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LiRa [457]
3 years ago
8

You borrow money for 4 years. The total amount that you repay is $7,840, which includes $840 in simple interest. How much was th

e principal? What was the annual interest rate?
Mathematics
1 answer:
Lina20 [59]3 years ago
6 0

Answer:

  • principal: $7000
  • interest rate: 3%

Step-by-step explanation:

amount repaid = principal + interest

$7840 = principal + $840

$7000 = principal . . . . . . . . subtract $840 from both sides of the equation

___

I = Prt

840 = 7000·r·4

840/(4·7000) = r = 0.03 = 3%

The principal was $7000; the interest rate was 3%.

You might be interested in
Please help!! i need 15 & 17!
Ludmilka [50]

Answer:

15. Answer: length = 15 ft; width = 3 ft

16. Answer: base = 14 cm; height = 5 cm

17. Answer: x² - 5x - 24 = 0

Step-by-step explanation:

15.

area of rectangle = length * width

length = x - 2

width = x - 14

area = (x - 2) (x - 14)

We are shown the area to be 45 ft².

We set the expression of the area equal to the given area and solve the quadratic equation for x.

(x - 2)(x - 14) = 45

x² - 14x - 2x + 28 - 45 = 0

x² - 16x - 17 = 0

(x - 17)(x + 1) = 0

x - 17 = 0  or  x + 1 = 0

x = 17  or x = -1

We discard the negative answer, x = -1, since it would give negative length and width.

x = 17

length = x - 2 = 17 - 2 = 15

width = x - 14 = 17 - 14 = 3

Answer: length = 15 ft; width = 3 ft

16.

area = ½bh

area = ½(x - 5)(x - 14)

area = 35

½(x - 5)(x - 14) = 35

(x - 5)(x - 14) = 70

x² - 14x - 5x + 70 = 70

x² - 19x = 0

x(x - 19) = 0

x = 0  or  x - 19 = 0

We discard x = 0 since it would give negative dimensions.

x = 19

base = x - 5 = 19 - 5 = 14

height = x - 14 = 19 - 14 = 5

base = 14

height = 5

Answer: base = 14 cm; height = 5 cm

17.

A polynomial with solutions x = a and x = b can be found by multiplying (x - a) by (x - b). Here, the solutions are x = -3 and x = 8.

[x - (-3)](x - 8) = (x + 3)(x - 8) = x² - 8x + 3x - 24 = x² - 5x - 24

Answer: x² - 5x - 24 = 0

5 0
3 years ago
If y = 3x – 4 and the domain is { -3, -1, 4}, find the range. When the domain is -3, the range is ______. Show your work to find
Dafna1 [17]
<h2>Hello!</h2>

The answer is:

When the domain is -3, the range is -13.

<h2>Why?</h2>

To solve the problem, we need to remember that the domain is also known as the input of the function, and the range of the function is also known as the output of the function.

We are given the inputs and we are asked to calculate the output of the function at -3, so, evaluating -3 into the function, we have:

y=3x-4\\f(x)=3x-4\\f(-3)=3*(-3)-4=-9-4=-13\\

Hence, we have that when the domain is -3, the range is -13.

Have a nice day!

8 0
3 years ago
If the length of the line segment CD is 65% of the length of the line segment AB, what is the length of line segment CD? (AB is
Tcecarenko [31]

Answer:

8.45

Step-by-step explanation

Convert 65% in decimal form

0.65 x 13 = 8.45

5 0
3 years ago
Help pls pls pls pls pls
Mice21 [21]

Answer:

i don't understand this and i'm in high school how is this possible????????????

Step-by-step explanation:

6 0
3 years ago
Tell whether the angles are adjacent or vertical. Then find the value of x.
Paladinen [302]

Answer:

They are vertical. x=37 degrees

Step-by-step explanation:

If two lines form an x, then it's a vertical angle.

3x-4=107

3x=111

x=37

Hope this helped!

~Mschmindy

8 0
3 years ago
Read 2 more answers
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