Exam 14: Foundations: a Prelude to Functions

Choose the one alternative that best completes the statement or answers the question. Find the general form of the equation for the line with the given properties. -Slope $= - \frac { 2 } { 3 } ;$ containing the point $( 0,5 )$

Solve the problem. -If (-7, -3) is the endpoint of a line segment, and (-3, -5) is its midpoint, find the other endpoint.

Write the word or phrase that best completes each statement or answers the question. -Each month a beauty salon gives x manicures for $12.00/manicure. The cost to the owner of the beauty salon for each manicure is $7.35. The monthly fixed cost to maintain a manicure station is $120.00. Write an equation that relates the monthly profit, in dollars, to the number of manicures given each month. Then use the equation to find the monthly profit when 200 manicures are given in a month.

List the intercepts for the graph of the equation. - $x ^ { 2 } + y - 25 = 0$

Find the center (h, k) and radius r of the circle with the given equation. - $( x - 2 ) ^ { 2 } + y ^ { 2 } = 9$

Find the slope and y-intercept of the line. - $9 x - 5 y = 7$

Write the standard form of the equation of the circle with radius r and center (h, k). - $\mathrm { r } = 11 ; ( \mathrm { h } , \mathrm { k } ) = ( - 1,0 )$

List the intercepts for the graph of the equation. - $y = x ^ { 3 } - 27$

Graph the circle with radius r and center (h, k). - $r=3:(h, k)=(-3,-2)$

Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. - $y = \frac { x ^ { 2 } - 49 } { 7 x ^ { 4 } }$

Tell in which quadrant or on what coordinate axis the point lies. - $( - 10 , - 6 )$

Solve the problem. -The relationship between Celsius $\left( { } ^ { \circ } \mathrm { C } \right)$ and Fahrenheit $\left( { } ^ { \circ } \mathrm { F } \right)$ degrees of measuring temperature is linear. Find an equation relating ${ } ^ { \circ } \mathrm { C }$ and ${ } ^ { \circ } \mathrm { F }$ if $10 ^ { \circ } \mathrm { C }$ corresponds to $50 ^ { \circ } \mathrm { F }$ and $30 ^ { \circ } \mathrm { C }$ corresponds to $86 ^ { \circ } \mathrm { F }$ . Use the equation to find the Celsius measure of $31 ^ { \circ } \mathrm { F }$ .

Find an equation for the line with the given properties. -The solid line L contains the point (2, 1) and is parallel to the dotted line whose equation is y = 2x. Give the equation for the line L in slope-intercept form.

Find the distance d(P1, P2) between the points P1 and P2. - $\mathrm { P } _ { 1 } = ( - 3 , - 3 ) ; \mathrm { P } _ { 2 } = ( - 3,2 )$

Find the slope of the line through the points and interpret the slope. -

Solve the problem. -The medians of a triangle intersect at a point. The distance from the vertex to the point is exactly two-thirds of the distance from the vertex to the midpoint of the opposite side. Find the exact distance of that point from the Vertex A(3, 4) of a triangle, given that the other two vertices are at (0, 0) and (8, 0).

Solve the problem. -If a circle of radius 5 is made to roll along the x-axis, what is the equation for the path of the center of the circle?

Plot the point. - $(-2,6)$

Plot the point. - $(-3,-1)$

Write the equation in slope-intercept form. - $8 x + 7 y = 4$