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Ad libitum [116K]

3 years ago

11

It took Bill 2 hours biking at a speed of 10 miles per hour to bike along a trail in town. If Bella is walking the same trail at

a speed of 4 miles per hour, how long will it take her to complete the trail?

2 answers:

alexgriva [62]3 years ago

5 0

Answer:

5 hours

Step-by-step explanation:

10*2=20

20 divided by 4 is equal to 5 so the answer is 5 hours

OleMash [197]3 years ago

4 0

The trail is 20 miles so it will take her 5 hours

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What is √75 in simplest form? A. 25√3 B. 3√5 C 5√3 D. 5√50

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Hassan made a vegetable salad with 2 3/8 pounds of tomatoes, 1 1/4 pounds of asparagus, and 2 7/8 pounds of potatoes. How many p

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Step-by-step explanation:

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Which set of numbers could represent the lengths of the sides of a right triangle?

DiKsa [7]

Answer:

The first set: 8, 15, and 17.

Step-by-step explanation:

<h3>Pair: 8, 15, 17</h3>

By the pythagorean theorem, a triangle is a right triangle if and only if

$\text{longest side}^2 = \text{first shorter side}^2 + \text{second shorter side}^2$ .

In this case,

$\text{longest side}^2 = 17^2 = 289$ .

$\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 8^2 + 15^2\\ &=64 + 225 = 289 \end{aligned}$ .

In other words, indeed $\text{hypotenuse}^2 = \text{first leg}^2 + \text{second leg}^2$ . Hence, 8, 15, 17 does form a right triangle.

Similarly, check the other pairs. Keep in mind that the square of the longest side should be equal to the sum of the square of the two

<h3>Pair: 10, 15, 20</h3>

Factor out the common factor $2$ to simplify the calculations.

$\text{longest side}^2 = 20^2 = 400$

$\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 10^2 + 15^2\\ &=100 + 225 = 325 \end{aligned}$ .

$\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2$ .

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

<h3>Pair: 12, 18, 22</h3>

$\text{longest side}^2 = (2\times 11)^2 = 2^2 \times 121$ .

$\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= (2 \times 6)^2 + (2 \times 9)^2\\ &=2^2 \times(36 + 81) = 2^2 \times 117 \end{aligned}$ .

$\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2$ .

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

<h3>Pair: 7, 9, 11</h3>

$\text{longest side}^2 = 11^2 = 121$ .

<h3> $\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 7^2 + 9^2\\ &=49+ 81 = 130 \end{aligned}$ .</h3>

$\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2$ .

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

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