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Lelu [443]
3 years ago
13

What is the value of the x-coordinate of 2x+3y=144;y-x=24

Mathematics
1 answer:
erica [24]3 years ago
3 0

The value of x - coordinate is 14.4

<em><u>Solution:</u></em>

Given that we have to find the x -coordinate of the system

<em><u>Given system of equations are:</u></em>

2x + 3y = 144 -------- eqn 1

y - x = 24 --------- eqn 2

Solve the above system of equations to find the x - coordinate

From eqn 2,

y = 24 + x ------- eqn 3

Substitute eqn 3 in eqn 1

2x + 3(24 + x) = 144

2x + 72 + 3x = 144

Add the like terms

5x + 72 = 144

5x = 144 - 72

5x = 72

Divide 72 by 5

x = 14.4

Thus the x - coordinate of the system is 14.4

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Y = ax + 4x - 2 x= 1
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6 0
3 years ago
For the following amount at the given interest rate compounded​ continuously, find​ (a) the future value after 9 ​years, (b) the
Stella [2.4K]

Answer:

(a) The future value after 9 ​years is $7142.49.

(b) The effective rate is r_E=4.759 \:{\%}.

(c) The time to reach ​$13,000 is 21.88 years.

Step-by-step explanation:

The definition of Continuous Compounding is

If a deposit of P dollars is invested at a rate of interest r compounded continuously for t years, the compound amount is

A=Pe^{rt}

(a) From the information given

P=4700

r=4.65\%=\frac{4.65}{100} =0.0465

t=9 \:years

Applying the above formula we get that

A=4700e^{0.0465\cdot 9}\\A=7142.49

The future value after 9 ​years is $7142.49.

(b) The effective rate is given by

r_E=e^r-1

Therefore,

r_E=e^{0.0465}-1=0.04759\\r_E=4.759 \:{\%}

(c) To find the time to reach ​$13,000, we must solve the equation

13000=4700e^{0.0465\cdot t}

4700e^{0.0465t}=13000\\\\\frac{4700e^{0.0465t}}{4700}=\frac{13000}{4700}\\\\e^{0.0465t}=\frac{130}{47}\\\\\ln \left(e^{0.0465t}\right)=\ln \left(\frac{130}{47}\right)\\\\0.0465t\ln \left(e\right)=\ln \left(\frac{130}{47}\right)\\\\0.0465t=\ln \left(\frac{130}{47}\right)\\\\t=\frac{\ln \left(\frac{130}{47}\right)}{0.0465}\approx21.88

3 0
3 years ago
I need an explanation on how to work this out
rjkz [21]

Answer:

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360×7/15=168°

360×5/15=120°

360×2/15=48°

360×1/15=24°

now draw each one from the radius give to the clockwise

if you don't know what's clockwise direction, see it from your house or tell anybody in your home to tell you where is clockwise

after you finish drawing, label each section by writing the names on the correct sections ( you can write in or out of the circle)

6 0
3 years ago
Which fraction is equivalent to 15/30<br> A 3/4<br> B 2/4<br> C 3/5<br> D 5/6
Ratling [72]

Answer:

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Step-by-step explanation:

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3 years ago
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