Untitled Quiz

Questions and Answers

Solve $\frac{2}{5}y = \frac{3}{14}$

y = \frac{28}{15}

Name the property illustrated by $7(9+1)=(9+1)7$

Commutative property of addition

Solve $18 = 3 |4x-10|$

x = 4, 1

Write a linear equation.

y = 3x + 7 Signup and view all the answers

Write $-3y = -1 + 5x$ in standard form.

5x + 3y = 1 Signup and view all the answers

Find the x-intercept of $4x-2y=8$.

x = 2 Signup and view all the answers

What is the slope of the line $x = -2$?

no slope Signup and view all the answers

What is the slope of the line $y = -2$?

0 Signup and view all the answers

A system of linear equations has how many solutions?

None, one or infinitely many Signup and view all the answers

The system of equations $y = -3x + 5$ and $y = 3x - 7$ has how many solutions? What are they?

One, (2, -1) Signup and view all the answers

Find the minimum and maximum value of $f(x,y) = 3x + y$ for the feasible region above.

min = 0, max = 6 Signup and view all the answers

Determine whether $f(x) = 4x^2 - 16x + 6$ has a maximum or a minimum value and find that value.

(2, -10) min Signup and view all the answers

Write the quadratic equation that has the roots -2 and $\frac{1}{5}$.

5x^2 + 9x - 2 = 0 Signup and view all the answers

Solve by using the quadratic formula $3x^2 = 5x - 1$.

$\frac{5 + \sqrt{13}}{6}$ Signup and view all the answers

Simplify $(4 - 12i) - (-8 + 4i)$.

12 - 16i Signup and view all the answers

Find the points for #39.

(2,4) other points -> (0, -4) Signup and view all the answers

Find the points for #40.

(-1, -4) other points -> (0, -3) Signup and view all the answers

Simplify $(5x-4)^2$.

25x^2 - 40x + 16 Signup and view all the answers

Use synthetic division to simplify $(3x^3 - 2x + 5) / (x - 2)$.

3x^2 + 6x + 10 + \frac{25}{x-2} Signup and view all the answers

How many real zeros does the graph of the function have?

3 Signup and view all the answers

How many real zeros are located on the graph?

1, 3, between 4 & 5 Signup and view all the answers

Find $(f-g)(x)$ for $f(x) = x^2 + 8x$ and $g(x) = 3x + 5$.

x^2 + 5x - 5 Signup and view all the answers

Find the inverse of $f(x) = 3 + 5x$.

$\frac{x-3}{5}$ Signup and view all the answers

Graph $y > \sqrt{x} + 3$.

(0, 3) shade above Signup and view all the answers

Simplify $\sqrt[3]{256t^4}$.

4t\sqrt{4t} Signup and view all the answers

Simplify $\sqrt{32} - \sqrt{18} + \sqrt{54} + \sqrt{150}$.

$\sqrt{2} + 8\sqrt{16}$ Signup and view all the answers

Simplify $\frac{5}{2 - \sqrt{3}}$.

$10 + 5\sqrt{3}$ Signup and view all the answers

Simplify $\sqrt{5} + \sqrt{20} - \sqrt{27} + \sqrt{147}$.

$3\sqrt{5} + 4\sqrt{3}$ Signup and view all the answers

Find the domain and range of the function $y = (\frac{1}{2})(2)^x$.

D: all real #'s, R: y > 0 Signup and view all the answers

Write an exponential function that represents growth.

$y = \frac{1}{2}(\frac{5}{3})^x$ —> $y = \frac{1}{20}(\frac{5}{2})^x$ Signup and view all the answers

Solve $32^{x+3} = 4^{2x+7}$.

x = -1 Signup and view all the answers

Solve $64^{x} < 32^{x+2}$.

x < 10 Signup and view all the answers

Solve $\log_{\frac{1}{8}} x = -1$.

x = 8 Signup and view all the answers

Where is $\frac{x^2 - 4x + 4}{2x^2 - 3x - 2}$ undefined?

x /= (-\frac{1}{2}), 2 Signup and view all the answers

Simplify $\frac{(m + 2t - 3)}{(t^2 - 1)} * \frac{(3t - 3)}{(t^2 - 4t + 3)}$.

$\frac{5}{3(m - 2t)}$ Signup and view all the answers

Simplify $\frac{3b^2 - 12}{(6b^2 + 12b)} / \frac{(5b - 10)}{(10b^2 + 20b)}$.

b + 2 Signup and view all the answers

Simplify $\frac{30}{(m^2 - 25)} + \frac{3}{(m-5)}$.

$\frac{3m + 45}{(m + 5)(m - 5)}$ Signup and view all the answers

Find the LCM of $7m - 21$ and $14m - 42$.

14(m - 3) Signup and view all the answers

Find the LCM of $t^2 - t - 12$ and $14m - 42$.

(t - 4)(t + 3)(t + 6) Signup and view all the answers

If y varies inversely as x and y = 5 when x = 5 find y when x = 45.

$\frac{5}{9}$ Signup and view all the answers

Solve $7 - \frac{3}{m} > \frac{18}{m}$.

m > 3 Signup and view all the answers

Write the equation of the parabola in standard form $y = 2x^2 - 8x + 1$.

$y = 2(x - 2)^2 - 7$ Signup and view all the answers

Write the equation for a circle if the endpoints of the diameter are (-7, 1) and (5, 1).

$(x + 1)^2 + (y - 1)^2$ Signup and view all the answers

Find the 20th term of the arithmetic sequence in which $a_1 = 5$ and d = 4.

81 Signup and view all the answers

Write an equation for the nth term of the arithmetic sequence -7, -2, 3, 8,...

$a_n = 5n - 12$ Signup and view all the answers

Find two arithmetic means for 6, , , 30.

14, 22 Signup and view all the answers

Find $S_n$ for the arithmetic series in which $a_1 = 3$, d = $\frac{1}{2}$, and $a_n = \frac{17}{2}$.

69 Signup and view all the answers

Find $^22E(50-2x)$ when x = 18.

50 Signup and view all the answers

Find the sixth term of the geometric sequence for which $a_1 = 4$ and r = 3.

972 Signup and view all the answers

Find four geometric means for 486, , , , , 2.

164, 54, 18, 6 Signup and view all the answers

Write 0.63 as a fraction.

7/11 Signup and view all the answers

Write 0.735 as a fraction.

245/333 Signup and view all the answers

Use binomial theorem to find the third term in $(x + 3y)^5$.

90x^3y^2 Signup and view all the answers

A binomial distribution has a 65% rate of success in 15 trials. What is the probability to get exactly 12 successes?

0.11096 Signup and view all the answers

State if a binomial distribution exists. If so, give a random variable, n, p, and q.

Yes, only two answers: n=15, p=0.75, q=0.25 Signup and view all the answers

Find the range of variables that represents the middle 95% of the distribution.

11.2 < x < 21.6 Signup and view all the answers

What percent of the data will be less than 19?

84% Signup and view all the answers

Solve $x = \tan^{-1}(-\sqrt{3})$.

300°, 120° Signup and view all the answers

Study Notes

Algebraic Equations and Solutions

Solving the equation ( \frac{2}{5}y = \frac{3}{14} ) yields ( y = \frac{28}{15} ).
The system of equations ( y = -3x + 5 ) and ( y = 3x - 7 ) has one solution, which is the point ( (2, -1) ).
For ( 18 = 3 |4x-10| ), the solutions are ( x = 4 ) and ( x = 1 ).

Linear and Quadratic Functions

A linear equation example is ( y = 3x + 7 ).
The standard form transformation of ( -3y = -1 + 5x ) results in ( 5x + 3y = 1 ).
The quadratic function ( f(x) = 4x^2 - 16x + 6 ) has a minimum value at the vertex ( (2, -10) ).

Slope and Intercepts

The line represented by ( x = -2 ) is vertical and has no slope.
The line ( y = -2 ) is horizontal with a slope of ( 0 ).
The x-intercept of ( 4x - 2y = 8 ) is found at ( x = 2 ).

Inequalities and Graphing

To graph ( y > \sqrt{x} + 3 ), start at point ( (0, 3) ) and shade above the curve.
The domain of ( y = \frac{1}{2}(2)^x ) is all real numbers, and the range is ( y > 0 ).

Exponential and Logarithmic Functions

An exponential growth function can be represented as ( y = \frac{1}{2} \left(\frac{5}{3}\right)^x ).
Solving ( \log_{\frac{1}{8}} x = -1 ) yields ( x = 8 ).

Simplification Techniques

Simplifying ( (4 - 12i) - (-8 + 4i) ) results in ( 12 - 16i ).
The expression ( \sqrt{32} - \sqrt{18} + \sqrt{54} + \sqrt{150} ) simplifies to ( \sqrt{2} + 8\sqrt{16} ).

Sequences and Series

The 20th term of an arithmetic sequence starting at ( 5 ) with a common difference of ( 4 ) is ( 81 ).
The formula for the nth term of the arithmetic sequence ( -7, -2, 3, 8 ) is ( a_n = 5n - 12 ).

Circle and Parabola Equations

The standard equation for a circle with endpoints of the diameter at ( (-7, 1) ) and ( (5, 1) ) is ( (x + 1)^2 + (y - 1)^2 = r^2 ) where ( r ) is the radius.
The equation of the parabola ( y = 2x^2 - 8x + 1 ) in standard form is ( y = 2(x - 2)^2 - 7 ).

Binomial Theorem and Distributions

Using the binomial theorem, the third term in ( (x + 3y)^5 ) is ( 90x^3y^2 ).
A binomial distribution example includes a success rate of ( 65% ) in ( 15 ) trials, giving a probability of exactly ( 12 ) successes as ( 0.11096 ).

Miscellaneous

Write ( 0.63 ) as a fraction: ( \frac{7}{11} ).
Finding the sixth term for a geometric sequence where ( a_1 = 4 ) and ( r = 3 ) results in ( 972 ).
The range representing the middle ( 95% ) of a distribution is ( 11.2 < x < 21.6 ).
The value of ( m ) in the inequality ( 7 - \frac{3}{m} > \frac{18}{m} ) is ( m > 3 ).

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Untitled Quiz

Questions and Answers

Solve $\frac{2}{5}y = \frac{3}{14}$

Name the property illustrated by $7(9+1)=(9+1)7$

Solve $18 = 3 |4x-10|$

Write a linear equation.

Write $-3y = -1 + 5x$ in standard form.

Find the x-intercept of $4x-2y=8$.

What is the slope of the line $x = -2$?

What is the slope of the line $y = -2$?

A system of linear equations has how many solutions?

The system of equations $y = -3x + 5$ and $y = 3x - 7$ has how many solutions? What are they?

Find the minimum and maximum value of $f(x,y) = 3x + y$ for the feasible region above.

Determine whether $f(x) = 4x^2 - 16x + 6$ has a maximum or a minimum value and find that value.

Write the quadratic equation that has the roots -2 and $\frac{1}{5}$.

Solve by using the quadratic formula $3x^2 = 5x - 1$.

Simplify $(4 - 12i) - (-8 + 4i)$.

Find the points for #39.

Find the points for #40.

Simplify $(5x-4)^2$.

Use synthetic division to simplify $(3x^3 - 2x + 5) / (x - 2)$.

How many real zeros does the graph of the function have?

How many real zeros are located on the graph?

Find $(f-g)(x)$ for $f(x) = x^2 + 8x$ and $g(x) = 3x + 5$.

Find the inverse of $f(x) = 3 + 5x$.

Graph $y > \sqrt{x} + 3$.

Simplify $\sqrt[3]{256t^4}$.

Simplify $\sqrt{32} - \sqrt{18} + \sqrt{54} + \sqrt{150}$.

Simplify $\frac{5}{2 - \sqrt{3}}$.

Simplify $\sqrt{5} + \sqrt{20} - \sqrt{27} + \sqrt{147}$.

Find the domain and range of the function $y = (\frac{1}{2})(2)^x$.

Write an exponential function that represents growth.

Solve $32^{x+3} = 4^{2x+7}$.

Solve $64^{x} < 32^{x+2}$.

Solve $\log_{\frac{1}{8}} x = -1$.

Where is $\frac{x^2 - 4x + 4}{2x^2 - 3x - 2}$ undefined?

Simplify $\frac{(m + 2t - 3)}{(t^2 - 1)} * \frac{(3t - 3)}{(t^2 - 4t + 3)}$.

Simplify $\frac{3b^2 - 12}{(6b^2 + 12b)} / \frac{(5b - 10)}{(10b^2 + 20b)}$.

Simplify $\frac{30}{(m^2 - 25)} + \frac{3}{(m-5)}$.

Find the LCM of $7m - 21$ and $14m - 42$.

Find the LCM of $t^2 - t - 12$ and $14m - 42$.

If y varies inversely as x and y = 5 when x = 5 find y when x = 45.

Solve $7 - \frac{3}{m} > \frac{18}{m}$.

Write the equation of the parabola in standard form $y = 2x^2 - 8x + 1$.

Write the equation for a circle if the endpoints of the diameter are (-7, 1) and (5, 1).

Find the 20th term of the arithmetic sequence in which $a_1 = 5$ and d = 4.

Write an equation for the nth term of the arithmetic sequence -7, -2, 3, 8,...

Find two arithmetic means for 6, __, __, 30.

Find $S_n$ for the arithmetic series in which $a_1 = 3$, d = $\frac{1}{2}$, and $a_n = \frac{17}{2}$.

Find $^22E(50-2x)$ when x = 18.

Find the sixth term of the geometric sequence for which $a_1 = 4$ and r = 3.

Find four geometric means for 486, __, __, __, __, 2.

Write 0.63 as a fraction.

Write 0.735 as a fraction.

Use binomial theorem to find the third term in $(x + 3y)^5$.

A binomial distribution has a 65% rate of success in 15 trials. What is the probability to get exactly 12 successes?

State if a binomial distribution exists. If so, give a random variable, n, p, and q.

Find the range of variables that represents the middle 95% of the distribution.

What percent of the data will be less than 19?

Solve $x = \tan^{-1}(-\sqrt{3})$.

Study Notes

Algebraic Equations and Solutions

Linear and Quadratic Functions

Slope and Intercepts

Inequalities and Graphing

Exponential and Logarithmic Functions

Simplification Techniques

Sequences and Series

Circle and Parabola Equations

Binomial Theorem and Distributions

Miscellaneous

Studying That Suits You

More Quizzes Like This

Untitled Quiz

Untitled Quiz

Untitled Quiz

Untitled Quiz

Find two arithmetic means for 6, , , 30.

Find four geometric means for 486, , , , , 2.