Three vertices of a rectangle ABCD have the points A (–3, 4), B (5, 4), and C (5, –1). Find the coordinates of the 4th vertex, and determine the area of the rectangle.
(Hint: Area of a [latex] rectangle = length \times width [/latex])
Write the following equations in standard form:
a. [latex] \displaystyle{y = \frac{2}{3}x - 2} [/latex]
b. [latex] \displaystyle{6 - 2x + \frac{1}{4} = 0} [/latex]
Write the following equations in slope-intercept form:
a. [latex] 2x - 3y + 6 = 0 [/latex]
b. [latex] 3x + 4y - 5 = 0 [/latex]
Graph the equation [latex] 2x - 3y = 9 [/latex] using a table of values with 4 points.
Graph the equation [latex] 3y + 4x = 0 [/latex] using the x-intercept, y-intercept, and another point on the line.
Use the following slopes (m) and y-intercepts (b) to graph the equations:
a. [latex] \displaystyle{m = -\frac{1}{2}} [/latex], [latex] b = -4 [/latex]
b. [latex] \displaystyle{m = \frac{2}{3}} [/latex], [latex] b = -2 [/latex]
Determine the equation of the line, in standard form, that passes through the points P (–4, 5) and Q (1, 1).
Determine the equation of the line, in standard form, having an x-intercept equal to 5 and y-intercept equal to –3.
Determine the equation of a line, in standard form, that is parallel to [latex] 3x - 2y + 9 = 0 [/latex] and that passes through the point (–6, –3).
Determine the equation of the line, in standard form, that passes through the origin and that is perpendicular to the line passing through the points P(–3, 5) and Q(5, –1).
Solve the following system of equations by using the Graphing Method:
[latex] y = 3x + 6 [/latex]
[latex] 6x - 2y + 12 = 0 [/latex]
Sandra wants to join a tennis club, and is looking at two different options. Club A has a $180 membership fee, and an additional $20 fee per hour of court time. Club B doesn't have a membership fee, but has a $30 fee per hour of court time.
Write an equation in slope-intercept form to represent the total fees charged by each tennis club.
Sketch the graphs and label the lines.
Where do the lines intersect? What does this point represent?
What does the graph indicate regarding which tennis club Sandra should join?
Determine whether each of the following systems of equations has one solution, no solution, or infinitely many solutions without graphing.
[latex] 4x + 3y - 16 = 0 [/latex] and [latex] 2x - y + 2 = 0 [/latex]
[latex] x - 3y + 11 = 0 [/latex] and [latex] 2x - 6y + 4 = 0 [/latex]
[latex] y = 4x + 8 [/latex] and [latex] 8x - 2y + 8 = 0 [/latex]
Solve the following system of equations by using the Substitution Method:
[latex] 2x + 4y + 6 = 0 [/latex]
[latex] y - 3x + 9 = 0 [/latex]
Solve the following system of equations by using the Elimination Method:
[latex] 6x - 4y + 3 = 0 [/latex]
[latex] 4x - 6y - 3 = 0 [/latex]
Determine the value of two numbers if their sum is 65 and the difference between the larger number and the smaller number is 5.
In a coin box, there are three times as many quarters (25¢) as dimes (10¢). If the total value of all these coins is $21.25, how many quarters are there?
The cost of admission to a concert was $75 for adults and $50 for students. If 400 tickets were sold and $28,125 was collected, how many adult tickets were sold?
A soybean meal contains 20% protein and a cornmeal contains 14% protein. How many pounds of each should be mixed to make a 15-pound mixture that contains 16% protein?
Mythili paddled a canoe for three hours at a speed of 6 km/h with the current and it took five hours for the return trip against the same current. Calculate the average speed of the canoe in still water and the average speed of the current.