Answer:
D AND E
Step-by-step explanation:
Answer:
The answer is C ФωФ
Step-by-step explanation:
Longer leg = x + 4
Shorter leg = x
Hypotenuse = x + 8
Using Pythagorean Theorem:
a^2 + b^2 = c^2
(x + 4)^2 + x^2 = (x + 8)^2
x^2 + 8x + 16 + x^2 = x^2 + 16x + 64
2x^2 + 8x + 16 = x^2 + 16x + 64
2x^2 +8x = x^2 + 16x + 48
2x^2 - 8x = x^2 + 48
x^2 - 8x = 48
x^2 - 8x - 48 = 0
You can complete the square from here or use the quadratic formula.
Completing the square:
x^2 - 8x = 48
x^2 - 8x + (-8/2)^2 = 48 + (-8/2)^2
x^2 - 8x + 16 = 48 + 16
(x - 4)(x - 4) = 64 or (x - 4)^2 = 64
x - 4 = +√64 OR x - 4 = -√64
x - 4 = +8 OR x - 4 = -8
x = 12 OR x = -4
However, you can't use negative 4 as a length because your length needs to be a positive.
So x will be 12.
Shorter leg: 12
Longer leg: 12 + 4
Hypotenuse: 12 + 8
Answer:
- slope: 1
- equation: y = x +3
Step-by-step explanation:
The slope of the line between two points can be found using the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (2 -0)/(-1 -(-3)) = 2/2
m = 1 . . . . . the slope of the line is 1
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The value of the y-intercept can be found by solving the slope-intercept equation for b.
y = mx +b
b = y -mx
b = (0) -(1)(-3) = 3 . . . . . using point (x, y) = (-3, 0)
The equation of the line with slope 1 and y-intercept 3 can be written as ...
y = x +3
