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Keith_Richards [23]
3 years ago
9

Write a Mathematical proof to show (3x)(5y)(7z) is equivalent to 105xyz

Mathematics
2 answers:
larisa86 [58]3 years ago
7 0
=3*5*7 (xyz)
=15*7 xyz
=105xyz
pav-90 [236]3 years ago
6 0

(3x*5y)*7z

15xy*7z

105xyz

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Kristen invests $ 5745 in a bank. The bank 6.5% interest compounded monthly. How long must she leave the money in the bank for i
podryga [215]

Answer:

1. 10.7 years

2. 17.0 years

3. 2nd option

Step-by-step explanation:

Use formula for compounded interest

A=P\cdot \left(1+\dfrac{r}{n}\right)^{nt},

where

A is final value, P is initial value, r is interest rate (as decimal), n is number of periods and t is number of years.

In your case,

1. P=$5745, A=2P=$11490, n=12 (compounded monthly), r=0.065 (6.5%) and t is unknown. Then

11490=5745\cdot \left(1+\dfrac{0.065}{12}\right)^{12t},\\ \\2=(1.0054)^{12t},\\ \\12t=\log_{1.0054}2,\\ \\t=\dfrac{1}{12}\log_ {1.0054}2\approx 10.7\ years.

2. P=$5745, A=3P=$17235, n=12 (compounded monthly), r=0.065 (6.5%) and t is unknown. Then


17235=5745\cdot \left(1+\dfrac{0.065}{12}\right)^{12t},

3=(1.0054)^{12t},

12t=\log_{1.0054}3,

t=\dfrac{1}{12}\log_{1.0054}3\approx 17.0\ years.

3. <u>1 choice:</u> P=$5745, n=12 (compounded monthly), r=0.065 (6.5%), t=5 years and A is unknown. Then

A=5745\cdot \left(1+\dfrac{0.065}{12}\right)^{12\cdot 5},\\ \\A=5745\cdot (1.0054)^{60}\approx \$7936.39.

<u>2 choice:</u> P=$5745, n=4 (compounded monthly), r=0.0675 (6.75%), t=5 years and A is unknown. Then

A=5745\cdot \left(1+\dfrac{0.0675}{4}\right)^{4\cdot 5},\\ \\A=5745\cdot (1.0169)^{20}\approx \$8032.58.

The best will be 2nd option, because $8032.58>$7936.39

5 0
3 years ago
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poizon [28]
A isosceles triangle is a triangle who has two sides of the same length
7 0
3 years ago
W is the midpoint of VX. What is VX if VW=2x+5 and WX =4x-3
Novosadov [1.4K]

Answer:

<h2>VX = 26</h2>

Step-by-step explanation:

If W is the midpoint of VX then VW = WX. Therefore we have the equation:

2x + 5 = 4x - 3          <em>subtract 5 from both sides</em>

2x = 4x - 8       <em>subtract 4x from both sides</em>

-2x = -8        <em>divide both sides by (-2)</em>

x = 4

VX = VW + WX

VX = 2x + 5 + 4x - 3 = (2x + 4x) + (5 - 3) = 6x + 2

Put the value of x = 4 to 6x + 2:

VX = 6(4) + 2 = 24 + 2 = 26

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Find the radius of the button.<br><br> radius: __ in.
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Answer:

1 3/4 in

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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