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4 years ago

The sum of 3 consecutive even integers is 576. Find the integers

1 answer:

4 0

You can write the equation
x+1+x+3+x+5=576
Combine like terms
3x+9=576
Subtract 9 from both sides
3x+9-9=576-9
3x=567
Divide both sides by 3
3x/3=567/3
x=189
The first integer is 190, the second is 192 and the third is 194 (enter it into the original equation to get those answers)

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Karen has 7 over 8cup of ice cream. How many 1 over 3cup servings can she make?

STALIN [3.7K]

Answer:

1 and 5 over 24

Step-by-step explanation:

its right trust me because 1+1 is 3

8 0

3 years ago

A glass paperweight has a composite shape: a square pyramid fitting exacty on top of an 8 centimeter cube. The pyramid has a hei

ArbitrLikvidat [17]

Answer:

Part 1) The volume of the paperweight is $576\ cm^{3}$

Part 2) The total surface area of the paperweight is $400\ cm^{2}$

Step-by-step explanation:

Part 1) what is the volume of the paperweight?

we know that

The volume of the paperweight is equal to the volume of the square pyramid plus the volume of the cube

step 1

Find the volume of the pyramid

The volume of the pyramid is equal to

$V=\frac{1}{3}BH$

where

B is the area of the square base

H is the height of the pyramid

$B=8^{2}=64\ cm^{2}$

$H=3\ cm$

substitute

$V=\frac{1}{3}(64)(3)=64\ cm^{3}$

step 2

Find the volume of the cube

The volume of the cube is equal to

$V=b^{3}$

$V=8^{3}=512\ cm^{3}$

step 3

Find the volume of the paperweight

$64\ cm^{3}+512\ cm^{3}=576\ cm^{3}$

Part 2) what is the total surface area of the paperweight?

we know that

The total surface area of the paperweight is equal to the surface area of 5 faces of the cube plus the lateral area of the pyramid

step 1

Find the surface area of 5 faces of the cube

$SA=5b^{2}$

$SA=5(8^{2})=320\ cm^{2}$

step 2

Find the lateral area of the pyramid

$LA=4[\frac{1}{2}bh]$

$LA=4[\frac{1}{2}(8)(5)]=80\ cm^{2}$

step 3

Find the total surface area of the paperweight

$320\ cm^{2}+80\ cm^{2}=400\ cm^{2}$

8 0

3 years ago

Find the coordinates of the midpoint of the segment with the given endpoints.

uysha [10]

$(\frac{x_{1} + y_{1}}{2}, \frac{x_{2} + y_{2}}{2}) \\(\frac{6 + 10}{2}, \frac{-3 + 5}{2}) \\(\frac{16}{2}, \frac{2}{2}) \\(8, 1)$

8 0

3 years ago

Pam pays $8.00 for 1 yard of fabric. How much would the fabric cost per inch? Round your answer to the nearest cent, if necessar

Aloiza [94]

$8 per yard of fabric
1 yard is equal to 3 feet
8 divided by 3 = 2.67(rounded)
$2.67 per foot of fabric
1 foot is equal to 12 inches
2.67 divided by 12 =0.22(rounded)
1 inch of fabric cost $0.22

3 0

3 years ago

Can someone help or show me how to simplify this equation 22.5+7(n-3.4)

Scorpion4ik [409]

22.5+7 (n-3.4)=19.8n

We simplify the equation to the form, which is simple to understand
22.5+7(n-3.4)=19.8n

Reorder the terms in parentheses
22.5+(+7n-23.8)=19.8n

Remove unnecessary parentheses
+22.5+7n-23.8=+19.8n

We move all terms containing n to the left and all other terms to the right.
+7n-19.8n=-22.5+23.8

We simplify left and right side of the equation.
-12.8n=+1.3

We divide both sides of the equation by -12.8 to get n.
n=-0.1015625

5 0

3 years ago

Read 2 more answers