Block 5: Percents
Write 7% as a decimal
0.07
What does the value k represent in the equation y=kx?
Unit Rate
or
Constant of Proportionality
or
Slope
What do you call a letter or symbol that represents a quantity in an expression, equation, or inequality?
variable
In the equation y=3x+2, which number or variable is considered the input and which is considered the output?
y is the output
x is the input
True or False:
The number of solutions of a quadratic equation is always two.
True
Write a decimal to show the value of a percent increase of 35%
1.35
The equation y = 0.75x describes the relationship between the number of cushions, x, and the number of yards of fabric, y, needed to cover those x cushions. How many yards of fabric are needed to cover 16 cushions?
12 yards
What do you call ...
A point where a graph crosses the vertical axis.
The point where the x-coordinate must be zero.
y-intercept
The function y = −20x + 3000 models the amount of water in an above ground pool over time. y represents the amount of water left in the pool in gallons. x represents the time in minutes.
What does the slope of the function represent? What does the y-intercept of the function represent?
Slope: This represents the rate at which the water is leaving the tank. So, every minute, 20 gallons of water are leaving the pool.
y-int: This represents the amount of water in the pool at first. So, the pool had 3000 gallons of water in the beginning.
What is the inverse of squaring a number?
Square rooting a number
A rectangle has side-lengths of 4 in and 5 in. What will be the area of this rectangle if each side of the shape increases in size by 20%?
28.8 in2
A city designer builds a scale model of a building. The height of the model is 7% of the height of the original building. Write an equation that can be used to find the height of the model building.
y=0.07x
What do you call a rate that compares two quantities in a way that the second quantity is 1 unit?
Unit rate
The function y = −20x + 3000 models the amount of water in an above ground pool over time. y represents the amount of water left in the pool in gallons. x represents the time in minutes.
How long will it take the pool to drain?
150 minutes
The equation x2=25 has two solutions. What are they?
Write an expression equivalent to 25% of 200
0.25⋅200
or
200 − (0.75⋅200)
The price of a can of hairspray was increased by 34%. The original price was $4. Write an expression equivalent to the new price, in dollars?
1.34⋅4
or
4 + (0.34⋅4)
What is it called when we replace a variable in an expression with a number?
Substitution
If x=4 , what us the output of y = 2x2 + 4x + 3?
A digital designer uses a square grid to create an interactive smartphone map. The length of the side of this square is 11 inches. Write an expression to calculate the area using an exponent.
112
A triangle has a base of 3 cm and a height of 5 cm. What is the new area if each side increases by 10%?
9.075 cm2
The amount, y, a restaurant spends on food is given by the equation y = 0.30x. x is the restaurants total budget. The restaurant spends $6 thousand on food in a year. What is the restaurant's total budget?
$20,000
What do we call the product of a number and itself; an expression raised to an exponent of 2?
If x = −6, what is the value of y = 2x2 + 9?
81
For what values of x does x2 = 14?
round to the nearest hundredths
x ≈ 3.74 and x≈ -3.74