The lengths of the other two sides of the right triangle are 12 and 13
<h3>Pythagorean theorem </h3>
From the question, we are to determine the lengths of the other sides of the triangle
From the given information,
The other sides have lengths that are consecutive integers
Thus,
If the length of the other side is x
Then,
The hypotenuse will be x + 1
By the <em>Pythagorean theorem</em>, we can write that
(x+1)² = x² + 5²
(x+1)(x+1) = x² + 25
x² + x + x + 1 = x² + 25
x² - x² + x + x = 25 - 1
2x = 24
x = 24/2
x = 12
∴ The other leg of the right triangle is 12
Hypotenuse = x + 1 = 12 + 1 = 13
Hence, the lengths of the other two sides are 12 and 13
Learn more on Pythagorean theorem here: brainly.com/question/4584452
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7). C
8). 60
n = 5(10) + 10
n = 50 + 10
n = 60
9). 17
f(x) = -2x + 7 plug the -5 in for x
f(x) = -2(-5) + 7
= 10 + 7
= 17
10).
Answer: 39.2Check out the attached image
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Explanation:
Draw out the triangle or use the diagram provided by your teacher. It should look something similar to what I've attached.
Let m = length of side XZ
We are given that
angle Y = 75 degrees
angle Z = 67 degrees
which are the green angles shown in the diagram
Use the fact that the three angles (X,Y,Z) add to 180 degrees to find angle X
X+Y+Z = 180
X+75+67 = 180
X+142 = 180
X+142-142 = 180-142
X = 38
Now use the law of sines to find m
sin(X)/YZ = sin(Y)/XZ
sin(38)/25 = sin(75)/m
m*sin(38) = 25*sin(75)
m = 25*sin(75)/sin(38)
m = 39.22309 <<<--- make sure your calculator is in degree mode
m =
39.2So
XZ is roughly 39.2 feet in length
4.5 ft per second doesn't fit with the others.
The other three are similar because they are all in the unsimplified format of distance in a period of time, while the first one is just a simplified rate that could be used to multiply easily.