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2 years ago

The complement of an angle is one-sixth the measure of the supplement of the angle. What is the measure of the complement angle?

Mathematics

2 answers:

DochEvi [55]2 years ago

8 0

Answer:

Option C.

The measure of the complement angle is $18\°$

Step-by-step explanation:

Let

x-----> the angle

we know that

The complement of an angle is equal to $(90-x)\°$

The supplement of an angle is equal to $(180-x)\°$

we have

The complement of an angle is one-sixth the measure of the supplement of the angle

$(90-x)\°=(1/6)(180-x)\°$

solve for x

$(540-6x)\°=(180-x)\°\\ (6x-x)=(540-180)\°\\ (5x)=(360)\°\\ x=72\°$

Find the measure of the complement angle

$(90-x)\° ----> (90-72)=18\°$

Jet001 [13]2 years ago

4 0

Answer:

Option C. 18

Step-by-step explanation:

<h2><em><u>Let x be the given angle. </u></em></h2><h2><em><u>1 </u></em></h2><h2><em><u>6 </u></em></h2><h2><em><u>(180 − x) = (90 − x) </u></em></h2><h2><em><u>30 − </u></em></h2><h2><em><u>1 </u></em></h2><h2><em><u>6 </u></em></h2><h2><em><u>x = 90 − x </u></em></h2><h2><em><u>5 </u></em></h2><h2><em><u>6 </u></em></h2><h2><em><u>x = 60 </u></em></h2><h2><em><u>x = 72° </u></em></h2><h2><em><u> </u></em></h2><h2><em><u>The supplement angle to 72° is 108°. </u></em></h2><h2><em><u>The complement angle to 72° is 18°.</u></em></h2>

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You have 42 ft. of fencing (1 ft. segments) to make a rectangular garden. How much should each side be to maximize your total ar

Verizon [17]

Answer:

$Length=10.5\ ft$

$Width=10.5\ ft$

$Area=110.25\ ft^{2}$

Step-by-step explanation:

Let

x----> the length of the rectangular garden

y---> the width of the rectangular garden

we know that

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we have

$P=42\ ft$

$42=2(x+y)$

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$21=(x+y)$

$y=21-x$ ------> equation A

Remember that the area of rectangle is equal to

$A=xy$ ----> equation B

substitute equation A in equation B

$A=x(21-x)$

$A=21x-x^{2}$ ----> this is a vertical parabola open downward

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The y-coordinate of the vertex is the maximum area

The x-coordinate of the vertex is the length side of the rectangle that maximize the area

using a graphing tool

The vertex is the point $(10.5,110.25)$

see the attached figure

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Find the value of y

$y=21-10.5=10.5\ ft$

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2 years ago

Plz help me with it !

Kipish [7]

Answer: $\bold{-7+2\sqrt{14}+5\sqrt{7}-10\sqrt{2}}$

<u>Step-by-step explanation:</u>

$\dfrac{\sqrt7-5}{\sqrt7+\sqrt8}\bigg(\dfrac{\sqrt7-\sqrt8}{\sqrt7-\sqrt8}\bigg)=\dfrac{7-2\sqrt{14}-5\sqrt{7}+10\sqrt2}{7-8}=\dfrac{7-2\sqrt{14}-5\sqrt{7}+10\sqrt2}{-1}\\\\\\=\boxed{-7+2\sqrt{14}+5\sqrt{7}-10\sqrt2}$

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2 years ago