Paul has three​ cube-shaped boxes. Each box is a different size and they are stacked from the largest to the smallest. Some information about the boxes is given below. Answer questions 15 below.

The combined volume of the three boxes is​ 1,197 cubic inches.

The area of one face of the medium box is 49 square inches.

The volume of the smallest box is 218 cubic inches less than the volume of the medium box.

1. What is the volume of the medium​ box? Explain.

The edge length of the medium box is

â–Ľ

StartFraction StartRoot 49 EndRoot Over 2 EndFraction comma

StartRoot 49 EndRoot comma

RootIndex 3 StartRoot 49 EndRoot comma

StartFraction 49 Over 2 EndFraction comma

which equals

nothing. The volume of the box is the edge length

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squared,

doubled,

tripled,

cubed,

which equals

nothing

â–Ľ

cubic inch(es).

inch(es).

square inch(es).

Answer:

if you use the 10 feet ladder base is 6 feet

if you use 12 feet ladder base is 8.94 feet

if you use 15 feet ladder base is 12.69 feet

Step-by-step explanation:

you know the ladder length so you know the hypotenuse

you can use a^2 + b^2= c^2

for example you use the 10 feet ladder

8^2+b^2 = 10^2

64 + b^2 = 100

subtract 64 from both sides

b^2=36

to get rid of the exponent find square root

b= 6

you can plug in the different values like 15 or 12

(A−5)(A+4) I think that is the right answer

Answer:

It would be A

Step-by-step explanation:

when you rotate Clockwise goes -> Counterclockwise goes <-

So you want to go -> so we are going Clockwise because that brings us to the "square" that DOG is in and when you do CAT is still 2 spots farther to the right from DOG so you want to go 2 to the left.

CAT:

when you rotate it clockwise 90 degrees

C goes at  (0,6)

A goes at (4,-6)

T goes at (2, -2)

Answer:

The answer is 16.746667

Step-by-step explanation:

1) Simplify 3.14 × 16 to 50.24.

[tex]50.24 \div 3[/tex]

2) Simplify 50.24 ÷ 3 to 16.746667.

[tex]16.746667[/tex]

Therefor. the answer is 16.746667.

Answer:

I'm pretty sure it's just 7.0 because seven is the nearest 10th because it's only .1

Answer:

13/100 or 13% is equivalent to 0.13

Step-by-step explanation:

hope this helps

Answer:

I believe the third option is correct!

{(-5,1), (-3,2), (-1,3), (1,4), (3,5)}

Hope this helps!

Answer:

[tex]Area = 4h^2-56h +144[/tex]

Step-by-step explanation:

Given

See attachment for complete question

Required: The base area.

From the question, we have the initial dimensions to be:

[tex]Length = 12[/tex]

[tex]Width = 12[/tex]

h inch were removed from each corner to form the new base. So, the dimension of the new base is:

[tex]Base\ Length = Length - h - h[/tex]

[tex]Base\ Length = Length - 2h[/tex]

[tex]Base\ Width = Width - h-h[/tex]

[tex]Base\ Width = Width - 2h[/tex]

The area of the base is calculated by multiplying the base dimensions

[tex]Area = Base\ Length * Base\ Width[/tex]

[tex]Area = [Length - 2h] * [Width - 2h][/tex]

[tex]Area = [12 - 2h] * [12 - 2h][/tex]

Expand

[tex]Area = 12[12 - 2h] -2h [12 - 2h][/tex]

[tex]Area = 144 - 28h -28h + 4h^2[/tex]

[tex]Area = 144 -56h + 4h^2[/tex]

Rewrite as:

[tex]Area = 4h^2-56h +144[/tex]

Answer:

8 cm

Step-by-step explanation:

If the 16 cm is the diameter then the radius is 8 cm. To find the radius of a circle you simply divide two by the diameter. 16 ÷ 2 = 8

Answer:

the number is 5

Step-by-step explanation:

((n x 5 + 3.5) ÷ 2) -7.6 = 6.65

( 5n + 3.5) ÷ 2 = 14.25

5n + 3.5 = 28.5

5n = 25

n = 5

Answer:

93.5ft

Step-by-step explanation:

Veremos que en la imagen 10 hay 37 circulos, y la diferencia entre las imagenes 12 y 7 es de 20 circulos.

Primero, debemos contar la cantidad de circulos que tenemos en las imagenes mostradas.

Entonces podemos ver que en cada imagen se agregan 4 circulos, es decir tenemos una secuencia aritmetica, de tal forma que la imagen número N tendremos:

[tex]C_N = 1 + (N - 1)*4[/tex]

Entonces, cuantos circulos hay en la imagen 10? para ver eso reemplazamos N por 10.

[tex]C_{10} = 1 + (10 - 1)*4 = 37[/tex]

¿Cuántos círculos más tendrá la imagen 12 respecto de la imagen 7?

Para ver esto calculamos:

[tex]C_12 - C_7 = (1 + (12 - 1)*4) - (1 + (7 - 1)*4) = 11*4 - 6*4 = 20[/tex]

Es decir, la image 12 tiene 20 circulos más que la imagen 7.

Sí quieres aprender más sobre secuencias, puedes leer:

https://brainly.com/question/7882626

Answer:

$23.22 per day.

Step-by-step explanation:

For a general function f(x), the average rate of change between A and B (when B > A) is:

[tex]r = \frac{f(B) - f(A)}{B - A}[/tex]

In this case we know that the function is:

f(x) = 0.01*(2)^x

And we want to find the average rate of change from day 7 to day 14

Then if we use the above equation we get that the rate of change from day 7 to day 14 is:

[tex]r = \frac{0.01*(2)^{14} - 0.01*(2)^7}{14 - 7} = 23.22[/tex]

Because this equation is in dollars, we can conclude that the average rate of change between day 7 and day 14 is $23.22 per day.

An average rate of change between A and B (where B>A) for a generic function [tex]f(x)[/tex] is:

[tex]\to r=\frac{f(B)-f(A)}{B-A}\\\\[/tex]

[tex]\to f(x) = 0.01\times (2)^x[/tex]

[tex]\to r=\frac{0.01\times 2^{14} -0.01 \times 2^7}{14-7}=23.22[/tex]

Since this equation is stated in dollars, we can calculate that the average rate of change between days 7 and 14 is [tex]\$23.22[/tex] each day.

Learn more:

brainly.com/question/12997887

Answer:

20, 45

Step-by-step explanation:

A triangle has 180 degrees interior angle measure. One angle measure 115 so that means the other two angles  must add up to 65.

The remaning angles form a ratio of 4:9. This means we must split 65 into a ratio of. 4:9

A ratio partition parts of something. We can add the ratio intergers to find it full length.

4+9=13.

Divide 65/13=5.

Multiply 5x4 and 5x9 serpately.

We get 20 and 45

Answer: they are equal because the exponents are equal. Right there are in different order but they are still the same.

Step-by-step explanation:

Answer:

5(x-2)^2=20

5(x^2-4)=20

5x^2-20=20

5x^2-20-20=0

5x^2-40=0

5x^2+0x-40=0

Step-by-step explanation:

hope this is helpfull

Answer:

2:5 12:30(?)

Step-by-step explanation:

the first ones right I'm not sure about 12:30

Answer:

-10/7

Step-by-step explanation:

w - 5 = 8w + 5

w - 8w = 5 + 5

-7w = 10

w = - 10/7

Answer:

Step-by-step explanation:

To solve this equation, group like terms together:  'w' terms on the right and constants on the left:

-10 = 7w.  Then:

w = -10/7 (exact) or w ≈ 1.43

Answer: 13.) 49,  14.) 64

Step-by-step explanation:

7x7=49, 8x8=64

Answer:

1272 ft^2

Step-by-step explanation:

The area is 144*106= 15264 inches and to convert inches to feet we divide by 12 because a foot has 12 inches

15264/12 = 1272 ft^2

Answer:

y = x/x+3 is a rational function

Step-by-step explanation:

Here, we want to select the equation that is a rational function

rational functions are such that could be expressed as the division of one function by another

For example;

f(x) = g(x)/h(x)

is a rational function

so, if we applied this here,

we have it that;

y = x/x+ 3 is a rational function

Answer:

4 quarters in a gallon

Step-by-step explanation:

Answer:

x = 19.8

Step-by-step explanation:

Mathematically, when two triangles are similar, the ratio of their corresponding sides are equal

thus, we have it that;

16/28.8 = 11/x

16 * x = 11 * 28.8

x = (11 * 28.8)/16

x = 19.8

Answer:

the slope is -1.5

Step-by-step explanation:

Answer:

A≈166.28cm²

Step-by-step explanation:

A=[tex]\frac{3\sqrt{3} }{2} a^{2} = \frac{3 x \sqrt{3} }{2} x 8^{2} = 166.27688cm^{2}[/tex]