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3 years ago

An angle measures 24° more than the measure of its supplementary angle. What is the measure of each angle?

Mathematics

1 answer:

marin [14]3 years ago

8 0

Answer:

x = 78°; 102

Step-by-step explanation:

x = the angle

the supplement of angle = (180-x)

x + 24 = (180 -x)

x +24 = 180 -x

x = 156 -x

2x = 156

x = 78

The supplementary angle = 78 + 24 =102°

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James's Sister is arranging rows of beads. She has 56 yellow beads and 120 blue beads. She wants to arrange them so that all the

lora16 [44]

Answer:

Step-by-step explanation:

gcf 56, 120 = 8, 56/8=7, 120/8=15, 7+15=22. 22

6 0

3 years ago

How do I solve a+18=7a ?

Slav-nsk [51]

$a+18=7a \ \ \ |\hbox{subtract 7a from both sides} \\
-6a+18=0 \ \ \ |\hbox{subtract 18 from both sides} \\
-6a=-18 \ \ \ |\hbox{divide both sides by (-6)} \\
a=3$

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3 years ago

Read 2 more answers

PLEASE HELP .........

joja [24]

Answer:

11860.22 rev/hour

Step-by-step explanation:

The diameter if a cylinder, d = 21.02 inches

Radius, r = 10.51 inches

r = 0.875 feet

The linear speed of a point on the cylinder's surface is 18.12 ft/sec.

We need to find the angular speed of the cylinder.

The relation between the linear speed and the angular speed is given by :

$v=r\omega$

Where

$\omega$ is angular speed

$\omega=\dfrac{v}{r}\\\\\omega=\dfrac{18.12}{0.875}\\\\\omega=20.7\ rad/s$

$\omega=11860.22\ rev/hour$

So, the required angular speed of the cylinder is 11860.22 rev/hour.

4 0

3 years ago

Calculus piecewise function.

Kipish [7]

Part A

The notation $\lim_{x \to 2^{+}}f(x)$ means that we're approaching x = 2 from the right hand side (aka positive side). This is known as a right hand limit.

So we could start at say x = 2.5 and get closer to 2 by getting to x = 2.4 then to x = 2.3 then 2.2, 2.1, 2.01, 2.001, etc

We don't actually arrive at x = 2 itself. We simply move closer and closer.

Since we're on the positive or right hand side of 2, this means we go with the rule involving x > 2

Therefore f(x) = (x/2) + 1

Plug in x = 2 to find that...

f(x) = (x/2) + 1

f(2) = (2/2) + 1

f(2) = 2

This shows $\lim_{x \to 2^{+}}f(x) = 2$

Then for the left hand limit $\lim_{x \to 2^{-}}f(x)$ , we'll involve x < 2 and we go for the first piece. So,

f(x) = 3-x

f(2) = 3-2

f(2) = 1

Therefore, $\lim_{x \to 2^{-}}f(x) = 1$

===============================================================

Part B

Because $\lim_{x \to 2^{+}}f(x) \ne \lim_{x \to 2^{-}}f(x)$ this means that the limit $\lim_{x \to 2}f(x)$ does not exist.

If you are a visual learner, check out the graph below of the piecewise function. Notice the gap or disconnect at x = 2. This can be thought of as two roads that are disconnected. There's no way for a car to go from one road to the other. Because of this disconnect, the limit doesn't exist at x = 2.

===============================================================

Part C

You'll follow the same type of steps shown in part A.

However, keep in mind that x = 4 is above x = 2, so we'll deal with x > 2 only.

So you'd only involve the second piece f(x) = (x/2) + 1

You should find that f(4) = 3, and that both left and right hand limits equal this value. The left and right hand limits approach the same y value. The limit does exist here. There are no gaps to worry about when x = 4.

===============================================================

Part D

As mentioned earlier, since $\lim_{x \to 4^{+}}f(x) = \lim_{x \to 4^{-}}f(x) = 3$ , this means the limit $\lim_{x \to 4}f(x)$ does exist and it's equal to 3.