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3 years ago

8=8^4x? What goes on the question mark?

Mathematics

1 answer:

Lerok [7]3 years ago

4 0

Answer:

8^1 = 8

So, x has to be 1/4 to make the exponent 1, and to make it equal to 8.

Let me know if this helps!

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If MS = 20 m, MT = 9 m, and RM = 12 m, what is the value of IM?

Helga [31]

Given two similar right triangles MIT and MSR such that side MR is an extension of side MT, side MS is an extension of side MI and the side IT is parallel to side SR.

Also, give that <span>If MS = 20 m, MT = 9 m, and RM = 12 m. To find the value of IM, we recall that the ratio of any two sides of a similar figure is equal to the ratio of the corresponding sides of the other triangle.

i.e. IM / MT = MS / RM
</span> IM / 9 = 20 / 12
IM = (9 x 20) / 12 = 15

Therefore, the measure of side IM is 15 m.

3 0

3 years ago

Read 2 more answers

Find the rate of change for each set of ordered pairs. What is

weqwewe [10]

(0,-1), (3,8) is the answer

8 0

3 years ago

Keith wants to place a picture frame in the center of a wall that is 14 5/6

Luda [366]

Answer:

6 2/3 feet

Step-by-step explanation:

<u>Required distance d is same from both sides, added to width of the picture we get the width of the wall:</u>

2d + 1 1/2 = 14 5/6
2d = 14 5/6 - 1 1/2
2d = 13 2/6 = 13 1/3
d = 13 1/3 ÷ 2
d = 40/3 *1/2 = 40/6 = 6 4/6 = 6 2/3 feet

4 0

3 years ago

Rhee and Pamela are two of the 5 members of a band. Every week, the band picks two members at random to play on their own for fi

frozen [14]

There is a 40% chance that Rhee and Pamela will be chosen. I got my answer by dividing 2 and 5 to get the percent.

3 0

3 years ago

A homeowner plans to enclose a 200 square foot rectangular playground in his garden, with one side along the boundary of his pro

Anestetic [448]

Answer:

Therefore the length and width of the playground are 15.5 feet and 12.9 feet respectively.

Step-by-step explanation:

Given that, a homeowner plans to enclose a 200 square foot rectangle playground.

Let the width of the playground be y and the length of the playground be x which is the side along the boundary.

The perimeter of the playground is = 2(length +width)

=2(x+y) foot

The material costs $1 per foot.

Therefore total cost to give boundary of the play ground

=$[ 2(x+y)×1]

=$[2(x+y)]

But the neighbor will play one third of the side x foot.

So the neighbor will play $=\$(\frac13x)$

Now homeowner's total cost for the material is

$=\$[ 2(x+y)-\frac13x]$

$=\$[2x+2y-\frac13x]$

$=\$[2y+x+x-\frac13x]$

$=\$[2y+x+\frac{3x-x}{3}]$

$=\$[2y+x+\frac{2}{3}x]$

$=\$[2y+\frac53x]$

$\therefore C(x)=2y+\frac53x$

where C(x) is total cost of material in $.

Given that the area of the playground is 200.

We know that,

The area of a rectangle is =length×width

=xy square foot

∴xy=200

$\Rightarrow y=\frac{200}{x}$

Putting the value of y in C(x)

$\therefore C(x)=2(\frac{200}{x})+\frac53x$

The domain of C is $(0,\infty )$ .

$\therefore C(x)=2(\frac{200}{x})+\frac53x$

Differentiating with respect to x

$C'(x)= - \frac{400}{x^2}+\frac53$

Again differentiating with respect to x

$C''(x) = \frac{800}{x^3}$

To find the critical point set C'(x)=0

$\therefore 0= - \frac{400}{x^2}+\frac53$

$\Rightarrow \frac{400}{x^2}=\frac{5}{3}$

$\Rightarrow x^2 =\frac{400\times 3}{5}$

$\Rightarrow x=\sqrt{240}$

$\Rightarrow x=15.49 \approx15.5$

Therefore

$\left C''(x) \right|_{x=15.5}=\frac{800}{15.5^3}>0$

Therefore at x= 15.5 , C(x) is minimum.

Putting the value of x in $y=\frac{200}{x}$ we get

$\therefore y=\frac{200}{15.5}$

=12.9

Therefore the length and width of the playground are 15.5 feet and 12.9 feet respectively.

6 0

4 years ago