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andrew-mc [135]
3 years ago
6

Nine fewer than half a number is five more than four times the number. Define a variable, write an equation, and solve to find t

he number.
Mathematics
1 answer:
nignag [31]3 years ago
3 0
N = the number

0.5n - 9 = 4n + 5
(0.5n - 0.5n) - 9 = (4n - 0.5n) + 5
-9 = 3.5n + 5
(-9 - 5) = 3.5n + (5 - 5)
-14 = 3.5n
-14/3.5 = 3.5n/3.5
-4 = n

The number is -4.
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<em><u>The least amount of money you would need to invest per month is; $335</u></em>

<em><u>The anticipated rate of return on your investments is; 7%</u></em>

<em><u /></em>

  • Amount to have been saved at the end of 10 years ≥ $40,000

Number of years of savings = 10 years.

  • We want to find out the least amount to be invested per month.

There are 12 months in a year. Number of months in 10 years = 10 × 12 = 120 months.

  • Thus, amount to be saved monthly = 40000/12 = $333.33
  • Since the minimum amount he wants to save after 10 years is $40000, then we need to approximate the monthly savings in order.

Thus;

Monthly savings ≈ $335

  • Now, for the anticipated rate of return on the investment, we know from S & P's that the benchmark on good rate of return for investment is a minimum of 7%.

  • From online calculator, the worth of the investment after 10 years based on 7% rate of return yearly would be $57626.

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3 years ago
If line GH is perpendicular to line HJ, then GJ is ____ HJ.
valentinak56 [21]

Option A: >

Solution:

Given a triangle GHJ.

The line GH is perpendicular to line HJ.

This means the triangle is a right angled triangle.

In ΔGHJ, GH is the base of the triangle and

HJ is a height of the triangle.

Then the third side must be the hypotenuse of the right triangle.

We know that by the Pythagoras theorem,

(\text {Hypotenuse})^2=(\text{Base})^2+(\text{Height})^2

(\text {GJ})^2=(\text {GH})^2+(\text {HJ})^2

This clearly shows that the hypotenuse is greater than the height.

⇒ GJ > HJ

Option A: > is the correct answer.

If line GH is perpendicular to line HJ, then GJ is > HJ.

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Answer:

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Step-by-step explanation:

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8 0
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