Equations and Expressions
Simplify:
3x+5x−4
Answer:
8x−4
What is the slope of the line passing through points (3,5) and (7,13)?
m=2
Solve:
∣x∣=7
Answer: x=7 or x=−7
Define "system of equations."
A set of two or more equations with the same variables.
Evaluate:
5 ^2 −3×4
13
Solve:
5x−7=18
Answer:
x=5
Write the equation of a line with slope −3 and y-intercept 5.
y=−3x+5
∣3x−4∣=11
x=5 or x=−7/3
Solve the system graphically:
y=2x+1
y=−x+4
Answer: (1,3).
Write an equation for the line that passes through the points (0,−2) and (4,6)
y=2x−2
Solve:
2(3x−4)+5=21
Answer:
x=5
Convert
3x+4y=12
to slope-intercept form.
y=− 3/4 x+3
De2 xx 2/(3*x^2)scribe the transformation of:
y=|x| to
y=∣x−3∣+2
Shift right 3 units, up 2 units
What does it mean when two lines in a system are parallel?
No solution; the system is inconsistent.
Solve for x in terms of a:
3x+a=7
x= (7−a )/3
Solve the inequality:
4x−7≥2x+5
Answer:
x≥6
Graph the equation
y= 1/2 x−3
. What are the x- and y-intercepts?
X-intercept = (6,0), Y-intercept = (0,−3)
Graph the function: y=−∣x+1∣+3 , what is the vertex?
Vertex: (−1,3).
Graph the system and state the solution:
y=x+3
y=−2x+6
Answer: (1,4)
Solve the inequality and graph the solution on a number line:
−2x+5>1
x<2
A rectangle’s perimeter is 64 cm. If its length is three times its width, find the dimensions of the rectangle.
Length = 24 cm, Width = 8 cm
If a line has slope 2/3 and y-intercept −4, write it in standard form.
2x−3y=12
Solve:
|2x-5|≤9
−2≤x≤7
A company sells two types of candles, regular and scented. The total sales are $120. The number of scented candles sold was three times the number of regular candles. How many of each type were sold?
10 regular candles, 30 scented candles
The product of two consecutive positive integers is 72. Find the integers.
8 and 9