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2 years ago

Identify the terms in the expression. (Enter your answers as a comma-separated list.)

Mathematics

1 answer:

USPshnik [31]2 years ago

8 0

5y3+y+3

5y4+3

I'm not sure but I think it will help you out

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Remember to show work and explain. Use the math font.

MrMuchimi

Answer:

$\large\boxed{1.\ f^{-1}(x)=4\log(x\sqrt[4]2)}\\\\\boxed{2.\ f^{-1}(x)=\log(x^5+5)}\\\\\boxed{3.\ f^{-1}(x)=\sqrt{4^{x-1}}}$

Step-by-step explanation:

$\log_ab=c\iff a^c=b\\\\n\log_ab=\log_ab^n\\\\a^{\log_ab}=b\\\\\log_aa^n=n\\\\\log_{10}a=\log a\\=============================$

$1.\\y=\left(\dfrac{5^x}{2}\right)^\frac{1}{4}\\\\\text{Exchange x and y. Solve for y:}\\\\\left(\dfrac{5^y}{2}\right)^\frac{1}{4}=x\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\\dfrac{(5^y)^\frac{1}{4}}{2^\frac{1}{4}}=x\qquad\text{multiply both sides by }\ 2^\frac{1}{4}\\\\\left(5^y\right)^\frac{1}{4}=2^\frac{1}{4}x\qquad\text{use}\ (a^n)^m=a^{nm}\\\\5^{\frac{1}{4}y}=2^\frac{1}{4}x\qquad\log_5\ \text{of both sides}$

$\log_55^{\frac{1}{4}y}=\log_5\left(2^\frac{1}{4}x\right)\qquad\text{use}\ a^\frac{1}{n}=\sqrt[n]{a}\\\\\dfrac{1}{4}y=\log(x\sqrt[4]2)\qquad\text{multiply both sides by 4}\\\\y=4\log(x\sqrt[4]2)$

$--------------------------\\2.\\y=(10^x-5)^\frac{1}{5}\\\\\text{Exchange x and y. Solve for y:}\\\\(10^y-5)^\frac{1}{5}=x\qquad\text{5 power of both sides}\\\\\bigg[(10^y-5)^\frac{1}{5}\bigg]^5=x^5\qquad\text{use}\ (a^n)^m=a^{nm}\\\\(10^y-5)^{\frac{1}{5}\cdot5}=x^5\\\\10^y-5=x^5\qquad\text{add 5 to both sides}\\\\10^y=x^5+5\qquad\log\ \text{of both sides}\\\\\log10^y=\log(x^5+5)\Rightarrow y=\log(x^5+5)$

$--------------------------\\3.\\y=\log_4(4x^2)\\\\\text{Exchange x and y. Solve for y:}\\\\\log_4(4y^2)=x\Rightarrow4^{\log_4(4y^2)}=4^x\\\\4y^2=4^x\qquad\text{divide both sides by 4}\\\\y^2=\dfrac{4^x}{4}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\y^2=4^{x-1}\Rightarrow y=\sqrt{4^{x-1}}$

6 0

3 years ago

Cecil the acrobat walked three and one half feet on his tightrope, backed up 1 foot, then walked six and one half feet to get ba

Effectus [21]

3 1/2 - 1 + 6 1/2= 9 feet is how far he walked

3 0

3 years ago

1. James and Alexis simplified the expression 5 + 42 - 6/3. James' said the answer is

Trava [24]

Answer:

Step-by-step explanation:

5 + 4^2 - 6/3

= 5 + 16 - 2

= 21 - 2

= 19

4 0

2 years ago

The difference between two numbers is 3. Their sum if 27. What is the<br> smaller number?

nevsk [136]

Answer: The smaller number is 12

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Give the domain and range.

MA_775_DIABLO [31]

Answer:

Domain: {-3, 0 3}

Range: {0, 3}

Step-by-step explanation:

Recall that the Domain of a relationship associated with coordinate pairs of the form (x,y), is the set of all "x-values" given in the relationship.

The Range is the set of all "y-values" given in the relationship.

In our case, we have three coordinate points defining the relationship. These points have the following (x,y) coordinates (see attached image to see which coordinates are associated with each point):

(-3, 3), (0, 0), and (3, 3)

Therefore, the x values associated with these points are: -3, 0 and 3

therefore the Domain of the relationship is the set: { -3, 0, 3}

On the other hand, he y values associated with these points are: 3, 0, and again 3. So in fact there are just to distinct y-values: 0 and 3.

therefore the Range of the relationship is he set: {0, 3}

which corresponds to answer B.

6 0

3 years ago