Write the expression 4a - 6 as a product of two factors.

Find the shaded sector and the length of the arc. Round to the nearest hundredth.

Dovator [93]

Answer:

Step-by-step explanation:

I'll show you how to do the first one; the other are exactly the same, so pay attention.

The formula for arc length is

$AL=\frac{\theta}{360}*2\pi r$ where θ is the central angle's measure. It just so happens that the measure of the central angle is the same as the measure of the arc it intercepts. Our arc shows a measure of 40°; this measure is NOT the same as the length. Measures are in degrees while length is in inches, or cm, or meters, etc. Going off that info, our central angle measures 40°. Filling in the formula and using 3.1415 for π:

$AL=\frac{40}{360}*2(3.1415)(3)$ . I'm going to reduce that fraction a bit (and I'll use the same reduction in the Area of a sector coming up next):

$AL=\frac{1}{9}*2(3.1415)(3)$ which makes

AL = 2.09 units. Now for Area of the Sector. The formula is almost identical, but instead uses the idea that the area of a circle is πr²:

$A_s=\frac{\theta}{360}*\pi r^2$ where θ is, again, the measure of the central angle (which is the same as the measure of the arc it intercepts). Filling in:

$A_s=\frac{1}{9}*(3.1415)(3)^2$ which simplifies a bit to

$A_s=\frac{1}{9}*(3.1415)(9)$ . As you can see, the 9's cancel each other out, leaving you with

$A_s=3.14$ units²

7 0

3 years ago

Read 2 more answers

Use the following function rule to find the missing value in the table

gladu [14]

The answer is c) -14.8

6 0

3 years ago

Please answer both questions math

djyliett [7]

Answer:

$3$ and perpendicular

Step-by-step explanation:

It's important to remember that equations of lines are always set up in the format of $y=mx+c$ .

$y$ is the $y$ value, $m$ is the gradient/slope, $x$ is the $x$ value and $c$ is the y-intercept.

Therefore, we must always rearrange our line equations so that $y$ is the subject.

In the first question, we are given the equation $2x+6y=12$ .

We rearrange to make $y$ the subject:

$6y = 12-2x$

Then, we divide both sides by 6 to have the $y$ isolated:

$\frac{6}{6} y = \frac{12}{6} - \frac{2}{6}x\\\\ y = 2 - \frac{1}{3}x$

To find a perpendicular slope, we use the negative reciprocal of the original slope. The negative part of that means we negate the value (it becomes inverse) and the reciprocal part means that we flip the fraction.

So here, the slope is $-\frac{1}{3}$ .

So, the negative reciprocal of that would be $3$ because we inverse the sign (the negative becomes positive) and the fraction is flipped to create $\frac{3}{1}=3$ .

So, the perpendicular slope is $3$ .

In the second question, we have two equations. They both need to be rearranged to isolate the $y$ .

$4x-y=5\\4x = 5 + y\\y = 4x - 5\\\\4y = -x-12\\y = -\frac{1}{4}x - 3$

Look at the slopes of the two equations. If you look carefully, you will see that they are inverse of each other (one is positive and one is negative) and if you imagine $4 = \frac{4}{1}$ , the fraction is flipped.

This means that the values are negative reciprocals of each other, meaning the lines are perpendicular.

5 0

2 years ago

What quadrant contains -11pi/18 and what is the reference angle?

lina2011 [118]

Convert the angle into degrees so we can easily at what quadrant it lies
-11pi / 18 ( 180 / pi)= -110 degrees
to make it a positive angle add 360

-110 + 360= 250 degreesso it is in quadrant III
so the reference angle for quadrant III250 - 180= 70 degrees is the reference angle

4 0

3 years ago

Measure of the other acute angle?

leonid [27]

Step-by-step explanation:

step 1. the 3 internal angles of a triangle add up to 180°. let x be the 3rd angle

step 2. x + 34 + 72 = 180

step 3. x = 74°.

step 4. for problem 5 let the internal angles be a, b, and c

step 5. so b = 2a - 10, c = b + 25

step 6. we also know that a + b + c = 180

step 7. so a + (2a - 10) + (b + 25) = 180 by substitution

step 8. a + (2a - 10) + ((2a - 10) + 25) = 180 also by substitution

step 9. 3a - 10 + 2a + 15 = 180

step 10. 5a + 5 = 180

step 11. a = 35°

step 12. therefore b = 2a - 10 = 60°, c = 85°.

3 0

3 years ago

Write the expression 4a - 6 as a product of two factors.​

Write the expression 4a - 6 as a product of two factors.