Algebra Review

The coordinates of the vertices of rectangle MNOP are: M(-2,1) N(4,3) O(5,0) P(-1, -2)

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A letter is chosen at random from the name Antarctica. What is the probability that the chosen letter is a vowel?

1. Count the total number of vowels: 4 2. Count the total number of letters: 10 3. 4/10 reduces to 2/5

a(b - c²) = ? given: a = 2/3 b = 3/4 c = 1/2

2/3 ( 3/4 - 1/4) remember to square 1/2 num and denom 2/3(3/4) - 2/3(1/4) distribute 6/12 - 2/12 multiply upstairs and downstairs 4/12 reduces to 1/3

1/3 + (-1/4)

Get common denominators by multiplying denominators Multiply numerator and denominator 1/3 by 4 Multiply numerator and denominator (-1/4) by 3 4/12 + (-3/12) = 1/12

State hypothesis: "If I complete my algebra homework daily, then I will learn the concepts."

I complete my algebra homework daily.

Name the set of numbers to which the real number "the square root of 196" does NOT belong

It is not an irrational number.

Sasha drove from her house to the grocery store in 20 minutes. Her return trip took 15 minutes. If the store is 7 miles from her house, what was Sasha's average speed for the round trip, in miles per hour?

Lesson 3-9

solve: (-3/4)y = 8/20

Multiply both sides by the reciprocal of (-3/4) which is (-4/3) (-4/3) (-3/4)y = (8/20) (-4/3) Multiply upstairs and downstairs (12/12)y = (32/60) 12/12 equals 1 y = 32/60 which reduces to 4/10 which reduces to 2/5

Evaluate this absolute value problem: | x-2 | + 3/4 Given: x = 11/5

Substitute 11/5 for x | 11/5-2 | + 3/4 | 11/5-10/5 | + 3/4 1/5 + 3/4 now get a common denominator 4/20 + 15/20 = 19/20

Write algebraic expression for the sum of n and 5

n + 5

Write algebraic expression for the difference of n and 5

n - 5

Write algebraic expression for the difference of n and 5

n divided by 5

Does this equation have a solution of (-2)? 4 = 3n - 2 Show why or why not.

no

Does this equation have a solution of (-2)? 4n + 3 = 11 Show why or why not.

no

Put this into y = mx + b form: 3x + 2y = 12

y = -3/2 + 6

Put this into y = mx + b form: 3x + 2y = - 12

y = -3/2 x + (-6)

Put this into y = mx + b form: 3x - 2y = -12

y =3/2 + 6

7 - 3x = 4 + 9x

-12x = -3 x = (-3/-12) reduces to 1/4

Solve 5/6 h = -30

-180 divided by 5 h = (-36)

Translate this sentence into an equation: "Twelve times a number r is the same as two times the sum of r and p."

12r = 2(r + p)

A car dealership has 180 cars on their lot. If they increase their inventory by 25%, how many cars will be on the lot?

225

Put this into y = mx + b form: 3x - 2y = 12

3x - 2y = 12 solve for y -2y = -3x + 12 divide by -2 y = (-3)/(-2) + 12/(-2) y =3/2 + (-6)

Solve 5(a - 12) = 8(3a + 2)

5a - 60 = 24a + 16 -19a = 76 a = (-4)

Simplify 7(x - y) - 2(y - x) + 4x

7x - 7y - 2y + 2x + 4x distribute 7x - 9y + 6x combine like terms 13x - 9y final answer

Find f(x) = 4x-5 Given f(3a + 1)

f(x) = 4x-5 Substitute 3a + 1 into the equation for x f(3a + 1) = 4(3a + 1) - 5 Now solve: 4(3a + 1) - 5 Distribute 12a + 4 - 5 12a + (-1) final answer Homes

What does the y = mx + b form tell you?

m is the slope (rise over run) b is the y-intercept which means that this is where the line crosses the y axis

Does this equation have a solution of (-2)? 3(n+1) = 2 Show why or why not.

no

Does this equation have a solution of (-2)? 5(1 + n) = (-5) Show why or why not.

yes

4v(squared) - [n² - 3s] Given n = 8, s = 4, v = 7

4(49) - [64 - 3(4)] 196 - [64 - 12] 196 - 52 = 144

Write algebraic expression for the product of n and 5

5n

Solve 2 1/3 - 5/6 = t

Change 2 1/3 to an improper fraction: multiply from right to left 3 x 2 then add numerator 1 2 1/3 = 7/3 Continue with problem: 7/3 - 5/6 = t Now you need to find a common denominator 14/6 - 5/6 = 9/6 9/6 reduces to 1 1/2

Simplify 9a² + 7a + 4a² + 2a

Combine like terms 13a² + 9a