Plot Twist!
Find the x-intercept and y-intercept of the line 2x-3y=6.
What are (3,0) and (0,-2)?
How can you tell the difference between a linear equation that has no solution and a linear equation that has infinite solutions?
What are:
No solution: the variable terms cancel, but you get a false statement.
Infinite solutions: the variable terms cancel, and you get a true statement.
A gym charges a $25 membership fee plus $12 per month. Write a function for the total cost after m months.
What is T(m)=25+12m?
Simplify \sqrt(-180).
What is 6i\sqrt5?
Solve the equation x^2-2x-48 = 0 by factoring.
What is x = 8 and x = -6?
Solve the inequality \frac{2}{3}x- \frac{1}{4}x \leq 3 + \frac{5}{6}x. Write your answer in interval notation.
What is [-\frac{36}{5}, \infty)?
How do you know when a system has one solution, no solution, or infinite solutions?
What is
Find the x-intercept and y-intercept of the line y=-\frac{3}{4}x+2.
What are (\frac{8}{3},0) and (0,2)?
Solve: 3(2−4x)−2(x−6)=5(2x+1)
What is x=\frac{13}{24}?
The length of a rectangle is five more than triple its width. If the perimeter is 138, what are the dimensions of the rectangle? Find an equation involving the width, w, to get the answer.
What is w=16 and l=53?
Simplify \sqrt{-\frac{289}{169}}
What is \frac{17}{13}i?
Solve the equation (x-3)^2 + 8 = 20.
What is x = 3 + 2\sqrt{3} and x = 3- 2\sqrt{3}?
Solve the absolute value inequality \abs{2x-11} + 7 < 12. Write your answer in interval notation.
What is (3, 8)?
Solve using the substitution method:
{(4x+y=-1),(-6x-2y=3):}
What is (\frac{1}{2},-3) ?
Find the exact distance between (-3,2) and (4,-1).
What is sqrt{58}?
Solve: \frac{1}{2}x+\frac{3}{4}x=5−\frac{6}{7}x
What is x=\frac{140}{59}?
A business has a startup cost of $120,000. Each meal costs $10 to make and is sold for $15. How many meals must they make to break even?
What is 24000 meals?
Write your final answer in standard form a + bi, where i = \sqrt(-1). Subtract: (-2+6i)-(3-i).
What is -5 + 7i?
Solve the equation x^2 -8x -10 = 0 by completing the square.
What is x = \sqrt{26} + 4 and x = -\sqrt{26} + 4?
Solve absolute value inequality \abs{3x + 4} -5 \geq 1. Write your answer in interval notation.
What is (-\infty, -\frac{10}{3}]\cup[\frac{2}{3}, \infty)?
Solve using the substitution method: {(3x-4y=-22),(2x+2y=-10):}
What is (-6,1)?
Find the coordinates of the midpoint of the segment connecting the points (4,6) and (-3,-2).
What is (\frac{1}{2},2)?
Find the equation of a line passing through (2,-3) and (-4,-1)
What is y=-\frac{1}{3}x-\frac{7}{3}?
Two 5G data plans are being compared.
Plan A has a fixed cost of $35 each month, plus $15 for each gigabyte of data.
Plan B has a fixed cost of $75 each month, plus $5 for each gigabyte.
a. Create a function for each plan.
b. How many gigabytes make the plans cost the same?
What are A(g)=15g+35, B(g)=5g+75, and g=4?
Write your final answer in standard form a + bi, where i = \sqrt(-1). Multiply: (3-3i)(2-2i)
What is -12i?
Solve the equation 3x^2-4x-2 = 0 using the quadratic formula.
What is x = \frac{2\pm \sqrt(10)}{3}?
Solve the absolute value inequality \abs{3x-2} + 1 \geq 10. Write your solution in interval notation.
What is (- \infty, -\frac{7}{3}] \cup [\frac{11}{3}, \infty)?
Solve using any method: {(2x-5y=3),(6x-9=15y):}
What is infinitely many solutions?
The distance between the points (1,-3) and (a,5) is 10. What are the possible values for a?
What is a=-5,7?
Find the equation of a line passing through (3,-5) that is perpendicular to 5x+3y=15
What is y=\frac{3}{5}x-\frac{34}{5}?
Two moving truck companies are being compared.
Company A charges a fixed rental fee of $42, plus $1.80 for each mile driven.
Company B charges a fixed rental fee of $18, plus a $2.40 for each mile driven.
a) Create a cost function for both companies.
b) How many mile will it take for both companies to cost the same?
c) Which company is less expensive for a trip of 60 miles?
What are A(m) = 42 + 1.80m, B(m) = 18 + 2.40 m, m = 40, and Company A is less expensive for 60 miles at $150.
Write your final answer in standard form a + bi, where i = \sqrt(-1). Divide: (1+4i) \div (3-2i).
What is -\frac{5}{13} + \frac{14i}{13}?
Solve the equation 5x^2 +4 = 6x using the quadratic formula.
What is x= \frac{3}{5} \pm \frac{i\sqrt{11}}{5}?
Solve the absolute value inequality 2\abs{3x-4} - 5 \geq x+8. Write your answer in interval notation.
What is (-\infty, \-frac{5}{7}] \cup [\frac{21}{5}, \infty)?
Solve using any method:
{(y=3x+8),(6x=2y+10):}
What is no solution?