The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May her driving cost was $380 for 480 mi and in June her cost was $450 for 830 mi. Assume that there is a linear relationship between the monthly cost C of driving a car and the distance x driven. Express the monthly cost C as a function of the distance driven d assuming that a linear relationship gives a suitable model.

the model is

C(x) = 0.2x + 284

Step-by-step explanation:

let x represent the distance driven in a month.

Let y represent the monthly cost for driving x miles.

If we plot y on the vertical axis and x on the horizontal axis, a straight line would be formed. The slope of the straight line would be

Slope, m = (450 - 380)/(830 - 480)

m = 70/350 = 0.2

The equation of the straight line can be represented in the slope-intercept form, y = mx + c

Where

c = intercept

m = slope

To determine the intercept, we would substitute x = 480, y = 380 and m = 0.2 into y = mx + c. It becomes

380 = 0.2 × 480 + c

380 = 96 + c

c = 380 - 96

c = 284

Therefore, the linear model is

y = 0.2x + 284

C(x) = 0.2x + 284

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc

dilation scale factor 2: starting with δabc, draw the dilation image of the triangle with a center at the origin and a scale factor of two. notice that every coordinate of the original triangle has been multiplied by the scale factor (x2). dilation with scale factor 2, multiply by 2.