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2 years ago

Which expression is equivalent to log w (x^2 -6)^4/ 3 sqrt x^2+8?

Mathematics

1 answer:

evablogger [386]2 years ago

3 0

Answer:

C $4\log_w(x^2-6)-\dfrac{1}{3}\log_w(x^2+8)$

Step-by-step explanation:

First use the property of logarithms

$\log _ab-\log_ac=\log_a\dfrac{b}{c}.$

For the given expression you get

$\log_w\dfrac{(x^2-6)^4}{\sqrt[3]{x^2+8} }=\log_w(x^2-6)^4-\log_w\sqrt[3]{x^2+8}=\log_w(x^2-6)^4-\log_w(x^2+8)^{\frac{1}{3}}$

Now use property of logarithms

$\log_ab^k=k\log_ab.$

For your simplified expression, you get

$\log_w(x^2-6)^4-\log_w(x^2+8)^{\frac{1}{3}}=4\log_w(x^2-6)-\dfrac{1}{3}\log_w(x^2+8).$

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Select all polynomials that are divisible by (x-1)(x−1)left parenthesis, x, minus, 1, right parenthesis. Choose all answers that

alexdok [17]

Answer:

Step-by-step explanation:

For us to be able to determine the polynomials that are divisible by (x-1), this means that x-1 must be a factor for the functon to be able to divide any of the polynimial.

Since x-1 is a factor, we can get the value of x

x-1 = 0

x =0+1

x = 1

Next is for to substitute x - 1 into the polynomial and see the ones that will give us zero

For A(x)=3x^3+2x^2-x

A(1) = 3(1)^3+2(1)^2-(1)

A(1) = 3+2-(1)

A(1) = 5-1

A(1) = 4

Since A(1) ≠ 0, then x-1 is not divisible by the polynomial function.

For B(x)=5x^3-4x^2-x

B(1)=5(1)^3-4(1)^2-1

B(1)=5-4-1

B(1)=1-1 = 0

Since B(1) = 0, hence x-1 is divisible by 5x^3-4x^2-x

For the polynomial C(x)= 2x^3-3x^2+2x-1

C(1)=2(1)^3-3(1)^2+2(1)-1

C(1)=2-3+2-1

C(1)= -1+1

C(1)= 0

Since C(1) = 0, hence x-1 is divisible by the

For the polynomial D(x)=x^3+2x^2+3x+2

D(1)=1^3+2(1)^2+3(1)+2

D(1)=1+2+3+2

D(x) = 8

Hence the polynomial D(x) is not divisible by x-1

Hence the correct options are B(x)=5x^3-4x^2-x and 2x^3-3x^2+2x-1

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2 years ago

at what x coordinate would a line whose equation is y=2x-3 intersect a perpendicular line whose y intercept is 17

Jlenok [28]

Answer:

Step-by-step explanation:hj

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1 year ago

Which function has a range of y < 3?

Setler79 [48]

Using a graphing tool

Let's graph each of the cases to determine the solution of the problem

case A) $y=3(2^{x})$

see the attached figure N $1$

The range is the interval--------> (0,∞)

$y> 0$

therefore

the function $y=3(2^{x})$ is not the solution

case B) $y=2(3^{x})$

see the attached figure N $2$

The range is the interval--------> (0,∞)

$y> 0$

therefore

the function $y=2(3^{x})$ is not the solution

case C) $y=-2^{x}+3$

see the attached figure N $3$

The range is the interval--------> (-∞,3)

$y< 3$

therefore

the function $y=-2^{x}+3$ is the solution

case D) $y=2^{x}-3$

see the attached figure N $4$

The range is the interval--------> (-3,∞)

$y>-3$

therefore

the function $y=2^{x}-3$ is not the solution

the answer is

$y=-2^{x}+3$

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2 years ago

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For every 1,000 feet you go up in elevation, the temperature decreases by about 3.3°F

Given:

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The top of the mountain is 5500 feet above you

Change (reduction) in temperature is 3.3 X 5500 / 1000

= 18.15°F

Temperature at the top of the mountain is 74°F – 18.15°F

= 55.85°F

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melisa1 [442]

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2 years ago

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