Direct Variation equation: y=kx, k=y/x
42/14=3
k=3
y=3x
y=3(90)
y=270
Answer:
5 x^2 y^ (-3) z = ?
Step-by-step explanation:
We know the volume of a rectangular prism is given by
V = l*w*h
V = 2x^2 * y^-2 * ?
We are given the volume
V =10x^4 y^-5 z
Set the two equal
10x^4 y^-5 z = 2x^2 * y^-2 * ?
Divide each side by 2x^2 y^-2
10x^4 y^-5 z /2x^2 y^-2 = 2x^2 * y^-2 * ?/2x^2 * y^-2
10x^4 y^-5 z/ 2x^2 y^-2 = ?
Simplifying
10/2 * x^4/x^2 y^-5/ y^-2 z = ?
We know that a^b/ a^c = a^(b-c)
5 x^ (4-2) y^(-5 - -2) z = ?
5 x^2 y^ (-5 +2) z = ?
5 x^2 y^ (-3) z = ?
Answer:
y = 17(2)^x
Step-by-step explanation:
If the graph of y = ab^x goes through (0, 17), then
17 = ab*0, or a = 17
Then the function is y = ab^x with a = 17, or
y = 17*b^x and we must find b.
If the graph of y = 17*b^x also goes through (6, 1088), then the following must be true: 1088 = 17*b^6
which reduces to 64 = b^6
Taking the sixth root of both sides, we get 64^(1/6) = b, and so b = 2
Then the desired exponential function is
y = 17(2)^x
If A and B are complementary angles, then they add up to 90 degrees.
So A + B = 90 => (x + 24) + (x + 16) = 90 => 2x + 40 = 90 => 2x = 50.
So x = 25, and thus, the measurement of B is (25 + 16) = 41.
The measurement of angle A is (25 + 24) = 49, and indeed they are complementary.
