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## Oscar Corporation is planning to construct an elliptical gate at its headquarters. The width of the ellipse will be 5 feet across and its maximum height along the center will be 3 feet. The company wants to place two bright spots at the foci of the ellipse. How far from the center of the ellipse will the spots be located?

Draw the elliptical gate and show the foci, the width, and height as in the figure below.
Note that
a = 5 ft, the width
b = 3 ft, the height

The center is at (0,0).
The foci are at (c, 0) and at (-c, 0).

The foci are related to a and b by
c² = a² – b²
= 5² – 3² = 16
c = +4 or -4

The foci are located 4 ft horizontally from the center of the ellipse.

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## A rectangle has a length of the cube root of 81 inches and a width of 3 to the 2 over 3 power inches. Find the area of the rectangle. Select one: a. 3 to the 2 over 3 power inches squared b. 3 to the 8 over 3 power inches squared c. 9 inches squared d. 9 to the 2 over 3 power inches squared

A rectangle has a length of the cube root of 81 inches and a width of 3 to the 2 over 3 power inches. Find the area of the rectangle. Select one: a. 3 to the 2 over 3 power inches squared b. 3 to the 8 over 3 power inches squared c. 9 inches squared d. 9 to the 2 over 3 power inches squared

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## Joshua wants to buy some land in Wyoming to start a free range chicken ranch. He wants the land to have a length 500 feet greater than the width, so the chickens have room to run. If the area of the land needs to be 1,742,400 square feet, what must the length be? Round answer to the nearest whole foot.

Joshua wants to buy some land in Wyoming to start a free range chicken ranch. He wants the land to have a length 500 feet greater than the width, so the chickens have room to run. If the area of the land needs to be 1,742,400 square feet, what must the length be? Round answer to the nearest whole foot.

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## Bruno is sewing a large rectangular tablecloth for a restaurant. He has 30 square feet of fabric, and the length of the table cloth needs to be 7.5 feet. What is the width of the tablecloth if he uses all of the fabric?

Bruno is sewing a large rectangular tablecloth for a restaurant. He has 30 square feet of fabric, and the length of the table cloth needs to be 7.5 feet. What is the width of the tablecloth if he uses all of the fabric?

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## The length of the base of a rectangular pyramid is tripled, the width of the base remains the same, and the height of the pyramid is divided by 7. What volume formula reflects these changes?

The volume of a rectangular pyramid is given by:

V=lbh/3

Where l is the length

b is the breath

and h is the height.

Now, l’,b’ and h’ be new length,breath and height

Then, l’=3l

b’=b

and h’=h/7

New volume=V’=l’b’h’/3

=

=

Hence, Volume formula which reflects these changes is:

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## Which equation can be used to calculate the area of the shaded triangle in the figure below? A rectangle is shown with a width of 6 ft and a length of 16 ft. There is a diagonal line through the rectangle, and the bottom half is shaded in grey. choices 2(16 × 6) = 192 square feet 2(16 + 6) = 44 square feet 1 over 2.(16 × 6) = 48 square feet 1 over 2.(6 + 16) = 11 square feet

Which equation can be used to calculate the area of the shaded triangle in the figure below? A rectangle is shown with a width of 6 ft and a length of 16 ft. There is a diagonal line through the rectangle, and the bottom half is shaded in grey. choices 2(16 × 6) = 192 square feet 2(16 + 6) = 44 square feet 1 over 2.(16 × 6) = 48 square feet 1 over 2.(6 + 16) = 11 square feet

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## A rectangular pool has a tile border around its perimeter that measures 66 feet. If the length of the pool is 18 feet, what is the width of the pool?

A rectangular pool has a tile border around its perimeter that measures 66 feet. If the length of the pool is 18 feet, what is the width of the pool?

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## A rectangular deck is 12ft by 14ft. When the length and width are increased by the same amount, the area becomes 288sq. ft. By how much were the dimensions increased?

A rectangular deck is 12ft by 14ft. When the length and width are increased by the same amount, the area becomes 288sq. ft. By how much were the dimensions increased?

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## Adenan makes a scale drawing of a rectangular flower box. The length is 5 in., and the width is 3 in. Adenan changes the scale of the drawing from 1 in. : 4 ft to 1 in. : 6 ft. Which statement about the dimensions of the flower box is true? A. The length of the flower box under the new scale is 15 ft. B. The length of the flower box under the old scale is 30 ft. C. The width of the flower box under the old scale is 12 ft. D. The width of the flower box under the new scale is 24 ft.

Since the scale is 1 inch = 6 feet, you would have to take the legth in inches of the scale drawing and multiply that by 6, so you would  have 5×6=30 for the length and 3×6=18 for the width under the new scale, both A and D are incorrect. In the old scale, 1 inch = 4 ft, so youu would take 5×4=20 for the length and 3×4=12 for the width, which would mean C is the correct answer.

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## Jared is building a rectangular prism garden box and wants to use soil that he already has in his shed. He decides that he wants the length of the garden box to be 2 feet longer than the width and the height to be 1 foot shorter than the width. Create an expression in terms of x, where x is the width of the garden, to demonstrate the volume of the garden box.

Jared is building a rectangular prism garden box and wants to use soil that he already has in his shed. He decides that he wants the length of the garden box to be 2 feet longer than the width and the height to be 1 foot shorter than the width. Create an expression in terms of x, where x is the width of the garden, to demonstrate the volume of the garden box.

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## Height of window 0.6 feet less than 2.5 times it width height of window 4.9 feet

Suggest you use some punctuation here:  “The height of window is 0.6 feet less than 2.5 times it width.  The height of window  is 4.9 feet.  Find the width of the window.”

height of window = 4.9 feet = 2.5(width) – 0.6 feet.

simplify this equation by adding 0.6 feet to both sides of the equation:

4.9 feet + 0.6 feet = 2.5 (width); find width:

5.5 feet = 2.5 (width)

Dividing both sides of this equation by 2.5 will result in an equation for the width of the window, in feet.

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## A rectangular photograph has an area of 104 square inches. if the width of the photograph is 5 inches less than its hight, find the dimensions

A rectangular photograph has an area of 104 square inches. if the width of the photograph is 5 inches less than its hight, find the dimensions

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## The perimeter of a rectangle is 20 feet. of all possible dimensions, the maximum area is 25 square feet when its length and width are both 5 feet. are there dimensions that yield a minimum area? explain.

Answer:  The correct option is (C). 10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared

Step-by-step explanation:  Given that the segment AB has point A located at (8, 9). The distance from A to B is 10 units.

We are to select the correct option that could be used to calculate the coordinates for point B.

Let, (x, y) be the co-ordinates of point B.

According to distance formula, the distance between two points (a, b) and (c, d) is given by

Therefore, the distance between the points A(8, 9) and B(x, y) is given by

Since, distance between A and B is 10 units, so

d = 10.

Therefore,

Thus, the correct statement is

10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared.

Option (C) is correct.

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## Larry wants to buy some carpeting for his living room. The length of the room is 3 times the width and the total area of the room is 27 square meters.

Answer:  The correct option is (C). 10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared

Step-by-step explanation:  Given that the segment AB has point A located at (8, 9). The distance from A to B is 10 units.

We are to select the correct option that could be used to calculate the coordinates for point B.

Let, (x, y) be the co-ordinates of point B.

According to distance formula, the distance between two points (a, b) and (c, d) is given by

Therefore, the distance between the points A(8, 9) and B(x, y) is given by

Since, distance between A and B is 10 units, so

d = 10.

Therefore,

Thus, the correct statement is

10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared.

Option (C) is correct.

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## Write an equation of an ellipse in standard form with the center at the origin and a height of 4 units and width of 5 units.

The standard form of equation of an ellipse is in the
form:

[(x – h)^2] / a^2 + [(y – k)^2] / b^2 = 1

Where, h and k are the center points, and a and b are one
half the length of the major and minor axis.

Since height is 4 units and width is 5 units, therefore:

a = 5 / 2 = 2.5

b = 4 / 2 = 2

and h = k = 0 (at the origin)

The standard equation then becomes:

x^2 / (2.5)^2 + y^2 / 2^2 = 1

x^2 / 6.25 + y^2 / 4 =1

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## Then length of a rectangle is 5 units longet than its width. which if the following represents its area in square units?5xx (5-x)x (x-5)x (x+5)2x+2 (x+5)

Then length of a rectangle is 5 units longet than its width. which if the following represents its area in square units?5xx (5-x)x (x-5)x (x+5)2x+2 (x+5)

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## Find the vertex, focus, directrix, and focal width of the parabola. -1/40 x^2=y

the vertex is at (0,0)

the focus is at (0, -10)

the directrix is y = 10

the focal width = |-40| = 40

Step-by-step explanation:

The equation of the parabola :

Which shows that the given parabola is a vertical parabola and the standard form of the vertical parabola is written as :

the vertex is at (h,k)

the focus is at (h,k+p)

the directrix is y = k−p

the focal width = |4p|

So, changing the given equation of parabola into standard form we get :

On comparing it with equation (1) we get

p = -10 , h = 0 , k = 0

Therefore, the vertex is at (0,0)

the focus is at (0, -10)

the directrix is y = 10

the focal width = |-40| = 40

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## Whats the perimeter of a rectangle with length 12 m and width 5m

Whats the perimeter of a rectangle with length 12 m and width 5m

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## If the telescope is 1 m deep and 8 m wide, how far is the focus from the vertex? 1 2 4 16 Find the vertex, focus, directrix, and focal width of the parabola. negative 1 divided by 12 times x squared = y

First, let me introduce the general equation of the parabola:

(x-h)^2 = +/- 4a(y-k) or (y-k)^2=+/- 4a(x-h), where

(h,k) are the coordinates of the vertex
a is the distance of the vertex to the focus
4a = length of lactus rectum or the focal width

If the equation contains (x-h)^2, then the parabola passes the x-axis twice. Similarly, (y-k)^2 passes the y-axis twice. If the sign is (-), it opens to the left(if y-axis) or downward (if x-axis). If the sign is (+), it opens to the right(if y-axis) or upward (if x-axis).

The equation of the parabola is -1/12 x^2 = y. Rearranging to the general form:

x^2 = -12y
Therefore,

-4a = -12
4a = 12
a = 3, and the parabola is facing downwards.

The vertex is (0,0) at the origin.
The focus is (0,-3). Since it is negative, the focus is situated downwards, hence -3.
The directrix is the mirror image of the focus. Hence, it is a line passing +3 on the y-axis. y=3
Focal width is 4a which is equal to 12 units.

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## A recatangle's length is 2 units more than twice its width.It's area is 40 square units.The equation w(2w+2)=40 can be used to find w,the width of the rectangle.What is the width of the rectangle?

A recatangle’s length is 2 units more than twice its width.It’s area is 40 square units.The equation w(2w+2)=40 can be used to find w,the width of the rectangle.What is the width of the rectangle?

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## During low tide, the beachfront in some places is about 350 from the ocean to the homes . High tide can change the width of a beach at a rate of -17 feet each hour . It takes 6 hours for the ocean to move from low to high tide . What is the change in the width of the beachfront from low to high tide ?

You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.

So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:

C (m,n) = m! / (n! * (m -n)! )

=> C (50,30) = 50! / (30! (50 – 30)! ) = (50!) / [30! (50 – 30)!] = 50! / [30! 20!] =

= 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.

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## The area of a rectangle is 35 feet^2, and the length of the rectangle is 8 feet less than three times the width. Find the dimensions of the rectangle

5 in 0.05 is 10 times greater than 5 in 0.005.

Step-by-step explanation:

To find : In which number does the digit 5 have greater value 0.05 or 0.005 how many times as great is it and how do you know ?

Solution :

According to the place value stem,

Ones      Tenths      Hundredths     Thousandths

0              0                   5                                           – 0.05

0              0                   0                        5                 – 0.005

In 0.05 5 is in hundredths place and in 0.005 5 is in thousandths place.

So, 5 in 0.05 is 10 times greater than 5 in 0.005.

As

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## Iris has a family photograph with a width of 8 in and height of 10 in. She wants to enlarg the photograph so that it’s width is 12 in. What will the height of the enlarged photograph be?

Answer:  The correct option is (C). 10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared

Step-by-step explanation:  Given that the segment AB has point A located at (8, 9). The distance from A to B is 10 units.

We are to select the correct option that could be used to calculate the coordinates for point B.

Let, (x, y) be the co-ordinates of point B.

According to distance formula, the distance between two points (a, b) and (c, d) is given by

Therefore, the distance between the points A(8, 9) and B(x, y) is given by

Since, distance between A and B is 10 units, so

d = 10.

Therefore,

Thus, the correct statement is

10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared.

Option (C) is correct.

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## The length of a rectangle is three times its width. if the perimeter of the rectangle is 98 cm , find its area.

5 in 0.05 is 10 times greater than 5 in 0.005.

Step-by-step explanation:

To find : In which number does the digit 5 have greater value 0.05 or 0.005 how many times as great is it and how do you know ?

Solution :

According to the place value stem,

Ones      Tenths      Hundredths     Thousandths

0              0                   5                                           – 0.05

0              0                   0                        5                 – 0.005

In 0.05 5 is in hundredths place and in 0.005 5 is in thousandths place.

So, 5 in 0.05 is 10 times greater than 5 in 0.005.

As

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## The area of a desk top is 8 3/4 square feet. If the length is 3 1/2 ft, find the width

Answer:  The correct option is (C). 10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared

Step-by-step explanation:  Given that the segment AB has point A located at (8, 9). The distance from A to B is 10 units.

We are to select the correct option that could be used to calculate the coordinates for point B.

Let, (x, y) be the co-ordinates of point B.

According to distance formula, the distance between two points (a, b) and (c, d) is given by

Therefore, the distance between the points A(8, 9) and B(x, y) is given by

Since, distance between A and B is 10 units, so

d = 10.

Therefore,

Thus, the correct statement is

10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared.

Option (C) is correct.