1) What is the volume of the container?

Simplify 25^ - 1/2 Please explain! I know the answer is 1/5 but why?

lisov135 [29]

$(25)^{-\frac{1}{2} }$

When the exponent is negative, you have to make the number a fraction(1 over the number).

For example:

$25^{-2} = \frac{1}{25^{2} }$

$x^{-1} =\frac{1}{x^{1} }$

This gets rid of the negative, but it leaves the exponent

$(25)^{-\frac{1}{2}} = \frac{1}{25^{1/2}}$

When an exponent is a fraction, it is the square root.

For example:

$x^{\frac{1}{3}} = \sqrt[3]{x}$

$x^{\frac{1}{2}} =\sqrt{x}$

$x^{\frac{1}{4}}=\sqrt[4]{x}$

So...

$\frac{1}{25^{1/2}} = \frac{1}{\sqrt{25} } = \frac{1}{5}$

3 0

3 years ago

Any help please I appreciate it thank you

Natali5045456 [20]

Answer:

20 feet

Step-by-step explanation:

Parimeter is how far you would walk if you made a lap around the shape, walking on the edge lines like a balance beam.

To find perimeter, we need to add up all the sides.

Because it's a square each side has the same length.

There are 4 sides.

5 x 4 = 20

or 5 + 5 + 5 + 5 = 20

The perimeter is 20 feet

7 0

3 years ago

Graph the system of equations. {8x+8y=642x−2y=−4

klemol [59]

The graph is attached.

Explanation:
We can use the x- and y-intercepts to graph. The x-intercept of the first equation is 8, and the y-intercept is 8. The x-intercept of the second equation is -2, and the y-intercept is 2.

x-intercepts are where the data crosses the x-axis. At every one of these points, the y-coordinate will be 0; therefore we can substitute 0 for y and solve to get the value of the x-intercept.

For the first equation, we would have
8x+8(0)=64
8x=64.

Divide both sides by 8:
8x/8 = 64/8
x=8.

For the second equation,
2x-2(0)=-4
2x=-4.

Divide both sides by 2:
2x/2 = -4/2
x=-2.

y-intercepts are where the data crosses the y-axis. At every one of these points, the x-coordinate will be 0; therefore we can substitute 0 for x and solve to get the value of the y-intercept.

For the first equation,
8(0)+8y=64
8y=64.

Divide both sides by 8:
8y/8 = 64/8
y=8.

For the second equation,
2(0)-2y=-4
-2y=-4.

Divide both sides by -2:
-2y/-2 = -4/-2
y=2.

Plot these points for both equations and connect them to draw the line.

6 0

3 years ago

Which expressions are equivalent to the one below? Check all that apply. 8^x

Dvinal [7]

$\bf a)\qquad \left( \cfrac{32}{4} \right)^x\implies \left( \cfrac{8}{1} \right)^x\implies (8)^x\implies 8^x
\\\\\\
b)\qquad x^4\impliedby \textit{nothing to simplify}
\\\\\\
c)\qquad 8\cdot 8^{x-1}\implies 8^1\cdot 8^{x-1}\impliedby \textit{same base, add the exponents}
\\\\\\
\left. \qquad \right.\left. \qquad \right.8^{1+x-1}\implies 8^x$

$\bf d)\qquad \cfrac{32^x}{4}\implies \cfrac{(2^5)^x}{2^2}\implies (2^5)^x\cdot 2^{-2}\implies 2^{5x}\cdot 2^{-2}\implies 2^{5x-2}
\\\\\\
e)\qquad \cfrac{32^x}{4^x}\implies \left( \cfrac{32}{4} \right)^x\implies \left( \cfrac{8}{1} \right)^x\implies 8^x
\\\\\\
f)\qquad 8\cdot 8^{x+1}\implies 8^1\cdot 8^{x+1}\implies 8^{1+x+1}\implies 8^{x+2}$

7 0

4 years ago

Write in slope-intercept form an equation of the line that passes through the given points.

Dahasolnce [82]

Find m or the slope of the two coordinates first.

M = y2-y1 / x2-x1

= 5 - (-1) / 1 - (-1)

= 6 / 2

= 3

Now that you have the slope, we can use the equation of a line which is :

y - y1 = m(x - x1)

Substitute any coordinate.

I'll go with (1, 5)

y - 5 = 3(x - 1)

y - 5 = 3x - 3

y = 3x + 2

And that's the equation in the slope intercept form or y=mx+b.

3 0

4 years ago