The ratio of width to height is 5 to 8. Using this ratio, you can determine the lengths.
1. 5/8=10/x
5x=80
x=16in
2. 5/8=15/x
5x=120
x=24in
3. 5/8 = 8/x
5x=64
x=12.8in
All you have to do is multiply 3/4 of a mile times two because she walked round trip. The answer is 1.5 miles
Answer:
Step-by-step explanation:
By definition, a relation is a function if and only if each input value have one and only one output value.
The input values are the x-values and the output values are the y-values.
Given the function f(x):
You need to substitute 
into this function:
And now you must evaluate in order to find the corresponding output value.
You get:
The function g(x) is:
Then, you need to substitute 
in the function:
And finally you must evaluate in order to find the corresponding output value. This is:
Answer:
k = 8
Step-by-step explanation:
Since the roots of the equation 3x² + 2x + k are x₁ and x₂ and 2x₁ = 3x₂.
By the roots of an equation, ax² + bx + c , where its roots are x₁ and x₂. It follows that sum of roots are x₁ + x₂ = -b/a and product of roots are x₁x₂ = c/a.
Comparing both equations, a = 3 b = 2 and c = k.
So, x₁ + x₂ = -b/a = -2/3 and x₁x₂ = c/a = k/3
x₁ + x₂ = -2/3 and x₁x₂ = k/3
3x₁ + 3x₂ = -2 (1) and 3x₁x₂ = k (2)
Since 2x₁ = -3x₂, and -2x₁ = 3x₂substituting this into equations (1) and (2) above, we have
3x₁ + 3x₂ = -2 (1) and 3x₁x₂ = k (2)
3x₁ + (-2x₁) = -2 and x₁(3x₂) = k
3x₁ - 2x₁ = -2 and x₁(3x₂) = k
x₁ = -2 and x₁(-2x₁) = k
x₁ = -2 and -2x₁² = k
Substituting x₁ = -2 into -2x₁² = k, we have
-2x₁² = k
-2(-2)² = k
2(4) = k
8 = k
So, k = 8
