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goldenfox [79]
3 years ago
5

Me Value of Money: Practice

Mathematics
1 answer:
Tatiana [17]3 years ago
3 0

Answer:

$3952.13

Step-by-step explanation:

Annuity amount = future value / annuity factor

Annuity factor = {[(1+r)^n] - 1} / r

FV = Future value = $75,000  

R = interest rate = 8%

N = number of years = 12

Annuity factor = [(1/08)^12 - 1 ] / 0.08 = 1.8977126

Annuity amount = $75,000 / 1.8977126 = $3952.13

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. Given ????(5, −4) and T(−8,12):
damaskus [11]

Answer:

a)y=\dfrac{13x}{16}-\dfrac{129}{16}

b)y = \dfrac{13x}{16}+ \dfrac{37}{2}

Step-by-step explanation:

Given two points: S(5,-4) and T(-8,12)

Since in both questions,a and b, we're asked to find lines that are perpendicular to ST. So, we'll do that first!

Perpendicular to ST:

the equation of any line is given by: y = mx + c where, m is the slope(also known as gradient), and c is the y-intercept.

to find the perpendicular of ST <u>we first need to find the gradient of ST, using the gradient formula.</u>

m = \dfrac{y_2 - y_1}{x_2 - x_1}

the coordinates of S and T can be used here. (it doesn't matter if you choose them in any order: S can be either x_1 and y_1 or x_2 and y_2)

m = \dfrac{12 - (-4)}{(-8) - 5}

m = \dfrac{-16}{13}

to find the perpendicular of this gradient: we'll use:

m_1m_2=-1

both m_1and m_2 denote slopes that are perpendicular to each other. So if m_1 = \dfrac{12 - (-4)}{(-8) - 5}, then we can solve for m_2 for the slop of ther perpendicular!

\left(\dfrac{-16}{13}\right)m_2=-1

m_2=\dfrac{13}{16}:: this is the slope of the perpendicular

a) Line through S and Perpendicular to ST

to find any equation of the line all we need is the slope m and the points (x,y). And plug into the equation: (y - y_1) = m(x-x_1)

side note: you can also use the y = mx + c to find the equation of the line. both of these equations are the same. but I prefer (and also recommend) to use the former equation since the value of 'c' comes out on its own.

(y - y_1) = m(x-x_1)

we have the slope of the perpendicular to ST i.e m=\dfrac{13}{16}

and the line should pass throught S as well, i.e (5,-4). Plugging all these values in the equation we'll get.

(y - (-4)) = \dfrac{13}{16}(x-5)

y +4 = \dfrac{13x}{16}-\dfrac{65}{16}

y = \dfrac{13x}{16}-\dfrac{65}{16}-4

y=\dfrac{13x}{16}-\dfrac{129}{16}

this is the equation of the line that is perpendicular to ST and passes through S

a) Line through T and Perpendicular to ST

we'll do the same thing for T(-8,12)

(y - y_1) = m(x-x_1)

(y -12) = \dfrac{13}{16}(x+8)

y = \dfrac{13x}{16}+ \dfrac{104}{16}+12

y = \dfrac{13x}{16}+ \dfrac{37}{2}

this is the equation of the line that is perpendicular to ST and passes through T

7 0
3 years ago
5.65 times 3.4 estimate
lidiya [134]
We can round 5.65 up to 6 and 3.4 down to 3.
3 * 6 = 18
now let's see how close our estimate is to the real answer
5.65 * 3.4 = 19.21
Our answer was pretty close to the real answer!

Hope I helped!
~ Zoe
3 0
3 years ago
Read 2 more answers
1.
9966 [12]

Answer: 30

Step-by-step explanation: square 24 and 18 (576 & 324) then add them together (900), then the square root of 900 is 30, so 30.

8 0
2 years ago
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It's make-your-own-dish night at your favorite pasta restaurant. The restaurant offers 5 types of pasta and 4 different sauces.
densk [106]

Answer:

there are 20 different combinations if that was the question.

Step-by-step explanation:

Formula :

Combination(event 1) times Combinations (Event2)

3 0
3 years ago
pepe is putting up a fence in his backyard to enclose a garden in form of a triangle. the garden already has sides enclosed with
Andrei [34K]

Answer:

20

Step-by-step explanation:

Because 8 times 5 is 40, and if it is a triangle then it should be 20 because area as a triangle is base times height divided by two.

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3 years ago
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