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2 years ago

If a^1/n=r then which of the following statements are true

Mathematics

2 answers:

posledela2 years ago

6 0

a. This is correct. When you transfer n to the other side, that would be the reciprocal power of a.

b. This is incorrect, because this contradicts with choice a.

c. This is correct. When a number is raised to a "1/n" fraction, that is equivalent to the nth root of the number.

d. This is incorrect, because it is not equivalent to the given equation.

Thus, the answers are A and C.

nlexa [21]2 years ago

4 0

Answer

a. r^n=a

c.^n√a=r

Explanation

solution 1

a⁽¹/ⁿ⁾ = r

Powering both sides of the equation by n;

a⁽¹/ⁿ ₓ ⁿ⁾ = rⁿ

a¹ = rⁿ

solution 2

Also,

a⁽¹/ⁿ⁾ = r

a⁽¹/ⁿ⁾ = ⁿ√a (nth root of a)

ⁿ√a = r

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What is the slope of the line that passes through the points (-2,5) and (3,-4) in the standard (x,y) coordinate plane

Scorpion4ik [409]

To find the slope between two coordinates, you use the formula:

m = y2 - y1/x2 - x1

If coordinate A is (-2, 5) and coordinate B is (3, -4), then:

y2 = -4

y1 = 5

x2 = 3

x1 = -2

So, just substitute the points into the formula.

m = -4 - 5/3 - (-2)

m = -9/5

The slope of the line is -9/5.

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2 years ago

If 9(1-x) = 27Y and x-y=-11/2, find the value of x + y.

Finger [1]

Answer:

-2.25

Step-by-step explanation:

9(1-x) = 27Y

9-9x =27y

-9x -27y = -9 multiply all terms by -1

9x +27y =9 equation (1)

x-y= -11/2 equation (2)

by solving 2 equations

x= -3.875

y= 1.625

∴ x+ y = 1.625 +(-3.875) = -2.25

5 0

2 years ago

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#6 I need help with that.

Alisiya [41]

Answer:

Answer is x= 15

Step-by-step explanation:

(3x+18)+(8x-3)=180

11x+15=180

11x=165

x=15

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2 years ago

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write the logarithm as a sum or difference of logarithms. simplify each term as much as possible. log4(6ab)

Dominik [7]

The logarithm written as a sum of logarithm and simplified as much as possible is $\frac{1}{2} +log_{4 }3 + log_{4 }a + log_{4 }b$

<h3>Simplifying Logarithms</h3>

From the question, we are to write the given logarithm expression as a sum or difference of logarithms

The given logarithm is

$log_{4 }6ab$

This can be written as

$log_{4 }6 \times a \times b$

From one of the rules of logarithm, we have that

$log_{x }yz= log_{x }y + log_{x }z$

Thus,

$log_{4 }6 \times a \times b$ becomes

$log_{4 }6 + log_{4 }a + log_{4 }b$

This can be further simplified into

$log_{4 }3 \times 2 + log_{4 }a + log_{4 }b$

$log_{4 }3 + log_{4 }2 + log_{4 }a + log_{4 }b$

If desired, this can be further simplified into

$log_{4 }3 + log_{2^{2} }2 + log_{4 }a + log_{4 }b$

$log_{4 }3 + \frac{1}{2} log_{2}2 + log_{4 }a + log_{4 }b$

$log_{4 }3 + \frac{1}{2} (1)+ log_{4 }a + log_{4 }b$

$\frac{1}{2} +log_{4 }3 + log_{4 }a + log_{4 }b$

Hence, the logarithm written as a sum of logarithm and simplified as much as possible is $\frac{1}{2} +log_{4 }3 + log_{4 }a + log_{4 }b$

Learn more on Simplifying logarithms here: brainly.com/question/17851187

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1 year ago

Boyle’s law states that the volume of a gas varies inversely with applied pressure. Suppose the pressure on 60 cubic meters of g

tatyana61 [14]

$\bf \qquad \qquad \textit{inverse proportional variation}
\\\\
\textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------$

$\bf \stackrel{\textit{the volume of a gas varies inversely with applied pressure}}{v=\cfrac{k}{p}}
\\\\\\
\textit{we also know that }
\begin{cases}
v=60\\
p=1
\end{cases}\implies 60=\cfrac{k}{1}\implies 60=k
\\\\\\
\boxed{v=\cfrac{60}{p}}
\\\\\\
\stackrel{\textit{now if we apply 3 atmospheres, p=3, what is \underline{v}?}}{v=\cfrac{60}{3}}$

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3 years ago

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