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3 years ago

18 Geometry question: Use an algebraic equation to find the measure of each angle that is representative in terms of X

Mathematics

1 answer:

Dmitrij [34]3 years ago

4 0

Answer:

12x - 28° = 116°

7x + 32° = 116°

Step-by-step explanation:

12x - 28° and 7x + 32° are vertical angles. Vertical angles are congruent.

Therefore, to find the measure of each angle, we have to set each equation equal to each other as follows:

12x - 28° = 7x + 32°

Collect like terms

12x - 7x = 28 + 32

5x = 60

Divide both sides by 5

5x/5 = 60/5

x = 12

✔️12x - 28°

Plug in the value of x

12(12) - 28

= 144 - 28

= 116°

✔️7x + 32°

7(12) + 32

= 84 + 32

= 116°

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Three potential employees took an aptitude test. Each person took a different version of the test. The scores are reported below

Anastaziya [24]

Answer:

Nico

Step-by-step explanation:

In order to compare who had the best performance on the aptitude test, we can use Z score. Z score indicates how many standard deviation a result is over the mean. For this case the higher the result is, the best is the performance on the aptitude test.

Z score is expressed with the following formula:

Z=(X-μ)/σ

Where:

X is the test score

µ is the mean

σ is the standard deviation

Replacing in the formula we obtained

For Nico:

X = 88.3

µ = 66.2

σ = 13

Z=(88.3-66.2)/13=1.7

For Justin:

X = 226.2

µ = 216

σ = 17

Z=(226.2-216)/17=0.6

For Tera:

X = 7.97

µ = 7.2

σ = 0.7

Z=(7.97-7.2)/0.7=1.1

Nico had the higher Z score which means he had the better performance on the test and he should be offered the job.

3 0

3 years ago

Find the equation of a circle that has a diameter with the endpoints given by the points A(-4,9) and B (- 2, - 3) )

Aleksandr-060686 [28]

The equation of the circle is $(x+3)^{2}+(y-3)^{2}=37$

Explanation:

Given that the endpoints of the circle are A(-4,9) and B(-2,-3)

We need to determine the equation of the circle.

Center:

The center of the circle can be determined using the midpoint formula,

$Center=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

Substituting the coordinates A(-4,9) and B(-2,-3), we get,

$Center=(\frac{-4-2}{2},\frac{9-3}{2})$

$Center=(\frac{-6}{2},\frac{6}{2})$

$Center=(-3,3)$

Thus, the center of the circle is (-3,3)

Radius:

The radius of the circle can be determined using the distance formula,

$r=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$

Substituting the center (-3,3) and the endpoint (-4,9), we get,

$r=\sqrt{\left(-4+3\right)^{2}+\left(9-3\right)^{2}}$

$r=\sqrt{\left(-1\right)^{2}+\left(6\right)^{2}}$

$r=\sqrt{1+36}$

$r=\sqrt{37}$

Thus, the radius of the circle is $\sqrt{37}$

Equation of the circle:

The standard form of the equation of the circle is given by

$(x-a)^{2}+(y-b)^{2}=r^{2}$

where (a,b) is the center and r is the radius.

Substituting the values, we have,

$(x+3)^{2}+(y-3)^{2}=(\sqrt{37})^{2}$

$(x+3)^{2}+(y-3)^{2}=37$

Thus, the equation of the circle is $(x+3)^{2}+(y-3)^{2}=37$

7 0

3 years ago

What’s the unit rate for this? please help!!

Lapatulllka [165]

Hello! Thank you for asking this question on Brainly!

Your question is:

What is the unit rate of 72 ounces for 12 servings?

Divide 72 by 12 to get your answer!

The best possible choice would be D. 6 ounces per serving.

Have a nice day!

:)

3 0

3 years ago

Please help me solve 4 inequalities and show work. Will get brainiest!!

FrozenT [24]

1. y ≤ 4x/3+5
2. y< 6x/4+3

5 0

3 years ago

Antonio gave 21 tomatoes to his neighbor and 15 to his brother .he had 72 tomatoes before giving some away .how many tomatoes do

Butoxors [25]

He has 36 tomatoes left. Since he had 72 tomatoes in the beginning but gave away 21 to his neighbor and 15 to his brother, you have to subtract those two values from 72. The equation would be 72-21-15 which results in 36. Therefore, Antonio has 36 tomatoes left.

8 0

3 years ago

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