Algebra 2 August 2016 Flashcards

Questions and Answers

Which equation has 1-i as a solution?

X^2 + 2x + 2 = 0

X^2 - 2x + 2 = 0 (correct)

X^2 + 2x + 1 = 0

X^2 - 1 = 0

Which statement(s) about statistical studies is true?

I, only — A survey of all English classes in a high school would be a good sample to determine the number of hours students throughout the school spend studying. (correct)

II, only — A survey of students from one class would adequately represent the whole school.

Neither I nor II is true.

Both I and II are true.

To the nearest tenth, what is the value of x that satisfies $2^x = -2x + 11$?

2.6

What is the probability that a randomly selected 60 watt lightbulb's lifespan will be between 1440 and 1465 hours?

0.8415 Signup and view all the answers

Which factorization is incorrect?

M^3 + 3m^2 - 4m + 12 = (m - 2)^2(m + 3) Signup and view all the answers

What is the highest ticket price to the nearest dollar that can be charged so that Sally's high school does not lose money on the event?

8 Signup and view all the answers

What is the probability that a randomly selected person texts over 50 messages per month, given they are between the ages of 16 and 23?

157/229 Signup and view all the answers

What is a recursive formula for the sequence 18, 9, 4.5...?

G1 = 18; Gn = (1/2)G_{n-1} Signup and view all the answers

If Kristen runs 8 miles in week one, what expression can help her find the total number of miles over the course of her 6-week training program?

6E 8(1.10)^{n-1} where n=1 Signup and view all the answers

Over which interval is the height of the sine wave decreasing only?

(100, 300) Signup and view all the answers

The expression $(x^3 + 2x^2 + x + 6)/(x + 2)$ is equivalent to?

X^2 + 1 + 4/(x + 2) Signup and view all the answers

Given this output, what is the margin of error for the poll at a 95% confidence level?

0.03 Signup and view all the answers

Which statement is not correct regarding the depreciation of a car represented by $v=32,000(0.81)^{(t/12)}$?

The car lost approximately 19% of its value each month. Signup and view all the answers

Which equation represents an odd function?

Y = sin x Signup and view all the answers

What is the completely factored form of $2d^4 + 6d^3 - 18d^2 - 54d$?

2d(d + 3)^2(d - 3) Signup and view all the answers

Which diagram shows an angle rotation of one radian on the unit circle?

Choice (1) Signup and view all the answers

When the equation is solved for J in terms of F and W, what does J equal?

FW / (W - F) Signup and view all the answers

The sequence $a_1 = 6$ and $a_n = 3a_{n-1}$ can also be written as?

a_n = 2 * 3^n Signup and view all the answers

Which equation represents the set of points equidistant from line L and point R shown on the graph?

Y = -rac{1}{8}(x - 2)^2 + 1 Signup and view all the answers

Mr. Fairson gave his class three mathematical rules. Which rules can be proved for all real numbers?

1 and 3 Signup and view all the answers

What is the remainder when $p(x)$ is divided by $x + 4$?

0 Signup and view all the answers

Which expression can be used to calculate the amount Remi would owe in dollars after one year if she did not make payments on a $300 payday loan?

300(1.30)^{365/14} Signup and view all the answers

Which value is not contained in the solution of the systems shown below?

2 Signup and view all the answers

Assuming a growth rate of 1.5%, what equation can predict the population of New York State t years after 2010, given the population was approximately 19,378,000?

P_0 = 19,378,000; P_t = 1.015P_{t-1} Signup and view all the answers

Study Notes

Algebraic Solutions and Functions

The equation (X^2-2x+2=0) has the complex solution (1-i).
The function representing revenue from ticket sales for a spring musical is (R(t)=-33t^2+360t) with a fixed production cost (C(t)=700+5t).
The incorrect factorization of (M^3+3m^2-4m+12) is ( (m-2)^2(m+3) ).

Statistical Studies and Probability

A survey of all English classes in a high school is a representative sample for studying student study hours.
For ages between 16 and 23, the probability of texting over 50 messages per month is calculated as ( \frac{157}{229} ).
Assuming a 95% confidence level, the margin of error for a poll is approximately 0.03.

Calculating Values and Sequences

The solution for the equation (2^x=-2x+11) rounded to the nearest tenth is 2.6.
A recursive formula for the sequence 18, 9, 4.5... is (G_1=18; G_n=(1/2)G_{n-1}).
The sequence defined by (a_1=6) and (a_n=3a_{n-1}) simplifies to (a_n=2\cdot3^n).
The total number of miles Kristen will run during her 6-week training program can be formulated as (E = 8(1.10)^{n-1}) where (n=1).

Statistical Distributions and Probabilities

The lifespan of a 60-watt lightbulb is normally distributed with a mean of 1450 hours and standard deviation of 8.5 hours, with a probability of lasting between 1440 and 1465 hours being 0.8415.
The population of New York State in 2010 was approximately 19.4 million, experiencing a growth rate of 1.5% annually, represented by (Pt = 1.015P_{t-1}).

Geometry and Functions

A sine function representing light waves increases through the origin, and the height decreases in the interval (100, 300).
The equation for a set of points equidistant from line (L) and point (R) is (y=-\frac{1}{8}(x-2)^2+1).
The expression for the division of ( \frac{x^3+2x^2+x+6}{x+2} ) simplifies to (x^2+1+\frac{4}{x+2}).

Miscellaneous Mathematics

The completely factored form of (2d^4+6d^3-18d^2-54d) is (2d(d+3)^2(d-3)).
The remainder when dividing (p(x)) by (x+4) is 0, indicating (x+4) is a factor of (p(x)).
The equation for calculating the amount owed on a $300 payday loan after one year with 30% interest compounded every 14 days is (300(1.30)^{365/14}).
The odd function is represented by the equation (y=\sin x).

Logical Proofs

Among the provided mathematical rules, rules 1 and 3 can be proved for all real numbers.
A statement about the value of a car after 10 months, represented by (v=32000(0.81)^{t/12}), incorrectly states that the car loses 19% of its value each month.

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Flashcards covering various algebra 2 topics, including equations, statistical studies, and exponential functions.