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3 years ago

1. Which of the following is the equation of a circle with center (a, −b) and radius r?

Mathematics

2 answers:

choli [55]3 years ago

5 0

Answer:

Step-by-step explanation:

Thepotemich [5.8K]3 years ago

4 0

Answer:

1) A

2) D

Step-by-step explanation:

1) The equation of a circle is (x-h)²+(y-k)²=r² where (h,k) is the center and "r" is the radius of the circle. With a center of (a,-b) the equation of the circle is (x-a)²+(y+b)²=r² making A the correct answer.

2) Convert from general form into standard form:

Given: x²+y²-4x-2y+4=1

Rearrange: x²-4x+4+y²-2y=1

Set right side equal to 0: x²-4x+4+y²-2y-1=0

Complete the square: x²-4x+4+y²-2y-1+2=0+2

Evaluate: x²-4x+4+y²-2y+1=2

Condense: (x-2)²+(y-1)²=2

Therefore, the center of the circle is D) (2,1)

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tatuchka [14]

Answer:

$65.52

Step-by-step explanation:

52 x 6% = 3.12. Multiply the price of the meal by the percentage of sales tax

52 x 20% = 10.4. Multiply the price of the meal by tip percent

$3.12 is the sales tax on the meal

$10.40 is the tip amount

$52 + $3.12 + $10.40 = $65.52

Add sales tax and the tip amount to the price of the meal to find the total

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2 years ago

The ellipse with x-intercepts (2, 0) and (-2, 0); y-intercepts (0, 4) and (0, -4).

masya89 [10]

Answer:

$\dfrac{x^2}{4}+\dfrac{y^2}{16}=1$

Step-by-step explanation:

If the ellipse has its x-intercepts at points (2, 0) and (-2, 0) and y-intercepts at points (0, 4) and (0, -4), then its symmetric across the y-axis and across the x-axis.

Moreover,

$a=2\\ \\b=4$

The equation of such ellipse is

$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$

Hence, the equation of the ellipse is

$\dfrac{x^2}{2^2}+\dfrac{y^2}{4^2}=1\\ \\ \\\dfrac{x^2}{4}+\dfrac{y^2}{16}=1$

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How is the function, y=x-3 related to y = x? Graph the function by translating the parent function.

aliina [53]

It is 3 units down to parent function

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3 years ago

Marissa bought 60 horns for her New Year’s Eve party for $83.40.

anzhelika [568]

That would cost her $25.02

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Julio bought tables and chairs for his restaurant. He bought 16 total items and spent $1800. Each table cost $150 and each chair

uysha [10]

Answer:

He bought 6 chairs and 10 tables.

Step-by-step explanation:

x+y = 16

he spent = $1800

1 chair = $50

y chairs = $50y

1 table = $150

x chairs = $150x

so, 150x+50y = 1800

we got two equations :

x+ y = 16

150x+50y = 1800

Using. substitution method,

x+y = 16

so, x = 16-y

Now

150x+50y =1800

or, 150(16-y) + 50y = 1800

or, 2400-150y+50y = 1800

or, 2400-1800 = 150y-50y

or, 600=100y

so, y = 6

now,

x+y = 16

or, x + 6 = 16

so, x = 10

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2 years ago