Use the given conditions to write an equation for the line in point-slope form and slope-intercept form.

2 angles are supplementary. The measure of one angle is one-third of the other. Find the measure of BOTH angles.

morpeh [17]

Answer:

45° and 135°

Step-by-step explanation:

let one angle be "x" and the other be "y"

Angles which are supplementary total to 180°. This can be represented with the equation:

x + y = 180

If angle "x" is a third of angle "y", the situation is represented with this equation:

(1/3)x = y

Since fractions are difficult to work with, multiply the whole equation by 3.

(1/3)x = y <= X 3

x = 3y

Use the equations x+y=180 and x=3y.

You can substitute x=3y into x+y=180.

x + y = 180

(3y) + y = 180 <=combine like terms

4y = 180 <=isolate y by dividing both sides by 4

y = 45

Substitute y=45 itno the equation x+y=180 to find x.

x + y = 180

x + 45 = 180 <=isolate x by subtracting 45 from both sides

x = 135

Therefore the angles are 45° and 135°.

5 0

3 years ago

Read 2 more answers

How do you find the perimeter on a coordinate plane

hoa [83]

Answer: You draw the shape on the coordinate plan and then you can count the number of unit squares

Step-by-step explanation:

4 0

1 year ago

Write the set builder notation {8}

timofeeve [1]

Step-by-step explanation:

$\{8 \} = \{x : x = n, \: n \in \:N, \: \: 7 < n > 9 \: \}$

5 0

3 years ago

6. A sector of a circle is a region bound by an arc and the two radii that share the arc's endpoints. Suppose you have a dartboa

Aliun [14]

Given the dartboard of diameter $20in$ , divided into 20 congruent sectors,

The central angle is $18^\circ$

The fraction of a circle taken up by one sector is $\frac{1}{20}$

The area of one sector is $15.7in^2$ to the nearest tenth

The area of a circle is given by the formula

$A=\pi r^2$

A sector of a circle is a fraction of a circle. The fraction is given by $\frac{\theta}{360^\circ}$ . Where $\theta$ is the angle subtended by the sector at the center of the circle.

The formula for computing the area of a sector, given the angle at the center is

$A_s=\dfrac{\theta}{360^\circ}\times \pi r^2$

<h3>Given information</h3>

We given a circle (the dartboard) with diameter of $20in$ , divided into 20 equal(or, congruent) sectors

<h3>Part I: Finding the central angle</h3>

To find the central angle, divide $360^\circ$ by the number of sectors. Let $\alpha$ denote the central angle, then

$\alpha=\dfrac{360^\circ}{20}\\\\\alpha=18^\circ$

<h3>Part II: Find the fraction of the circle that one sector takes</h3>

The fraction of the circle that one sector takes up is found by dividing the angle a sector takes up by $360^\circ$ . The angle has already been computed in Part I (the central angle, $\alpha$ ). The fraction is

$f=\dfrac{\alpha}{360^\circ}\\\\f=\dfrac{18^\circ}{360^\circ}=\dfrac{1}{20}$

<h3>Part III: Find the area of one sector to the nearest tenth</h3>

The area of one sector can be gotten by multiplying the fraction gotten from Part II, with the area formula. That is

$A_s=f\times \pi r^2\\=\dfrac{1}{20}\times3.14\times\left(\dfrac{20}{2}\right)^2\\\\=\dfrac{1}{20}\times3.14\times10^2=15.7in^2$

Learn more about sectors of a circle brainly.com/question/3432053

8 0

2 years ago

Choose the correct answer below. A. Increasing the level of confidence has no effect on the interval. B. Increasing the level of

murzikaleks [220]

Answer:

$ME = t_{\alpha/2} \frac{s}{\sqrt{n}}$

And the width for the confidence interval is given by:

$Width =2ME=2t_{\alpha/2} \frac{s}{\sqrt{n}}$

And we want to see the effect if we increase the confidence level for a interval. On this case if we increase the confidence level then the critical value for the confidence interval $t_{\alpha/2}$ would be higher and then the width of the interval would increase. So then the best answer for this case would be:

B. Increasing the level of confidence widens the interval.

Step-by-step explanation:

Let's assume that we have a parameter of interest $\mu$ who represent for example the true mean for a population. And we can construct a confidence interval in order to estimate this parameter if we know the distribution for the statistic let's say $\bar X$ and for this particular example the confidence interval is given by:

$\bar X \pm ME$

Where ME represent the margin of error for the estimation and this margin of error is given by:

$ME = t_{\alpha/2} \frac{s}{\sqrt{n}}$

And the width for the confidence interval is given by:

$Width =2ME=2t_{\alpha/2} \frac{s}{\sqrt{n}}$

And we want to see the effect if we increase the confidence level for a interval. On this case if we increase the confidence level then the critical value for the confidence interval $t_{\alpha/2}$ would be higher and then the width of the interval would increase. So then the best answer for this case would be:

B. Increasing the level of confidence widens the interval.

3 0

3 years ago