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3 years ago

PLZ HELP ME

Mathematics

1 answer:

creativ13 [48]3 years ago

8 0

Answer:

$2x + 1200$

Step-by-step explanation:

$.5x + 300 \\ 3(.5x + 300) = 1.5x + 900\\ 2(1.5x + 900) = 3x + 1800 \\ \frac{2}{3} (3x + 1800) = 2x + 1200$

Each new line represents the change stated in the question.

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You purchase a stereo system for $830. The value of the stereo system decreases 13% each year. a. Write an exponential decay mod

lorasvet [3.4K]

Answer:

a. $y=830*(0.87)^x$

b. The value of stereo system after 2 years will be $628.23.

c. After approximately 4.98 years the stereo will be worth half the original value.

Step-by-step explanation:

Let x be the number of years.

We have been given that you purchased a stereo system for $830. The value of the stereo system decreases 13% each year.

a. Since we know that an exponential function is in form: $y=a*b^x$ , where,

a = Initial value,

b = For decay b is in form (1-r), where r is rate in decimal form.

Let us convert our given rate in decimal form.

$13\%=\frac{13}{100}=0.13$

Upon substituting our given values in exponential decay function we will get

$y=830*(1-0.13)^x$

$y=830*(0.87)^x$

Therefore, the exponential model $y=830*(0.87)^x$ represents the value of the stereo system in terms of the number of years since the purchase.

b. To find the value of stereo system after 2 years we will substitute x=2 in our model.

$y=830*(0.87)^2$

$y=830*0.7569$

$y=628.227\approx 628.23$

Therefore, the value of stereo system after 2 years will be $628.23.

c. The half of the original price will be $\frac{830}{2}=415$ .

Let us substitute y=415 in our model to find the time it will take the stereo to be worth half the original value.

$415=830*(0.87)^x$

Upon dividing both sides of our equation by 830 we will get,

$\frac{415}{830}=\frac{830*(0.87)^x}{830}$

$0.5=0.87^x$

Let us take natural log of both sides of our equation.

$ln(0.5)=ln(0.87^x)$

Using natural log property $ln(a^b)=b*ln(a)$ we will get,

$ln(0.5)=x*ln(0.87)$

$\frac{ln(0.5)}{ln(0.87)}=\frac{x*ln(0.87)}{ln(0.87)}$

$\frac{ln(0.5)}{ln(0.87)}=x$

$\frac{-0.6931471805599}{-0.139262067}=x$

$x=4.977286\approx 4.98$

Therefore, after approximately 4.98 years the stereo will be worth half the original value.

5 0

3 years ago

How much does Jimmy earn each week, and

Kisachek [45]

Answer:

we need more info to answer this question

4 0

2 years ago

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The lateral area of a cylinder is 325 pi inch^2. The radius is 13 in. Find the surface area and volume. Please show all work!!!

USPshnik [31]

Answer:

Surface area = 663π in².
Volume = (676/3)π in² ≈ 225.33 π in²

Explanation:

1) We know the radius and the lateral area.

2) With the radius you can find the areas of the top and the bottom.

For that, you use the formula:

area of the top = area of the bottom = π r²

∴ π (13 in)² = 169π in² (each)

3) Then, the surface area is the sum of the lateral area and the two bases (top and bottom)

surface area = lateral area + bottom area + top area = 325π in² + 2×169π in² = 663π in².

3) You can also find the height of the cylinder.

Use the formula: lateral area = 2π r h

∴ h = lateral area / [2 π r]

⇒ h = 325 π / [ 2π (13) ] = 12.5 in

4) With the height you can find the volume.

Use the formula: V = (4/3) π r³

∴ V = (4/3) π (13 in)³ = (676/3)π in² ≈ 225.33 π in²

8 0

3 years ago

Please help! Will give the brainiest!!

Eduardwww [97]

Answer:

1. SSS; Triangle ABC is congruent to Triangle DEF; sorry there's no triangle symbol on here.

2. HL; CBA is congruent to ZYX; or ABC is congruent to XYZ

Step-by-step explanation:

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2 years ago

Help me on this please

Solnce55 [7]

Answer:

Step-by-step explanation:

8 0

3 years ago

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