Fractions
The fully simplified version of 5/15
What is 1/3?
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5/15 divided by 5/5
Lines that cross and make a 90 degree angle are called:
Perpendicular
A _____________ of linear equations is a collection of two or more lines with the same variables.
What is a System?
Simplify the expression: 3(4y)
12y
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3 * 4y = 12y
An electric scooter company in Chicago charges a $1 flat fee to unlock a scooter, and an additional $0.15 for every minute you ride. Write an equation to model this information and identify the rate of change:
y = 0.15x + 1, The rate of change is 0.15
The fully simplified version of 18/72
What is 1/4?
18/72 divided by 18/18
Any line parallel to y = 3x + 5 has a slope of:
3
What is Intersect?
Simplify the expression completely: -2x(3x – 1) – (4x + 5)
-6x2 – 2x – 5
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-6x2 + 2x – (4x + 5)
-6x2 + 2x – 4x – 5
-6x2 – 2x – 5
Aarov works in sales for a software company, and he gets both a base salary and earns commission for selling the company’s products. He uses the equation y = 40,000 + 0.3x to predict his total salary in dollars, given he makes x dollars in sales. What is his base salary?
He has a base salary of $40,000
_____ and 7/12 make a whole.
5/12
Any line perpendicular to y = 3x + 5 will have the slope of:
-1/3
Find the solution to this system:
y – x = 3
y = -4x – 2
(-1,2)
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1st: make sure all equations are in slope-intercept form
2nd: set equations equal to each other and solve for x
3rd: plug back into one of the equations to solve for y
4th: Set answers for x and y as ordered pair
The amount Mike gets paid weekly can be represented by the expression 2.50a + 290, where a is the number of cell phone accessories he sells that week. What is the constant term in this expression and what does it represent?
290, the amount he is guaranteed to be paid each week.
Identify the rate of change in the following scenario: Poyraz has $35,000 in his savings account. Each month he spends $1,800.
- $1,800
Simplify the expression: 1/2 + 3/4
1 and 1/4
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1/2 + 3/4
1/2 * 2/2 = 2/4
2/4 + 3/4 = 5/4 or 1 and 1/4
Parallel Lines
If the equations have the same ________ and a different ________, the system has no solution.
slope, y-intercept
If a = 4y + 2z and b = z – y, what is the value of a + b, in terms of y and z?
3y + 3z
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4y + 2z + z - y
4y - y + 2z + z
3y + 3z
A bike rental service in New York City charges $13.50 to rent a bike for one hour, then $4.50 for each additional hour. Write an expression to model how much it would cost to rent a bike for n hours.
9 + 4.50n
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13.50 - 4.50 = 9 ---> 9 is the base price.
$9 + $4.50 an hour
9 + 4.50n
Simplify the expression by changing the whole number into a fraction: 7 + 8/3
9 and 2/3
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7 + 8/3
7/1 + 8/3
7/1 * 3/3 = 21/3
21/3 + 8/3 = 29/3 or 9 and 2/3
Find the slope of a line parallel to 2y - 3 = 10x + 4
5
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2y - 3 = 10x + 4
+3 +3
2y = 10x + 7
/2 /2
y = 5x + 7/2
Is the ordered pair (5, -1) a solution to the equation? 4y - x = 21
No, (5,1) is not a solution to the equation
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4(-1) - 5 = 21
-4 - 5 does not equal 21
Simplify the expression: n – [3n – (1 – 2n)]
-4n + 1
A taqueria in Pilsen, Chicago spends approximately $1.25 on ingredients for each taco they make. The shop-owner spends an estimated $175 on rent and electricity each week. The taqueria's total costs the week before were $546.25, how many tacos did they sell the week before?
x = 297; The taqueria sold 297 tacos the week before.
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546.25 = 175 + 1.25x
546.25 - 175 = 1.25x
371.25/1.25= 1.25x/1.25
297 = x