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serious [3.7K]
3 years ago
8

How can I solve this? and can you please tell me how step by step.

Mathematics
2 answers:
Ludmilka [50]3 years ago
8 0

Answer:27/343 or 0.0787172

Step-by-step explanation:

First you need to place the exponent on both the numerator and the demonimator to make 3 to the power of 3 over 7 to the power of 3

Next you evaluate the numerator so 3 to the power of 3 is 27

and 7 to the power of 3 is 343 so your answer in fraction form is 27/343

you can also change into a decimal if you divide the fraction if you need to

Hope this helps

Scorpion4ik [409]3 years ago
4 0

Answer:

(\frac{27}{343})

Step-by-step explanation:

This is what you start off with (\frac{3}{7})^{3}

(\frac{3}{7})^{3} is also equal to (\frac{3}{7})(\frac{3}{7})}(\frac{3}{7}) because the original equation is (\frac{3}{7}) multiplied by itself 3 times.

(\frac{3}{7})(\frac{3}{7})}(\frac{3}{7})

Multiply the first two fractions straight across

(\frac{9}{49})(\frac{3}{7})

Multiply the answer of multiplying the two fractions by (\frac{3}{7})

(\frac{27}{343})

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Show work please<br> \sqrt(x+12)-\sqrt(2x+1)=1
Nesterboy [21]

Answer:

x=4

Step-by-step explanation:

Given \displaystyle\\\sqrt{x+12}-\sqrt{2x+1}=1, start by squaring both sides to work towards isolating x:

\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2

Recall (a-b)^2=a^2-2ab+b^2 and \sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}:

\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2\\\implies x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1

Isolate the radical:

\displaystyle\\x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1\\\implies -2\sqrt{(x+12)(2x+1)}=-3x-12\\\implies \sqrt{(x+12)(2x+1)}=\frac{-3x-12}{-2}

Square both sides:

\displaystyle\\(x+12)(2x+1)=\left(\frac{-3x-12}{-2}\right)^2

Expand using FOIL and (a+b)^2=a^2+2ab+b^2:

\displaystyle\\2x^2+25x+12=\frac{9}{4}x^2+18x+36

Move everything to one side to get a quadratic:

\displaystyle-\frac{1}{4}x^2+7x-24=0

Solving using the quadratic formula:

A quadratic in ax^2+bx+c has real solutions \displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}. In \displaystyle-\frac{1}{4}x^2+7x-24, assign values:

\displaystyle \\a=-\frac{1}{4}\\b=7\\c=-24

Solving yields:

\displaystyle\\x=\frac{-7\pm \sqrt{7^2-4\left(-\frac{1}{4}\right)\left(-24\right)}}{2\left(-\frac{1}{4}\right)}\\\\x=\frac{-7\pm \sqrt{25}}{-\frac{1}{2}}\\\\\begin{cases}x=\frac{-7+5}{-0.5}=\frac{-2}{-0.5}=\boxed{4}\\x=\frac{-7-5}{-0.5}=\frac{-12}{-0.5}=24 \:(\text{Extraneous})\end{cases}

Only x=4 works when plugged in the original equation. Therefore, x=24 is extraneous and the only solution is \boxed{x=4}

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3 years ago
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the ratio of cats to dogs is 5 to 4 if there are a total of 63 cats and dogs how many dogs are there and how many cats ate there
Illusion [34]

Answer:

Number of cats is (5/9)(63) = 35, and number of dogs is (4/9)(63) = 28

Step-by-step explanation:

The given ratio is 5 to 4.  Sum these up, obtaining 9.  Then (5/9) of the whole represents the number of cats, and (4/9) of the whole represents the number of dogs.

Number of cats is (5/9)(63) = 35, and

number of dogs is (4/9)(63) = 28

As a check:  35 + 28 = 63.

7 0
3 years ago
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ladessa [460]

Step-by-step explanation:

given

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Writing In slope intercept form , y = mx + c

y = -3x + 9

comparing the given equation with y = mx + c

slope (m) = - 3

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Hope it will help :)

3 0
3 years ago
Write an equation for the nth term of the arithmetic sequence. Then find a50.
julia-pushkina [17]

Step-by-step explanation:

Since the sequence above is an arithmetic sequence

For an nth term in an arithmetic sequence

A(n) = a + ( n - 1)d

where a is the first term

n is the number of terms

d is the common difference

From the question

a = 1/3

d = 1/2 - 1/3 = 1/6 or 2/3 - 1/2 = 1/6

Substitute the values into the above formula

That's

<h3>A(n) =  \frac{1}{3}  + (n - 1) \frac{1}{6}  \\  =  \frac{1}{ 3}  -  \frac{1}{6}   +  \frac{1}{6} n</h3>

So the nth term of the sequence is

<h3>A(n) =  \frac{1}{6}  +  \frac{1}{6}n</h3>

For a50 since we are finding the 50th term

n = 50

So we have

<h3>A(50) =  \frac{1}{6}  +  \frac{1}{6} (50) \\  =  \frac{1}{6}  +  \frac{25}{3}</h3>

We have the final answer as

<h3>A(50) =  \frac{17}{2}</h3>

Hope this helps you

4 0
3 years ago
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