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1 year ago

3. Which of the following is a solution to the equation 16 = 4x – 4? (1 point)

1 answer:

8 0

-4 x = -4 -16 = 4x = -20

divide both sides of the equation by -4
-The answer to your question is 5, or x = 5! Hope this helps

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Simplify each expression. Assume that all variables are positive.

kozerog [31]

Q1. The answer is $\frac{8x^{3}y^{6} }{27}$

$( \frac{16 x^{5} y^{10}}{81x y^{2} } )^{ \frac{3}{4} }= ( \frac{16}{81}* \frac{ x^{5} }{x}* \frac{ y^{10} }{y^{2}} )^{ \frac{3}{4} } \\ \\ 
 \frac{ x^{a} }{ x^{b} }= x^{a-b} \\ \\ 
( \frac{16}{81}* \frac{ x^{5} }{x}*\frac{ y^{10} }{y^{2}} )^{ \frac{3}{4} }}=( \frac{16}{81 }* x^{5-1}* y^{10-2})^{ \frac{3}{4} }=( \frac{16}{81 }* x^{4}* y^{8})^{ \frac{3}{4} }= \\ \\ = (\frac{16}{18} )^{ \frac{3}{4} }*(x^{4})^{ \frac{3}{4} }*(y^{8})^{ \frac{3}{4} }=$
$\frac{(16)^{ \frac{3}{4} }}{(18)^{ \frac{3}{4} }}*(x^{4})^{ \frac{3}{4} }*(y^{8})^{ \frac{3}{4} }=\frac{( 2^{4} )^{ \frac{3}{4} }}{( 3^{4} )^{ \frac{3}{4} }}*(x^{4})^{ \frac{3}{4} }*(y^{8})^{ \frac{3}{4} } \\ \\ 
 (x^{a} )^{b} = x^{a*b} \\ \\ 
\frac{( 2^{4} )^{ \frac{3}{4} }}{( 3^{4} )^{ \frac{3}{4} }}*(x^{4})^{ \frac{3}{4} }*(y^{8})^{ \frac{3}{4} } = \frac{ 2^{4* \frac{3}{4} } }{ 3^{4* \frac{3}{4} } } * x^{4* \frac{3}{4} } * y^{8*\frac{3}{4}} = \frac{ 2^{3} }{ 3^{3} } * x^{3} *y^{6} =$
$= \frac{8x^{3}y^{6} }{27}$

Q2. The answer is 1/16

$(-64) ^ \frac{-2}{3} =(-1* 2^{6} ) ^ \frac{-2}{3}=(-1)^ \frac{-2}{3} *(2^{6} ) ^ \frac{-2}{3} \\\\x^{-a} = \frac{1}{ x^{a} } \\\\(-1)^ \frac{-2}{3} *(2^{6} ) ^ \frac{-2}{3} = \frac{1}{(-1)^ \frac{2}{3}} *\frac{1}{(2^{6})^ \frac{2}{3}} \\ \\ (x^{a} )^{b}=x^{a*b} \\\\x^{ \frac{a}{b} = \sqrt[b]{ x^{a} } } \\ \\ 
$
$\frac{1}{(-1)^ \frac{2}{3}} *\frac{1}{2^{6*\frac{2}{3}}} = \frac{1}{ \sqrt[3]{(-1)^{2} } } * \frac{1}{ 2^{4} } = \frac{1}{ \sqrt[3]{1} } * \frac{1}{16} = \frac{1}{1} * \frac{1}{16}= \frac{1}{16}$

Q3. The answer is $a^{ \frac{7}{6} }$

$a^{ \frac{2}{3} } * a^{ \frac{1}{2} } \\ \\ 
 x^{a}* x^{b} =x^{a+b} \\ \\ 
a^{ \frac{2}{3} } * a^{ \frac{1}{2} }= a^{ \frac{2}{3} + \frac{1}{2} } =a^{ \frac{2*2}{3*2} + \frac{1*3}{2*3} }=a^{ \frac{4}{6} + \frac{3}{6} }=a^{ \frac{4+3}{6} }=a^{ \frac{7}{6} }$

7 0

2 years ago

When you find the surface area of a cube, you ________ the length of the cube and<br> multiply by 6

Papessa [141]

Answer:

The word for the blank would be "square".

Step-by-step explanation:

Since the area of a face of a cube would be square its side length, the total surface area of a cube would be that times 6.

Hope this helped!

8 0

2 years ago

Read 2 more answers

Help me! Will give 18 Points and will mark a person as brainiest to the first person who answers!

Reika [66]

Answer:

-201.1

-200.9

-200

201

201.8

Step-by-step explanation:

For the given statement we have come to know that number in the line who have negative vales are less than the positive value

so in the number line we can see that

-201.1 is negative value in the number line and it has least value so

next value is -200.9 who is also negative and least but greater than -201.1

moving towards next we can see the value of 200 who is also negative but greater than from -200.9 so moving towards next

we can see that 201.8 is positive value so it is greater from all the past values

next the value 201 is greater than 200

so after these explanation you can see that numbers moving from negative to positive values and its show greatest values as well

hope it will be brainliest to you .

thank you

4 0

3 years ago

35 POINTS!!! The measures of the angles in a quadrilateral are represented by x, 2x, 3x, and 3x. Write an equation that would al

Marina86 [1]

Answer:

The value of x is 40.

Step-by-step explanation:

The measures of the angles in a quadrilateral are represented by x, 2x, 3x, and 3x.

According to the angle sum property of quadrilateral, the sum of interior angles of a quadrilateral is always 360 degree.

Since the measures of the angles in a quadrilateral are represented by x, 2x, 3x, and 3x, therefore

$x+2x+3x+3x=360$

This is the equation which is used to solve for the value of x.

$9x=360$

$x=\frac{360}{9}$

$x=40$

Therefore the value of x is 40.

6 0

3 years ago

A triangle has side lengths of 8 8 inches, 12 12 inches, and 16 16 inches. Determine whether this is a right triangle and why. C

arlik [135]

Answer:

It is not a right triangle

Step-by-step explanation:

A triangle has side lengths of 8 inches, 12 inches, and 16 inches.

To determine if it is a Right Triangle, we make use of the Pythagoras Theorem, i.e.

$Hypotenuse^2=Opposite^2+Adjacent^2$

Now the Hypotenuse is always the longest side

$16^{2} =8^2+12^2\\256=64+144\\256=208$

The equality above is not true and in fact

$256\neq 208$

Therefore the 3 numbers do not satisfy Pythagoras theorem and cannot be the lengths of a right triangle.

7 0

2 years ago

Read 2 more answers