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lubasha [3.4K]
3 years ago
15

The distance between the points (−5, 1) and (2, −1).

Mathematics
2 answers:
devlian [24]3 years ago
8 0
Here u go :) hope it helps

jarptica [38.1K]3 years ago
7 0

Answer: The distance \sqrt{53}  which reduces to 7.28

Step-by-step explanation:

To find the distance between these two coordinates, find the difference of the y coordinates and x coordinates and square them then add them together to find their square root.

The y coordinates are 1 and -1.

The x coordinates are -5 and 2.

So -1-1 = -2

-5 - 2= - 7   Find their absolute values.

The absolute value of -2 is 2  and the absolute value of -7 is 7.

2^2 + 7^2 = d^2     where d is the distance.

4 +49  = d^2

53=  d^2  

d= \sqrt{53}  

d= 7.28

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Ira Lisetskai [31]

Answer:

Equation is  A = 5000(1.015)^(4t)

Her investment will be worth $10,000 in about <u>11.63888 years</u>

Rounding up to the nearest whole number gets to <u>12 years</u>

==========================================================

Explanation:

Part 1) Finding the equation

The compound interest formula is

A = P(1+r/n)^(n*t)

Here are the variables

  • A = final amount
  • P = starting amount, or deposit, or principal
  • r = interest rate in decimal form
  • n = number of times money is compounded per year
  • t = number of years

In this case,

  • P = 5000
  • r = 0.06 from the 6% annual interest
  • n = 4 times a year is the compounding frequency
  • t = unknown amount of time

Therefore, the equation is

A = P(1+r/n)^(n*t)

A = 5000(1+0.06/4)^(4t)

A = 5000(1.015)^(4t)

The decimal value is exact.

--------------------------

Part 2) Let's plug in A = 10,000 and solve for t.

You'll need to use logarithms to isolate the exponent.

A = 5000(1.015)^(4t)

10,000 = 5000(1.015)^(4t)

10,000/5000 = (1.015)^(4t)

2 = (1.015)^(4t)

Log[ 2 ] = Log[ (1.015)^(4t) ]

Log(2) = 4t*Log( 1.015 )

4t = Log(2)/Log(1.015)

4t = 46.5555256308062

t = 46.5555256308062/4

t = 11.6388814077015

t = 11.63888

It takes about 11.63888 years for the investment to reach $10,000.

Therefore, at the 12 year mark is when the investment is more than $10,000.

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