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3 years ago

Find the equation of the line that

Mathematics

1 answer:

olganol [36]3 years ago

5 0

Answer:

y= $\frac{1}{2}x-2$

Step-by-step explanation:

Perpendicular lines have negative reciprocal gradients(slopes) so the slope of your new line would be 1/2. Then you use the point to find the new y-intercept

y=mx+b

2= $\frac{1}{2}$ (8)+b

2=4+b

B=-2

y= $\frac{1}{2}x-2$

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Paul wants to buy a car. He needs to take out a loan for $7000. The car salesman offers him a loan with an interest rate of 8%,

Alisiya [41]

Answer:

a. It will take approximately 40 months

b. The total amount Paul has to pay is approximately $8,000

c. The amount Paul pays each month is approximately $316.59

d. The amount Paul has to pay is approximately $7,598.16

e. Lower monthly payment

f. Lower total payment amount (amount to be paid)

Step-by-step explanation:

a. The loan amount, PV = $7,000

The annual interest rate, r = 8%

Option 1; The amount of equal monthly payment to repay the loan = $200

Option 2; The number of equal monthly payment to repay the loan = 24

The formula for the present value of an annuity is given as follows;

$PMT = \dfrac{\dfrac{r}{12} \times PV}{1 - \left (1 + \dfrac{r}{12} \right)^{-n}}$

Where;

PMT = The monthly payment

n = The number of months

Where PMT = $200, we have;

$200 = \dfrac{\dfrac{0.08}{12} \times 7,000}{1 - \left (1 + \dfrac{0.08}{12} \right)^{-n}}$

$1 - \dfrac{\dfrac{0.08}{12} \times 7,000}{200} = \left (1 + \dfrac{0.08}{12} \right)^{-n}$

$1 - \dfrac{7}{30} = \dfrac{23}{30} = \left ( \dfrac{151}{150} \right)^{-n}$

$-n = \dfrac{ ln \left(\dfrac{23}{30} \right)}{ln\left(\dfrac{151}{150} \right) } \approx -39.988$

∴ The number of months it will take for Paul to repay the loan, n ≈ 39.988 ≈ 40 months

b. The total amount Paul has to pay, A = PMT × n

Therefore, b plugging in the values of PMT, and 'n', we get;

A ≈ $200 × 40 = $8,000

c. Using option 2, we have;

n = 24

Therefore;

$PMT = \dfrac{\dfrac{0.08}{12} \times 7,000}{1 - \left (1 + \dfrac{0.08}{12} \right)^{-24}} \approx 316.59$

The monthly payment, PMT ≈ $316.59

d. The total amount Paul has to pay using option 2, A ≈ 316.59 × 24 = 7,598.16

The total amount Paul has to pay using option 2, A ≈ $7,598.16

e. A reason why Paul might choose option 1 is that option 1 offers lower monthly payment

f. A reason why Paul may choose option 2 is that option 2 offers a lower total amount that he has to pay.

5 0

3 years ago

If Z=3 and Z*Y=12 what does Y+5 equal

TEA [102]

Y=4, therefore Y+5=9

3 0

3 years ago

45.5

sergey [27]

Answer:

The answer is 31.1%!

Hope this helps! If so, please mark my answer as brainliest :)

3 0

3 years ago

Read 2 more answers

Can somebody explain in great detail how to find a and b??

adoni [48]

So you know that this triangle must be a 45-45-90 degree triangle (you can tell this from the picture!)

The side that is length 4 is opposite from the 45 degree angle, and remember that congruent angles also give you congruent sides. This means that the length of a must be equal to the length of 4, because both are located opposite a 45 degree angle.

To find b, you must know that the hypotenuse of a 45-45-90 triangle is just equal to a $\sqrt{2}$ . Thus, the length of b= 4 rt. 2

4 0

3 years ago

Read 2 more answers

A bag contains 9 red, 7 blue, and 4 yellow marbles. If a marble is chosen at random from the bag, what is the probability that i

34kurt

Answer:

Step-by-step explanation:

if you add all the numbers together you get a total of 20. if you add the non yellow marbles together you get 16. so the fraction is 16/20. then you shorten the fractions by dividing the numbers. both are divisible by 4, so the final answer is 4/5.

5 0

3 years ago