In a direct variation, when the independent variable increase the dependent variable also increases. In this case, the independent variable is the time (time is always independent) and the miles driven by Steve is the dependent variable. This means, the miles driven increase as time pass.

3 0

3 years ago

Y=x^2 -9x at x = 4 Find an equation of the tangent an an equation of the normal

Montano1993 [528]

The tangent line to y = f(x) at a point (a, f(a) ) has slope dy/dx at x = a. So first compute the derivative:

y = x² - 9x → dy/dx = 2x - 9

When x = 4, the function takes on a value of

y = 4² - 9•4 = -20

and the derivative is

dy/dx (4) = 2•4 - 9 = -1

Then use the point-slope formula to get the equation of the tangent line:

y - (-20) = -1 (x - 4)

y + 20 = -x + 4

y = -x - 24

The normal line is perpendicular to the tangent, so its slope is -1/(-1) = 1. It passes through the same point, so its equation is

y - (-20) = 1 (x - 4)

y + 20 = x - 4

y = x - 24

3 0

3 years ago

Write an equivalent expression to

mel-nik [20]

1. Distributive Property.
4(3a + 7) + 3(2a + 5)
12a + 28 + 6a + 20

2. Combine like terms
12a + 28 + 6a + 20
18a +48

The equivalent expression is 18a + 48. If a = anything then the expressions will still be equivalent.

5 0

3 years ago