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2 years ago

PLS HELP ON MATH QUIZ PT.2

Mathematics

1 answer:

vredina [299]2 years ago

4 0

Given:

In the given figure, $m\angle 1=(3x+12)^\circ, m\angle 2=(3x+18)^\circ, m\angle 3=(7x+10)^\circ$ .

To find:

The measure of angle 3.

Solution:

According to the exterior angle theorem of a triangle, the measure of exterior angle is equal to the sum of two opposite interior angles of a triangle.

Using exterior angle theorem of a triangle, we get

$m\angle 3=m\angle 1+m\angle 2$

$7x+10=(3x+12)+(3x+18)$

$7x+10=6x+30$

$7x-6x=30-10$

$x=20$

The value of x is 20. So, the measure of angle 3 is:

$m\angle 3=(7x+10)^\circ$

$m\angle 3=(7(20)+10)^\circ$

$m\angle 3=(140+10)^\circ$

$m\angle 3=150^\circ$

Therefore, the measure of angle 3 is 150 degrees.

You might be interested in

If cos A = 3 over 11, then which of the following is correct?

ziro4ka [17]

Answer: The answer is (a) sec A = 11 over 3.

Step-by-step explanation: Given that Cosine of an angle 'A' is 3 over 11,

i.e.,

$\cos A=\dfrac{3}{11}.$

And we need to find which one of the given four options is correct.

We have the following relations between cosine, secant and cosecant of an angle from trigonometry.

$\sec A=\dfrac{1}{\cos A}~~\textup{and}~~\csc A=\dfrac{1}{\sqrt{1-\cos^2 A}}.$

Therefore,

$\sec A=\dfrac{11}{3}$

and

$\csc A=\dfrac{1}{\sqrt{1-\frac{9}{121}}}=\dfrac{1}{\sqrt{\frac{112}{121}}}=\dfrac{11}{4\sqrt 7}.$

Thus, the correct option is (a) sec A = 11 over 3.

3 0

3 years ago

Is the triangle obtuse, acute, equilateral or right?

Stells [14]

9514 1404 393

Answer:

obtuse

Step-by-step explanation:

The law of cosines tells you ...

b² = a² +c² -2ac·cos(B)

Substituting for a²+c² using the given equation, we have ...

b² = b²·cos(B)² -2ac·cos(B)

We can subtract b² to get a quadratic in standard form for cos(B).

b²·cos(B)² -2ac·cos(B) -b² = 0

Solving this using the quadratic formula gives ...

$\cos(B)=\dfrac{-(-2ac)\pm\sqrt{(-2ac)^2-4(b^2)(-b^2)}}{2b^2}\\\\\cos(B)=\dfrac{ac}{b^2}\pm\sqrt{\left(\dfrac{ac}{b^2}\right)^2+1}$

The fraction ac/b² is always positive, so the term on the right (the square root) is always greater than 1. The value of cos(B) cannot be greater than 1, so the only viable value for cos(B) is ...

$\cos(B)=\dfrac{ac}{b^2}-\sqrt{\left(\dfrac{ac}{b^2}\right)^2+1}$

The value of the radical is necessarily greater than ac/b², so cos(B) is necessarily negative. When cos(B) < 0, B > 90°. The triangle is obtuse.

4 0

2 years ago

Read 2 more answers

teacher gives 5 students a multiple choice test, in which each problem is worth 1 point and there is no penalty with negative po

mamaluj [8]

The mean is the average value of a given set of numbers, and the median is the number in the middle of a set of numbers arranged in increasing order

The correct values as response to the questions are;

The minimum possible top score is 21

The maximum possible top score is 32

The minimum of the possible standard deviation is approximately 1.26

The maximum of the possible standard deviation is approximately 11.7

The reason the above values are correct are as follows:

The given parameters are;

The number of students that take the test, n = 5

The amount of points for each problem = 1 point

The median score = 9

The mean Score = 10

Required:

The minimum possible score;

The maximum possible top score

The minimum of the possible standard deviations

The maximum of the possible standard deviations

Solution:

Given that there is a score (the median) which is 9, we have;

The scores obtainable in the test is Scores ≥ 9

Therefore, for a score of 10, we have;

The minimum total points obtainable = Mean × Number of students

Therefore;

Total minimum total points obtainable by the 5 students = 5 × 10 = 50

The minimum possible top score

By arrangement, with the median at the middle, the minimum possible top score is given as follows;

0, 0, 9, 20, 21

Therefore, the minimum possible top score is 21

The maximum possible top score

The maximum possible top score is similarly given by arrangement of the numbers as follows'

0, 0, 9, 9, 32

The maximum possible top score is 32

The minimum standard deviation

By arrangement and selection, the minimum standard deviation is given as follows;

The minimum of the possible standard deviations of (9, 9, 9, 11, 12) ≈ 1.26

The maximum of the possible standard deviation

The maximum of the possible standard deviation is given as follows;

The maximum of the possible standard deviation of (0, 0, 9, 9, 32) ≈ 11.7

Learn more about mean and median here:

brainly.com/question/17012793

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2 years ago

Isaiah is having his house painted. He paid $525 for the required materials, and he will pay $30 an hour for the painters to com

alukav5142 [94]

Answer:

Step-by-step explanation:

x is the amount of hours it will take. Since he pays $30 per hour, your answer would be 30x + 525

7 0

2 years ago

Solve. -1/2 + (3/4 x 4/9)

max2010maxim [7]

-0.16666666666 which equals -1/16.

4 0

3 years ago