Answer:
qt's length = 16
Step-by-step explanation:
The problem states that qrs is a right triangle,
where qr = 20
sr =?
qs = 25
qt =?
1)
Calculate sr
hypotenuse² = base² + height²
sq² = sr² + rq²
25² - 20² = sr²
sr = √(25² - 20²)
sr = 15
2)
When altitude rt is dropped to hypotenuse qs, it creates
two right triangles: rtq and rts.
Δrtq
height = rt
base= tq = 25 - x
hypotenuse = qt = 20
Δrts
height = rt
base= ts = x
hypotenuse = sr = 15
Both triangles share the same height, which is rt
Using the Pythagorean theorem:
Δ rtq Δ rts
hypotenuse² - base² = height²
20² - (25 - x)² = 15² - x²
400 - (625 + x² - 50x) = 225 - x²
400 - 625 - x² + 50x = 225 - x²
-225 - x² + 50x - 225 + x² = 0
-450 + 50 x = 0
50x = 450
x = 450/50
x = 9
Base of Δ rtq = tq = 25 - x
tq = 25 - 9
tq = 16
2G=B+3
G=B-4
2(B-4)=B+3
2B-8=B+3
B=11
Bert possesses 11 cents
The possible sets of integers that yield a product of -11 include (-1, 1, 11), (-11, -1, -1), and (-11, 1, 1). An integer can be understood as a whole number encompassing zero, both positive and negative values. Given that the product should equal −11, and knowing the factors of 11 are 1 and 11, we conclude with the different possible integer combinations.
