Solve the equations using addition or subtraction.<br> 5.5=-2+d

Consider circle H with a 3 centimeter radius. If the length of minor arc RT is

djyliett [7]

Answer:

$\angle RST=20^{\circ}$

$\angle RST=\frac{\pi}{9}$

Step-by-step explanation:

Please consider the attached graph of circle.

We have been given that circle H has a radius of 3 centimeters. The length of minor arc RT is $\frac{2}{3}\pi$ . We are asked to find the measure of angle RST.

We will use arc length formula to find central angle.

$\text{Arc length}=r\cdot \theta$ , where theta is central angle in radians.

Upon substituting our given values in arc length formula, we will get:

$r\cdot \theta=\frac{2}{3}\pi$

$3\cdot \theta=\frac{2}{3}\pi$

$\frac{3\cdot \theta}{3}=\frac{\frac{2\pi}{3}}{3}$

$\theta=\frac{2\pi}{3\cdot 3}$

$\theta=\frac{2\pi}{9}$

We know that the measure of inscribed angle is half the measure of central angle.

$\angle RST=\frac{1}{2}\angle RHT$

$\angle RST=\frac{1}{2}\cdot \frac{2\pi}{9}$

$\angle RST=\frac{\pi}{9}$

The measure of angle RST is in radians, we will convert it in degrees as:

$\angle RST=\frac{\pi}{9}\times \frac{180^{\circ}}{\pi}$

$\angle RST=20^{\circ}$

Therefore, measure of angle is $\frac{\pi}{9}$ in radians or 20 degrees.

6 0

2 years ago

Read 2 more answers

A 5-pound bag of dog food costs $2.10. What is the unit price?<br> per pound<br> Submit

blondinia [14]

Answer:

.42 per pound

Step-by-step explanation:

6 0

2 years ago

The lengths of text messages are normally distributed with a population standard deviation of 3 characters and an unknown popula

slava [35]

Answer:

25.4, 28.6

Step-by-step explanation:

Given parameters

sample size, n = 24

sample mean, X = 27

population standard deviation, s = 3

critical value, Zα/2, where α = 0.01

99% confidence Interval, CI, is given as follows

CI = X ± Zα/2 × (s/√n)

Zα/2 = Z0.01/2 = Z0.005 = 2.576

CI = 27 ± 2.576 × (3/√24)

= (25.42 ,28.57)

5 0

2 years ago

A pizza had 9/10 left before Lucas ate 4/5 of the pizza. How much pizza is left over?

Allushta [10]

Step-by-step explanation:

always try to bring fractions you need to compare to the same denominator (bottom number).

we have 9/10 of the pizza left.

then 4/5 if the pizza are eaten.

how to compare 9/10 with 4/5 ?

by bringing 4/5 also to a fraction of 10ths.

what do I need to multiply 5 with to get 10 ?

right, 2.

since we don't want to change the overall value of the original fraction, we need to multiply both levels (numerator and denominator) by that same factor :

4/5 × 2/2 = 8/10

aha !

that we can compare with 9/10.

so, when Lucas ate 4/5 (= 8/10) of the pizza, when there was originally 9/10 left, then we have 1/10 of the pizza left.

5 0

2 years ago

Esther is participating in a walk-a-thon. She will raise 5 dollars for her charity for each lap she walks.

avanturin [10]

Answer:

independent variable = number of laps;

dependent variable = number of dollars

Step-by-step explanation:

If we were to put this information into a slope-intercept form equation, the equation would be: y = 5x (dollars raised = 5 dollars per lap walked). In this case, we are going to use the variables l and d instead of x and y, respectively. The equation instead of being y = 5x, it is going to be d = 5l. In the slope-intercept form X will always be the independent variable and y the dependent variable, because the number we get for Y totally depends on what you plugged in for X. In this equation, l is the independent variable (the number of laps she walks) and d is the dependent variable (number of dollars).

6 0

3 years ago

Read 2 more answers

Solve the equations using addition or subtraction. 5.5=-2+d