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2 years ago

A triangle with an area of 2/3 cm² is dilated by a factor of 6.

Mathematics

2 answers:

vazorg [7]2 years ago

6 0

By the word "dilation" we mean to say that the dimension of the new triangle is 6 times longer than the dimensions of the former triangle. The ratio between the area of the new triangle and the old one is equal to the square of the ratio of their sides. If we let x be the area of the larger triangle then,
(x / 2/3 cm²) = (6/1)²
The value of x from the equation is 24. Thus, the area of the larger triangle is equal to 24 cm².

Nataly [62]2 years ago

4 0

Answer:

24 cm²

Proof in Photo:

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The population of a city is modeled by the equation P(t)=232012e0.23t where t is measure in years. If the city continues to grow

Gennadij [26K]

In around 6.35 years, the population will be 1 million.

<h3> how many years will it take for the population to reach one million?</h3>

The population is modeled by the exponential equation:

$P(t) = 232,012*e^{0.23*t}$

Then we just need to solve the equation for t:

$P(t) = 232,012*e^{0.23*t} = 1,000,000$

Let's solve that:

$232,012*e^{0.23*t} = 1,000,000\\\\e^{0.23*t} = 1,000,000/232,012 = 4.31\\$

If we apply the natural logarithm to both sides:

$ln(e^{0.23*t}) = ln(4.31)\\\\0.23*t = ln(4.31)\\\\t = ln(4.31)/0.23 = 6.35$

So in around 6.35 years, the population will be 1 million.

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1 year ago

What is the area of the triangle that is 30 m base in the height of 12 m in a straight line of 13

Reika [66]

Answer:

Step-by-step explanation:

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2 years ago

What is the greatest common factor of 16ab3 + 4a2b + 8ab ?

ziro4ka [17]

Answer:

2ab(3b^2+2a+4)

Step-by-step explanation:

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Factor out the common terms

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3 years ago

The senior class want to play a practical joke on the principal, who was a former college basketball star. They want to fill his

steposvetlana [31]

The number of basketball that will fill up the entire office is approximately 16,615.

Recall:

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Volume of a rectangular prism = $l \times w \times h$

Given:

Diameter of basketball = 9.5 in.

Radius of the ball = 1/2 of 9.5 = 4.75 in.

Radius of the ball in ft = 0.4 ft (12 inches = 1 ft)

Dimension of the office (rectangular prism) = 20 ft by 18 ft by 12 ft

First, find the volume of the basketball:

Volume of ball = $\frac{4}{3} \pi r^3 = \frac{4}{3} \times \pi \times 4.75^3\\$

Volume of basketball = $448.92 $ in^3$

Convert to $ft^3$

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Therefore,

Volume of basketball = $\frac{448.92}{1728} = 0.26 $ ft^3$

Find the volume of the office (rectangular prism):

Volume of the office = $20 \times 18 \times 12 = 4,320 $ ft^3$

Number of basket ball that will fill the office = Volume of office / volume of basketball

Thus:

Number of basket ball that will fill the office = $\frac{4,320}{0.26} = 16,615$

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2 years ago

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Therefore, the correct answer is the first option. The paint will not fill the tray by 44.59 in³.

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2 years ago

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