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fiasKO [112]
2 years ago
10

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:
cestrela7 [59]2 years ago
7 0

Answer:

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\°

Alona [7]2 years ago
6 0

Answer:

18⁰

Step-by-step explanation:

Angle = x

Complement = 90 - x

Supplement = 180 - x

Given:

90 - x = 1/6 × (180 - x)

540 - 6x = 180 - x

5x = 360

x = 72

Complement = 90 - 72 = 18⁰

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Maksim231197 [3]

Answer: (6+7\sqrt{3},0)\text{ and }(6-7\sqrt{3},0) are the required points.

or  (18.124,0) and ( -6.124,0) are the required points.

Step-by-step explanation:

Let (x,0) be the point on x -axis that are 14 units from the point (6,-7) .

Then by distance formula , we have

\sqrt{(x-6)^2+(0-(-7))^2}=14\ \ \ [\ \because distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}]

Taking square on both the sides , we get

(x-6)^2+7^2=14^2\\\\\Rightarrow\ x^2+6^2-2(6)x+49=196\\\\\Rightarrow\ x^2+36-12x=147\\\\\Rightarrow\ x^2-12x=111\\\\\Rightarrow\ x^2-12x-111=0

Using quadratic formula : x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}

x=\dfrac{12\pm\sqrt{(-12)^2-4(1)(-111)}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{144+444}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{588}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{2^2\times7^2\times3}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm14\sqrt{3}}{2}\\\\\Rightarrow\ x=6\pm7\sqrt{3}

so, (6+7\sqrt{3},0)\text{ and }(6-7\sqrt{3},0) are the required points.

since \sqrt{3}=1.732

so, (6+7(1.732),0)\text{ and }(6-7(1.732),0) are the required points.

i.e. (18.124,0) and ( -6.124,0) are the required points.

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3 years ago
4(x-6)&lt;-2x+6 what is the solution to the inequality <br> _
Cloud [144]
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4(x - 6) \leq -2x + 6
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All is left to do is add and subtract to get the x variable all alone.

4x - 24  \leq -2x + 6
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In order to be in the solution set, x has to be less than or equal to 5.

In interval notation: [5, -∞)
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Adam is going to cook a turkey for 14 people and wants to allow 3/4 lb of turkey for each person. 1lb = 450g
Zarrin [17]
(You forgot to add the question, but I guess you want to know the mass of the turkey for 14 people :p )
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So to know the total mass of the turkey, you multiply the mass for one person by the total  number of people:
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Hope this Helps! :)
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