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mote1985 [20]
1 year ago
14

The mayor of Brookmarsh is running a campaign to revitalize his city. Currently, the population of Brookmarsh is 10,000 and is i

ncreasing at a rate of 2% per year. The mayor predicts that the population will continue to grow in this manner, and that in "t" years, the population will be at least 15,000.
Write an inequality in terms of "t" that models the situation.
Mathematics
1 answer:
lisabon 2012 [21]1 year ago
8 0
The equation correctly modeled would be

1000+.02t = 15000
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Which graph represents the function of f(x) = the quantity of 9 x squared plus 9 x minus 18, all over 3 x plus 6
lora16 [44]

Answer:

The answer is the option C

graph of 3x minus 3, with discontinuity at negative 2, negative 9

Step-by-step explanation:

we have

f(x)=\frac{9x^{2}+9x-18}{3x+6}

Simplify

f(x)=9\frac{(x^{2}+x-2)}{3(x+2)}

f(x)=3\frac{(x^{2}+x-2)}{(x+2)}

Step 1

Convert to a factored form the numerator

x^{2}+x-2=0    

Group terms that contain the same variable, and move the constant to the opposite side of the equation

x^{2}+x=2

Complete the square. Remember to balance the equation by adding the same constants to each side.

x^{2}+x+0.25=2+0.25

x^{2}+x+0.25=2.25

Rewrite as perfect squares

(x+0.5)^{2}=2.25

Square root both sides

x+0.5=(+/-)1.5

x=-0.5(+/-)1.5

x=-0.5+1.5=1

x=-0.5-1.5=-2

so

x^{2}+x-2=(x-1)(x+2)  

Step 2

Simplify the function f(x)

f(x)=3\frac{(x^{2}+x-2)}{(x+2)}=3\frac{(x-1)(x+2)}{(x+2)}

The domain of the function f(x) is all real numbers except the number x=-2

Because the denominator can not be zero

f(x)=3\frac{(x-1)(x+2)}{(x+2)}=3(x-1)=3x-3  

f(x)=3x-3  ------> with a discontinuity at x=-2

f(-2)=3(-2)-3=-9

The discontinuity is at point (-2,-9)

the answer in the attached figure

8 0
2 years ago
Read 2 more answers
A giraffe measures 17 feet tall . A gorilla mesures 63 inches tall. How many feet taller is the giraffe than the gorilla
9966 [12]

Answer:

11.75 feet

Step-by-step explanation:

17 times 12 = 204 inches

204 - 63 = 141 inches

141/12 = 11.75 feet

4 0
1 year ago
Jill is standing at the base of her apartment building. She measures the angle of elevation to the top of a nearby tower to be 4
almond37 [142]
1) From the measure of 40°, you can write:

tan(40°) = 100/x, where x is the base from the building to the tower

⇒x=100/tan(40°) = 119,18 m

2) From the measure of 30°, you can write

tan(30°) = y / 119,18, where y is the height from the roof of Jill's building to the top of the tower.

Then, y = tan(30°) * 119,18 = 68,81 m

3) The height of Jill's building is 100 - 68,81 = 31,19 m
4 0
1 year ago
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Explain why you would make one of the addends a tens number when solving an addition problem
leonid [27]
<span> You refer to a multiple of ten. As a multiple of ten you can just add it to another number easier than a "ones number".</span>
4 0
1 year ago
A craft vendor must sell at least $300 worth of merchandise to make a profit. Scarves sell for $10 each and hats sell for $20 ea
valina [46]
There is a missing graph in the problem given. However, we can simply solve the equation using the given data.

Items to be sold: scarves and hats. Minimum of 20 items sold in all.
Scarves sell for 10 each and hats sell for 20 each. Must sell at least 300 worth of merchandise to make profit. 

Let s represent scarves and h represent hats.

10s + 20h <u>></u> 300
s + h <u>></u> 20

We use inequality because the problem states "at least". 

s + h = 20
10s + 20h = 300

s = 20 - h
10(20-h) + 20h = 300
200 - 10h + 20h = 300
10h = 300 - 200
10h = 100
h = 100/10
h = 10

s = 20 - h
s = 20 - 10
s = 10

s + h <u>></u> 20
10 + 10 <u>></u> 20

10s + 20h <u>></u> 300
10(10) + 20(10) <u>></u> 300
100 + 200 <u>></u> 300

7 0
1 year ago
Read 2 more answers
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