.

(b) It would take approximately 6.24 years for the investment to be worth at least $40,000.

(a) To find the value of r, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

A = Final amount

P = Principal amount (initial investment)

r = Annual interest rate (in decimal form)

n = Number of times interest is compounded per year

t = Number of years

In this case, the principal amount P is $6000, the final amount A is $16000, the number of years t is 10, and the interest is compounded annually (n = 1). We need to solve for r.

16000 = 6000(1 + r/1)^(1*10)

Dividing both sides by 6000:

16000/6000 = (1 + r)^10

Simplifying the left side:

2.6667 = (1 + r)^10

Taking the 10th root of both sides:

(1 + r) = (2.6667)^(1/10)

(1 + r) ≈ 1.1479

Subtracting 1 from both sides:

r ≈ 1.1479 - 1

r ≈ 0.1479

Therefore, the annual interest rate is approximately 14.79%.

(b) To find the time taken for the investment to be worth at least $40,000, we can again use the compound interest formula and solve for t:

40000 = 6000(1 + 0.1479/1)^(1*t)

Dividing both sides by 6000:

40000/6000 = (1 + 0.1479)^t

6.6667 = (1.1479)^t

Taking the logarithm (base 1.1479) of both sides:

log base 1.1479 (6.6667) = t

t ≈ 6.24

Therefore, it would take approximately 6.24 years for the investment to be worth at least $40,000.

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A group of friends orders a pizza. One person ate 1/4 of the pizza, one ate 1/8 of the pizza, and another ate 1/3 of the pizza. How much is left??

Answers

Answer:

Step-by-step explanation:

Pls help!
I’ll mark whoever gets this right in four hours brainiest!

The area below is a field (inside the track). What is the amount of money necessary to re-sod the field at $4.99/m (small two beside m)?

Answers

[tex]{\huge{\bold{\underline{\pink{\mathfrak{Answer}}}}}}[/tex]

______________________________________

→ To calculate the area of the field:

A = length x height

A = 100 m x 50 m

A = 5000 m²

______________________________________

→ To calculate the amount of money:

Cost = A x cost per square meter

Cost = 5000 m² x $4.99/m²

Cost = $24,950

______________________________________

→ Therefore, it would cost $24,950.

9. Consider the following short run production function: Q=61² -0.41³ a. Find the value of L that maximizes output b. Find the value of L that maximizes marginal product c. Find the value of L that maximizes average product​

Answers

a. The value of L that maximizes output is approximately L ≈ 99.19.

b. The value of L that maximizes marginal product is approximately L ≈ 124.19.

c. The value of L that maximizes average product is approximately L ≈ 100.17.

To find the value of L that maximizes output (Q) in the short run production function Q = 61² - 0.41³, we need to find the value of L that yields the highest possible output.

a. To maximize output, we take the derivative of the production function with respect to L and set it equal to zero:

dQ/dL = 2(61)L - 3(0.41²)L² = 0

Simplifying the equation, we have:

122L - 1.23L² = 0

Factoring out L, we get:

L(122 - 1.23L) = 0

Setting each factor equal to zero, we have:

L = 0 (one possible solution)

122 - 1.23L = 0

Solving the second equation, we find:

L ≈ 99.19

Therefore, the value of L that maximizes output is approximately L ≈ 99.19.

b. To find the value of L that maximizes marginal product (MP), we take the derivative of the production function with respect to L:

dMP/dL = 2(61) - 6(0.41²)L

Setting this derivative equal to zero, we have:

2(61) - 6(0.41²)L = 0

Simplifying the equation, we find:

122 - 0.984L = 0

Solving for L, we have:

L ≈ 124.19

Therefore, the value of L that maximizes marginal product is approximately L ≈ 124.19.

c. To find the value of L that maximizes average product (AP), we use the formula:

AP = Q/L

Taking the derivative of AP with respect to L, we have:

dAP/dL = (dQ/dL)/L - (Q/L²)

Setting this derivative equal to zero, we find:

[(2(61)L - 3(0.41²)L²)/L] - [(61² - 0.41³)/L²] = 0

Simplifying the equation, we have:

2(61) - 3(0.41²)L = (61² - 0.41³)/L

Rearranging the equation, we get:

L³ = (61² - 0.41³)/(2(61) - 3(0.41²))

Solving for L, we find:

L ≈ 100.17

Therefore, the value of L that maximizes average product is approximately L ≈ 100.17.

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What is the solution to the inequality below?
2-2x>-20
A. x<11
B. x<10
C. x<9
D. x>12

Answers

Answer:

A

Step-by-step explanation:

subtract 2 from both sides and then divide by -2 on both sides.

when dividing by a negative sign, remember to switch the inequality sign (in this case from > to <)

To pay for a home improvement project that totals $20,000, a homeowner is choosing between two different credit card loans with an interest rate of 9%. The first credit card compounds interest quarterly, while the second credit card compounds monthly. The homeowner plans to pay off the loan in 10 years.

Part A: Determine the total value of the loan with the quarterly compounded interest. Show all work and round your answer to the nearest hundredth. (4 points)

Part B: Determine the total value of the loan with the monthly compounded interest. Show all work and round your answer to the nearest hundredth. (4 points)

Part C: What is the difference between the total interest accrued on each loan? Explain your answer in complete sentences. (2 points)



Please only responded if you know how to do it, will give the brainiest to however answers it correctly

Answers

The total value of the loan with quarterly compounded interest is approximately $45,288.38, while the total value of the loan with monthly compounded interest is approximately $45,634.84. The difference in total interest accrued is approximately $346.46.

Part A: To determine the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:

A = P(1 + r/n)^(nt),

where:

A is the total value of the loan,

P is the principal amount (initial loan amount),

r is the interest rate (in decimal form),

n is the number of times interest is compounded per year,

and t is the number of years.

Given:

P = $20,000,

r = 9% or 0.09,

n = 4 (quarterly compounding),

t = 10 years.

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/4)^(4*10).

Calculating this value, we find:

A ≈ $45,288.38.

Therefore, the total value of the loan with quarterly compounded interest is approximately $45,288.38.

Part B: To determine the total value of the loan with monthly compounded interest, we follow the same formula but with a different value for n:

n = 12 (monthly compounding).

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/12)^(12*10).

Calculating this value, we find:

A ≈ $45,634.84.

Therefore, the total value of the loan with monthly compounded interest is approximately $45,634.84.

Part C: The difference between the total interest accrued on each loan can be calculated by subtracting the principal amount from the total value of each loan.

For the loan with quarterly compounding:

Total interest = Total value - Principal

Total interest = $45,288.38 - $20,000

Total interest ≈ $25,288.38.

For the loan with monthly compounding:

Total interest = Total value - Principal

Total interest = $45,634.84 - $20,000

Total interest ≈ $25,634.84.

The difference between the total interest accrued on each loan is approximately $346.46.

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PLEASE HELP
A formula connecting speed (s), distance (d) and time (t) is s = d/t d = 160 to 2 significant figures t=7,2 to 2 significant figures Work out the upper and lower bounds for s. Give your answers to 3 significant figures.​

Answers

Answer:

upper: 23.1lower: 21.4

Step-by-step explanation:

You want the upper and lower bounds for speed, given that distance 160 was traveled in time 7.2 (both to 2 significant figures).

Speed

As the problem statement tells you, speed is proportional to distance and inversely proportional to time.

Bounds

The upper bound for speed will be the upper bound for distance divided by the lower bound for time.

  165/7.15 ≈ 23.1 . . . . . speed units (maximum)

The lower bound will be the lower bound for distance divided by the upper bound for time.

  155/7.25 ≈ 21.4 . . . . . speed units (minimum)

__

Additional comment

Dividing the nominal values, the nominal speed is 22.22... speed units. Rounded to 2 sf, this would be 22 speed units. The implied bounds are 22±0.5. You can see that the upper and lower bounds computed here are actually about 22.25±0.85.

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A = 11 + 2 (x-6) + 4 (-3-6)

Answers

Answer:

A = 2x - 37

Step-by-step explanation:

A

= 11 + 2(x - 6) + 4(-3 - 6)

= 11 + 2x - 12 - 12 - 24

= 2x - 37

write an equation of the form y=mx for the line shown below (-1,4)

Answers

The equation of the Line of the form y = mx is y = -x + 3.

To write an equation of the form y = mx for the line shown below (-1,4), we need to determine the slope (m) of the line first.

Let (x₁, y₁) = (-1, 4) be a point on the line. Now let's find another point on the line. Let's say we have another point (x₂, y₂) = (1, 2).The slope (m) of the line can be calculated using the formula:m = (y₂ - y₁) / (x₂ - x₁)Substituting the values,

we get:m = (2 - 4) / (1 - (-1))= -2 / 2= -1

Now that we know the slope of the line, we can use the point-slope form of the equation of a line to write the equation of the line:y - y₁ = m(x - x₁)Substituting the values, we get:y - 4 = -1(x - (-1))y - 4 = -1(x + 1)y - 4 = -x - 1y = -x - 1 + 4y = -x + 3

Therefore, the equation of the line is y = -x + 3 in slope-intercept form. Since the question specifically asks for the equation of the form y = mx, we can rewrite the equation in this form by factoring out the slope:y = -x + 3y = (-1)x + 3

Thus, the equation of the line of the form y = mx is y = -x + 3.

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4, 36, 18, 6, 45, 15, 8, 44 what is the next number

Answers

The next number that continues the sequence: 4, 36, 18, 6, 45, 15, 8, 44 is 11.

How to derive the next value of a sequence

Let us identify each of the numbers position:

n₁ = 4,

n₂ = 36,

n₃ = 18,

n₄ = 6,

n₅ = 45,

n₆ = 15,

n₇ = 8,

n₈ = 44

n₁, n₄, n₇ formed a sequence such that the common difference is:

d = n₄ - n₁ = n₇ - n₄ = 2

The next value (n₁₀) in this sequence will be

n₁₀ = n₇ + d

n₁₀ = 8 + 2 = 10

But we need to calculate n₉:

Consider the following,

n₂ and n₃

n₂/n₃ = 36/18 = 2

n₅ and n₆

n₅/n₆ = 45/15 = 3

n₈ and n₉

n₈/n₉ = 44/n₉ = 4

n₉ = 44/4 = 11

Therefore the 9th and 10th positions of the sequence are 11 and 10 respectively.

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Which of the lines or segments below is tangent to circle P?

A) <—>
ZM
B)——
EX
C)——
LE
D)<—>
TX

Answers

Answer:

A) Line ZM is tangent to circle P.

Let g(x) be the indicated transformation of f(x) = −|3x| − 4. Stretch the graph of f(x) = −|3x| − 4 vertically by a factor of 3 and reflect it across the x-axis. Identify the rule and graph of g(x).

Answers

The final rule for g(x) is g(x) = 3|3x| + 12.

To stretch the graph of f(x) = −|3x| − 4 vertically by a factor of 3, we multiply the function by 3. This will result in a vertical stretching of the graph.

So, the rule for g(x) is g(x) = 3f(x).

Now, let's find the expression for g(x) using the given function f(x) = −|3x| − 4:

g(x) = 3f(x)

g(x) = 3(-|3x| - 4)

g(x) = -3|3x| - 12

This is the expression for g(x), which represents the transformed graph.

To reflect the graph of g(x) across the x-axis, we change the sign of the function. This means that the negative sign in front of the absolute value will become positive, and the positive sign in front of the constant term will become negative.

Therefore, the final rule for g(x) is g(x) = 3|3x| + 12.

Now, let's consider the graph of g(x). The graph will have the same shape as f(x), but it will be stretched vertically by a factor of 3 and reflected across the x-axis.

The original graph of f(x) = −|3x| − 4 is a V-shaped graph that opens downward and passes through the point (0, -4). The transformed graph of g(x) will have a steeper V-shape, opening downward, and passing through the point (0, 12) instead of (0, -4).

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g(x)+4(5-x) , find g(-7)

Answers

The value of the function g(-7) when evaluated is 48

How to evaluate the function

From the question, we have the following parameters that can be used in our computation:

g(x) = 4(5 - x)

Also, we have

g(-7)

The above means that the value of x is

x = -7

Substitute the known values in the above equation, so, we have the following representation

g(-7) = 4(5 + 7)

Evaluate

g(-7) = 48

Hence, the function when evaluated is 48

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Given rhombus LMNO below. If m

Answers

The measure of angle LOP is given as follows:

m < LOP = 52º.

How to obtain the angle measure?

The segment OP bisects the angle O of the rhombus into two smaller angles, which are NOP and LOP.

.

A bisection means that the larger angle is divided into two smaller angles of equal measure.

The measure of angle NOP is given as follows:

m < NOP = 52º.

Hence the measure of angle LOP is given as follows:

m < LOP = 52º.

Missing Information

The final sentence is to find the measure of angle LOP.

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Find the savings plan balance after 12 months with an APR of 3% and monthly payments of $200

Answers

To find the savings plan balance after 12 months with an APR of 3% and monthly payments of $200, you can use the formula for the future value of an annuity. So the savings plan balance after 12 months with an APR of 3% and monthly payments of $200 is $2,492.80.

The formula for the future value of an annuity: FV = PMT * [(1 + r/n)^(n*t) - 1] / (r/n), where: FV is the future value of the annuity, PMT is the periodic payment, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

Using this formula, we have r = 3% = 0.03n = 12 (monthly payments)t = 12/12 = 1 year PMT

= $200FV

= 200 * [(1 + 0.03/12)^(12*1) - 1] / (0.03/12)FV

= 200 * [(1.0025)^12 - 1] / (0.0025)FV

= 200 * 0.03115 / 0.0025FV = $2,492.80

Therefore, the savings plan balance after 12 months with an APR of 3% and monthly payments of $200 is $2,492.80.

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Which of the following is the best use for the sign chart when graphing
rational functions?
OA. To check whether F(x) is a straight or curved line for values of x
B. To check whether F(x) has a positive or negative slope
OC. To check whether F(x) reaches a maximum or a minimum
OD. To check whether F(x) is positive or negative for values of x

Answers

The best use for a sign chart when graphing rational functions is Option D: To check whether F(x) is positive or negative for values of x.

A sign chart, also known as an interval chart, is a tool used to determine the sign (positive or negative) of a function over different intervals. When graphing rational functions, it is essential to identify the intervals where the function is positive or negative.

By constructing a sign chart for the rational function, you can analyze the behavior of the function and determine its sign over different intervals. This information is crucial for sketching an accurate graph of the rational function.

The sign chart helps identify intervals where the function is positive (above the x-axis) or negative (below the x-axis), which directly impacts the shape and position of the graph. It provides information about the regions where the function is increasing or decreasing.

The best use for a sign chart when graphing rational functions is Option D: To check whether F(x) is positive or negative for values of x. Options A, B, and C are not the best uses for a sign chart when graphing rational functions. Checking whether the function is a straight or curved line (Option A), the slope (Option B).

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Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 41 minutes and standard deviation 19 minutes. A researcher observed 17 students who entered the library to study. Round all answers to 4 decimal places where possible.

What is the distribution of
?
~ N(
,
)
What is the distribution of

?

~ N(
,
)
What is the distribution of
?
~ N(
,
)
If one randomly selected student is timed, find the probability that this student's time will be between 37 and 43 minutes.
For the 17 students, find the probability that their average time studying is between 37 and 43 minutes.
Find the probability that the randomly selected 17 students will have a total study time less than 731 minutes.
For part e) and f), is the assumption of normal necessary? YesNo
The top 15% of the total study time for groups of 17 students will be given a sticker that says "Great dedication". What is the least total time that a group can study and still receive a sticker?
minutes

Answers

A. The distribution of the time spent is X ~ N(41, 19²)

B. The distribution of the sample mean is x-bar ~ N(41, (19²)/17)

C. The distribution of the total study time is X_total ~ N(17 × 41, 17 × 19²)

D. The probability is 0.3168

E. The probability is 0.6837

F. The probability is 0.6368

G. The least total time that a group of 17 students can study and still receive a sticker for "Great dedication" is approximately 350.3618 minutes.

How did we get the values?

To answer these questions, use the properties of the normal distribution. Given the mean and standard deviation provided, calculate the required probabilities and values.

a) The distribution of the time spent studying by a single student is given by:

X ~ N(41, 19²)

b) The distribution of the sample mean for a sample size of 17 students is given by:

x-bar ~ N(41, (19²)/17)

c) The distribution of the total study time for 17 students is given by:

X_total ~ N(17 × 41, 17 × 19²)

d) To find the probability that a randomly selected student's time is between 37 and 43 minutes, use the normal distribution:

P(37 ≤ X ≤ 43) = P((37 - 41) / 19 ≤ Z ≤ (43 - 41) / 19)

Using standard normal distribution tables or a calculator, find the corresponding probabilities for Z = -0.2105 and Z = 0.1053:

P(37 ≤ X ≤ 43) ≈ P(-0.2105 ≤ Z ≤ 0.1053) ≈ 0.3168

e) To find the probability that the average time studying for the 17 students is between 37 and 43 minutes, use the distribution of the sample mean:

P(37 ≤ x-bar ≤ 43) = P((37 - 41) / (19 / √(17)) ≤ Z ≤ (43 - 41) / (19 / √(17)))

Again, using standard normal distribution tables or a calculator, find the corresponding probabilities for Z = -0.8292 and Z = 0.8292:

P(37 ≤ x-bar ≤ 43) ≈ P(-0.8292 ≤ Z ≤ 0.8292) ≈ 0.6837

f) To find the probability that the randomly selected 17 students will have a total study time less than 731 minutes, use the distribution of the total study time:

P(X_total < 731) = P((X_total - (17 × 41)) / (√(17) × 19) < (731 - (17 * 41)) / (√(17) × 19))

Again, using standard normal distribution tables or a calculator, find the corresponding probability for Z ≈ 0.3503:

P(X_total < 731) ≈ P(Z < 0.3503) ≈ 0.6368

g) Yes, the assumption of normality is necessary for parts e) and f) since we are using the properties of the normal distribution.

h) To find the least total time that a group of 17 students can study and still receive a sticker for "Great dedication," find the cutoff point where the top 15% of the distribution lies.

Using the inverse normal distribution (also known as the Z-score or percent-point function), we can find the Z-score corresponding to the top 15% of the distribution. The Z-score for the top 15% is approximately 1.0364.

Now, solve for the least total time using the formula for the total study time:

X_total = (Z × √(17) × 19) + (17 × 41)

Substituting Z = 1.0364, we can calculate:

X_total ≈ (1.0364 × √(17) × 19) + (17 × 41) ≈ 350.3618

Therefore, the least total time that a group of 17 students can study and still receive a sticker for "Great dedication" is approximately 350.3618 minutes.

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