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3 years ago

Please help me on number 11 if you know how to :) !

Mathematics

1 answer:

NemiM [27]3 years ago

8 0

Answer:

(x, y) = (25, 18)

Step-by-step explanation:

Use the angle sum theorem. You can write equations for the right angle and for the linear angle.

(x +11) +(3y) = 90 . . . . sum of angles making the right angle

(y +7) +90 +65 = 180 . . . . sum of angles making the linear angle

From the second equation, we have ...

y = 18 . . . . subtract 162

Substituting into the first equation gives ...

x + 11 + 3(18) = 90

x = 25 . . . . subtract 65

The values of x and y are 25 and 18, respectively.

_____

<em>Check</em>

VQ = 18+7 = 25

QR = 25 +11 = 36

RS = 3·18 = 54

ST = 65

The totals are 36 +54 = 90; 25 +36 +54 +65 = 180, as required.

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Evaluate the question

Vesna [10]

Answer:

we conclude that:

$\frac{2^{-\frac{4}{3}}}{54^{-\frac{4}{3}}}=81$

Step-by-step explanation:

Given the expression

$\frac{2^{-\frac{4}{3}}}{54^{-\frac{4}{3}}}$

$\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}\:=\:x^{a-b}$

$\frac{2^{-\frac{4}{3}}}{54^{-\frac{4}{3}}}=\left(\frac{2}{54}\right)^{-\frac{4}{3}}$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}$

$=\frac{1}{\left(\frac{2}{54}\right)^{\frac{4}{3}}}$

$=\left(\frac{1}{27}\right)^{-\frac{4}{3}}$

$\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}$

$=\frac{1}{\frac{1^{\frac{4}{3}}}{27^{\frac{4}{3}}}}$

$=\frac{1}{\frac{1^{\frac{4}{3}}}{81}}$ ∵ $27^{\frac{4}{3}}=81$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{1}{\frac{b}{c}}=\frac{c}{b}$

$=\frac{81}{1^{\frac{1}{3}}}$

$\mathrm{Apply\:rule}\:1^a=1$

$=\frac{81}{1}$

$=81$

Therefore, we conclude that:

$\frac{2^{-\frac{4}{3}}}{54^{-\frac{4}{3}}}=81$

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3 years ago

1. A theater group bought supplies to construct the set of a play. Lumber cost $135.86, paint cost $62.91, and hardware cost $27

OleMash [197]

Answer:

The answers are:

a. $226.40

b. 12.2%

c. 87.8%

Step-by-step explanation:

In order to find the total cost, add all three costs together.

135.86 + 62.91 + 27.63 = 226.40

Now to find the percentage cost of the hardware, divide the hardware cost by the total cost.

27.63/226.40 = 12.2%

And since we know that the hardware cost 12.2%, we can find the percentage of the other costs by subtracting the percentage cost of the hardware from 100.

100% - 12.2% = 87.8%

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3 years ago