The correct equation for the parabola is [tex]x^2 = 16(y - 4)[/tex].
The standard equation of the parabola in the graph can be determined based on its characteristics.
Given:
Vertex: (0, 4)
Focus: (4, 4)
P (the distance from the vertex to the focus or directrix): 4
We can conclude that the parabola opens to the right because the axis is horizontal.
The standard equation of a parabola with a horizontal axis and vertex (h, k) is given by:
[tex](x - h)^2 = 4p(y - k)[/tex]
In this case, the vertex is (0, 4), so the equation becomes:
[tex](x - 0)^2 = 4p(y - 4)[/tex]
Now, we need to determine the value of p. The distance from the vertex to the focus is p, which is 4 in this case.
Therefore, the standard equation of the parabola in the graph is:
[tex]x^2 = 4(4)(y - 4)\\x^2 = 16(y - 4)[/tex]
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Please help me asap
Answer:
A. x+y+z=35,000
4x+6y+12x-194,000
2y-z=0
Step-by-step explanation:
The system of equations is:
x + y + z = 35,000 (total investment is $35,000) 4x + 6y + 12z = 19,400 (the investor wants an annual return of $1940 on the three investments) y = 2z (the client wants to invest twice as much in A bonds as in B bonds)
The answer is A.
The first equation represents the total amount of money invested in the three types of bonds. The second equation represents the total annual return on the investments, which is equal to the sum of the individual returns on each type of bond. The third equation represents the client's preference for investing in A bonds over B bonds.
The system of equations can be used to solve for the values of x, y, and z, which represent the amounts invested in AAA, A, and B bonds, respectively.
Answer:
[tex]\textsf{A.} \quad \begin{cases}x+y+z=35000\\4x+6y+12z=194000\\2z-y=0\end{cases}[/tex]
Step-by-step explanation:
A system of equations is a set of two or more equations with the same variables. It allows us to model and solve problems that involve multiple equations and unknowns.
An investment firm recommends that a client invest in bonds rated AAA, A, and B. The definition of the variables are:
Let x be the number of AAA bonds.Let y be the number of A bonds.Let z be the number of B bonds.The average yield on each of the three bonds is:
AAA bonds = 4%A bonds = 6%B bonds = 12%We have been told that the total investment is $35,000. Therefore, the equation that represents this is the sum of the three investments equal to 35,000:
[tex]x+y+z=35000[/tex]
To find the annual return on each investment, multiply the number of bonds by the average yield (in decimal form). Given the investor wants a total annual return of $1940 on the three investments, the equation that represents this is the sum of the product of the investment amount for each bond type and its corresponding yield, equal to $1940.
[tex]0.04x+0.06y+0.12z=1940[/tex]
Multiply all terms by 100:
[tex]4x+6y+12z=194000[/tex]
Finally, given the client wants to invest twice as much in A bonds as in B bonds, the equation is:
[tex]y=2z[/tex]
Subtract y from both sides of the equation:
[tex]2z-y=0[/tex]
Therefore, the system of equations the models the given scenario is:
[tex]\begin{cases}x+y+z=35000\\4x+6y+12z=194000\\2z-y=0\end{cases}[/tex]
Help me please. You can get 20 points
a. The marginal profit function Py is Py = -30x + 47y - 915 and
b. Change in profit if price increase by 1 cent is 831 cents.
Understanding Profit FunctionTo find the marginal profit functions Px and Py, we need to find the partial derivatives of the profit function P(x, y) with respect to x and y, respectively.
Given:
P(x, y) = (x - 40)(55 - 4x + 5y) + (y - 45)(70 + 5x - 7y)
a. Marginal profit function Px:
To find Px, we differentiate P(x, y) with respect to x while treating y as a constant:
Px = ∂P/∂x = (∂/∂x) [(x - 40)(55 - 4x + 5y) + (y - 45)(70 + 5x - 7y)]
Expanding the terms and simplifying:
Px = (55 - 4x + 5y) + (x - 40)(-4) + (70 + 5x - 7y)(5)
Simplifying further:
Px = 55 - 4x + 5y - 4x + 40 + 350 + 5x - 7y
Combining like terms:
Px = 355 - 3x - 2y
b. Marginal profit function Py:
Similarly, to find Py, we differentiate P(x, y) with respect to y while treating x as a constant:
Py = ∂P/∂y = (∂/∂y) [(x - 40)(55 - 4x + 5y) + (y - 45)(70 + 5x - 7y)]
Expanding the terms and simplifying:
Py = (x - 40)(5) + (70 + 5x - 7y)(-7) + (y - 45)(5)
Simplifying further:
Py = 5x - 200 - 7y - 490 - 35x + 49y + 5y - 225
Combining like terms:
Py = -30x + 47y - 915
This is the profit function Py.
b. Estimating the daily change in profit:
To estimate the daily change in profit, we need to evaluate Px and Py at the given prices and calculate the change in profit when the prices are increased as specified.
Given initial prices:
First brand price (x) = 70 cents
Second brand price (y) = 73 cents
To estimate the change in profit, we substitute the initial prices into Px and Py and calculate the results:
Px(70, 73) = 355 - 3(70) - 2(73)
= 355 - 210 - 146
= -1
Py(70, 73) = -30(70) + 47(73) - 915
= -2100 + 3431 - 915
= 416
The daily change in profit can be estimated by multiplying the changes in price (1 cent for the first brand and 2 cents for the second brand) with the respective marginal profit functions:
Change in profit = ΔP ≈ Px(70, 73) * 1 + Py(70, 73) * 2
≈ -1 * 1 + 416 * 2
≈ -1 + 832
≈ 831 cents
Therefore, the estimated daily change in profit when the salesperson increases the price of the first label by 1 cent and the price of the second label by 2 cents is 831 cents.
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What is the axis of symmetry of h(x) = 6x2 − 60x + 147?
x = −5
x = −3
x = 3
x = 5
polynomial standard form of x^2-x^6+x^8-5 ?
The standard form of the polynomial x^2 - x^6 + x^8 - 5 is:
x^8 - x^6 + x^2 - 5
To express the polynomial x^2 - x^6 + x^8 - 5 in standard form, we arrange the terms in descending order of their exponents.
The given polynomial can be rewritten as:
x^8 - x^6 + x^2 - 5
In the standard form of a polynomial, the terms are arranged in descending order of their exponents. So, let's rearrange the terms:
x^8 - x^6 + x^2 - 5
The standard form of the polynomial x^2 - x^6 + x^8 - 5 is:
x^8 - x^6 + x^2 - 5
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What graph represents the piecewise-defined function ? y={6 if x <-3, 3 if -32
The graph of the piecewise-defined function will consist of two horizontal line segments.
The piecewise-defined function can be represented using a graph with two separate segments.
First, let's consider the segment where the value of y is 6 when x is less than -3. This means that for any x-value less than -3, the corresponding y-value is 6. This segment will be a horizontal line parallel to the x-axis, located at the y-coordinate of 6.
Next, let's consider the segment where the value of y is 3 when x is greater than or equal to -3 and less than or equal to 2. This means that for any x-value between -3 and 2 (inclusive), the corresponding y-value is 3. This segment will also be a horizontal line parallel to the x-axis, located at the y-coordinate of 3.
To summarize:
For x < -3, y = 6.
For -3 ≤ x ≤ 2, y = 3.
Therefore, Two horizontal line segments make up the graph of the piecewise-defined function. One segment will be located at y = 6, and the other segment will be located at y = 3. The vertical range of the graph will extend to include both y-values (6 and 3), while the horizontal range will depend on the given x-values and the interval specified.
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a^3(b+c)/(a-b)(a-c) + b^3(c+a)/(b-c)(b-a) + a^3(a+b)/(c-a)(c-b) = ab+bc+ca
The value of the algebraic expression is ab+bc+ca.
What is algebraic equation?An algebraic equation is a mathematical statement that contains two equated algebraic expressions formulated by applying algebraic operations such as addition, subtraction, multiplication, division, raising to a power, and extraction of a root to a set of variables
The equation A^3(b+c)/(a-b)(a-c) + b^3(c+a)/(b-c)(b-a) + a^3(a+b)/(c-a)(c-b) = ab+bc+ca
(a-b, a-c, b-c, b-a, c-a, c-b).
Simplifying each fraction, we get
(a^3b + a^3c)/(a^2 - ab - ac + b^2 - bc + c^2) + (b^3c + b^3a)/(b^2 - bc - ba + c^2 - ac + a^2) + (a^4 + a^3b)/(c^2 - ac - ab + b^2 - bc + a^2).
(a-b)(a-c), (b-c)(b-a), and (c-a)(c-b),
ab+bc+ca.
Therefore, the equation A^3(b+c)/(a-b)(a-c) + b^3(c+a)/(b-c)(b-a) + a^3(a+b)/(c-a)(c-b) = ab+bc+ca
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Given that the two expression(r+ a)(r – 15) and r² – br-75 are indentical calculate the value of b
Answer:
b = 10
Step-by-step explanation:
expand expression and compare like terms.
(r + a)(r - 15) ← expand using FOIL
= r² - 15r + ar - 15a ← factor out r from second/ third terms
= r² + r(a - 15) - 15a
compare with r² - br - 75
then
- 15a = - 75 ( divide both sides by - 15 )
a = 5
and
a - 15 = - b ← substitute a = 5
5 - 15 = - b
- 10 = - b ( multiply both sides by - 1 )
10 = b
What fraction subtracted from 5/12 will yield an answer that is equal to the difference between 2/3 and 1/2?
The fraction that, when subtracted from 5/12, yields the same result as the difference between 2/3 and 1/2, is 1/4.
To find the fraction that, when subtracted from 5/12, gives the same result as the difference between 2/3 and 1/2, we need to compute both the difference and the subtraction, and then find the fraction that represents their equality.
The difference between 2/3 and 1/2 can be found by subtracting the two fractions:
2/3 - 1/2 = (4/6) - (3/6) = 1/6
Now, let's represent the fraction we are looking for as "x." We can set up the equation:
5/12 - x = 1/6
To solve for "x," we need to isolate it on one side of the equation. We can do this by subtracting 5/12 from both sides:
-x = 1/6 - 5/12
To simplify the right side, we need a common denominator, which is 12:
-x = 2/12 - 5/12
Now we can combine the numerators:
-x = (2 - 5)/12 = -3/12 = -1/4
To solve for "x," we multiply both sides of the equation by -1:
x = 1/4
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You have found a store that is unique. All the shirts sell for a set price and all the pants are also priced the same in the entire store! You have purchased 3 shirts and 2 pants for $104.81 and your friend has purchased 2 shirts and one pant for $61.33. Set up and solve a system of linear equations. How much is one shirt?
Answer:
17.85$
Step-by-step explanation:
Let x be 1 shirt price
Let y be 1 pant price
we have the following equation
3x+2y = 104.81$ (1)
2x+y = 61.33$ => multiply two sides by 2 => 4x + 2y = 122.66 (2)
=> (2) - (1) => x = 17.85$
So one shirt is 17.85$
Use the graph of the function f to find the approximations of the given values.
b. f(4)
d. f(12) − f(4) / 12 − 4
Answer:
b. f(4) = -12
d. (f(12) - f(4))/(12 - 4) = (12 - (-12))/8 = 24/8
= 3
raj bought 300 mangoes at per 10 mangoes for RS 100 and sold them at a profit of 25% at what rate he sell per 15 mangoes
Raj would sell 15 mangoes at a rate of Rs 187.50 in order to achieve a profit of 25%.
To find the selling rate per 15 mangoes, we need to consider the buying price, profit percentage, and the number of mangoes.
Given:
Number of mangoes bought = 300
Buying price for 10 mangoes = Rs 100
Profit percentage = 25%
Calculate the cost price of 1 mango.
Cost price per mango = Buying price for 10 mangoes / 10
Cost price per mango = Rs 100 / 10
Cost price per mango = Rs 10
Calculate the selling price of 1 mango, including the profit.
Profit per mango = Cost price per mango * Profit percentage
Profit per mango = Rs 10 * 25/100
Profit per mango = Rs 2.50
Selling price per mango = Cost price per mango + Profit per mango
Selling price per mango = Rs 10 + Rs 2.50
Selling price per mango = Rs 12.50
Calculate the selling price for 15 mangoes.
Selling price per 15 mangoes = Selling price per mango * 15
Selling price per 15 mangoes = Rs 12.50 * 15
Selling price per 15 mangoes = Rs 187.50
Therefore, Raj would sell 15 mangoes at a rate of Rs 187.50 in order to achieve a profit of 25%.
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need help with this question trying to figure out this question
3x-15=x+33
or, 3x-2x=33+15
THEREFORE X=48 UNITS
THIS IS THE CORRECT QNSWER
how to calculate Bi weekly pay?
Calculating bi-weekly pay involves determining the total earnings for a two-week period. Here's the process 1. Determine the hourly rate: Start by determining the hourly rate of pay. For example, let's say the hourly rate is $15.
2. Calculate regular earnings: Determine the number of hours worked in a two-week period. Let's assume 80 hours. Multiply the hourly rate by the number of hours worked to calculate the regular earnings: $15/hour x 80 hours = $1200.
3. Calculate overtime (if applicable): If there are any overtime hours, calculate the overtime earnings separately. Typically, overtime is paid at a higher rate (e.g., 1.5 times the regular hourly rate) for hours worked beyond a certain threshold (e.g., 40 hours per week). Multiply the overtime hours by the overtime rate and add this amount to the regular earnings.
4. Deduct taxes and other withholdings: Subtract the applicable taxes and other withholdings from the total earnings. This may include federal income tax, state income tax, Social Security tax, Medicare tax, and any other deductions.
5. Determine the net pay: Subtract the deductions from the total earnings to calculate the net pay—the amount the employee takes home after taxes and withholdings.
It's important to note that bi-weekly pay may also include additional components such as bonuses, commissions, or other allowances. These should be factored into the calculations accordingly.
By following these steps, you can calculate an employee's bi-weekly pay based on their hourly rate, hours worked, and any additional components or deductions involved.
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The solution to this problem
Answer:
3.1+2=8
2.3-4=2
Step-by-step explanation:
Answer:
(Multiply 2y-x=2 by a 3 so that the x can be canceled)
3(2y-x=2)
=6y-3x=6 (add this to 3x+y=8)
(the +3x and -3x cancel)
3x+y=8
+6y-3x=6
_______
7y=14 (divide 14÷7)
●y=2
(take 3x+y=8 and place y=2 to find x)
3x+(2)=8 (and solve for x)
3x=6
●x=2
final answer:
(2,2)
The paint needed for a 980 ft2 room costs $35.25 per gallon. What is the total cost of the paint
needed to paint the room?
Note: Assume that one gallon of paint will cover a total of 350 square feet.
O $88.60
O $98.70
O $88.12
O $89.07
Answer:
$98.70
Step-by-step explanation:
Number of gallons = Area of room / Coverage per gallon
Number of gallons = 980 ft^2 / 350 ft^2/gallon
Number of gallons = 2.8 gallons
Therefore, we need 2.8 gallons of paint to cover the room. The cost of one gallon of paint is given as $35.25, so the total cost of the paint needed to paint the room is:
Total cost = Number of gallons × Cost per gallon
Total cost = 2.8 gallons × $35.25/gallon
Total cost = $98.70
So, the total cost of the paint needed to paint the room is $98.70.
Factor the polynomial: 2x(x - 3) + 9(x - 3)
The answer is:
(x - 3)(2x + 9)
Work/explanation:
Since (x-3) appears in both terms, we move it to the first place:
(x - 3)
We need to have another term; for that other term, we take what's left, and put that as our other term.
As a result, we have:
(x - 3)(2x + 9)
Hence, this is the answer.
The following sentence shows one of the steps to construct a regular hexagon inscribed in a circle.
"Make a point A anywhere in the circumference for the first vertex. Place the compass on point A and draw an arc to create the next vertex of the hexagon."
Which of the following statements should be added to make this step correct?
The width of the compass needs to be set to equal half the radius of the circle.
The width of the compass needs to be set to equal the radius of the circle.
The width of the compass needs to be set to equal the diameter of the circle.
Answer:
the width of the compass needs to be set to equal half of the radius of the circle
What is 52% of 78? Round to one decimal place.
Answer:
40.6
Step-by-step explanation:
Step 1: Convert 52% to a decimal:
We can find 52% of 78 by multiplying the decimal form of the percentage by 78.To convert a percentage to a decimal, imagine the percentage sign as a decimal place with two 0s after the decimal. Thus, imagine 52% as 52.00.Then, you move the decimal two places to the left (this is the same as dividing by 100 since a percentage is always out of 100):Thus, 52% as a decimal is 0.52.
Step 2: Multiply 0.52 by 78 and round to one decimal place:
Now we can multiply 0.52 by 78 and round to one decimal place to find 52% of 78:
0.52 * 78
40.56
40.6
Thus, 52% of 78 is about 40.6,
. If the cone has a height of 10 cm and a diameter of 18 cm, what is its volume?
Answer:
[tex]\Huge \boxed{\boxed{\bf{Volume = 848.23 cm^3}}}[/tex]
Step-by-step explanation:
To calculate the volume of a cone with a height of 10 cm and a diameter of 18 cm, we can use the formula:
[tex]\LARGE \boxed{\tt{V = \frac{1}{3} \times \pi \times r^2 \times h}}[/tex]
➤V = volume
➤r = radius
➤h = height
Since the diameter is 18 cm, the radius is half of that, which is 9 cm. Now, we can plug in the values:
[tex]\tt{V = \frac{1}{3} \times \pi \times (9)^2 \times 10}[/tex][tex]\tt{V = \frac{1}{3} \times \pi \times 81 \times 10}[/tex][tex]\tt{V = \pi \times 270}[/tex]The volume of the cone is [tex]\tt{270\pi \approx 848.23 \texttt{ cm}^3}[/tex]
__________________________________________________________
Assume the average nightly payroll for a city’s downtown restaurants on the weekend is $2200 with a standard deviation of $300. The distribution has a bell-shaped curve. A manager wants to be 99% sure he has this cost covered for the next four weeks and puts away $10,000. Will he have enough? Use your z-score formula result to justify your answer. Please respond with the dollar amount and round to the nearest dollar.
Hint: Round your z-value to the hundredths place and direction of the graph will matter.
Given statement solution is :- The manager will have enough funds, and the amount set aside ($10,000) is sufficient to cover the payroll for the next four weeks.
To determine if the manager will have enough funds to cover the nightly payroll for the next four weeks, we need to calculate the total cost for four weeks and compare it to the amount set aside.
The nightly payroll has a mean of $2200 and a standard deviation of $300. Since there are seven nights in a week, the weekly payroll can be calculated as:
Weekly Payroll = Nightly Payroll * Number of Nights in a Week
= $2200 * 7
= $15,400
To calculate the total cost for four weeks, we multiply the weekly payroll by four:
Total Cost for Four Weeks = Weekly Payroll * Number of Weeks
= $15,400 * 4
= $61,600
Now, let's calculate the z-score using the formula:
z = (X - μ) / σ
Where:
X = Total Cost for Four Weeks
μ = Mean of the distribution
σ = Standard deviation of the distribution
z = ($61,600 - $2200) / $300
z = $59,400 / $300
z ≈ 198
To determine if the manager will have enough funds to cover the payroll, we need to find the proportion of the distribution that is less than or equal to the z-score. This can be done by consulting a standard normal distribution table or using statistical software.
For a z-score of 198, the proportion in the tail of the distribution is essentially 1 (or 100%). This means that the manager is virtually guaranteed to have enough funds to cover the payroll for the next four weeks.
Since the manager has set aside $10,000, which is less than the calculated total cost of $61,600, he will indeed have enough funds to cover the payroll.
Therefore, the manager will have enough funds, and the amount set aside ($10,000) is sufficient to cover the payroll for the next four weeks.
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Question 9 of 30
What is the surface area of the solid?
41
OA. 84 square feet
OB. 50 square feet
O C. 100 square feet
OD. 56 square feet
7 ft
2 ft
Answer:
Step-by-step explanation:
What is the length of EF in the right triangle below?
D
26
10
E
F
The measure of side length EF in the right triangle is 24.
What is the measure of side length EF?The Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
It is expressed as;
c² = a² + b²
From the diagram:
Hypotenuse DE = c = 26
Leg DF = a = 10
Leg EF = b = ?
Plug in the values and solve for b:
c² = a² + b²
26² = 10² + b²
676 = 100 + b²
b² = 676 - 100
b² = 576
b = +√576 ( we take the positive value since we are dealing with dimensions)
b = 24
Therefore, the length EF is 24.
Option C)24 is the correct answer.
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If set is equivalent to the set of natural numbers that are multiples of 4
Answer:
2 4 8 16 and so on and so forth
express 30.725 correct to one decimal place
Answer:
30.7
Step-by-step explanation:
30.725 to one decimal place is 30.7. To round/correct to one decimal place, it would be the tenths. So, look at the hundredths place number (2), and if its greater than 5, add 1 to the tenths place (7 changes to 8), and if its less than 5, don't do anything (7 stays as 7).
Hope this helps! :)
Answer:
The value corrected to one decimal place is 30.7
Step-by-step explanation:
The value 30.725 has three decimal places. The number 7 is in the one's place, the number 2 is in the tenth place, and the number 5 is in the hundredth place.
To round off, if the value in a place is equal to or above 5, the previous place number is increased by one; else it remains the same. In this case, the hundredth place is 5, so we add 1 to the tenth place. This gives us 2 + 1 = 3. Therefore, the number is expressed with two decimal places as 30.73.
To express it as one decimal place, we look at the value in the tenth place, which is 3. As 3 is less than 5, the one's place remains the same.
Thus, the value is 30.7 when expressed with one decimal place.
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Please Solve, Thank you!
The graph which shows the interval notation of the inequality 3 > - x > - 7 is option C.
How to solve inequality using graph?3 > - x > - 7
Break the compound inequality into two and solve each
3 > - x
divide both sides by -1
-3 < x
- x > - 7
divide both sides by -1
x < 7
So the solution to the inequality is
-3 < x < 7
Therefore, it can be interpreted that x is greater than -3 and less than 7
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Find the inverse of the matrix, use an algorithm for finding A^-1 by row reducing [A I]
[------------------]
| 1 0 -3 | 1 0 0 |
| 3 1 -4 | 0 1 0 |
| 4 2 -4 | 0 0 1 |
[------------------]
Answer:
A: A^-1 = [[-2,-3,-1.5],[-2,-4,-2.5],[-1,1,-.5]]
Step-by-step explanation:
Answer:
To find the inverse of the matrix A, we will use the row reduction method. We will augment matrix A with the identity matrix I and perform row operations until A is transformed into the identity matrix. The resulting matrix on the right side will be the inverse of A.
Step-by-step explanation:
Augment the matrix A with the identity matrix I:
[ 1 0 -3 | 1 0 0 ]
[ 3 1 -4 | 0 1 0 ]
[ 4 2 -4 | 0 0 1 ]
Perform row operations to transform the left side of the augmented matrix into the identity matrix:
R2 = R2 - 3R1
R3 = R3 - 4R1
[ 1 0 -3 | 1 0 0 ]
[ 0 1 5 | -3 1 0 ]
[ 0 2 8 | -4 0 1 ]
Perform row operations to further transform the left side of the augmented matrix into the identity matrix:
R3 = R3 - 2R2
[ 1 0 -3 | 1 0 0 ]
[ 0 1 5 | -3 1 0 ]
[ 0 0 -2 | 2 -2 1 ]
Multiply the third row by -1/2 to make the pivot element of the third row equal to 1:
R3 = (-1/2) * R3
[ 1 0 -3 | 1 0 0 ]
[ 0 1 5 | -3 1 0 ]
[ 0 0 1 | -1 1 -1/2 ]
Perform row operations to further transform the left side of the augmented matrix into the identity matrix:
R1 = R1 + 3R3
R2 = R2 - 5R3
[ 1 0 0 | 2 0 3/2 ]
[ 0 1 0 | 2 -4 5/2 ]
[ 0 0 1 | -1 1 -1/2 ]
The resulting matrix on the right side of the augmented matrix is the inverse of matrix A:
[ 2 0 3/2 ]
[ 2 -4 5/2 ]
[ -1 1 -1/2 ]
Therefore, the inverse of matrix A is:
[ 2 0 3/2 ]
[ 2 -4 5/2 ]
[ -1 1 -1/2 ]
If the park was 1/8 of mile and 1/2 how many miles total
Answer: 5/8 miles
Step-by-step explanation:
1/8+1/2 is the equation. First, you have to make the denominators equal. So, we have to turn 2 into 8. Since you multiply 2 by 4 to get 8, multiply the numerator (1) by 4 as well. This leaves you with 1/8+4/8. Now add the numerators together to get 5/8.
5.3 Suppose the radius of a second solid metal ball, B₂, is half the radius of ball B₁. Suppose ball B₂ was put into the tank of water instead of ball B₁. Would the surface of the water be 4cm below the top of the tank? Explain your answer. (5)
If ball B₂ is placed in the tank instead of B₁, the surface of the water would not be 4cm below the top of the tank. It would be lower than that, indicating that ball B₂ causes a lesser rise in the water level due to its smaller volume.
No, the surface of the water would not be 4cm below the top of the tank if ball B₂ with a radius half of B₁ was placed in the tank instead.
The water level in a tank is determined by the volume of the object submerged in it, not just the radius of the object. The volume of a sphere is directly proportional to the cube of its radius.
Let's assume the radius of ball B₁ is r. Then, the radius of ball B₂ would be (1/2) * r.
The volume of ball B₁ can be calculated as V₁ = (4/3) * π * r³.
Similarly, the volume of ball B₂ can be calculated as V₂ = (4/3) * π * (1/2 * r)³ = (1/6) * (4/3) * π * r³.
The volume of water displaced by ball B₁ would be equal to V₁, which would cause the water level to rise.
However, the volume of water displaced by ball B₂ would be equal to V₂, which is only (1/6) of V₁. This means that ball B₂ would displace less water compared to B₁, resulting in a lower rise in the water level.
Therefore, if ball B₂ is placed in the tank instead of B₁, the surface of the water would not be 4cm below the top of the tank. It would be lower than that, indicating that ball B₂ causes a lesser rise in the water level due to its smaller volume.
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If A is the set of positive integers defined as
A = {x:x²+x-6=0}. Find the value of X satisfying the
solution set.
The value of x that satisfies the equation x² + x - 6 = 0 is x = 2 or x = -3.
To find the value of x that satisfies the equation x² + x - 6 = 0, we can solve the quadratic equation by factoring or using the quadratic formula.
Option 1: Factoring
To factor the quadratic equation, we need to find two numbers whose product is -6 and whose sum is +1 (the coefficient of x).
The numbers that satisfy this condition are +3 and -2.
Therefore, we can rewrite the equation as (x + 3)(x - 2) = 0.
Setting each factor equal to zero, we have x + 3 = 0 or x - 2 = 0.
Solving these equations gives x = -3 or x = 2.
Option 2: Quadratic Formula
The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b² - 4ac)) / (2a).
In our equation, a = 1, b = 1, and c = -6.
Substituting these values into the formula, we have:
x = (-1 ± √(1² - 4(1)(-6))) / (2(1)).
Simplifying the expression inside the square root, we get:
x = (-1 ± √(1 + 24)) / 2.
x = (-1 ± √25) / 2.
x = (-1 ± 5) / 2.
This gives us two solutions: x = (-1 + 5) / 2 = 4 / 2 = 2, and x = (-1 - 5) / 2 = -6 / 2 = -3.
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What is the length of leg s of the triangle below?
45
1012
A. 10-2
OB. 10
O C. 1
OD. 5√2
E 5
45
F. 5.6
Answer:
B
Step-by-step explanation:
