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gtnhenbr [62]
3 years ago
11

Write an equation of a line in slope intercept form that is parallel to y = 3x+6 and passes through the point (-10, 2.5)

Mathematics
1 answer:
TiliK225 [7]3 years ago
3 0

1) Line should be parallel to y = 3x+6, so slope of this line should be =3.

y=mx +b

y=3x +b

Now we have to find b (y-intercept), using the point (-10, 2.5).

2.5 = 3*(-10)+b

b=2.5+30=32.5

y=3x + 32.5

2) The line should be perpendicular to y = -4x -2, so its slope is going to be negative reciprocal m= 1/4.

Now we have to find b (y-intercept), using the point (-16, -11).

y=(1/4)x +b

-11=(1/4)*(-16) + b

-11 = -4 +b

b = -7

y=(1/4)x - 7

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Suppose a population is growing by 8% each year. How many years will it take the population to double?
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ANSWER

\text{9 years}

EXPLANATION

We want to find the number of years that it will take the population to double.

To do this, we have to apply the exponential growth function:

y=a(1+r)^t

where y = final value

a = initial value

r = rate of growth

t = time (in years)

For the population to double, it means that the final value must be 2 times the initial value:

y=2a

Substitute the given values into the function above:

\begin{gathered} 2a=a(1+\frac{8}{100})^t \\ \frac{2a}{a}=(1+0.08)^t=1.08^t \\ 2=1.08^t \end{gathered}

To solve further, convert the function from an exponential function to a logarithmic function as follows:

\log _{1.08}2=t

Solve for t:

\begin{gathered} \frac{\log _{10}2}{\log _{10}1.08}=t \\ \Rightarrow t=9\text{ years} \end{gathered}

It will take 9 years for the population to double.

4 0
1 year ago
Help me pls only 10points
NeX [460]

y=-7x+8

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B. No solutions

3 0
3 years ago
If this is the graph of f(x)=a^(x+h)+k, then: <br> A. a&lt; 0<br> B. k&gt; 1<br> C. 0 D. a&gt; 1
lyudmila [28]

Answer:

Option D. is the right choice.

Step-by-step explanation:

D. a > 1 is the right answer.

Best Regards!

4 0
3 years ago
Make a down payment of $1500 and finance the rest of $20000 at 1.9% interest rate, making equal monthly payments for 5 years.
Rudik [331]
We know that we have to m<span>ake a down payment of $1500 and finance the rest of $20000 at a 1.9% interest rate, making equal monthly payments for 5 years. Our first step to solve this problem would be to convert 5 years into months. 

1 year = 12 months 

12 * 5 = 60 months 

Therefore, in 5 years there are 60 months. 

Now lets solve this problem step by step. 

Subtract the down payment from $20,000

</span>$20000-$1500=$18500

Multiply the remaining number by the interest rate. 

$18500 *1.9 = $35150 

Divide 35150 by number of months in 5 years (60)

$35150 / 60 = $585 

<span>Therefore, you have to pay $585 per month. </span>
7 0
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