Answer:
Longer side = 84 meters
Shorter side = 80 meters
Step-by-step explanation:
The hypotenuse is the longest side of the right angle triangle. Let x represent the length of the longer side of the triangle. The difference between the other two sides is 4 meters. It means that the length of the shorter side is x - 4
Applying Pythagoras theorem which is expressed as
Hypotenuse² = longer side² + shorter side²
Therefore,
116² = x² + (x - 4)²
13456 = x² + x² - 4x - 4x + 16
2x² - 8x + 16 - 13456 = 0
2x² - 8x - 13440 = 0
Dividing through by 2, it becomes
x² - 4x - 6720
x² + 80x - 84x - 6720 = 0
x(x + 80) - 84(x + 80) = 0
x - 84 = 0 or x + 80 = 0
x = 84 or x = - 80
Since the length cannot be negative, then
x = 84
Length of shorter side is
84 - 4 = 80
Answer:
a=-1
Step-by-step explanation:
a(n) = -6+3(n-1)
a(n) = -6+3n-3
a(n) -n=-6+3n-n-3
a=-6+3-3
+3 +3
a3=-3
---- ----
3 3
a=-1
Answer:
Given: Population of ducks in lake, last year is 60.
Also, the population of ducks this year decreased by 1/4 th over the last year.
So, the population of ducks this year is = 60*(1-1/4)
= 60*(3/4)
= 45
Therefore, the population of ducks this year is 45 ducks.
No, she didn't because 5:7 and 12:8 are not equivalent ratios
Answer:
x = -3 ; y = -6
Step-by-step explanation:
x = y + 3
-2x + 4y = -18
-2(y+3) + 4y = -18
-2y -6 + 4y = -18
2y = -12
y = -6
x = -6+3
x = -3
