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2 years ago

Complete the square please.

Mathematics

1 answer:

Aleks04 [339]2 years ago

3 0

Answer:

(x-3)^2 + (y+2)^2 = 9^2

Step-by-step explanation:

x^2 -6x+y^2+4y-68 = 0

Complete the square

x^2 -6x+y^2+4y-68+68 = 0+68

x^2 -6x+y^2+4y = 68

Find the term to add for x

-6 /2 = -3 -3^2 = 9

Find the term to add for y

4/2 =2 2^2 = 4

Add 9 and 4

x^2 -6x+9+y^2+4y+4 = 68+9+4

(x-3)^2 + (y+2)^2 = 81

(x-3)^2 + (y+2)^2 = 9^2

The standard form is

(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius

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Can somebody help me think it’s b but I’m not sure can ya help me ? Be 100%

QveST [7]

Yes, it’s option one where y is neg five

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2 years ago

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Answer:

Yes, look at the explanation:

Step-by-step explanation:

Calculate how many miles a car can drive with 1 gallon: 285 miles ÷ 10 = 28.5 miles with one gallon
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3 years ago

1. Find the volume of a sphere with a radius of 10 inches. Use 3.14 for pi.

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Answer: $1256in^{2}$

Step-by-step explanation:

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I hope this helped

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3 years ago

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Show division using an array 1. 24÷4 Quotient= Remainder=

Lana71 [14]

Answer:

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Step-by-step explanation:

24 divided by 4 is 6.

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2 years ago

PLEASE HELP ASAP! I don’t recall how to do this!

MakcuM [25]

Answer:

Step-by-step explanation:

For a. we start by dividing both sides by 200:

$(1.05)^x=1.885$

In order to solve for x, we have to get it out from its position of an exponent. Do that by taking the natural log of both sides:

$ln(1.05)^x=ln(1.885)$

Applying the power rule for logs lets us now bring down the x in front of the ln:

x * ln(1.05) = ln(1.885)

Now we can divide both sides by ln(1.05) to solve for x:

$x=\frac{ln(1.885)}{ln(1.05)}$

Do this on your calculator to find that

x = 12.99294297

For b. we will first apply the rule for "undoing" the addition of logs by multipllying:

$ln(x*x^2)=5$

Simplifying gives you

$ln(x^3)=5$

Applying the power rule allows us to bring down the 3 in front of the ln:

3 * ln(x) = 5

Now we can divide both sides by 3 to get

$ln(x)=\frac{5}{3}$

Take the inverse ln by raising each side to e:

$e^{ln(x)}=e^{\frac{5}{3}}$

The "e" and the ln on the left undo each other, leaving you with just x; and raising e to the power or 5/3 gives you that

x = 5.29449005

For c. begin by dividing both sides by 20 to get:

$\frac{1}{2}=e^{.1x}$

"Undo" that e by taking the ln of both sides:

$ln(.5)=ln(e^{.1x})$

When the ln and the e undo each other on the right you're left with just .1x; on the left we have, from our calculators:

-.6931471806 = .1x

x = -6.931471806

Question d. is a bit more complicated than the others. Begin by turning the base of 4 into a base of 2 so they are "like" in a sense:

$(2^2)^x-6(2)^x=-8$

Now we will bring over the -8 by adding:

$(2^2)^x-6(2)^x+8=0$

We can turn this into a quadratic of sorts and factor it, but we have to use a u substitution. Let's let $u=2^x$

When we do that, we can rewrite the polynomial as

$u^2-6u+8=0$

This factors very nicely into u = 4 and u = 2

But don't forget the substitution that we made earlier to make this easy to factor. Now we have to put it back in:

$2^x=4,2^x=2$

For the first solution, we will change the base of 4 into a 2 again like we did in the beginning:

$2^2=2^x$

Now that the bases are the same, we can say that

x = 2

For the second solution, we will raise the 2 on the right to a power of 1 to get:

$2^x=2^1$

Now that the bases are the same, we can say that

x = 1

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2 years ago