Simplify where a = 9 and b = 8 2a

Two triangular prisms are similar. The perimeter of each face of one prism is double the perimeter of the

shepuryov [24]

The area of a shape is the amount of space it can occupy.

The surface area of the larger prism is 4 times the surface area of the smaller prism.

Let the dimension of one side of the smaller prism be: l and w

Let the dimension of one side of the bigger prism be: L and W

So, we have:

$L = 2l$

$W =2w$

The area of these corresponding sides are:

$A_1 =l \times w$ ---- the first

$A_1 = lw$

While, the area of the second is:

$A_2 =2l\times 2w\\$

$A_2 =4lw$

The ratio of these two sides are:

$Ratio = A_1 : A_4$

This gives

$Ratio = lw : 4lw$

Cancel out common terms

$Ratio = 1 : 4$

Express as fractions

$Ratio = \frac 14$

Also, we have:

$Ratio = \frac{Small}{Large}$

This gives

$\frac{Small}{Large} = \frac 14$

Cross multiply

$Large = 4 \tiimes Small$

$Large = 4\4Small$

Hence, option (c) is true

Read more about areas at:

brainly.com/question/6465134

4 0

2 years ago

The legs of a right triangle measure 8 cm and 6 cm respectively. How long is the longest side of the triangle?

Masja [62]

Answer:

b. 10

Step-by-step explanation:

Based on the Pythagoras Theorem, the longest side of a right-angled triangle is: $\sqrt{a^{2}+b^{2} }$ where a and b are the legs of the triangle.

Longest side of triangle = $\sqrt{8^{2}+6^{2}}$

= $\sqrt{64+36}$

= $\sqrt{100}$

= 10

5 0

3 years ago

Round 117.22666 to the nearest tenths

zzz [600]

Answer:

117.2

Step-by-step explanation:

Rounding a number to the nearest tenth:

A number rounded to the nearest tenth will have one decimal place.

To do this, we look at the second decimal digit.

If it is less than 5, the first decimal digit is kept.

Otherwise, one is added to the first decimal digit.

In this question:

117.22666

The second decimal digit is 2, which means that we keep the first decimal digit which is also 2.

So, the number rounded to the nearest tenth is 117.2.

6 0

3 years ago

What is the setting for "the three brass pennies"

lara [203]

Three brass pennies is the short story and the setting of this story is Ancient Chinese city.

The theme of the story is about desires and happiness. It is not necessary that what we desire bring happiness in our lives. Sometimes we think and desire for something that may be it brings happiness but instead of happiness it causes trouble.

7 0

3 years ago

A railroad track runs parallel to a highway from City A to City B. An express train and an automobile leave City A at the same t

Nookie1986 [14]

City A is far from City B by 170 miles

Step-by-step explanation:

A railroad track runs parallel to a highway from City A to City B

An express train and an automobile leave City A at the same time
The train travels 85 mph
The automobile travels at 50 mph
The train arrives 1 hour and 24 minutes before the automobile arrives

We need to find how far is City A from City B

Assume that the distance from City A to City B is x mile

∵ Distance = Speed × Time

∴ Time = $\frac{Distance}{Speed}$

∵ The speed of the train = 85 mph

∵ Distance between city A and city B = x miles

∴ The time for the train = $\frac{x}{85}$ hours

∵ The speed of the automobile = 50 mph

∵ Distance between city A and city B = x miles

∴ The time for the automobile = $\frac{x}{50}$ hours

The train takes time less because it travels by high speed

∵ The train arrives 1 hour and 24 minutes early then the automobile

- Change the time to hour only

∵ 1 hour = 60 minutes

∴ 24 minutes = $\frac{24}{60}$ hour

∴ 24 minutes = 0.4 hour

∴ The train arrives 1.4 hours early then the automobile

Now lets subtract the time of the train from the time of the automobile and equate the answer by 1.4

∵ $\frac{x}{50}-\frac{x}{85}=1.4$

- Multiply each numerator by the other denominator and multiply

the two denominators to make the two fraction a single fraction

∴ $\frac{85x-50x}{(50)(85)}=1.4$

∴ $\frac{35x}{4250}=1.4$

- Multiply both sides by 4250 to cancel the denominator

∴ 35x = 5950

- Divide both sides by 35

∴ x = 170

City A is far from City B by 170 miles

Learn more:

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7 0

3 years ago