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3 years ago

Are the angles with the given measures complementary, supplementary, or neither?

1 answer:

4 0

The two angles are supplementary angles. Two angles are considered to be supplementary when the sum of the measurement of their angles is 180 degrees. The measurement of angle T is 76 degrees and the measurement of angle U is 104 degrees. If you try to add the measurement of the two angles, the answer would be 180 degrees. Therefore, the two angles are supplementary angles.

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How would the average rate of change over years 1 to 5 and years 6 to 10 be affected if the population increased at a rate of 8%

Sever21 [200]

Answer:

(A): As year increases the number of pikas reduces.

(B): As year increases the number of pikas increases as opposed to when the rate reduces.

Step-by-step explanation:

See comment for complete question

Given

$a = 144$ --- Initial Population

$r = 8\%$ --- rate

(A) WHEN THE RATE DECREASES

First, we need to write out the function when the population decreases.

This is given as:

$f(x) = a(1-r)^x$

Substitute values for a and r

$f(x) = 144(1-8\%)^x$

Convert % to decimal

$f(x) = 144(1-0.08)^x$

$f(x) = 144(0.92)^x$

Next, we calculate the average rate of change for both intervals using:

$Rate = \frac{f(b) - f(a)}{b-a}$

For 1 to 5:

$Rate = \frac{f(5) - f(1)}{5-1}$

$Rate = \frac{f(5) - f(1)}{4}$

Calculate f(5) and f(1)

$f(x) = 144(0.92)^x$

$f(1) = 144*0.92^1 =144*0.92=132.48$

$f(5) = 144*0.92^5 =144*0.66=95.04$

$Rate = \frac{95.04 - 132.48 }{4}$

$Rate = \frac{-37.44}{4}$

$Rate = -9.36$

For 6 to 10:

$Rate = \frac{f(10) - f(6)}{10-6}$

$Rate = \frac{f(10) - f(6)}{4}$

Calculate f(6) and f(10)

$f(x) = 144(0.92)^x$

$f(6) = 144*0.92^6 =144*0.61=87.84$

$f(10) = 144*0.92^{10} =144*0.43=61.92$

$Rate = \frac{61.92-87.84}{4}$

$Rate = \frac{-25.92}{4}$

$Rate = -6.48$

So, we have:

$Rate = -9.36$ for year 1 to 5

This means that the number of pikas reduces by 9.36 yearly

$Rate = -6.48$ for year 6 to 10

This means that the number of pikas reduces by 6.48 yearly

So, we can say that, as year increases the number of pikas reduces.

(B) WHEN THE RATE INCREASES

First, we need to write out the function when the population decreases.

This is given as:

$f(x) = a(1-r)^x$

Substitute values for a and r

$f(x) = 144(1+8\%)^x$

Convert % to decimal

$f(x) = 144(1+0.08)^x$

$f(x) = 144(1.08)^x$

Next, we calculate the average rate of change for both intervals using:

$Rate = \frac{f(b) - f(a)}{b-a}$

For 1 to 5:

$Rate = \frac{f(5) - f(1)}{5-1}$

$Rate = \frac{f(5) - f(1)}{4}$

Calculate f(5) and f(1)

$f(x) = 144(1.08)^x$

$f(1) = 144(1.08)^1 = 144*1.08= 155.52$

$f(5) = 144(1.08)^5 = 144*1.47= 211.68$

$Rate = \frac{211.68 - 155.52}{4}$

$Rate = \frac{56.16}{4}$

$Rate = 14.04$

For 6 to 10:

$Rate = \frac{f(10) - f(6)}{10-6}$

$Rate = \frac{f(10) - f(6)}{4}$

Calculate f(6) and f(10)

$f(x) = 144(1.08)^x$

$f(6) = 144(1.08)^6 = 228.52$

$f(10) = 144(1.08)^{10} = 310.89$

$Rate = \frac{310.89-228.52}{4}$

$Rate = \frac{82.37}{4}$

$Rate = 20.59$

So, we have:

$Rate = 14.04$ for year 1 to 5

This means that the number of pikas increases by 14.04 yearly

$Rate = 20.59$ for year 6 to 10

This means that the number of pikas increases by 20.59 yearly

So, we can say that, as year increases the number of pikas increases as opposed to when the rate reduces.

5 0

3 years ago

What is the slope of a line that has an x-intercept of 6 and a y-intercept of 0

ankoles [38]

x intercept of 6 means (6,0) is on the line

y intercept of 0 means (0,0) is on the line

so the slope is (0-0)/(6-0) = 0

Answer: 0

Note: The question is actually bad; the line through the origin with slope zero is the X axis itself in which case it wouldn't be right to call the X intercept (just) (6,0).

7 0

3 years ago

3/(2x-1)+4=6x/(2x-1)

andrew-mc [135]

Answer: x = 1/2

Explanation:
3/(2x-1)+4=6x/(2x-1)

Make both sides has the same denominator:

3/2x-1 + 4(2x-1)/(2x-1) = 6x/2x-1

Cut down all the denominator:

3 + 8x -4= 6x
8x - 1 = 6x
2x = 1
X= 1/2

5 0

3 years ago

What is the volume of a cube with edge length 2/3 yard

KiRa [710]

(2/3)^3 = 8/27 cubic yards

4 0

3 years ago

A new bank customer with $2,500 wants to open a money market account. The bank is offering a simple interest rate of 1.9%.

Alika [10]

Answer:

He will earn $69000

Step-by-step explanation:

Think about it. The illuminati is real and 420 is a number. Its quite easy math. Now please go and **** yourself

8 0

3 years ago

Read 2 more answers