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3 years ago

Simplify.Simplify. 62+42 62+42

Mathematics

1 answer:

valentina_108 [34]3 years ago

6 0

Answer:

104

Step-by-step explanation:

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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

Gemma's mean speed on her drive home from Chicago is 59mph. If the total trip is 295 miles, how long should she expect the drive

SCORPION-xisa [38]

Answer:

5 hours

Step-by-step explanation:

If shes going 59mph and the total trip is 295mph

then you would divid 295 by 59 and get 5

5 0

2 years ago

Find the possible values of s in the inequality 12s-20 <3s-25

GaryK [48]

12s - 20 < 3s - 25 |+20

12s < 3s - 5 |-3s

9s < -5 |:9

s < -5/9

Answer: Any number from the set (-∞, -5/9).

7 0

2 years ago

Please answer this correctly

ra1l [238]

Answer:

42 13/20 km

Step-by-step explanation:

10 3/10+9 7/20+14 7/10+ 8 9/20=41+ (6+7+14+9)/20=41 + 1 13/20= 42 13/20 km

4 0

3 years ago

A plan shows a length 3cm. If the scale is 2cm:5m-what is the actual length?

posledela

Answer:

7.5m

Step-by-step explanation:

1cm:2.5m

3cm:7.5m

8 0

3 years ago