What number is not part of the solution set to the inequality below?

w−10≤16

A) 11

B) 15

C) 26

D) 27?

A table of values for g(x) has been completed below;

x            f(x)          g(x)

-2           3             8

0             1             7

1             -4             1

3            -2             3

In Mathematics and Geometry, the translation a geometric figure upward simply means adding a digit to the value on the positive y-coordinate (y-axis) of the pre-image;

g(x) = f(x) + N

Since the parent function f(x) was translated 5 units up, we have the following transformed function;

g(x) = f(x) + 5

Therefore, the table of values should be completed as follows;

x            f(x)          g(x)

-2           3             8

0             1             7

1             -4             1

3            -2             3

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The point P should be chosen at 1.07 units to maximize the angle.

From the figure, let the distance of point P from point A on line segment AB be x and let the angle opposite side a be M and the angle opposite side c be N.

Using pythagoras theorem,

tan M = a/(b - x)

M = tan⁻¹(a/(b - x))

Also, we can say that:

tan N = c/x

N = tan⁻¹(c/x)

Angle θ is given by:

θ = 180 - M - N

θ = 180 - tan⁻¹(a/(b - x)) - tan⁻¹(c/x)

Given that a = 3 units, b = 5 units, and c = 8 units. Thus:

θ = 180 - tan⁻¹(3/(5 - x)) - tan⁻¹(8/x)

To maximize angle θ, the differentiation of θ with respect to x must be equal to zero.

i.e. dθ/dx = - 3/(x² - 10x + 34) + 8/(x² + 64) = 0

8/(x² + 64) = 3/(x² - 10x + 34)

8(x² - 10x + 34) = 3(x² + 64)

8x² - 80x + 272 = 3x² + 192

5x² - 80x + 80 = 0

Using quadratic equation calculator gives:

x = 1.0718

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To calculate the interest earned in 3 months, we need to first find the monthly interest rate.

The annual interest rate is 14%, so the monthly interest rate is:

14% / 12 months = 1.1667% per month

Next, we can calculate the interest earned in 3 months by multiplying the monthly interest rate by the principal (the amount in the savings account):

3 months * 1.1667% per month * $13,163 = $485.95

Therefore, Janelle will earn $485.95 in interest in 3 months.

A payday loan for $2300 due in 13 days with a rate of $120, because it has the shorter period and this will have a higher effective interest rate, Therefore option B is correct.

The effective interest rate (EIR) takes into account the whole value of the loan such as fees and the period of the loan.

In this situation, both loans have the equal rate of $120, so the full price is the same.

However, the mortgage due in thirteen days has a shorter length, meaning that the hobby is being charged over a shorter amount of time, resulting in a better effective interest rate compared to the mortgage due in 15 days.

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The best prediction of a person's blood pressure if he or she worked 32 hours a week is given as follows:

J. 125.

To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.

The points for the data-set in this problem are given as follows:

(75, 172), (41, 130), (85, 170), (56, 142), (25, 125), (60, 141), (48, 138).

Inserting these points into a calculator, the linear regression equation predicting the blood pressure of a person that works x hours a week is given as follows:

y = 0.86x + 97.47

Hence the prediction when x = 32 is given as follows:

y = 0.86(32) + 97.47

y = 125.

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The correct statement regarding whether we can prove that the lines are parallel is:

Yes. Alternate Interior Angles Converse.

Alternate interior angles happen when there are two parallel lines cut by a transversal lines.

The two alternate exterior angles are positioned on the inside of the two parallel lines, and on opposite sides of the transversal line, and they are congruent.

The red sectors represents that the angles are alternate interior angles for the problem, hence the correct option is given as follows:

Yes. Alternate Interior Angles Converse.

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An equation that could represent the graph of P(x) include the following: p(x) = -3/4(x - 2)²(x + 1).

In Mathematics and Geometry, the graph of a polynomial function touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.

Also, the graph has a zero of multiplicity 2 at x = 2 and zero of multiplicity 2 at x = -1;

x = 2 ⇒ x - 2 = 0.

(x - 2)²

x = -1 ⇒ x + 1 = 0.

(x + 1)²

In this context, an equation that represent the polynomial function is given by:

p(x) = a(x - 2)²(x + 1)²

By evaluating and solving for the leading coefficient "a" in this polynomial function based on the y-intercept (0, -3), we have;

-3 = a(0 - 2)²(0 + 1)²

-3 = a4

a = 3/4.

Therefore, the required polynomial function is given by:

p(x) = -3/4(x - 2)²(x + 1)

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The equation of the circle is (x – 3)² + (y + 1)² = 25.

D. is the answer.

The general equation of a circle is given by:

(x – h)² + (y – k)² = r²,

where (h, k) is the coordinate of the circle's center, and r is the radius.

Thus, (h, k) = (3, -1) and the circle passes through (-2, -1) i.e. (x, y) =  (-2, -1). Substituting into the equation, we can get the radius. That is:

(x – h)² + (y – k)² = r²

(-2 – 3)² + (-1 – (-1))² = r²

(-5)² = r²

25 = r²

r² = 25

Substitute only h, k and r² back into the general equation to get the equation of the graph. That is:

(x – h)² + (y – k)² = r²

(x – 3)² + (y – (-1))² = 2

(x – 3)² + (y + 1)² = 25

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It is not worth the extra drive to the store across town for the cheaper chicken.

To determine if it is worth the extra drive to the store across town for the cheaper chicken, we need to consider the cost of gas and the time spent driving.

First, let's calculate the cost difference between the two stores. For 7 pounds of chicken, the neighborhood store would cost $3.59/pound x 7 pounds = $25.13. The store across town would cost $3.29/pound x 7 pounds = $23.03. So, by going to the store across town, we would save $2.10 on chicken.

Next, let's calculate the cost of gas. To drive to the store across town and back, we will travel a total of 17.6 miles (8.8 miles each way). With a car that averages 24 miles per gallon, we will use approximately 0.73 gallons of gas for this trip (17.6 miles / 24 mpg). At a cost of $3.85 per gallon, the cost of gas for this trip would be approximately $2.81.

Now, let's consider the time spent driving. Driving to the neighborhood store and back would take approximately 16 minutes (8 minutes each way). Driving to the store across town and back would take approximately 48 minutes (24 minutes each way). So, by going to the store across town, we would spend an extra 32 minutes driving.

In summary, if we go to the store across town for the cheaper chicken, we will save $2.10 on chicken, but spend $2.81 on gas and an extra 32 minutes driving. In this case, the cost of gas and time spent driving outweighs the savings on chicken.

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Complete question is:

you need to buy some chicken for dinner tonight. You found an ad showing that the store across town has it on sale for 3.29 a pound which is cheaper that your usual neighborhood store which sells it for $3.59 a pound. Is it worth the extra drive?

Information you'll need:

How much chicken will you be buying? 7 pounds

How much far are the two stores? My neighborhood store is 2.3 miles away, and takes about 8 minutes. The store across town is 8.8 miles away, and takes about 24 minutes.

How kind of mileage does your car get? It averages about 24 miles per gallon in the city.

How many gallons does your car hold? About 16 gallons

How much is gas? About $3.85/gallon right now.

Answer:

A. Circle

To draw a regular polygon, one can use a circle as a geometric figure. A regular polygon is a polygon with all sides and angles equal. By inscribing a polygon inside a circle, the vertices of the polygon are evenly spaced on the circumference of the circle, and the radius of the circle is equal to the distance between the center of the circle and the vertices of the polygon. This ensures that all sides of the polygon are of equal length, and all angles between the sides are equal. Therefore, by using a circle as a geometric figure, Rachael can draw a regular polygon with ease.

Walton's actual check average is $9.52

The actual food cost is lower than the flexible budget by $5020

We have ,

Net income considered a vital financial metric of an organization, delineates the earned sum after deducting expenses and taxes from total revenue.

The measure is indicative of the profitability status of an entity, portraying cash flow left over subsequent to settling all obligations. To uncover net income, business expenditures spanning across areas such as salaries, interest payments and rents alongside taxations are subtracted from entire receipts.

Ascertaining net income facilitates assessing the fiscal robustness and future prospects of a company for interested investors.

Hence, Walton's actual check average is $9.52

The actual food cost is lower than the flexible budget by $5020

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The requreid,
(a) Approximate values of the given numbers are π ≈ 3.1, √6 ≈ 2.4, 2√6 ≈ 4.8, and √7 ≈ 2.6.
(b) √6  < √7 <  π  < 2√6

(a)

π ≈ 3.1 (since π is between 3 and 4, and is closer to 3.1 than to 3.2)

√6 ≈ 2.4 (since 6 is between 4 and 9, and the square root of 6 is closer to 2.4 than to 2.5)

2√6 ≈ 4.8 (since 2√6 is approximately twice the value of √6, which is 2.4)

√7 ≈ 2.6 (since 7 is between 4 and 9, and the square root of 7 is closer to 2.6 than to 2.7)

(b)

Order from least to greatest:

√6  < √7 <  π  < 2√6

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Answer: 96 cm2

Step-by-step explanation:

Surface area of a cube= (x)^2(6)

First we find the area of one face of the cube which is; 4x4 or 4^2 = 16

We know that a cube has 6 faces, therefore we take the area of one face multiply the total number of faces: 16x6= 96 cm2

Answer:

A=25%

B=6.25%

C=3.125%

D=12.5%

F=~12.5%

Step-by-step explanation:

they look like it

i cant read the letters so not sure.

if its by scale then im right

Answer:

Piece A- 25%

Piece B- 6.25%

Piece C- 3.125%

Piece D- 15.625%

Piece E- 37.5%

Piece F- 12.5%

Step-by-step explanation:

To find each shape's area as a percentage, each shape should be compared to the whole larger square, so we will first find the total area in the large square.

The question states that the square is 4cm x 4 cm, and using the equation for the area of a square, length x width, we know that the large square's area is 16cm squared.

Square A is 2cm long and 2cm wide, so similarly, we can use the length x width formula to get 4cm squared for its area. To find its percentage relative to the larger square, we must divide its area, 4, by the large square's area, 16. 4/16 = 0.25, which can be converted to a percentage by multiplying it by 100%. This means that piece A takes up 25% of the large square's area.

Square B is 1cm long and 1cm wide. Once again, we will multiply its length and width to get an area of 1cm squared. Again, we must divide this number by the total area of the large square. 1/16= 0.0625, or, after converting it to a percentage, 6.25%.

Piece C is triangular, and so we will use the formula for an area of a triangle instead: Base x height x 1/2. We know from seeing it above square B that its base is 1cm wide. It also ends vertically at square A. Because it starts after square B, which is 1cm long, and square A is 2cm long, we know that the triangle's height is 2cm - 1cm, or, 1cm long. The base multiplied by the height is 1, and dividing it by 2 gets us 1/2cm squared for its area. To find the percentage, we divide 1/2 by 16, which gives us 0.03125, or 3.125%.

Piece D is an irregular shape, however we can instead imagine it as two separate shapes- a square near the bottom and a triangle on top. The square section is 1cm wide, since the large square's side is 4cm and so far, squares A and B are lying on that side, taking up 3cm. it is also as tall as square B, making it 1cm long vertically. Using the formula for the area of a square, length x width, we know that the area of that section is 1cm squared.

The triangle section is right on top of it, making its base 1cm wide as well. The side of the triangle goes until the top of the large square, and because the square section already took up 1cm of the 4cm long side, we know that the triangle is 3cm tall. Using the area of a triangle formula, base x height x 1/2, we can multiply 1 x 3 x 1/2 to get an area of 3/2cm squared.

To find the total area of piece D, we then have to add the area of the square and triangle sections together. 1 + 3/2 = 5/2cm squared area total. Dividing 5/2 by 16 gets 0.15625, or 15.625% of the large square's area.

Piece E as well can be split up into a square and a triangle. The square section ends where square A ends, and takes up half of the large square's side, meaning it is 2cm wide and 2 cm long. Multiplying its length and width gets an area of 4cm squared.

The triangle also takes up half of the larger square's side horizontally and vertically, so it has a base and height of 2cm. Using the area of a triangle formula, base x height x 1/2, we can get 2 x 2 x 1/2, or 2cm squared for its area.

Adding the areas of the square and triangle sections, Piece E will have a total area of 6cm squared. Then, we divide that by 16, and 6/16= 0.375, or 37.5% of the large square's area.

Piece F is diagonal, so it is harder to tell the measurements of its base and height. however, we know that its sides are the hypotenuses of two other triangles we have measured. The hypotenuse is the longest side of a triangle, facing opposite of its 90 degree angle. If we name the hypotenuse "c" and the other two sides of the triangles "a" and "b", we can use the Pythagorean theorem, a^2+b^2=c^2, to find the lengths of Piece F.

For piece C, the base and height of the triangle are both 1cm, so if those are a and b, then 1^2+1^2=c^2, with c being the base of piece F. 1*1=1, so 1+1=c^2, making c^2=2. We can then isolate c by taking the square root of both sides, making c=[tex]\sqrt{2}[/tex].

We can do the same thing with the triangle taken from piece E, though this time a and b will both equal 2cm.  If we plug those values into the equation, then 2^2+2^2=c^2. 2*2=4, so 4+4=c^2, or c^2=8. Taking the square root of both sides, we find that c=[tex]\sqrt{8}[/tex].

Basically, piece F has a base of [tex]\sqrt{2}[/tex]cm, and a height of [tex]\sqrt{8}[/tex]cm. We can plug those into the equation for the area of a triangle, base x height x 1/2, to get [tex]\sqrt{8}[/tex] x [tex]\sqrt{2}[/tex] x 1/2, or 2cm squared for the area of piece F. 2/16= 0.125, so piece F takes up 12.5% of the large square's area.  

The rule for the geometric sequence is [tex]a_n = a_{n-1} * (1/2).[/tex]

The sequence that is geometric is: 5, 10, 30, 60, ...

To determine if a sequence is geometric, we look for a common ratio between consecutive terms. If the ratio between any two consecutive terms is the same, then the sequence is geometric.

For the first sequence, the differences between consecutive terms are 1, 2, 3, 4, which are not constant. Therefore, the first sequence is not geometric.

For the second sequence, the ratio between consecutive terms is 486/972 = 1/2, and the ratio between any two consecutive terms is the same (1/2). Therefore, the second sequence is geometric.

For the third sequence, the differences between consecutive terms are 25, 25, 25, which are constant. Therefore, the third sequence is not geometric.

For the fourth sequence, the ratio between consecutive terms is 10/5 = 2, the ratio between the second and third term is 30/10 = 3, and the ratio between the third and fourth term is 60/30 = 2. Therefore, the fourth sequence is geometric.

The rule for the geometric sequence is that each term is found by multiplying the previous term by a constant factor, called the common ratio. In the second sequence, the common ratio is 1/2, and the rule is:

[tex]a_n = a_{n-1} * (1/2)[/tex]

where a_n represents the nth term in the sequence. So, for example, the fourth term in the sequence can be found by:

[tex]a_4 = a_3 * (1/2)[/tex] = 121.5 * (1/2) = 60

Therefore, the rule for the geometric sequence is[tex]a_n = a_{n-1} * (1/2).[/tex]

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Answer:

hope this helps

Step-by-step explanation:

The measure of arc XW in the circle shown in the image above is calculated as: m(XW) = 108°.

To find the measure of the arc indicated in the circle, recall that a circle measures 360 degrees.

Therefore, create an equation to find x as shown below:

m(XW) + m(XY) + m(WY) = 360° [full circle]

Given the following:

m(XW) = 37x - 3

m(XY) = 32x - 2

m(WY) = 51x + 5

Plug in the values:

37x - 3 + 32x - 2 + 51x + 5 = 360

Combine like terms:

120x = 360

Divide both sides by 120:

120x/120 = 360/120

x = 3

m(XW) = 37x - 3 = 37(3) - 3

m(XW) = 108°

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The required, we get a population of 543694 after 12 years.

To find the population of the city after 12 years, we need to apply the formula for compounding:

[tex]A = P(1 + r/n)^{(nt)}[/tex]

In this case, P = 210,000, r = 0.0825 (8.25% expressed as a decimal), n = 1 (since the growth is yearly), and t = 12. Plugging in these values, we get:

A = 210,000(1 + 0.0825/1)¹ˣ¹²

A = 210,000(1.0825)¹²

A ≈ 543693.51

Rounding this to the nearest whole number, we get a population of 543694 after 12 years.

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The graph doesn't represent a one-to-one function because certain y-values between 0 and 2 are paired with multiple x-values(D). A one-to-one function requires each x-value and y-value to be paired uniquely.

Based on your question, it seems that the graph is displaying a situation where certain y-values between 0 and 2 are associated with multiple x-values(D). In this case, the graph does not represent a one-to-one function. This is because a one-to-one function, by definition, must have each y-value corresponding to exactly one x-value and each x-value corresponding to exactly one y-value. Passing through the origin, or being defined for all x-values, is not a necessary condition for a function to be one-to-one. The key definition of one-to-one functions lies in the uniqueness of the pairs.

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The word problem makes use of the division number sentence to find the answer which is given as 4 apples

Division number sentence: 40 ÷ 10 = 4

Multiplication number sentence: 10 × (1/4) = 2.5

Word problem:

Mr. Oliveras has 40 apples and wants to divide them equally among 10 students. How many apples does each student receive?

This can be solved using the division number sentence: 40 ÷ 10 = 4.

Each student gets 4 apples.

Therefore, the word problem makes use of the division number sentence to find the answer which is given as 4 apples

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The end behavior of the cube root function represented by the graph is B. As x decreases in value, f ⁡ ( x ) increases in value. As x increases in value, f ⁡ ( x ) decreases in value.

The given data is

(-5, 2)

(0, 1) = y-axis at 1 unit

(2, 0) = intercepts the x-axis at 2 units

(3, -2)

(6, -5)

Examining the increasing and decreasing trend as represented by the ordered pairs it shows that

x ⇒ -∞ f(x) ⇒ ∞

x ⇒ ∞ f(x) ⇒ -∞

This end behavior is described by option B.

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Answers:

8

6

1

3

Reason:

Add 5 to each value in the f(x) column.

Example: 3+5 = 8 for the first row.

This will shift each point 5 units up. This is because we're moving 5 units up the y axis.

The solution to the equation 3x(x + 4) + 3(x + 4) = 0 is x = -4 or x = -1.

Given the equation in the question:

3x(x + 4) + 3(x + 4) = 0

To determine the solution to the equation.

First, factor out the common factor of (x + 4) from the left-hand side of the equation:

3x(x + 4) + 3(x + 4) = 0

3(x + 4)(x + 1) = 0

The equation is now in factored form, and we can use the zero product property to find the values of x that satisfy the equation:

3(x + 4)(x + 1) = 0

(x + 4)(x + 1) = 0 (Divide both sides by 3)

Using the zero product property, we know that:

(x + 4) = 0 and (x + 1) = 0

Solving for x, we get:

x + 4 = 0 and x + 1 = 0

x = -4 and x = -1

Therefore, the solution s are x = -4 and x = -1.

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The surface of area of the rectangular prism is 52 cm².

A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.

The surface of area of a rectangular prism is expressed as;

SA = 2( wl + hl + hw )

Where w is the width, h is height and l is length

From the diagram:

Length l = 3cm

Width w = 2cm

Height h = 4cm

Plug these values into the above formula and solve for the surafce area.

SA = 2( wl + hl + hw )

SA = 2( 2×3 + 4×3 + 4×2 )

SA = 2( 6 + 12 + 8 )

SA = 2( 26 )

SA = 52 cm²

Therefore, the surface area is 52 cm².

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Answer:

Find the incenter of the triangle

Step-by-step explanation:

Step 1: We draw angle bisectors for 2 angles and mark their intersection.

Step 2: Next, we drop a perpendicular line from the incenter of the circle to one edge of the triangle.

When solved, the expressions below that will have a 1 in the tenths place is A) 24.321 x 100 and  C) 96.51 x 10

From the question we were told to find the the expressions that will have a 1 in the tenths place which implies that we will need to find the simplification of each expression by perforimgmultiplication operation on eaqch of the given expression which can be done  as ;

The first option;

24.321 x 100 = 2432.1

The second option;

25.671 x 10 = 256.71

The third option;

96.51 x 10 = 965.1

The fifth option;

89.15 x 100 = 8915

We can see that in option A and option C that the have a 1 in the tenths place.

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Answer:

the depth of the pool, in feet, before Mr. Richardson started draining it

Step-by-step explanation:

y = -0.5x + 4 is the in the slope-intercept form, whose general form is

y = mx + b, where m is the slope of the line and b is the y-intercept.  The y-intercept is where the line intersects the x axis and in order to intercept the y-axis, x has to be 0.

Thus, when the y-intercept is 4, we know that x-value is automatically 4 and therefore Mr. Richardson's pool was already at a depth of 4 feet before the draining began.

Answer:

The correct answer is 4) 4.25; a puppy who is just born is predicted to weigh 4.25 ounces.

Step-by-step explanation:

The w-intercept of the line of fit is the value of w when d = 0. In other words, it is the predicted weight of a puppy when it is born.

From the equation w = 4.25 + 0.4d, we can see that when d = 0, the value of w is:

w = 4.25 + 0.4(0) = 4.25

Therefore, the w-intercept of the line of fit is 4.25.

This means that a puppy who is just born is predicted to weigh 4.25 ounces.

So, the correct answer is 4) 4.25; a puppy who is just born is predicted to weigh 4.25 ounces.