short leg: x
long leg: 5x + 19
hypotenuse: 5x + 20
(short leg)² + (long leg)² = hypotenuse
(x)² + (5x + 19)² = (5x + 20)²
x² + 25x² + 190x + 361 = 25x² + 200x + 400
x² - 10x - 39 = 0 <em>subtracted 25x², 200x, and 400 from both sides</em>
(x - 13)(x + 3) = 0
x - 13 = 0 , x + 3 = 0
x = 13 x = -3 <em>length cannot be negative so disregard -3</em>
long leg: 5x + 19 = 5(13) + 19 = 65 + 19 = 84
hypotenuse: 5x + 20 = 5(13) + 20 = 65 + 20 = 85
Answer: short leg = 13, long leg = 84, hypotenuse = 85
Answer:
88%
Step-by-step explanation:
First we multiply the mean by 5.
77.4 x 5 = 387
Then we add all of the test scores.
88 + 77 + 70 + 72 = 299
We subtract the total of the scores from 387, which we got from mulitplying the mean by 5.
387 - 299 = 88
Therefore, Tom's score on his fifth test was an 88%.
Hope this helps!
If these are the choices:
A. 8m – 38
B. 8m + 7
C. 8m + 31
<span>D. 2m – 38
Solution:
6(2m - 1) - 4(m + 8)
distributive property of multiplication:
6(2m) + 6(-1) -4(m) -4(8)
12m - 6 -4m -32
combine like terms:
12m - 4m - 6 - 32
8m - 38 choice A. </span>
Answer:
0.3125
Step-by-step explanation:
When a fair coin is tossed we find that
there are only two outcomes
Each toss is independent of the other
Hence if Xis no of heads then X is binomial with n = 5 and p = 0.5
Using binomial formula we can find probability for getting 3 heads exactly.
Required probability
= P(X=3)
=
Answer: The outbound trip is 18 miles per hour
Step-by-step explanation:
Let x represent the speed of the plane.
An aircraft carrier made a trip. Let us assume that this trip was outbound. The trip there took 5 hours.
Distance = speed × time. Therefore
Distance = 5x
The trip back took 6 hours. It averaged 3 mph faster on the trip there then on the return trip. This means that the speed on the trip back is x - 3 mph.
Distance = 6(x-3) = 6x - 18
Since the distance is the same,
5x = 6x - 18
6x - 5x = 18
x = 18
The speed on return or inbound trip would be 18 - 3 = 15 mph