What multiplies to 42 and adds to -27

Answers

Answer 1

Answer: Consider ways to multiply to get 42. Then see if the numbers can be used to make -27.

42 = 21 × 2...not going to work.
42 = 14 × 3...not going to work. (Though -14 and -3 add to -17)
42 = 7 × 6...not going to work.

There are no whole number solutions to this question.

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Audrey is buying a new car for $32,998.00. She plans to make a down payment of $4,200.00. If she's to make monthly payments of $525 for the next five years, what APR has she paid?A. 37%
B. .37%
C. 3%
D. 3.7%

Answers

This question is an annuity problem with cost of the car = $32,998, the present value of the annuity (PV) is given by the difference between the cost of the car and the down payment = $32,998 - $4,200 = $28,798. The monthly payments (P) = $525 and the number of number of years (n) = 5 years and the number of payments in a year (t) is 12 payments (i.e. monthly) The formula for the present value of an annuity is given by PV = (1 - (1 + r/t)^-nt) / (r/t) 28798 = 525(1 - (1 + r/12)^-(5 x 12)) / (r/12) 28798r / 12 = 525(1 - (1 + r/12)^-60) 28798r / (12 x 525) = 1 - (1 + r/12)^-60 2057r / 450 = 1 - (1 + r/12)^-60 Substituting option A (r = 37% = 0.37) 2057r / 450 = 2057(0.37) / 450 = 761.09 / 450 = 1.691 1 - (1 + r/12)^60 = 1 - (1 + 0.37/12)^-60 = 1 - 0.1617 = 0.8383 Therefore, r is not 37% Substituting option D (r = 3.7% = 0.037) 2057r / 450 = 2057(0.037) / 450 = 76.109 / 450 = 0.1691 1 - (1 + r/12)^60 = 1 - (1 + 0.037/12)^-60 = 1 - 0.8313 = 0.1687 Therefore, r is approximately 3.7%

To solve this we are going to use the loan payment formula: $P= ( (r)/(n)(PV))/(1-(1+ (r)/(n))^(-nt) )$

where

$P$ is the amount of the regular payment

$PV$ is the present debt

$r$ is APR in decimal form

$n$ is the number of payments per year

$t$ is the time in years

We know from our problem that Audrey is making a down payment of $4,200.00; since the cost of the car is $32,998.00, the present deb will be the cost of the car minus the down payment, so $PV=32998-4200=28798$ . We also know that she is going to make monthly payments of $525 for the next five years, so $n=12$ and $t=12$ . Let's replace the values in our formula:

$P= ( (r)/(n)(PV))/(1-(1+ (r)/(n))^(-nt) )$

$525= ( (r)/(12)(28798))/(1-(1+ (r)/(12))^(-(12)(5)) )$

We have two ways of finding the APR: we can solve for $r$ in our equation, which is extremely difficult, or we can evaluate the given APRs and check for which one both sides of the equation are almost the same. Since the second is way easier, we are going to use it.

A. 37%

The APR should be in decimal form, so we need to convert it first; to do it we are going to divide the APR by 100%

$r=(37)/(100) =0.37$

Let's replace the ARP in decimal form in our equation

$525= ( (0.37)/(12)(28798))/(1-(1+ (0.37)/(12))^(-(12)(5)) )$

$525=1059.20$

$529\neq 1059.20$

Since 529 is not equal to 1059.20, 37% is not the APR of the loan.

B. .37%

- Convert the APR to decimal form

$r=(0.37)/(100) =0.0037$

- Replace the APR

$525= ( (0.0037)/(12)(28798))/(1-(1+ (0.0037)/(12))^(-(12)(5)) )$

$525=484.49$

Since 525 is not equal to 484.59, .37% is not the APR of the loan.

C. 3%

- Convert the APR to decimal form

$r=(3)/(100) =0.03$

- Replace the APR

$525= ( (0.03)/(12)(28798))/(1-(1+ (0.03)/(12))^(-(12)(5)) )$

$525=517.46$

Since 525 is not equal to 517.46, 3% is not the APR of the loan.

D. 3.7%

- Convert the APR to decimal form

$r=(3.7)/(100) =0.037$

- Replace the APR

$525= ( (0.037)/(12)(28798))/(1-(1+ (0.037)/(12))^(-(12)(5)) )$

$525=526.47$

Since 525 is almost equal to 526.47, 3.7% is the APR of the loan.

We can conclude that the correct answer is D. 3.7%

What is the square root of 325

Answers

$√(325)=√(25\cdot13)=√(25)\cdot√(13)=5√(13)\approx18.03$

$√(325)=5√(13)\approx18$

True or false: The midpoint of a given line segment must lie on the given line segment?

Answers

Answer:
True

Explanation:
A midpoint of a line is defined as half the distance between these two points.
Therefore, to get this midpoint, we should first connect the endpoints of the line and then get the half the distance

This means that the midpoint must lie on the given line segment

Hope this helps :)

True. The midpoint of a given line segment must lie on the given line segment because it is the half way point of the line.

Scott puts some sports in rowhe makes 6 rows with 5 stickers in each row.If he puts the same number of stikers in 5 equal row how many stickers would be in each row? How do you know

Answers

We know that Scott has put 6 rows with 5 stickers each.

The total number of stickers available with Scott = 5*6 = 30 stickers

These 30 stickers are now placed in 5 rows with equal number of stickers in each row.

Number of stickers in each row= Total number of stickers available/number of rows

Number of stickers in each row = 30/5 = 6 stickers

Number of stickers in each row now would be = 6 stickers

What is the square root of 2?

Answers

Hi There!

What is the square root of 2?

The answer is 1.4 or 1.41421356237

The answer is not 1.4

The answer is 2

Solve 64x^3 +1 =0the back of the texts books gives me the answers -1/4 and 1 plus or minus i√3 all over 8
I understand where the -1/4 comes from . I just don't understand the second answer. I know they used the quadratic formula to get it but I always end up with something to totally different

Answers

Expand the expression using the formula:
$a^3+b^3=(a+b)(a^2 - ab + b^2)$

$64x^3+1=0 \n(4x)^3+1^3=0 \n(4x+1)((4x)^2- 4x * 1+1^2)=0 \n(4x+1)(16x^2-4x+1)=0 \n4x+1=0 \ \lor \ 16x^2-4x+1=0$

The first equation:
$4x+1=0 \n 4x=-1 \n x=-(1)/(4)$

The second equation:
$16x^2-4x+1=0 \n \na=16 \n b=-4 \n c=1 \n b^2-4ac=(-4)^2-4 * 16 * 1=16-64=-48 \n√(b^2-4ac)=√(-48)=√(48) * √(-1)=√(16 * 3) * √(-1)=\pm 4√(3) i \n \nx=(-b \pm √(b^2-4ac))/(2a)=(-(-4) \pm 4√(3)i)/(2 * 16)=(4 \pm 4√(3)i)/(32)=(4(1 \pm √(3)i))/(4 * 8)=(1 \pm √(3)i)/(8) \nx=(1-√(3)i)/(8) \ \lor \ x=(1+√(3)i)/(8)$

The final answer:
$\boxed{x=-(1)/(4) \hbox{ or } x=(1-√(3)i)/(8) \hbox{ or } x=(1+√(3)i)/(8)}$

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