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3 years ago

Can the set of lengths be the side lengths of a right triangle?

Mathematics

2 answers:

ElenaW [278]3 years ago

7 0

Answer: Hello there!

We know that in a right triangle, the sum of the squares of the cathetus is equal to the square of the hypotenuse.

the smaller sides given are:

7ft and 12ft, and the longest is 17ft

so if this triangle is a right triangle, we should have that:

7^2 + 12^2 = 17^2

17^2 = 289

7^2 + 12^2 = 193

The terms are different, which means that this is not a right triangle, then the correct answer is B.

andreyandreev [35.5K]3 years ago

4 0

Answer:

B. No.

Step-by-step explanation:

We have been given 3 side lengths 7 ft, 12 ft, 17 ft. We are asked to determine, whether the given set of lengths can form a right triangle or not.

We will use Pythagoras theorem to solve our given problem, which states that the square of hypotenuse of a right triangle is equal to the sum of squares of two legs of right triangle.

$17^2=12^2+7^2$

$289=144+49$

$289>193$

Since the sum of squares of both legs is less than square of hypotenuse, therefore, the given set of lengths can not be the side lengths of a right triangle.

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3 years ago

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3 years ago

Brandon is paid 150% of his regular hourly rate for overtime hours. He is paid \$45.00 an hour for overtime hoursWhat is his reg

Ne4ueva [31]

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Let the payment for regular hours be $x

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3 years ago

= table shows a hot air balloon's height h, in feet, during a descent at various times t, in seconds.

denpristay [2]

Answer:

A. Slope is -12 feet per second

B. Yes, it is constant.

<u>Skills needed: Linear Equations, Substitution and Division</u>

Step-by-step explanation:

1) Solving Part A (we need to find the slope):

The slope is $\frac{y_2-y_1}{x_2-x_1}$ --> $y_1$ , $y_2$ , $x_1$ , and $x_2$ are all values from the table. We know that the left column is the x-values, and the right column is the y-values as that is the conventional way of depicting them.

2) Using the y-values of 1150 and 1090, and their corresponding x-values (5 and 10 respectively), we can get the slope:

- $\frac{y_2-y_1}{x_2-x_1}$ ==> $\frac{1090-1150}{10-5}$ ==> $1090-1150=-60, 10-5=5$ ==> $\frac{-60}{5}$

$\frac{-60}{5} =-12$ , so the slope is -12.

==================================================================

1) Part B (analysis)

We can see that no matter what 2 y-values and their corresponding x values we use, the slope always is the same. This means that the rate of change is constant.

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