8. Each box in a set of decorative storage boxes is a cube.
a) The sides of the smallest box are 30% of the length of the sides of the largest
box. The volume of the largest box is 7784 cubic inches more than the
volume of the smallest box. Define one or more variables, and write an
equation that represents the situation.
b) What are the lengths of the sides of the largest and smallest boxes?
c) Two of the other boxes have a total volume of 2457 cubic inches. The length
of the sides of the smaller of these boxes is 75% of those of the larger box.
Write and solve an equation to find the lengths of the sides of the boxes.

Answer:

5 ig

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

4x2= 8

8+2= 10

------

2x2 = 4

4-1=

3

-----

10-3=7

Given:

The figure of a right angle triangle.

[tex]a=b[/tex]

Hypotenuse = [tex]9\sqrt{2}[/tex] in.

To find:

The missing lengths of the sides.

Solution:

In the given right angle triangle both legs a and b are equal, and hypotenuse is [tex]9\sqrt{2}[/tex] in.

Using Pythagoras theorem, we get

[tex]Hyponteuse^2=Base^2+Perpendicular^2[/tex]

[tex](9\sqrt{2})^2=(a)^2+(b)^2[/tex]

[tex]81(2)=(a)^2+(a)^2[/tex]                    [tex][\because a=b][/tex]

[tex]81(2)=2(a)^2[/tex]

Divide both sides by 2.

[tex]81=(a)^2[/tex]

Taking square root on both sides.

[tex]\pm \sqrt{81}=a[/tex]

[tex]\pm 9=a[/tex]

Side cannot be negative. So,

[tex]9=a[/tex]

Thus, the missing side lengths are a=9 in and b=9 in.

Therefore, the correct option is C.

[tex]5x - 3[/tex]

Step-by-step explanation:

1) Expand by distributing terms.

[tex]5 + 6x - 8 - x[/tex]

2) Collect like terms.

[tex](5 - 8) + (6x - x)[/tex]

3) Simplify.

[tex] - 3 + 5x[/tex]

4) Regroup terms.

[tex]5x - 3[/tex]

Therefor the answer for this equation will be, 5x - 3.

Answer:

5x-3

Step-by-step explanation:

distribute 2 to 3x and -4

then you get 5+6x-8-x

combine like terms

5-8; 6x-x

you get: 5x-3

hopes this helps

Answer:

b. V = 336 ft³

Step-by-step explanation:

[tex]V = \frac{1}{2}bhl\\b = 14\\h = 8\\l = 6\\V = \frac{1}{2}(14)(8)(6)\\V = 336 ft^{3}[/tex]

Given:

A rectangular piece of land has an area of [tex]\dfrac{3}{4}[/tex] square mile.

The land is [tex]2\dfrac{1}{2}[/tex] miles long.

To find:

The width of the rectangular land.

Solution:

We have,

Area of a rectangle =  [tex]\dfrac{3}{4}[/tex] square mile.

Length = [tex]2\dfrac{1}{2}[/tex] miles

We know that, area of a rectangle is

[tex]A=l\times b[/tex]

[tex]\dfrac{3}{4}=2\dfrac{1}{2}\times b[/tex]

[tex]\dfrac{3}{4}=\dfrac{2(2)+1}{2}b[/tex]

[tex]\dfrac{3}{4}=\dfrac{5}{2}b[/tex]

Multiply both sides by [tex]\dfrac{2}{5}[/tex], we get

[tex]\dfrac{2}{5}\times \dfrac{3}{4}=\dfrac{2}{5}\times \dfrac{5}{2}b[/tex]

[tex]\dfrac{6}{20}=b[/tex]

[tex]\dfrac{3}{10}=b[/tex]

Therefore, the width of the land is [tex]\dfrac{3}{10}[/tex] miles.

Answer:

The slope of the line is -3/1

Step-by-step explanation:

Using the rise over run method I calculated that the slope is -3/1 because every block that the line goes over it goes 3 down.

Answer:

Slope of the Line = 3.

7 + x/4 = 15

x/4 = 15 - 7

x/4 = 8

x = 8 · 4

x = 32

Answer: x=32

Step-by-step explanation:

Given

7+x/4=15

Subtract 7 on both sides

7+x/4-7=15-7

x/4=8

Multiply 4 on both sides

x/4 ×4=8×4

x=32

Hope this helps!! :)

Please let me know if you have any questions

Answer:

nine is the area I think

Step-by-step explanation:

base times height is width

Answer:

27 in. ^2

Step-by-step explanation:

Ok. Let's start by reflecting on what the definition of lateral area is. In this case, it's all the faces except the 2 equilateral triangle faces. So, let's find the rectangular faces. Length for all of them is 9, width for all of them is 1. So, area is 9 for all 3 lateral faces. 3*9=27.

Answer: 39°

Step-by-step explanation:

This is a right triangle, meaning one of the angles is a 90° angle. Angle CBA in this case is the 90° angle. In order to figure out the measure of ABD, you subtract the measure of CBA by the measure of CBD, which is 51°.

90 - 51 = 39

Thus, the measure of ABD is 39°

Answer:

Step-by-step explanation:

3.8

Hope it helps

Please mark brainest

Answer:

70

Step-by-step explanation:

the sum of the three is 180, so c is 60, a is 70, and b is 50.

Answer:

Elga is 32 years old.

Step-by-step explanation:

Let Alvin's age = A

Let Elga's age = E

Alvin is 10 years younger than Elga, so A = E - 10

The sum of their ages is 54, so A + E = 54

Replace the A in the second equation with E - 10, then solve for E.

A + E = 54 becomes (E - 10) + E = 54

Combine like terms

2E - 10 = 54

Add 10 to both sides

2E = 64

Divide both sides by 2

E = 32

Answer:

20

Step-by-step explanation:

LC = 1/2 LH

2LC = LH

2(10) = LH

LH = 20

Answer:

20

Step-by-step explanation:

Answer:

third and fourth one.

Not sure tho

Answer:

5: c, 3: a

Step-by-step explanation:

Answer: n^2+5n+4r+7

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]8.5+50\%\times8.5=8.5+0.5\times8.5=8.5+4.25=12.75[/tex]

Answer:

angle x=10

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

got it right on edjenuity

Answer:

you literally just translate each shape by the number of squares specified.

Step-by-step explanation:

for example, move shape 1 5 squares to the right, then 4 down. it will be in the middle area of quadrant 1 (where it already is).

Answer:

hope this helps you out good luck

Answer: answer is d

Step-by-step explanation:

i would explain but im helping 7 other people rn

Answer: c = 1.05p

Step-by-step explanation:

Price of the hat = p

Percentage increase in the price of the hat = 5%

The equation to calculate the increase of the total cost, c, of the hat will be:

c = p + (5% × p)

= p + (5/100 × p)

= p + (0.05 × p)

= p + 0.05p

c = 1.05p

Answer:

B

Step-by-step explanation:

when the arrow is pointing toward the left side that means less than side. When the arrow is pointing towards the right side that means greater than.

Answer:

B, because that symbol means at least so you would go to the negative side which is on the left it has to start from 4 which is correct and this means negative: - The 0 is the origin so from the origin to the left side is negative from the origin to the right side is positive you want to look for negative because it's negative 4.

Answer:

[tex]1\frac{3}{5}[/tex] or 1.4 as a decimal

since i don't know which way you need

Step-by-step explanation:

Answer:

a = 9

b = 6

I hope you can do the rest yoyrself, as I coulsnt find how to type it out ;-;

Answer:

1) 117

2) 9

3) 45 or -45

Step-by-step explanation:

a=9

b=6

1) a²+b²=9²+6²=81+36=117

2) (a-b)²=(9-6)²=3²=9

3) a²-b²=81-36=45

It’s also possible that a=6 and b=9, in which case

1) (same)

2) (same)

3) 36-81=-45

Answer:

When we have a set of N elements, the number of combinations of K elements (such that N ≤ K) from these N elements is:

[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]

Then if we have 8 different types of carpet, and we want to see how many different samples of 3 types we can choose, we just need to replace N by 8, and K by 3 in the above equation:

[tex]C(8, 3) = \frac{8!}{(8 - 3)!*3!} = \frac{8!}{5!*3!} = \frac{8*7*6}{3*2} = 56[/tex]

So there are 56 different samples.

Now we can do the same, but this time we want to use 5 types of carpet, then we will have K = 5.

[tex]C(8, 5) = \frac{8!}{(8 - 5)!*5!} = \frac{8!}{3!*5!} = 56[/tex]

Again, we have 56 different samples.