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vekshin1
3 years ago
6

If two angles from a linear pair and the m<1=2x+20 and m<2=48x find the measure of each angle

Mathematics
1 answer:
il63 [147K]3 years ago
5 0

The measures of two angles in a linear pair add to 180 deg.

m<1 + m<2 = 180

2x + 20 + 48x = 180

50x + 20 = 180

50x = 160

x = 3.2

m<1 = 2x + 20 = 2(3.2) + 20 = 6.4 + 20 = 26.4

m<2 = 48x = 48(3.2) = 153.6

Answer: m<1 = 26.4 deg; m<2 = 153.6 deg

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Find all of the equilibrium solutions. Enter your answer as a list of ordered pairs (R,W), where R is the number of rabbits and
zloy xaker [14]

Answer:

(0,0)   (4000,0) and (500,79)

Step-by-step explanation:

Given

See attachment for complete question

Required

Determine the equilibrium solutions

We have:

\frac{dR}{dt} = 0.09R(1 - 0.00025R) - 0.001RW

\frac{dW}{dt} = -0.02W + 0.00004RW

To solve this, we first equate \frac{dR}{dt} and \frac{dW}{dt} to 0.

So, we have:

0.09R(1 - 0.00025R) - 0.001RW = 0

-0.02W + 0.00004RW = 0

Factor out R in 0.09R(1 - 0.00025R) - 0.001RW = 0

R(0.09(1 - 0.00025R) - 0.001W) = 0

Split

R = 0   or 0.09(1 - 0.00025R) - 0.001W = 0

R = 0   or  0.09 - 2.25 * 10^{-5}R - 0.001W = 0

Factor out W in -0.02W + 0.00004RW = 0

W(-0.02 + 0.00004R) = 0

Split

W = 0 or -0.02 + 0.00004R = 0

Solve for R

-0.02 + 0.00004R = 0

0.00004R = 0.02

Make R the subject

R = \frac{0.02}{0.00004}

R = 500

When R = 500, we have:

0.09 - 2.25 * 10^{-5}R - 0.001W = 0

0.09 -2.25 * 10^{-5} * 500 - 0.001W = 0

0.09 -0.01125 - 0.001W = 0

0.07875 - 0.001W = 0

Collect like terms

- 0.001W = -0.07875

Solve for W

W = \frac{-0.07875}{ - 0.001}

W = 78.75

W \approx 79

(R,W) \to (500,79)

When W = 0, we have:

0.09 - 2.25 * 10^{-5}R - 0.001W = 0

0.09 - 2.25 * 10^{-5}R - 0.001*0 = 0

0.09 - 2.25 * 10^{-5}R = 0

Collect like terms

- 2.25 * 10^{-5}R = -0.09

Solve for R

R = \frac{-0.09}{- 2.25 * 10^{-5}}

R = 4000

So, we have:

(R,W) \to (4000,0)

When R =0, we have:

-0.02W + 0.00004RW = 0

-0.02W + 0.00004W*0 = 0

-0.02W + 0 = 0

-0.02W = 0

W=0

So, we have:

(R,W) \to (0,0)

Hence, the points of equilibrium are:

(0,0)   (4000,0) and (500,79)

4 0
3 years ago
David received $50 dollars for working at his father’s store. He spent $20 dollars at the movies, and $10 dollars buying comic b
statuscvo [17]
Total amount of money received by David for working at his father's store = $50
Amount of money spent by David at the movies = $20
Amount of money spent by David buying comics books = $10
Amount of money spent by David buying candy = $5
Then
Total amount spent by David = (20 + 10 + 5) dollars
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Amount of money saved by David = (50 - 35 ) dollars
                                                       = 15 dollars
So
The ratio of the amount of money David
spent to the amount of money David saved = 35:15
                                                                      = 7:3
So the ratio of the amount of money David spent to the amount of money David saved is 7:3
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3 years ago
How many different arrangements of 3 letters can be formed if the First letter must be W or K
Llana [10]
You would do 2 · 26 · 26 = 1,352 different arrangements 
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The bottom part of this block is a rectangular prism. The top part is a square
dedylja [7]

Answer:

I think you need 8 papers

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2 years ago
75 pins of juice in 5 containers find the rate and unit rate
Eva8 [605]

Answer: 15 juice pins per container

75 Juice pins ÷ 5

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=

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= 15 Juice pins per Container


4 0
3 years ago
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