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DENIUS [597]
2 years ago
10

The measure of the supplement of an angle exceeds three times the measure of the complement of the angle by 12. Find the measure

of half of the supplement.​
Mathematics
1 answer:
satela [25.4K]2 years ago
8 0

Answer:

  64.5°

Step-by-step explanation:

The supplement of angle x is 180-x. The complement of the same angle is 90-x, which is 90 less than the supplement.

We can let 'a' represent half the measure of the supplement. Then 2a is the measure of the supplement, and we are given the relation ...

  2a -(3(2a-90)) = 12

  2a -6a +270 = 12 . . . simplify

  258 = 4a . . . . . . . . . . add 4a-12

  a = 64.5

The measure of half the supplement is 64.5 degrees.

_____

<em>Additional comment</em>

Then the supplement of the angle is 129°, and the angle is 51°. Its complement is 39°. 3 times the complement is 117°, which is 12° less than the supplement, as required.

__

There are many ways to assign the variable(s) in this problem. Here, we chose one that is pretty direct: the value of the variable answers the question. If you let the variable represent the angle, its complement, or its supplement, then additional work is required to answer the question after the value of the variable is found.

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Write a cubic function whose graph goes through the points: (-5, 0) (1, 0) (2, -2) (4, 0)
Free_Kalibri [48]

Answer:

f(x) = \frac{1}{7}(x+5)(x-1)(x-4)

Step-by-step explanation:

Let the equation of the give cubic function is,

f(x) = p(x - a)(x - b)(x - c)

Here, a, b, c and d are the x-intercepts of the given graph.

Since, x-intercepts given in the graph are x = -5, 1 and 4,

Equation of the curve will be,

f(x) = p(x + 5)(x - 1)(x - 4)

Since, the graph of this function passes through (2, -2) also

-2 = p(2 + 5)(2 - 1)(2 - 4)

-2 = -p(14)

p = \frac{2}{14}

p = \frac{1}{7}

Therefore, equation will be,

f(x) = \frac{1}{7}(x+5)(x-1)(x-4)

5 0
3 years ago
An open-top rectangular box with square base is to be made from 100 square feet of material, as shown.
-Dominant- [34]

The largest possible volume of the given box is; 96.28 ft³

<h3>How to maximize volume of a box?</h3>

Let b be the length and the width of the base (length and width are the same since the base is square).

Let h be the height of the box.

The surface area of the box is;

S = b² + 4bh

We are given S = 100 ft². Thus;

b² + 4bh = 100

h = (100 - b²)/4b

Volume of the box in terms of b will be;

V(b) = b²h = b² * (100 - b²)/4b

V(b) = 25b - b³/4

The volume is maximum when dV/db = 0. Thus;

dV/db = 25 - 3b²/4

25 - 3b²/4 = 0

√(100/3) = b

b = 5.77 ft

Thus;

h = (100 - (√(100/3)²)/4(5.77)

h = 2.8885 ft

Thus;

Largest volume = [√(100/3)]² * 2.8885

Largest Volume = 96.28 ft³

Read more about Maximizing Volume at; brainly.com/question/1869299

#SPJ1

4 0
1 year ago
Alyssa took a math test for 20 questions and she answered 16 questions correctly in order to get an a she needs to answer at lea
Elenna [48]

Answer:

She did not qualify the exam.

Step-by-step explanation:

Given data

Total no of question in a test = 20

No. of question answered correctly = 16

Percentage of question answered correctly

(\frac{16}{20}) 100 = 80

But in order to get in the exam the student must have to score at least 90 %. But she got only 80 % so she did not qualify the exam.

6 0
3 years ago
I need help on my homework
soldi70 [24.7K]

Answer:

\displaystyle m\angle AED=32.5^\circ

Step-by-step explanation:

<u>Angles in a Circle</u>

An exterior angle of a circle is an angle whose vertex is outside a circle and the sides of the angle are secants or tangents of the circle.

Segments AE and DE are secants of the given circle. They form an exterior angle called AED.

The measure of an exterior angle is equal to half the difference of the measure of their intercepted arcs.

Intercepted arcs in the given circle are AD=113° and BC=48°. The exterior angle is:

\displaystyle m\angle AED=\frac{AD-BC}{2}

\displaystyle m\angle AED=\frac{113^\circ-48^\circ}{2}=\frac{65^\circ}{2}

\displaystyle m\angle AED=32.5^\circ

8 0
2 years ago
Another easy question need fast please
Tresset [83]

Answer:

30.25

Step-by-step explanation:

All angles of a line must add up to 180. Since we already know that one angle is 90 degrees, we know that the other angles should add up to 90 degrees in order for all of the angles to add up to 180 degrees:

(3x-7)+(x+8)=90

4x+1=90

4x=89

x=22.25

22.25+8= 30.25

3 0
2 years ago
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