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sveta [45]
3 years ago
10

The graph of the equation x^2+6x+y^2-16y=-9 is a circle. Choose True or False for each statement

Mathematics
1 answer:
BigorU [14]3 years ago
7 0

Answer:

see the explanation

Step-by-step explanation:

we have

x^2+6x+y^2-16y=-9

<u><em>Convert the equation of the circle in center radius form</em></u>

Group terms that contain the same variable

(x^2+6x)+(y^2-16y)=-9

Complete the square twice. Remember to balance the equation by adding the same constants to each side

(x^2+6x+9)+(y^2-16y+64)=-9+9+64

(x^2+6x+9)+(y^2-16y+64)=64

Rewrite as perfect squares

(x+3)^2+(y-8)^2=8^2

The center of the circle is (-3,8)

The radius of the circle is 8 units

<u><em>Verify each statement</em></u>

A. The center of the circle is (3,-8).

False

The center of the circle is (-3,8)

B. The circle is tangent to the x-axis

True

The circle is tangent to x=5 and x=-11 and is tangent to y=0 and y=16

Remember that y=0 is the x-axis

C. The circle has a radius of 64

False

The radius of the circle is 8 units

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Simplify this radical.
Zielflug [23.3K]

Answer:

3\sqrt{10}

Step-by-step explanation:

Assuming you mean \sqrt{90}

Using the rule of radicals

\sqrt{a} × \sqrt{b} ⇔ \sqrt{ab} , then

\sqrt{90}

= \sqrt{9(10)}

= \sqrt{9 × \sqrt{10}

= 3\sqrt{10}

6 0
3 years ago
HELP PLEASE NOW GUVUDYGYESDTIXJRXZTKXRX
kramer

Answer:

He should cross multiply 90 and 60, and then divide by 100. The answer is 54.

6 0
3 years ago
I need answers for 1 , 2, 4​
andreyandreev [35.5K]

Answer:

(3) x ≥ -3

(4) 2.5 gallons

(4) -12x + 36

Step-by-step explanation:

<em>Hey there!</em>

1)

Well its a solid dot meaning it will be equal to.

So we can cross out 1 and 2.

And it's going to the right meaning x is greater than or equal to -3.

(3) x ≥ -3

2)

Well if each milk container has 1 quart then there is 10 quarts.

And there is 4 quarts in a gallon, meaning there is 2.5 gallons of milk.

(4) 2.5 gallons

4)

16 - 4(3x - 5)

16 - 12x + 20

-12x + 36

(4) -12x + 36

<em>Hope this helps :)</em>

3 0
3 years ago
Sin law or cos law?!!!!!!!!!!!!! ​
MA_775_DIABLO [31]

Answer:

Law of Sines

Step-by-step explanation:

Law of Sines: \frac{A}{sina} =\frac{B}{sinb} =\frac{C}{sinc}

Step 1: Solve for m∠B

\frac{25}{sin36} =\frac{27}{sinx}

25sinx = 27sin36°

sinx = 27sin36°/25

x = sin^{-1}(\frac{27sin36}{25} )

m∠B ≈ 39.4°

Step 3: Find m∠C

180 - (36 + 39.4)

180 - 75.4

m∠C = 104.6°

5 0
3 years ago
Solve for x &amp; y. 30x−42y=−6 and 5x−7y=−1
vladimir1956 [14]
Um.. Both of those equations are the exact same. Divide both sides of the first equation by 6. You get:

\frac{30x  - 42y}{6} = \frac{-6}{6} \\ 5x - 7y = -1

That is the exact same as the second equation. This system has an infinite number of solutions. 5x - 7y = -1 is a line, so basically every point on that line is a solution to the system.

For example, x = 0 and y = \frac{1}{7} would work, but so would x = 1 and y = \frac{6}{7}
4 0
3 years ago
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