Resources

Resources

Nth roots

Your answer should be in the form

p(x)+\frac{k}{x-3}

p

is a polynomial and

k

\frac{x^2+4}{x-3}

Liz solved the equation

3(n - 2) = -6 + 4n - n

. Here are her last two steps:

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3n - 6 = -6 + 3n

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-6 = -6

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Which statement is true about the equation?

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(A)The solution is

n = -6

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(B)There is no solution because

-6 = -6

is a true equation.

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(C)There are infinitely many solutions because

-6 = -6

is a true equation.

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(D)The solution is

(-6, 6)

f(x)=-6 x^{3}-6 x

f(-x)

first and then determine whether the function is even, odd, or neither. Write even if the function is even, odd if the function is odd, and neither if the function is neither even nor odd.

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f(-x)=

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\square

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Even/Odd/Neither:

\square

2

. Let's say and urite whether thes

x

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y

is an odd number between

2

4 . y

\qquad

vedanta Excel in Mothematies - Book

5

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188

KHORN MIDDLE SCHOOL-INT) Hudson Ough

04

16

24

5

53

10

2

5

8

80 b 8

10

0

1

reasoning Use the Distributive Property to write an expresslon equivalent to

4(c+8)

. Use pencil and paper. Write the algebraic expression

4(c+8)

in words. Then write the equivalent expression in words. Describe the similarities and the differences in the two statements.

(c+8)=

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oxed{ ext{(Simplify your answer.)}} Get more help - Clear all check an: hp

f(x)=(2 x-1)(3 x+5)(x+1)

x=-\frac{5}{3}, x=-1

x=\frac{1}{2}

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What is the sign of

f

on the interval

-\frac{5}{3}<x<\frac{1}{2}

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1

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f

is always positive on the interval.

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f

is always negative on the interval.

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f

is sometimes positive and sometimes negative on the interval.

f(x)=x(x+3)(x+1)(x-4)

x=-3, x=-1, x=0

x=4

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What is the sign of

f

on the interval

-1<x<4

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1

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f

is always positive on the interval.

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f

is always negative on the interval.

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f

is sometimes positive and sometimes negative on the interval.

f(x)=(x-1)(4 x+3)(3 x-8)

x=-\frac{3}{4}, x=1

x=\frac{8}{3}

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What is the sign of

f

on the interval

-\frac{3}{4}<x<1

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1

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f

is always positive on the interval.

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f

is always negative on the interval.

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f

is sometimes positive and sometimes negative on the interval.

f(x)=(3 x-2)(x+4)(9 x+5)

x=-4, x=-\frac{5}{9}

x=\frac{2}{3}

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What is the sign of

f

on the interval

-\frac{5}{9}<x<\frac{2}{3}

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1

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f

is always positive on the interval.

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f

is always negative on the interval.

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f

is sometimes positive and sometimes negative on the interval.

f(x)=(5 x+1)(4 x-8)(x+6)

x=-6, x=-\frac{1}{5}

x=2

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What is the sign of

f

on the interval

-\frac{1}{5}<x<2

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1

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f

is always positive on the interval.

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f

is always negative on the interval.

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f

is sometimes positive and sometimes negative on the interval.

f(x)=(2 x-1)(3 x-5)(x-4)(3 x+6)

x=-2, x=\frac{1}{2}, x=\frac{5}{3}

x=4

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What is the sign of

f

on the interval

\frac{1}{2}<x<\frac{5}{3}

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1

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f

is always positive on the interval.

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f

is always negative on the interval.

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f

is sometimes positive and sometimes negative on the interval.

The polynomial function

f

f(c)=(c-k)(c^{2}-4c+4)

k

is a constant. The value

2

f

. What is the remainder of

f(c)

when divided by

(c-2)?

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ifferentiability - System of Equations

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4 / 5

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Determine the values of

a

b

which would result in the function

f(x)

being differentiable at

x=-1

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f(x)=\left\{\begin{array}{lll} a x-3 & \text { for } & x \leq-1 \\ 2 b x^{2}-4 x+9 & \text { for } & x>-1 \end{array}\right.

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1

2

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a=\square \quad b=\square \quad \text { Submit Answer }

Given the function

f(x)=-5 x-1

f(x)-1

as a simplified polynomial?

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-90^{\circ} \leq \theta \leq 90^{\circ}

. Find the value of

\theta

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\begin{array}{l} \sin (\theta)=-\frac{\sqrt{3}}{2} \\ \theta=\square \end{array}

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The resistance of a circuit formed by connecting two resistors in parallel is given by

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\frac{1}{\frac{1}{R_{1}}+\frac{1}{R_{2}}} .

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Find the resistance of the circuit if

R_{1}=8

R_{2}=12

. The solution is a fraction whose numerator is

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and whose denominator is

A natural number,

N

4

less than another natural number,

M

. The sum of the reciprocals of

M

N

5

times the reciprocal of twice the value of

M

. What are the two numbers?

M

T

are odd numbers, and

M

is a multiple of

T

, which of the following must be true?

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M + T

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MT

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M - T

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M \div T

State why the following expression is not a polynomial.

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4 \mathrm{x}^{-1}+6 \mathrm{x}

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Choose the correct answer below.

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A. The exponent of the variable is a rational number.

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B. The exponent of the variable is a negative integer.

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C. The expression is a quotient of polynomials, which cannot be simplified to a polynomial.

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D. The exponent of the variable is an irrational number.

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26

35

(1

point) I Cuestion Attempt:

1

1

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14

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=15\quad=16\quad=17\quad=18\quad=19

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Translate the sentence into an equation.

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Twice the difference of a number and

5

7

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Use the variable

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y

for the unknown number.

The table shows the values of an even function for some inputs.

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\begin{array}{c|c} x & f(x) \\hline -4 & 2 \ -3 & \ -2 & 8 \ -1 & \ 0 & 10 \ 1 & \ 2 & \ 3 & \ 4 & 0 \ \end{array}

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Complete the table.

f

be a twice differentiable function, and let

f(-3)=-4

f^{\prime}(-3)=0

f^{\prime \prime}(-3)=1

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What occurs in the graph of

f

(-3,-4)

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1

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(-3,-4)

is a minimum point.

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(-3,-4)

is a maximum point.

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(C) There's not enough information to tell.

f

be a twice differentiable function, and let

f(1)=-7

f^{\prime}(1)=0

f^{\prime \prime}(1)=-2

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What occurs in the graph of

f

(1,-7)

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1

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(1,-7)

is a minimum point.

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(1,-7)

is a maximum point.

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(C) There's not enough information to tell.

f(x)=\frac{6 x+5}{2-\sqrt{14+5 x}}

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We want to find

\lim _{x \rightarrow-2} f(x)

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What happens when we use direct substitution?

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1

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(A) The limit exists, and we found it!

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(B) The limit doesn't exist (probably an asymptote).

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(C) The result is indeterminate.