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Olegator [25]
3 years ago
10

Slove system of equations y=2x-3 y=x^2-2x-8

Mathematics
1 answer:
Fiesta28 [93]3 years ago
3 0

Answer:

2 solutions:

x=5 and y=7

x=-1 and y=-5

Step-by-step explanation:

y=2x-3

y=x^2-2x-8

y=y   so:

2x-3=x^2-2x-8

simplifying to:

x^2-4x-5=0

factoring to:

(x-5)(x+1)=0

x=5 or x=-1

if x=5 then y=2(5)-3=7

if x=-1 then y=2(-1)-3=-5

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A company makes candles in the shape of a right cone. The lateral surface of each candle is covered with
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Answer:

The amount of paper needed = 363.3 in²

Total amount of paper and plastic needed = 564.3 in

Step-by-step explanation:

As the diagram isn't given.

Consider a right cone shown in the ATTACHMENT.

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r = 8 in

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First find the value of hypotenuse s by using Pythagoras theorem

<h3>Find Lateral Area:</h3>

The amount of paper needed to cover the candle is lateral area, which is given by:

L=\pi\cdot{r}\cdot{s}\\L =\pi\cdot8\cdot14.422\\L=363.3in^2\\

<h3>Find Surface Area:</h3>

Total amount of paper and plastic is the surface area:

S=L+\pi{r}^2\\S=363.3+\pi(8)^2\\S=564.26in^2

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3 years ago
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What is the equation, in standard form, of a parabola that models the values in the table? x~ -1 0 2
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<h2>Steps</h2>
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So firstly, since (0,5) is one of our values we can plug it into the standard form equation to solve for the c variable (since 0 will cancel out the a and b variable):

5=a*0^2+b*0+c\\5=c

Now we know that the value of c is 5. Next, plug in (-1,12) into the standard form equation and simplify (remember to also plug in 5 for the c variable):

12=a*(-1)^2+b*(-1)+5\\12=a-b+5\\7=a-b

Next, plug (2,15) into the standard form equation and simplify:

15=a*2^2+b*2+5\\15=4a+2b+5\\10=4a+2b\\5=2a+b

Now, with our last two simplified equations we will create a system of equations:

7=a-b\\5=2a+b

Now, I will be using the elimination method with this system. With the system, add up the equations together and you will get:

12=3a

From here, we can solve for the a variable. With it, just divide both sides by 3:

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Now that we know the value of a, plug it into either equation to solve for the b variable:

7=4-b\\3=-b\\-3=b\\\\5=2(4)+b\\5=8+b\\-3=b

<h2>Answer</h2>

Putting all of our obtained values together, your final answer is:

f(x)=4x^2-3x+5

8 0
3 years ago
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