Find the distance between the points L (7,-1) and M (-2,4)

What is the correct expanded form of -3(4 + 2n) ?

lys-0071 [83]

Answer:

-3(4+2n) multiply -3 by 4 and 2n

-12-6n

3 0

3 years ago

Read 2 more answers

Madelyn is working two summer jobs, making $20 per hour lifeguarding and making $12 per hour clearing tables. In a given week, s

Kamila [148]

Answer:

The possible values of the number of hours clearing tables are 2 , 3 , 4 , 5 hours

Step-by-step explanation:

* <em>Lets explain how to solve the problem</em>

- Madelyn is making $20 per hour life guarding

- She is making $12 per hour clearing tables

- She can work no more than 13 total hours

∴ The greatest time she can work is 13 hours (≤)

- She must earn no less than $180

∴ The least money she wants to earn is $180 (≥)

- If Madelyn worked 8 hours life guarding and assume that she

worked x hours clearing tables

∵ She can work no more than 13 hours

∴ 8 + x ≤ 13

- Subtract 8 from both sides

∴ x ≤ 5 ⇒ (1)

∵ She must earn no less than $180

∴ 8 × 20 + x × 12 ≥ 180

∴ 160 + 12x ≥ 180

- Subtract 60 from both sides

∴ 12x ≥ 20 ⇒ (2)

- From equation (1) ⇒ x = 1 , 2 , 3 , 4 , 5

- Substitute x in equation (2) by these values to find the right values

of x

# If x = 1

∴ 12(1) ≥ 20

- But 12 is less than 20

∴ x can not be 1

# x = 2

∴ 12(2) ≥ 20

∴ 24 ≥ 20

- 24 is greater than 20 then x can be 2

∵ 3 , 4 , 5 greater than 2

∴ All of them give answers greater than 20

∴ x can be 3 , 4, 5

∵ x represents the number of hours for clearing tables

∴ The possible values of the number of hours clearing tables are

2 , 3 , 4 , 5 hours

5 0

4 years ago

Give at least five problems solving about area of a sector of a circle.

Katyanochek1 [597]

See below for the examples of sectors and arcs of a circle

<h3>Area of sector of a circle</h3>

The area of a sector is calculated as:

$A = \frac{\theta}{360} * \pi r^2$ ---- when the angle is in degrees

$A = \frac{\theta}{2} *r^2$ ---- when the angle is in radians

Take for instance, we have the following problems involving sector areas

Calculate the area of a sector where the radius of the circle is 7, and

The central angle is 30 degrees
The central angle is π/12 rad
The central angle is 90 degrees
The central angle is π/4 rad
The central angle is 180 degrees

Using the above formulas, the sector areas are:

1. $A = \frac{30}{360}* \frac{22}{7} * 7^2 = 12.83$

2. $A = \frac{\pi}{12} * 7^2 = 12.83$

3. $A = \frac{90}{360}* \frac{22}{7} * 7^2 = 38.5$

4. $A = \frac{\pi}{2} * 7^2 = 38.5$

5. $A = \frac{180}{360}* \frac{22}{7} * 7^2 = 77$

<h3>Examples of arc length</h3>

The length of an arc is calculated as:

$L= \frac{\theta}{360} * 2\pi r$ ---- when the angle is in degrees

$L = r\theta$ ---- when the angle is in radians

Take for instance, we have the following problems involving arc lengths

Calculate the length of an arc where the radius of the circle is 7, and

The central angle is 30 degrees
The central angle is π/12 rad
The central angle is 90 degrees
The central angle is π/4 rad
The central angle is 180 degrees

Using the above formulas, the arc lengths are:

1. $L = \frac{30}{360}* 2 * \frac{22}{7} * 7 = 3.7$

2. $L = \frac{\pi}{12} * 7 = 3.7$

3. $L = \frac{90}{360}*2 * \frac{22}{7} * 7 = 11.0$

4. $L = \frac{\pi}{4} * 7 = 11$

5. $L = \frac{180}{360}*2 * \frac{22}{7} * 7 = 22$

<h3>Examples of the arcs of a circle</h3>

The examples include:

A parabolic path
Distance in a curve
Curved bridges
Pizza
Bows