abeka 10th grade algebra 2 test 12

What is the determinant of the matrix: [1, 5] [3, -1]

(1×-1)-(3×5)=-16

solve and place on a number line: x² + 7x - 18 ≥ 0

(x+9) (x-2) = 0 x + 9 = 0 x = -9 x- 2 = 0 x = 2 closed dot on -9 line goes to left closed dot on +2 lines goes to right

solve and make a number line: |x − 4| < 5

-5 < x - 4 < 5 -1 < x < 9 open dot on -1 and +9 then line between -1 to +9

Write csc θ using the reciprocal identity.

1/sinθ

determine the next term of the arithmetic sequence: 25, 14, 3, -8...

14-25= -11 -8 + -11 = -19

Based on the formula for permutation correctly set up ₁₅P₈

15!/(15 - 8)!

condense each logarithmic expression into a single logarithm: 2 log x + 3 log y

2 log x + 3 log y = log x² + log y³ = log x²y³

Convert 200° to radians.

200°×π/180°= 10π/9

which of the following correctly states the empirical rule? 28-52-75.6 60-75-90.1 68-85-95.5 68-95-99.7

68-95-99.7

standard form of complex numbers

8-4i

What is the argument in the logarithmic function 2 = log₃ 9 ?

9

what is the compounded continuously intrest formula?

A=Peʳ ᵗ

In which quadrant does θ lie given the conditions tan θ< 0 & sin θ < 0?

Cosine Quadrant IV

What is the equation for standard deviation?

Look up equation for standard deviation

Which of the following events are mutually exclusive according to the following information? A desk has 12 items: 4 yellow books , 3 red books, 2 red erasers , 2 yellow erasers, and 1 brown eraser.

a brown item or a book

Find the domain of this function ƒ(x)= x-12 over x-2

all real numbers except 2

Find the 6th term of an sequence in which the first term is 7 and the common difference is 4.

a₆ = a₁ + ( n - 1) a₆= 7+ (6 - 1)4 a₆ = 7 + (5)(4) a₆ = 27

type of sequence which gradually approaches a specific number

convergent

Rewrite log₃ 22 using the change of base formula.

log 22 over log 3

Describes 2 characteristics simultaneously by listing the frequencies of one characteristic in rows and the other in columns?

two-way frequency table

x⁴ - 10x² + 16 = 0 (using U substitution)

u² - 10u + 16 =0 (u - 2)(u - 8) = 0 X² = u x² =2 x² =8 So x=±√2 and x=±2√2

What is the standard deviation for a sampling distribution where the σₓ = 2.3 and the sample size= 5

σₓ= 2.3/√5 = 1.02.... = 1.0

Table A. Areas of Standard Normal Distribution Which of the following is the area above a z-score of 0.5?

30.9%

If a 3×4 matrix and a 4×2 matrix were multiplied, what would be the dimensions of the resulting matrix?

3×2

What is the summation for this series 5 ∑3i i=1

5 3∑i i=1 3[5(5 + 1)/2] 3[5(6)/2] 3(15)= 45

Table A. Areas of Standard Normal Distribution Which of the following is the area below a z-score of -1.5?

6.7%

Type of data that must be measured

continuous

When calculating a probability, which type of events will influence each others probability of occurring?

dependent

which of the following probability distributions can be visualized by a histogram? Continuous, discrete, geometric, or uniform

discrete

Which type of sequence does the common ratio generate the next term?

geometric

determine if the graph will have vertical translation, horizontal translation, vertical translation, vertical stretch, or vertical compression: ƒ(x) = (x - 1)²

horizontal translation

determine if the graph will have vertical translation, horizontal translation, vertical reflection, vertical stretch, or vertical compression: f(x) = -x²

vertical reflection

determine if the graph will have vertical translation, horizontal translation, vertical translation, vertical stretch, or vertical compression: f(x) = 5x²

vertical stretch

determine if the graph will have vertical translation, horizontal translation, vertical translation, vertical stretch, or vertical compression: ƒ(x) = x² + 8

vertical translation

Which of the following systems results from the elementary row operation (ERO) performed on the given system? Eq 1↔Eq 2: 2x + 3y - 7z = 5 (Eq 1) x + y - 2z = 11 (Eq 2) 4x - 10y + 15z = 7 (Eq 3)

x + y - 2z = 11 (Eq 2) 2x + 3y - 7z = 5 (Eq 1) 4x - 10y + 15z =7 (Eq 3)

solve and make a number line: (x + 4)( x + 1)( x - 3) < 0

x = -4, -1, 3 open dot on -4 with line to the left open dot on -1 and +3 with a line from -1 to +3

When using Cramer's rule to solve a system of equations, which of the following expressions gives the x-value of the solution (x, y)

x=|X| over |A|

solve and make a number line: x² > 4

x² = 4 x = ± 2 open dot on -2 line goes from there to the left open dot on +2 line goes from there to the right

Let x and y be inversely related. If y=3 when x=4, find y when x=1

y=12

Rewrite the exponential equation 6²=36 as a logarithmic equation.

y=log∨b x 2=log₆ 36

calculate the z-score: µ = 40 σ = 3 x = 44

z = x - µ / σ = 44-40 / 3 = 4/3 = 1.3333... = 1.3

What is the solution for 2 cos θ = 1 for all angles [0°, 360°]?

θ=60°, 300°

Completely factor x⁶- y⁶

(x + y)(x² - xy + y²)(x - y)(x² + xy + y²)

Which of he following items would NOT be used for geometric probability? Area of a dartboard Length of time Number of pencils Volume of a tub

Number of pencils

Read the information below and identify the objective function. Mr. Edwards is selling 50 baseball cards and 20 football cards. However he only has enough space to display 55 cards. The expected profit of each baseball card is $10, while the expected profit from each football card is $8. Use x to represent baseball cards and y to represent football cards.

P = 10x + 8y

Table A. Areas of Standard Normal Distribution Which of the following is the area between a z-score of -0.3and 0.6?

P(-0.3 < z < 0.6) = P(z < 0.6) - (z < - 0.3) = 0.726 - 0.382 =0.344 =34.4%

The correct combination notation is...

nCr (formula) ₁₂C₅ (example)

when a sampling distribution has a larger deviation then normal deviation is it a central limit theorem or not?

not central limit theorem

Definition for tan θ in terms of opp., adj., and hyp.?

opp. /adj.

Which is not a measure of center? Mean, median, mode or range

range