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Svetllana [295]

2 years ago

14

Pablo folds a straw into a triangle with side lengths of 4x2−3 inches, 4x2−2 inches, and 4x2−1 inches. Which expression can be u

sed to find the perimeter of the triangle, and what is the perimeter when x = 1.5?

2 answers:

Lesechka [4]2 years ago

9 0

Answer:

The answer to your question a) Perimeter = 12x² - 6 b) Perimeter = 21 in

Step-by-step explanation:

Data

side 1 = 4x² - 3

side 2 = 4x² - 2

side 3 = 4x² - 1

Process

1.- Calculate the perimeter of a triangle

Perimeter = side 1 + side 2 + side 3

-Substitution

Perimeter = (4x² - 3) + (4x² - 2) + (4x² - 1)

-Simplification

Perimeter = 4x² - 3 + 4x² - 2 + 4x² - 1

Perimeter = 12x² - 6

2.- Find the perimeter when x = 1.5

Perimeter = 12(1.5)² - 6

-Simplification

Perimeter = 12(2.25) - 6

Perimeter = 27 - 6

-Result

Perimeter = 21 in

tatuchka [14]2 years ago

6 0

Answer:

Step-by-step explanation:

The formula for determining the perimeter of a triangle is expressed as

Perimeter = a + b + c

Where a, b and c are the lengths of each side of the triangle.

The side lengths of the triangular straw are 4x² - 3 inches, 4x² -2 inches, and 4x² - 1 inches. The expression for the perimeter is

4x² - 3 + 4x² -2 + 4x² - 1

= 4x² + 4x² + 4x² - 3 - 2 - 1

= 12x² - 6

When x = 1.5, then

Perimeter = 12(1.5)² - 6

Perimeter = 21 inches

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A company makes wax candles in the shape of a solid sphere. Suppose each candle has a diameter of 15 cm. If

jekas [21]

We have been given that a company makes wax candles in the shape of a solid sphere. Each candle has a diameter of 15 cm. We are asked to find the number of candles that company can make from 70,650 cubic cm of wax.

To solve our given problem, we will divide total volume of wax by volume of one candle.

Volume of each candle will be equal to volume of sphere.

$V=\frac{4}{3}\pi r^3$ , where r represents radius of sphere.

We know that radius is half the diameter, so radius of each candle will be $\frac{15}{2}=7.5$ cm.

$\text{Volume of one candle}=\frac{4}{3}\cdot 3.14\cdot (7.5\text{ cm})^3$

$\text{Volume of one candle}=\frac{4}{3}\cdot 3.14\cdot 421.875\text{ cm}^3$

$\text{Volume of one candle}=1766.25\text{ cm}^3$

Now we will divide 70,650 cubic cm of wax by volume of one candle.

$\text{Number of candles}=\frac{70,650\text{ cm}^3}{1766.25\text{ cm}^3}$

$\text{Number of candles}=\frac{70,650}{1766.25}$

$\text{Number of candles}=40$

Therefore, 40 candles can be made from 70,650 cubic cm of wax.

8 0

2 years ago

Find the area of the trapezoidal cross-section of the irrigation canal shown below. Your answer will be in terms of h, w, and θ.

Setler [38]

The answer is ：h^2/tanθ+wh

5 0

2 years ago

Yun was trying to factor 7x^2-14x7x

disa [49]

the width of Yun's area model is 7x units or ( x-2 )units .

<u>Step-by-step explanation:</u>

Here we have , Yun was trying to factor 7x^2-14x. He found that the greatest common factor of these terms was 7x and made an area model: What is the width of Yun's area model. Let's find out:

We know that area of rectangle :

⇒ $Area = length(width)$ .........(1)

Now , According to question we have

⇒ $Area = 7x^2-14x$

⇒ $Area = 7x(x-2)$

Comparing this equation to equation (1) we get that :

⇒ $width = 7x$ or , $width =x -2$

Therefore , the width of Yun's area model is 7x units or ( x-2 )units .

8 0

2 years ago

Read 2 more answers

A rocket is divided into three sections. The top section is one-eighth the length of the bottom section. The middle section is o

Ahat [919]

Answer:

312 ft

Step-by-step explanation:

The steps are as follows :

1. The problem can be described as an equation

$x + \frac{1}{2}x + \frac{1}{8}x = 312$

2. Convert all values on the left side into their equivalent fractional values

$\frac{8}{8}x + \frac{4}{8}x + \frac{1}{8} x = 312$

3. Combine like terms

$\frac{13}{8} x = 312$

4. Multiply both sides by the reciprocal of 13/8 to isolate variable X

$concept \: \: \: ({ \frac{8}{13} \times \frac{13}{8} }) = 1$

$\frac{8}{13} \times \frac{13}{8}x = 312 \: \times \frac{8}{13}$

5. Simplify

$x = 192$

6. Check answer by using it in the original equation

$(192) + \frac{1}{2}(192) + \frac{1}{8} (192) = 312$

4 0

2 years ago

Serena is single. She purchased her principal residence three years ago. She lived in the home until she sold it at a $300,000 g

Lesechka [4]

Answer: Long -term capital gain

Step-by-step explanation:

Serena is single, so based on the Taxpayer Relief Act of 1997, she would pay no capital gains tax on the first $250,000 gain.

Therefore, $300,000 - $250,000 = $50,000

<em>The remaining $50,000 gain is taxable because of her being single and it has been her principal residence for three years.</em>

7 0

2 years ago