A rectangular closet has a perimeter of 18 feet and an area of 20 square feet. What are the dimensions of the closet.

The unknown value in the table using the constant of proportionality is; 96

The constant of proportionality is the ratio of two proportional values at a constant value. Two variable values have a proportional relationship when either their ratio or their product gives a constant.

We are given the coordinates;

(12, 42), (18, 63), (40, y)

where x-values represents time in seconds and y-values represents number of pencils that were produced.

To find the constant of proportionality is as good as finding the slope between two consecutive points as;

m = (63 - 18)/(42 - 12)

m = (45/30)

m = 1.5

Thus to find the unknown value y, we will use the formula;

(y - y1)/x - x1) = m

So we will use the coordinates; (18, 63), (40, y)

Plugging them into the formula above will result in;

(y - 63)/(40 - 18) = 1.5

y - 63 = 1.5 * 22

y - 63 = 33

y = 33 + 63

y = 96

Thus, we can conclude that using the constant of proportionality, the number of pencils that were produced after a time of 40 seconds is 96 pencils.

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Answer:

- 2n + 6

Step-by-step explanation:

note that + (-) = -

5n + 6 + (- 7n)

= 5n + 6 - 7n ← collect like terms

= 5n - 7n + 6

= - 2n + 6

7×50×5 = 1750 minutes

1750minutes/60minutes = 29.161 hours

The polynomial which can be used to support the idea that the set of polynomials is closed under multiplication is: A. (5x - 1)(3x² + 4x).

A polynomial can be defined as a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations such as:

In Mathematics, a set is considered as closed under a multiplication operation, if the multiplication performed on two (2) elements of the set produces an element of the same set.

Note: The exponents of the variables are added when multiplying polynomials in accordance to the rules of exponents.

For option A, we have:

P = (5x - 1)(3x² + 4x)

P = 15x³ - 3x² + 20x² - 4x

P = 15x³ - 23x² - 4x.

For option B, we have:

P = (9x⁻³ - 5)(3x - 17)

P = 27x⁻² - 15x - 153x⁻³ + 85.

In conclusion, we can infer and logically deduce that the polynomial (5x - 1)(3x² + 4x) can be used to support the idea that the set of polynomials is closed under multiplication.

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Answer: x = 0

Step-by-step explanation:

Given equation (swapped position):

x + 3 - 5x = 3

Combine like terms:

(x - 5x) + 3 = 3

-4x + 3 = 3

Subtract 3 on both sides:

-4x + 3 - 3 = 3 - 3

-4x = 0

Divide -4 on both sides:

-4x / -4 = 0 / -4

[tex]\boxed{x=0}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The expression that completes the function b(x)​ is b(x) = 33741 * (1.028)^x

The given parameters are:

Initial value, a = 33741  

Rate, r = 2.8%

The cost of tuition each year since 2015 is represented as

B(x) = a * (1 + r)^x

This gives

B(x) = 33741 * (1 + 2.8%)^x

Evaluate

b(x) = 33741 * (1.028)^x

Hence, the expression that completes the function b(x)​ is b(x) = 33741 * (1.028)^x

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Complete question

A study estimates that the cost of tuition at a university will increase by 2.8% each year. The cost of tuition at the University in 2015 was $33,741 the function b(x) , models the estimated tuition cost , where x is the number of years since 2015.

Find the expression that completes the function b(x)​

Answer:

23

Step-by-step explanation:

  In arithmetic sequence, the difference between any consecutive terms is constant and the progression goes either in  ascending order or in descending order.

a = first term = 2

a₂ = 5

difference = d = second term - first term

                        = 5 - 2

                      d = 3

Formula for finding nth term in arithmetic sequence:

   [tex]\sf \boxed{t_n = a + (n-1)*d}[/tex]

     t₈ = 2 + (8 -1) * 3

        = 2 + 7 *3

        = 2 + 21

    t₈ = 23

Answer:

Step-by-step explanation:

The correct option is C. find the real range, find the interval width, and construct the frequency distribution.

To make the information easier to understand, frequency distributions are textured look which organise and present frequency counts. Absolute frequencies as well as frequency distributions, such as percentages or ratios, can be displayed in frequency distributions.

The real range is find by the following method-

The interval width is find by the following method-

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The correct question is-

The three steps for constructing a simple frequency distribution are -

Group of answer choices

A. find the observed range, find the interval width, and construct the frequency distribution

B. find the real range, count the scores, and construct the frequency distribution

C. find the real range, find the interval width, and construct the frequency distribution

D. all of the above

Answer:

For every x value, the y value would be double of the x value. (ex, x=2, y=4)

Step-by-step explanation:

If you look closely at every x value and see their y-values for the ordered pair, you will see that the x-value in question was doubled in order to find the y-value. This will result in the linear equation: [tex]y=2x[/tex].

Answer:

6288388288288828ffjfjjrjir

Answer:

y = -⅔x + 11/3

Step-by-step explanation:

The slope is

[tex] \frac{5 - 3}{ - 2 - 1} = - \frac{2}{3} [/tex]

Substituting into point-slope form,

y - 3 = -⅔(x - 1)

y - 3 = -⅔x + ⅔

y = -⅔x + 11/3

Answer:

50000

Step-by-step explanation:

Using

[tex]P(percentage) \times CP(cost \: price) = Sales \: Tax[/tex]

Putting the given values

P × 25000 = 1750

[tex]P = \frac{1750}{25000} [/tex]

[tex]P = 0.07 \times 100[/tex]

[tex]P = 7\%[/tex]

Now

For purchase price of a new car.

[tex]P \times CP=Sales \: Tax[/tex]

[tex]7 \times CP = 3500[/tex]

[tex]CP = 50000[/tex]

Hope it helps you, any confusions you may ask!

The widgets should be sold for $22.08 for the company to make the maximum profit.

To maximize a function, y = f(x), we differentiate it with respect to x, to get y' = f'(x). Equate it to zero to get the points on inflections.

Differentiate y' = f'(x) again with respect to x, to get y'' = f''(x), and put in the points of inflections to check whether y'' is greater than or less than zero. If it is greater than zero, then we have a minimum, and if it is less than zero, then we have a maximum.

In the question, we are given a profit function y, with respect to the sale price of each widget x. We are asked to find the sale price that maximizes the profit.

The function given is:

y = -30x² + 1325x - 8569.

Differentiating this with respect to x, we get:

y' = -60x + 1325.

To find the point of inflection, we equate this to zero, to get:

0 = -60x+ 1325,

or, x = 1325/60 = 22.0833

Now, we differentiate, y' = -60x + 1325, with respect to x, to get:

y'' = -60 < 0, thus we have a maximum at x = 22.0833.

Thus, the widgets should be sold for $22.08 for the company to make the maximum profit.

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the actual height of the backboard is 8.18 feet.

A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)

Given

We have been given that Derek places  a standard 12-inch ruler next to the goal post and measures the shadow of the ruler and the backboard. If the ruler has a shadow of 10 inches. We are asked t find the height of the backboard, if the backboard has a shadow of 8.5 feet.

We will use proportions to solve our given problem as ratio between sides ruler will be equal to ratio of sides of background.

[tex]\frac{Actual height of ruler}{Shadow of ruler} = \frac{Actual height of black board}{Shadow of black board} \\\\\frac{12}{11} =\frac{Actual height of black board}{7.5} \\\\Actual height of black board = \frac{12}{11} * 7.5 = 8.18\\[/tex]

Therefore, the actual height of the back-board is 8.18 feet.

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Considering that it is a triangle, the range of the possible lengths, x, of the third side of the tile is: (1, 17).

In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.

Hence, if 9 is the greater side:

8 + x > 9

x > 1.

If 8 and 9 are the smaller sides:

x < 8 + 9

x < 17.

Hence the range of possible lengths is:

(1, 17).

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x would be the side-length of a square that has the same area as a rectangle with width b and length a.

√(a*b) = x

Notice that you have two "lengths" which are a and b.

And you want to find x such that:

a/x = x/b

Now, notice that w e can rewrite the above expressions as:

a*b  = x*x

This means that x would be the side-length of a square that has the same area as a rectangle with width b and length a.

Now, if you know the values of a and b (you can get these by using a ruler for example)

Then you can replace them in the equation:

a*b = x*x

√(a*b) = x

And find the value of x that meets the given condition.

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Answer:

150 + 1.5d

Step-by-step explanation:

increase 120 by d%

d% = d/100

So, increasing 120 by d % means

120 + (d/100 * 120)

= 120 + 1.2d

Then increase this by 25%

= (120 + 1.2d) + 25/100(120 + 1.2d)

= 120 + 1.2d + (120+1.2d)/4

= 120 + 1.2d + 30 + 0.3d

= 120 + 30 + 1.2d + 0.3d

= 150 + 1.5d

so here you the answer is 9

I give u the answers of first and second one.

thank you

brainlist please

Answer:

First answer is 9 or 1 . Second answer is 7 or -7.

Step-by-step explanation:

[tex](x-5)^{2} =16[/tex]

[tex]x-5 = 4[/tex]  or [tex]x - 5 =-4[/tex]

so [tex]x = 9[/tex] or [tex]x = 1[/tex]

[tex]2x^{2} = 98[/tex]

[tex]x^{2} =49[/tex]

[tex]x=7[/tex] or [tex]x = -7[/tex]

The value of x when y = 1.728 and z = 5 in the inverse variation y = (k × x²) / z³ is 36

The types of variation are;

y = (k × x²) / z³

where,

If y = 12, x = 4 and z = 2

y = (k × x²) / z³

12 = (k × 4²) / 2³

12 × 2³ = k × 4²

12 × 8 = k × 16

96 = 16k

k = 6

Find x when y = 1.728 and z = 5

y = (k × x²) / z³

1.728 = (6 × x) / 5³

1.728 × 5³ = 6x

1.728 × 125 = 6x

216 = 6x

x = 216/6

x = 36

Therefore, value of x when y = 1.728 and z = 5 in the inverse variation y = (k × x²) / z³ is 36

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The complete question:

A baby's t-shirt requires 4/5 yards of fabric. How many t-shirts can be made from 48 yards? A book is on sale at a 30% discount. If the sales price is $28, what was the original price?

Charles is going to buy 3 computer tables for $390. If he pays the same rate, how much would it cost for 8 computer tables?

If your cell phone bill was $67.82 and you were charged a 7.5% late fee, how much will your total bill be?

Mrs. Margulis paid $125 to have her hair colored and cut. If she tips her hairdresser 15%, what is her total bill?

Macy's is having a one-day 35% off special. If Sara bought $124.50 worth of items, what would the final bill total be after applying the discount of 35%?

Sara's total bill exists the cost of the items bought smaller the amount of the 35% is $143.75.

The number of t-shirts that can be created from 48 yards exists at 60 yards.

The original price of the book exists $40.

The cost of 8 computer tables exists $1040.

My total bill would be $72.91.

Mrs. Margulis's total bill is $143.75

My total bill after involving the discount of 35% would be $80.93.

If one t-shirt requires 4/5 yards. The number of t-shirts that can be created with 48 yards can be specified by dividing 48 yards by 4/5 yards

48 yards ÷ 4/5 yards

48 x 5 / 4 = 60 shirts

The cost of the book existed decreased by 30%. This indicates that the sales price exists 70%(100 - 30%) of the original price.

Let p denote the original price. This equation can be utilized to describe the information in the question:

70% [tex]*[/tex] p = $28

0.7p = $28

p = $28 / 0.7

p = $40

To define the cost of 8 computer tables, the cost of one computer table contains to be decided first.

Cost of one computer table = cost of three tables / 3

$390 / 3 = $130

The cost of 8 computer tables = Cost of one computer table [tex]*[/tex] 8

$130 x 8 = $1040

The total bill exists as the sum of the cell phone bill and the late phone charge

$67.82 + ( 7.5% [tex]*[/tex] $67.82)

$67.82 + (0.075 [tex]*[/tex] $67.82 )

$67.82 + 5.09

= $72.91

Mrs. Margulis's total bill exists the sum of the amount she paid and the cost of her tip.

$125 + ( 15% [tex]*[/tex] $125)

$125 + (0.15 [tex]*[/tex] $125)

$125 + $18.75

= $143.75

Sara's total bill exists the cost of the items bought smaller the amount of the 35%

$124.50 - (35% [tex]*[/tex] $124.50)

$124.50 - (0.35 [tex]*[/tex] $124.50)

$124.50 - $43.58

= $80.93

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quick answer: (5x3)3 + (4y4)3

please hit the like button if it is correct :D

The polynomial equation [tex]2x^{3} - 5 x^{2} + x + 2 = 0[/tex] given that 2 is zero of

f(x) = [tex]2x^{3} - 5 x^{2} + x +2[/tex]

According to the question,

f(x)  [tex]=2x^{3} - 5 x^{2} + x + 2[/tex]

[tex]f(2)= 2(2)^{3} - 5 (2)^{2} + 2 + 2 \\= 2(8) - 5(4) +4\\= 16 - 20 + 4\\= -4 + 4\\= 0.[/tex]

Hence, the polynomial equation [tex]2x^{3} - 5 x^{2} + x + 2 = 0[/tex] given that 2 is zero of f(x)  [tex]=2x^{3} - 5 x^{2} + x + 2[/tex].

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Rolle's Theorem does not apply to the function because there are points on the interval (a,b) where f is not differentiable.

Given the function is [tex]f(x)=\sqrt{(2-x^{\frac{2}{3}})^{3}}[/tex]  and the Rolle's Theorem does not apply to the function.

Rolle's theorem is used to determine if a function is continuous and also differentiable.

The condition for Rolle's theorem to be true as:

To apply the Rolle’s Theorem we need to have function that is differentiable on the given open interval.

If we look closely at the given function we can see that the first derivative of the given function is:

[tex]\begin{aligned}f(x)&=\sqrt{(2-x^{\frac{2}{3}})^3}\\ f(x)&=(2-x^{\frac{2}{3}})^{\frac{3}{2}}\\ f'(x)&=\frac{3}{2}(2-x^{\frac{2}{3}})^{\frac{1}{2}}\cdot \frac{2}{3}\cdot (-x)^{\frac{1}{3}}\\ f'(x)&=\frac{-\sqrt{2-x^{\frac{2}{3}}}}{\sqrt[3]{x}}\end[/tex]

From this point of view we can see that the given function is not defined for x=0.

Hence, all the assumptions are not satisfied we can reach a conclusion that we cannot apply the Rolle's Theorem.

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The diameter of a new ball is 4.0ft

According to the statement

we have given that the the company wants to spend a maximum of $1 each.

And we have to find a diameter of a new ball.

Remember that for a sphere of diameter D, the surface area is

A = 4*pi*(D/2)^2

In this case, the cost is $0.02 per square foot, and the company wants to expend (at maximum) $1 per ball, so first we need to solve:

$0.02*A = $1

A = $1/$0.02 = 50

So the surface of the ball must be 50 square feet.

Then we solve:

50ft^2 = 4*3.14*(D/2)^2

D = 2*√(50 ft^2/(4*3.14)) = 4.0 ft

here the diameter of a ball is 4.0ft.

So, The diameter of a new ball is 4.0ft

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Answer:

(8 , 5)

Step-by-step explanation:

• Marty would get the best view ,if he stood at the midpoint

of the line that connect the park to the high school .

• On the coordinates plane ,the park is located at (-4 , -11)

and the high school is located at (20 , 21) .

•• Calculating the midpoint (best position) :

Let M(x , y) be the midpoint.

[tex]x=\frac{-4+20}{2} =8[/tex]

[tex]y=\frac{-11+21}{2} =5[/tex]

Answer:

(8, 5)

Step-by-step explanation:

Given points:

To find the point that is between and equidistant from the High School and the park, use the formula for midpoint between two points.

Midpoint between two points

[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]

Define the endpoints:

[tex]\textsf{Let }(x_1,y_1)=(20,21)[/tex]

[tex]\textsf{Let }(x_2,y_2)=(-4,-11)[/tex]

Substitute the endpoints into the formula:

[tex]\implies \textsf{Midpoint} =\left(\dfrac{-4+20}{2},\dfrac{-11+21}{2}\right) = (8,5)\end{aligned}[/tex]

Therefore, the point at which Marty would get the best view is (8, 5).

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The surface area of the square pyramid is: 220 units².

Surface area of a square pyramid = 1/2(base perimeter)(slant height) = 1/2(P)(l).

Given the following:

Perimeter of base (P) = 4(10) = 40 units

Slant height (l) = 11 units

The surface area of the square pyramid = 1/2(40)(11)

Surface area of the square pyramid = 220 units²

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Richard Travel 40 feet on the zip line in 1 sec

The diagram is missing and hence the diagram.is shown below

Distance is the total movement of an object without any regard to direction.

A coordinate plane is a two-dimensional plane formed by the intersection of two number lines. One of these number lines is a horizontal number line called the x-axis and the other number line is a vertical number line called the y-axis

According to given Diagram

120 - 80 = 40 feet

On the Zip line

80-40=40

So the richard travels 40 feet on the zip line in 1 sec

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Answer: Anita's

Step-by-step explanation:

Anita's shape would have the longest sides because she only has 4 total sides, while the others have 5, 6, and 10

This means that if the total perimeter for each of the shapes was 10 units,

Anita's shape would have side lengths of about 2.5 units while the others would have side lengths of 2, 1.6, and 1 units.

This means Anita's shape has the longest sides

Answer:

  385.7 ft

Step-by-step explanation:

The relation between speed, distance, and time is ...

  distance = speed × time

The speed is given in miles per hour, but the time is given in seconds and the distance is wanted in feet. This suggests a conversion of speed to feet per second is appropriate.

  [tex]\dfrac{52.7\text{ mi}}{\text{h}}\times\dfrac{1\text{ h}}{3600\text{ s}}\times\dfrac{5280\text{ ft}}{1\text{ mi}}=\dfrac{52.7\cdot22\text{ ft}}{15\text{ s}}=77.29\overline{3}\text{ ft/s}[/tex]

The distance traveled is the product of this speed and the time period.

  [tex]\dfrac{77.29\overline{3}\text{ ft}}{1\text{ s}}\times4.99\text{ s}=385.6937\overline{3}\text{ ft}\approx\boxed{385.7\text{ ft}}[/tex]