Algebra II Regents Review

solve a system of equations algebriacally

2x+y-z=19 -3x+2y+4z=-9 5x-2y=2z=7 2x+y-z=19 (-3x+2y+42=-9 5X-2y+22=& 2x+6z=-2 2(5)+6Z=-2 10+6z=-2 -10. -10 6z=-12/6 z=-2 4x+2y-22=38 5x-2y=2z=7 9x=45/9 x=5 2(5)+y(-2)=19 y=7

y = −2 x + 1 4 3x − 4z = 2 3x − y = 16 For the system shown above, what is the value of Z

3x−(−2x+14)=16 3(6)−4z=2 5x = 30 −4z = −16 x=6 z=4

Which expression is equivalent to 16x^4-64

(4x6^2+8)(4X^2-8)

Last year, the total revenue for Home Style, a national restaurant chain, increased 5.25% over the previous year. If this trend were to continue, which expression could the company's chief financial officer use to approximate their monthly percent increase in revenue? [Let m represent months.]

1.0525 ^1/12 ≈ 1.00427

2x^3-15x^2+31X-3=(x-4)(2x^2+1X+3)+K Determine the Values of H and K to correctly complete the identity stated above ALGEBRAICALLY!!

2x^3+hx^2+3-3X-3x^2-4hx-12+k 2x^3-10x^2+11x-7=2x^2+hx^2-8x^2-4hx+3x+k-12 2x^2-2x+3 R5 x-4 √2x^3-10x^2+11x-7 +. 2x^3+3x^2 -2x^2=11x + 2x^2=3X 3x-7 -3x=12 5 k=5 H=-2

(2x-7)(3x^2-3x-2)

6x^3-6X6^2-4X-21x^2+21x+14 6x^3-27X^2=4x+21x+14 6x^3-27X^2+17x+14

Seth's parents gave him $5000 to invest for his 16th birthday. He is considering two investment options. Option A will pay him 4.5% interest compounded annually. Option B will pay him 4.6% compounded quarterly. Write a function of option A and option B that calculates the value of each account after n years. Seth plans to use the money after he graduates from college in 6 years. Determine how much more money option B will earn than option A to the nearest cent. Algebraically determine, to the nearest tenth of a year, how long it would take for option B to double Seth's initial investment.

A = 5000(1.045)n 4n 4n − 5000(1.045)6 ≈ 6578.87 − 6511.30 ≈ 67.57 10000 = 5000^1 + .046 4 2 = 1.01154n n= log2 4 log 2 = 4n ⋅ log 1.0115 B = 50001 + .046 4 log 1.0115 n ≈ 15.2

Quadrants

All students take classes. Sine and cosecant are positive in quadrants 1 and 2. Cosine and secant are positive in quadrants 1 and 4. Tangent and cotangent are positive in quadrants 1 and 3.

The Ferris wheel at the landmark Navy Pier in Chicago takes 7 minutes to make one full rotation. The height, H, in feet, above the ground of one of the six-person cars can be modeled by in minutes. Using H(t) for one full rotation, this car's minimum height, in feet, is H(t) = 70 sin 2πt − 1.75 + 80, where t is time,

H(t) is at a minimum at 70(−1) + 80 = 10

Converting radians to degrees and minutes

Multiply by 180 and then divide by pi. The part before the decimal is the degrees. Multiply the decimal by 60 to find the minutes.

Converting between logarithm and exponent form

To convert from logarithmic form to exponent form the base remains the base and the rest of the stuff crosses. the b and the n can never be negative.

Factoring out a -1

To factor out a -1, remove the negative and change the signs of the terms

Rationalizing the denominator

To rationalize a denominator multiply the numerator (top) and denominator (bottom) by the conjugate of the denominator (bottom).

Absolute value inequalities

To solve absolute value inequalities Isolate the absolute value on one side of the equation. Change the inequality sign and the sign(s) of the terms on the right to the opposite signs. If the original inequality has a greater than or greater than or equal to (≥ or >) sign use or between your solutions. Solution is <(≤) x or x >(≥) solution. If the original inequality has a less than or less than or equal to (≤ or <) write as an interval. Solution <(≤) x <(≤) solution. You have to divide by a negative, do not forget to flip the inequality sign.

Equations with fractions

To solve equations with fraction, find a common denominator. Drop the denominators Solve the resulting equation. Check the answer(s) in the denominators for extraneous roots.

Find the Vertex and directrix of y=1/24(x+2)^2+5

Vertex(-2,5) Directrixy=-1

If the Function f(x) has zeroes at -4 and 10, then which of the following would have zeroes at -2 and 5

f(1/2x)

Discriminant (describe the roots)

if the discriminant is 0, the roots are real, rational and equal. if the discriminant is negative, the roots are complex or imaginary. if the discriminant is a perfect square, the roots are real, rational, and unequal. if the discriminant is not a perfect square, the roots are real, irrational, and unequal

If the linear function y=-2x+10 had a domain given by [-1,4] then which of the following is its range?

substitute in f(-1)=-2(-1)+10=12 f(-4)=2(3)+10= -2

The graphs of the equations y = x 2 + 4x − 1 and y + 3 = x are drawn on the same set of axes. One solution to this system is

x2 +4x−1=x−3 y + 3 = −1 y = −4 x = −2 , − 1 x2 +3x+2=0 (x + 2)(x + 1) = 0