The Cotton family purchases a glass sculpture in the shape of a rectangler pyrimad.The base measures 7 1/2 inches by 5 inches.If the volume of the sculpture is 75 cubic inches, what isthe height of the pyrimad, in inches?
Answer Choices:
A) 15in
B) 6in
C) 2in
D) 37.5in

Answer:

22.4

Step-by-step explanation:

Is means equals and of means multiply

W = 28% * 80

Change to decimal form

W = .28 * 80

W = 22.4

28 percent of 80 is 22.4

Answer:

22.4

Step-by-step explanation:

80/x = 100/28

80/x = 3.57142857143

times both sides by x

x cancels out on the left and leaves on the right 3.57142857143 x

80/3.57142857143 = x

22.4 = x

The correct option is c.

The area of the figure is [tex]\( 320 \)[/tex] square millimeters.

To find the area of the given figure, which is composed of a triangle and a rectangle, follow these steps:

1. Calculate the area of the rectangle: The area of a rectangle is found by multiplying the length by the width. From the figure, we see that the length is 20 mm and the width is 15 mm. So, the area [tex]\( A_{\text{rectangle}} \)[/tex] is:

[tex]\[ A_{\text{rectangle}} = \text{length} \times \text{width} = 20 \, \text{mm} \times 15 \, \text{mm} \][/tex]

2. Calculate the area of the triangle: The area of a triangle is found by using the formula [tex]\( \frac{1}{2} \times \text{base} \times \text{height} \)[/tex]. The base of the triangle is 20 mm (same as the length of the rectangle) and the height, which is the perpendicular distance from the base to the opposite vertex, is 2 mm. So, the area [tex]\( A_{\text{triangle}} \)[/tex] is:

[tex]\[ A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 20 \, \text{mm} \times 2 \, \text{mm} \][/tex]

3. Add the areas of the rectangle and triangle to find the total area: The total area [tex]\( A_{\text{total}} \)[/tex] is the sum of [tex]\( A_{\text{rectangle}} \)[/tex] and [tex]\( A_{\text{triangle}} \)[/tex].

 [tex]\[ A_{\text{total}} = A_{\text{rectangle}} + A_{\text{triangle}} \][/tex]

Now let's calculate the areas with the given dimensions.

The area of the rectangle is [tex]\( 300 \)[/tex] square millimeters, and the area of the triangle is [tex]\( 20 \)[/tex] square millimeters. Adding these together gives us the total area of the figure:

[tex]\[ A_{\text{total}} = A_{\text{rectangle}} + A_{\text{triangle}} = 300 \, \text{mm}^2 + 20 \, \text{mm}^2 = 320 \, \text{mm}^2 \][/tex]

Therefore, the answer is [tex]\( 320 \)[/tex] square millimeters.

The options are give here:

A. 175 square millimeters.

B. 200 square millimeters.

C. 320 square millimeters.

D. 350 square millimeters.

Answer:

[tex]\large{\boxed{\text{the multiplication property of equality}}}[/tex]

Step-by-step explanation:

[tex]\dfrac{3x}{5}+5=20\qquad\text{subtract 5 from both sides}\\\boxed{\text{the subtraction property of equality}}\\\\\dfrac{3x}{5}+5-5=20-5\\\\\dfrac{3x}{5}=15\qquad\text{multiply both sides by}\ \dfrac{5}{3}\\\boxed{\text{the multiplication property of equality}}\\\\\dfrac{3\!\!\!\!\diagup^1}{5\!\!\!\!\diagup_1}\cdot\dfrac{5\!\!\!\!\diagup^1x}{3\!\!\!\!\diagup_1}=\dfrac{5}{3\!\!\!\!\diagup_1}\cdot15\!\!\!\!\!\diagup^5\\\\x=(5)(5)\\\\x=25[/tex]

Answer: C

Step-by-step explanation:

Answer:

Part a) The weight of the original statue is [tex]9,483\ pounds[/tex]

The ratio of the height of the original statue to the height of the small statue is 8.4

The ratio of the weights or volumes is [tex]8.4^{3}[/tex]

Part b)  [tex]221,184\ pounds[/tex]

Step-by-step explanation:

Part a)

we know that

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor and the ratio of its volumes or weights is equal to the scale factor elevated to the cube

step 1

Find the scale factor

remember that

[tex]1\ ft=12\ in[/tex]

The original statue is 7 ft tall

Convert to inches

[tex]7\ ft=7*12=84\ in[/tex]

Divide the height of the original statue by the height of the model to find the scale factor

[tex]\frac{84}{10}=8.4[/tex]

step 2

Find the ratio of its weights

Let

z-----> the scale factor

x-----> the weight of the original statue

y----> the weight of the model

so

[tex]z^{3}=\frac{x}{y}[/tex]

we have

[tex]z=8.4[/tex]

[tex]y=16\ lb[/tex]

substitute

[tex]8.4^{3}=\frac{x}{16}[/tex]

[tex]x=16(8.4^{3})=9,483\ pounds[/tex]

The weight of the original statue is [tex]9,483\ pounds[/tex]

The ratio of the height of the original statue to the height of the small statue is 8.4

The ratio of the weights or volumes is [tex]8.4^{3}[/tex]

Part b) If the original statue were 20 ft tall, how much would it weight?

step 1

Find the scale factor

remember that

[tex]1\ ft=12\ in[/tex]

The original statue is 20 ft tall

Convert to inches

[tex]20\ ft=20*12=240\ in[/tex]

Divide the height of the original statue by the height of the model to find the scale factor

[tex]\frac{240}{10}=24[/tex]

step 2

Find the ratio of its weights

Let

z-----> the scale factor

x-----> the weight of the original statue

y----> the weight of the model

so

[tex]z^{3}=\frac{x}{y}[/tex]

we have

[tex]z=24[/tex]

[tex]y=16\ lb[/tex]

substitute

[tex]24^{3}=\frac{x}{16}[/tex]

[tex]x=16(24^{3})=221,184\ pounds[/tex]

Answer:

x = 5

Step-by-step explanation:

As you know 32 = 2^5

so

2^x = 32

2^x = 2^5

Since both have same base 2

x = 5

32=2^x

Prime factors of 32

32 = 2 * 16

16 = 2 * 8

8 = 2 * 4

4 = 2 * 2

32 = 2*2*2*2*2

32 = 2^5

x=5

Hope this helps :)

Answer:

15625

Step-by-step explanation:

5x5=25

25 x 25 x 25=15625

Answer:

1. A(3/2,6)

B(15,33)

2.A(2/9,1/3)

B(2/3,-1/3)

Step-by-step explanation:

1) y−2x=3; A(...; 6), B(15; ...)

We know y =6

Substitute this into the equation

6 -2x =3

Subtract 6 from each side

6-6 -2x=3-6

-2x = -3

Divide by -2

x = -3/-2

x = 3/2

A(3/2,6)

We know x = 15

y - 2(15) =3

y - 30 = 3

Add 30 to each side

y-30+30 = 3+30

y = 33

B(15,33)

2) 4.5x+3y=2; A(...; 1/3 ), B( 2/3 ; ...)

We know y = 1/3

4.5x + 3(1/3) = 2

4.5x +1 =2

Subtract 1 from each side

4.5x +1-1=2-1

4.5x = 1

Divide each side by 4.5

x = 1/4.5

x = 10/45

x =2/9

A(2/9,1/3)

Let x =2/3

4.5(2/3) +3y =2

3 +3y =2

Subtract 3 from each side

3-3+3y = 2-3

3y = -1

Divide by 3

y = -1/3

B(2/3,-1/3)

Answer:

1. A(3/2;6) B(15;33)

slope=2

2. A(2/9;1/3) B(2/3;-1/3)

slope=-1.5

Step-by-step explanation:

Hope this helps,

Have a great day

Answer: B

Step-by-step explanation:

If she bought 9 packs of pens at 2.50$ each then she spent 22.50$ on pens. If you add up the packs and multiply by the price you get your answer. 2.50 * (2+3+4) = 22.50$

Answer:

[tex]1,125\ ft^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of the triangular prism that will be covered with insulation is equal to the area of the two triangular faces plus the two lateral rectangular faces

so

[tex]SA=2[\frac{1}{2}(15)(15)]+2[(30)(15)]= 1,125\ ft^{2}[/tex]

Answer:

See attached picture.

y-intercept at (0,5) and asymptote at y = 4.

Step-by-step explanation:

This graph has a base 3/4 that is less than 1. This means it will start high and end low.

It has also been shifted up 4 units by adding 4. This means the asymptote moves to from y = 0 to y =4. The y-intercept of the parent function will also move from (0,1) to (0,5).

Answer:

a. 267 hrs b.

Step-by-step explanation:

a.)4 secs divided by 5 gals is .8 secs per gal, multiply by 20,000 gals, is 16,000 secs, divide that by 60 secs in an hour and you get 266.666 hrs

b.)42 hrs with both hoses

.8 secs per gal and 7.2 secs per gal = 8 secs per gal

20,000 = 8 gals per hour = 2500 secs  divided by 60 secs per hour = 41.66

(2b^3 -7b^2) + (3b^2 + 3b^3) =

2b^3 + 3b^3 -7b^2 + 3b^2=

5b^3 -4b^2

Answer:

x=4

Step-by-step explanation:

We can find the length of RT by using the Pythagorean theorem

sin theta = opposite side/ hypotenuse

sin 60 = 2 sqrt(3)/ RT

Multiply each side by RT

RT sin 60 = 2 sqrt(3)

Divide by sin 60

RT = 2 sqrt(3)/ sin 60

RT = 4

Then

tan theta = opposite side/ adjacent side

tan 45 = x/RT

tan 45 = x/4

4 tan 45 = x

4 = x

Answer:

The answer is 1/4

The decimal form is:0.25

Step-by-step explanation:

2/1 x 1/8 + 2x 1/1 x 8+ 2/8= 2 (divide by) 2/ 8 (divide by) 2=1/4

(I added a 1 to 2 because you can't divide a fraction withour two numbers)

I AM NOT A PRO AT MATH ,SO IF I'M WRONG PLEASE LET ME KNOW :)

Answer:

A=376

the formula is (wl+hl+hw)

Step-by-step explanation:

Answer:

OPTION B:  [tex]2(3x+5)[/tex]

Step-by-step explanation:

To solve the exercise you can simplify the expression given in the problem, as following:

- Add the like terms:

[tex]3x+3x+5+5\\6x+10[/tex]

- Find the greatest common factor (GCF) of 6 and 10:

[tex]6=2*3\\10=2*5\\\\GCF=2[/tex]

- Factor ir out.

Then, you obtain the following equivalent expression:

[tex]2(3x+5)[/tex]

Answer:

6x + 10

Step-by-step explanation:

Combine like terms:

3x + 3x = 6x, and

5+5 = 10

and so the final sum is 6x + 10

Answer:

y = (-1/8)x + 10.5

Step-by-step explanation:

The given equation is y = 8x -1.  The slope is 8.

Any line perpendicular to the given equation/line has a slope which is the negative reciprocal of 8:  That would be -1/8.

We'll use the point-slope formula of a straight line to come up with a formula for this specific problem:   y - k = m(x - h), where (h, k) is the point in question and m is the slope.

Here we have y - 10 = (-1/8)(x - 4).  This is complete in itself,  But you could also present it in more compact form, as follows:

Add 10 to both sides.  We get y = (-1/8)(x - 4) + 10.

Perform the indicated mult.:  y = (-1/8)x + 1/2 + 10, or

                                                y = (-1/8)x + 10.5

Answer:

X is equal to 0.18

Step-by-step explanation:

X is that number

then

2X equal to 0.36

X equal to 0.36 divided 2

X is equal to 0.18

Best regards

it is a function because each input (x) has a unique output (y) that is not repeated

In order for a relationship between numbers x and y to be considered a function from x to y, you need to have one unique y for every x. This doesn’t mean that each y needs exactly one x; for instance, the function y = x² is a function from x to y and has two y values associated with most x values (x = 2 and x = -2, for instance, both give you y = 4).

Essentially, if we give a function some x value, we want to know exactly what y value we’re getting out of it.

The pictured table gives you two possible values for x = 2; given a 2 as input, we have no idea whether to go to 1 or 7 for our output, so it would not be a function from x to y.

(Interestingly, a function from y to x would satisfy that “one output per input” requirement, so if you wanted to impress your teacher, you could answer “yes, but only from y to x, NOT x to y”)

Answer:

The one that stands out as incorrect is B

Step-by-Step Explanation:

I'll assume that by 12, you meant 1/2 because if the scale factor is 12, then none of the choices are correct. B is the only one that stands out because while in the x, 10 does turn into 5 after being multiplied by 1/2, the 2 in the y remained the same instead of being turned into 1.

Answer:

This figure is dilated by a factor of 12, with the origin as center.  

Which statement is NOT correct?

A)R(2, 8) → R'(1, 4)

B)Q(10, 2) → Q'(5, 2)

C)P(2, -4) → P'(1, -2)

 D)S(-10, 2) → S'(-5, 1)

​

Step-by-step explanation:

As you can see in A,C and D, the x-coordinate and the y-coordinate is divided by 2.

E.g.  2 / 2 =1     8/2=4    so ⇒R'(1, 4)  

but in B, the first x-coordinate is divided by 2 but the y-coordinate is divided by 1.

Answer:

1. Volume of cube-shaped box = 91.125 cubic inches

2. Volume of shipping box = 729 cubic inches

3. 8 boxes of office supplies can be packed into the larger box for shipping.

Step-by-step explanation:

1.

The first question asks for the volume of a cube. The formula is  V = s^3, where, s is the side length and V is the volume. Thus plugging in, we get:

[tex]V=s^3\\V=(4\frac{1}{2})^3\\V=(4.5)^3\\V=91.125[/tex]

Volume of cube-shaped box = 91.125 cubic inches

2.

The second question asks for the volume of the shipping box. Since 3 measurements are given, the shipping box is a rectangular prism. The volume of a rectangular prism is  V = l * w * h, where

V is the volume

l is the length

w is the width, and

h is the height

Plugging in all the info we know (multiplying the 3 numbers - dimensions), we can get the volume of the shipping box. So:

[tex]V=lwh\\V=(18)(9)(4\frac{1}{2})\\V=(18)(9)(4.5)\\V=729[/tex]

Volume of shipping box = 729 cubic inches

3.

Since the volume of a single box of office supplies (cub-shape) is 91.125 cu. in., and the volume of larger shipping box is 729, we can divide 729 by 91.125 to find how many of them would fit the large box.

[tex]\frac{729}{91.125}=8[/tex]

Hence, 8 boxes of office supplies can be packed into the larger box for shipping.

Answer:

8

Step-by-step explanation:

4 1/2=9/2*9/2=81/4*9/2=729/8

9/1*9/2*18/1=1,458/2

1,458/2*8/729=11,664/1,458

=8

So eight boxs of office supplies can be packed.

Answer:

correct option is F

Step-by-step explanation:

Suppose there is a book the cost of which is $100

You got  successive discounts of 15% off and then 25% off

So after getting 15% discount cost of book=$85

again on $85 there is a discount of 25%

it means

25% discount on $85=[tex]\frac{25\times 85}{100} \\[/tex]

=$21.25

It means after successive discounts of 15% off and then 25% off cost of book=[tex]85-21.25[/tex]

after successive discounts of 15% off and then 25% off cost of book=$63.75

On the other hand if you got 40% discount on the same book which costs $100

then after discount of 40% its cost will be=$60

It means,Taking successive discounts of 15% off and then 25% off is not same as taking a one time discount of 40%.

Therefore correct option is F

Answer:

false

Step-by-step explanation:

got it right on edg

Answer:

The radius of the cone is [tex]5\ ft[/tex]

Step-by-step explanation:

we know that

The volume of a cone is equal to

[tex]V=\frac{1}{3}\pi r^{2}h[/tex]

In this problem we have

[tex]V=50\pi\ ft^{3}[/tex]

[tex]h=6\ ft[/tex]

substitute in the formula and solve for r

[tex]50\pi=\frac{1}{3}\pi r^{2}(6)[/tex]

Simplify

[tex]25=r^{2}[/tex]

square root both sides

[tex]r=5\ ft[/tex]

Answer:

5ft

Step-by-step explanation:

I did the test

Answer:

4 ft

Step-by-step explanation:

12 ft - 8 ft = 4ft

Best regards

Answer:

Step-by-step explanation:

The perimeter of the given figure is equal to the circumference of whole circle.

The formula of a circumference of a circle:

[tex]C=\pi d[/tex]

d - diameter

We have d = 70 cm. Substitute:

[tex]C=70\pi\ cm[/tex]

The area of given figure is equal to the area of rectangle 70cm × 35cm.

(look at the picture).

The area of a rectangle:

[tex]A=(70)(35)=2,450\ cm^2[/tex]

Answer:

3x + 20 = 152

x= 44

Step-by-step explanation:

The formula for distance is [tex]\sqrt{(x_{2} -x_{1}) } + (y_{2} -y_{1}) }}[/tex]

if we plug our points into the equation we get √68

is their operations that you didnt list

Answer: The answer is, 20x7y9z8.

Step-by-step explanation:

Answer:

y= -3/2x + 1

Step-by-step explanation:

The slope of this line is 2/3. The slope of the line perpendicular to this line will be the negative reciprocal or -3/2.

Write the equation using the slope m=-3/2 and the point slope form.

[tex]y-y_1=m(x-x_1)\\y--2=-\frac{3}{2}(x-4)\\y+2=-\frac{3}{2}(x-4)[/tex]

This is the equation of the line. You can convert it to slope intercept form:

[tex]y+2=-\frac{3}{2}(x-4)\\y+2 = -\frac{3}{2}x + 3\\y=-\frac{3}{2}x +1[/tex]

Square, Rectangle and Rhombus