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marishachu [46]
3 years ago
14

What values of c and d make the equation true?

Mathematics
1 answer:
saul85 [17]3 years ago
4 0

Answer:

Third option.

Step-by-step explanation:

You need to cube both sides of the equation. Remember the Power of a power property:

(a^m)^n=a^{mn

\sqrt[3]{162x^cy^5}=3x^2y(\sqrt[3]{6y^d})\\\\(\sqrt[3]{162x^cy^5})^3=(3x^2y(\sqrt[3]{6y^d}))^3\\\\162x^cy^5=27x^6y^36y^d

According to the Product of powers property:

(a^m)(a^n)=a^{(m+n)

Then. simplifying you get:

162x^cy^5=162x^6y^{(3+d)}

Now you need to compare the exponents. You can observe that the exponent of "x" on the right side is 6,  then the exponent of "x" on the left side must be 6. Therefore:

c=6

You can notice that the exponent of "y" on the left side is 5,  then the exponent of "x" on the left side must be 5 too. Therefore "d" is:

3+d=5\\d=5-3\\d=2

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The length of a rectangle is 3 feet more than twice the width. The perimeter is 128 feet. Find the length and width.
iragen [17]
We are going to consider a rectangle with length called "a" and width "b"  Then we know that perimeter is the sum of both sides 2*a + 2*b = 128  And also the following equation given by the question: a = 2*b + 3  So solving the first equation: 2*(2*b+3) + 2*b = 128 4*b+6+2*b=128 6*b = 122 b = 122/6 = 61/3  Then a=2*122/6+3 = 244/6+3 = 262/6 = 131/3  Solution:  Length = 131/3 Width = 61/3
7 0
3 years ago
HELP PLEASE!!!<br><br>Answer: ?​
padilas [110]

Answer:

third choice

Step-by-step explanation:

8 0
2 years ago
Simplify each expression as much as possible, and rationalize denominators when applicable. . √36/√18= ?
tino4ka555 [31]

Answer:

√2

Step-by-step explanation:

Solving the given expression step by step:

\frac{\sqrt{36} }{\sqrt{18} } = \frac{6}{3\sqrt{2} }\ \ \ [\because \sqrt{36} = 6 \ and \ \sqrt{18} = 3\sqrt{2}] \\ = \frac{3 \times 2}{3\sqrt{2} } = \frac{ 2}{\sqrt{2} }= \sqrt{2}

We rationalize denominator and change it into a simpler form as soon as possible.

7 0
3 years ago
Can someone help me?
Kitty [74]

Answer:

see explanation

Step-by-step explanation:

Given the width is \frac{1}{3} of the length, then

y - 4 = \frac{1}{3}(2y + 6)

Multiply through by 3 to clear the fraction

3y - 12 = 2y + 6 ( subtract 2y from both sides )

y - 12 = 6 ( add 12 to both sides )

y = 18

Thus

length = 2y + 6 = 2(18) + 6 = 36 + 6 = 42 in

width = y - 4 = 18 - 4 = 14 in

6 0
3 years ago
Please help me!
Tamiku [17]
Check the picture below.

notice the sides, now, on the second triangle, side 6 slants a bit more to fit in 13, on the third triangle, side 6 slants even further to fit 13 in, now, if 6 were to slant completely, it'll make a flat-line with side 5, and there will be a triangle no more.

but even if side 6 would stretch to a flat-line, 5+6 is just 11, whilst side 13 is longer than that, so no dice.

4 0
3 years ago
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