Algebra 1 study set

A twelve inch candle and an 18 inch candle are lit at 6pm. The 12-in. candle burns 0.5 inches every hour. The 18 inch candle burns two inches every hour. After how many hours will the two candles be the same height?

4

Write an equation or inequality to represent the situation. Josh has a $30 online gift voucher. He plans to buys as many books as he can. The cost of each book is $4. There is also a sinlge shipping charge of $2. How many books can he afford with out spending more than his gift voucher amount?

4x + 2 ≤ 30

one-variable inequalities

A linear inequality is an inequality in one variable that can be written in one of the following forms where a and b are real numbers and a≠0 a ≠ 0 : a+bx<0 a + b x < 0 ; a+bx≤0 a + b x ≤ 0 ; a+bx>0 a + b x > 0 ; a+bx≥0.

multi-step equations

A multi-step equation is an equation that takes two or more steps to solve.

What is the vertex of the function y = 2(x - 3)² + 8?

vertex (3, 8)

ten more than a number

x + 10

There are x students in the class. The office calls 5 students down. Write an expression for how many students are left in the class.

x - 5

-3(x - 4) + 2x = -6

x = 18

-6 + 4(5x - 11) + 3x = -4

x = 2

7x - 4(x + 2) - 4 = 9

x = 7

y = −3x + 5 5x − 4y = −3

(1, 2)

Simplify 8y(y - 4) + 3y(y + 2)

11y^2 - 26y

Michael and Kevin are running. Kevin gets a 3-mile head start and runs at a rate of 5.5 mi/h. Michael runs at a rate of 7 mi/h. How many hours will it take Michael to catch up with Kevin?

2

The profits of Mr. Unlucky's company can be represented by the equation y = -3x² + 18x - 4, where y is the amount of profit in thousands of dollars and x is the number of years of operation. What is the maximum profit?

23,000

Abigail tosses a coin off a bridge into the stream below. The distance, in feet, the coin is above the water is modeled by the equation y = -16x²+ 96x + 112. Where x represents time in seconds.What is the maximum height of the coin?

256

triple a number

3x

Write an equation or inequality to represent the situation. Brandon and John have $20 left for a cab fare home. The cab fare is $3 per mile plus a $2 fixed change. What is the maximum number of miles they will be able to travel in the cab?

3x + 2 ≤ 20

Write an equation or inequality to represent the situation. Tyrone's cell phone cots him $21 per month plus $3 for every 1GB of data downloaded. What is the limit to the number of GBs he can download to stay within his monthly budget of $30.

3x + 21 ≤ 30

(2x+y)(x+2y)

5xy+2x2+2y2

Carol has 9 more cakes than Joseph. Joseph has x cakes. Write an algebraic expression for the number of cakes Carol has.

9 + x

Taylor takes 9 minutes to run a mile. Adam take x fewer minutes than Taylor. Write an expression for how long it takes Adam to run a mile.

9 - x

multiplying monomials

A monomial is an expression of the form k⋅xⁿ, where k is a real number and n is a positive integer.

Writing Algebraic Expressions

In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations

Which number line represents the solution set for the inequality 3(8 - 4x) < 6(x - 5)?

Line 2.

Factor 2m^2 + 9m + 10

The correct answer is (2m + 5) (m + 2)

factor. v^2 - 10v + 16

The correct answer is (v-2) (v-8)

Order of operations

The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression.

What is the y-intercept of the graph of the function y = 2x² - 12x + 7?

(0, 7)

y = 6x − 11 −2x − 3y = −7

(2, 1)

Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost $15. She bought seven total shirts. How many fancy and plain shirts did Kristin buy?

(2, 5)

2x − 3y = −1 y = x − 1

(4, 3)

There are 13 animals in the barn. Some are chickens and some are pigs. There are 40 legs in all. How many pigs and chickens are there?

(7, 6)

A farmhouse shelters 10 animals. Some are pigs and some are ducks. Altogether there are 36 legs. How many ducks and pigs are there?

(8, 2)

What value of x is in solution set of 9(2x + 1) < 9x - 18?

-4

(3x+1)(x-2)

-5x+3x*2-2

(3x-3y)(2x-y)

-9xy+6x2+3y2

double a number

2x

Netflix charges David $15 per month for a membership, plus a $5 one-time fee for streaming on his phone. How many months will David have his membership for if Netflix charges him $50?

3

The profits of Mr. Unlucky's company can be represented by the equation y = -3x² + 18x - 4, where y is the amount of profit in hundreds of thousands of dollars and x is the number of years of operation. When will Unlucky's business show the maximum profit?

3

Graphing Quadratic Equations

A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape. The picture below shows three graphs, and they are all parabolas.

systems of equations

A set of two or more equations containing a set of common variables.

Foil Method in multiplying binomials

A technique for distributing two binomials.

Find the product. -a^2b^2c^2(a + b - c)

a^3b^2c^2 - a^2b^3c^2 + a^2b^2c^3

Simplify p(p - q) - q(q - p).

p^2 - q^2

nolan bought 2 burgers for $3.50 each and 3 medium French fries for $1.20 each. Write a numerical expression to represent this situation and then find the cost.

the answer is 2 × 3.50 + 3 × 1.20

Evaluate The Expression 3 + 1 - 4

the answer is 0

Evaluate The Expression 1 x -3 + 5

the answer is 2

george bought 4 oranges for 50 cents each and 1 apple for 80 cents. Write a numerical expression to represent this situation and then find the total cost in dollar.

the answer is 4 × 50 + 80

Evaluate The Expression 5 + 2/1

the answer is 7

peyton pays 20 dollars for materials to make earrings. She makes 10 earrings and sells 7 for 5 dollars and 3 for 2 dollars. Write a numerical expression to represent this situation and then find Martha's profit?

the answer is 7 × 5 + 3 × 2 - 20

factor u^2 +10u + 25

the correct answer is (u + 5)^2

factoring

the process of finding the factors: Factoring: Finding what to multiply together to get an expression. It is like "splitting" an expression into a multiplication of simpler expressions.

Solve the inequality. 2(4 + 2x) ≥ 5x + 5?

x ≤ 3

What are the x-intercepts of the function y = 0.2(x - 5)(x + 3)?

x=5 and x=-3