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1 year ago

What is the center and radius of -10x = -121 - y2 - x2 -22y

Mathematics

1 answer:

OlgaM077 [116]1 year ago

8 0

We need to find the center and the radius of

$-10x\: =\: -121\: -\: y^2\: -\: x^2\: -22y$

The general circle equation is the following

$(x-h)^2+(y-k)^2=r^2$

where

(h,k) is the center and

r is the radius

1. rearrange the equation

$(x^2-10x)+(y^2+22y+121)=0$

2. Add 25 on both sides

$(x^2-10x+25)+(y^2+22y+121)=25$

3. Factor

$(x-5)^2+(y+11)^2=5^2$

Now we have an equation that is very similar to the circle equation, so let's compare them

Center -> (h,k) = (5,-11)

radius -> r = 5

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Function A is a quadratic function with a vertex at (3, 4) and a leading coefficient of -1 Function B has the equation y = |x +

skad [1K]

With the information given, we deduce that the parabola is

$y=-(x-3)^2+4 = -(x^2-6x+9)+4 = -x^2+6x-5$

Reflecting a function over the x axis means to change its sign. After the reflection, the parabola becomes

$y=x^2-6x+5$

And to shift down a function, you subtract the shift from the equation: the equation becomes

$y=x^2-6x+5-2=x^2-6x+3$

Similarly, the other function is reflected over the x axis (sign change) and shifted up 3 (add 3 to the equation):

$|x+2|\mapsto -|x+2|\mapsto -|x+2|+3$

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8 0

4 years ago

The perimeter of a rectangle is 42 feet. The length decreased by three times the width is 1 foot. What are the dimensions of the

madreJ [45]

First you want to make an equation to express the problem. For this one in particular, let's make the length be represented by "L" and the width "W."

The length minus three times the width is 1 foot. This can be represented as L - 3W = 1. This means that L = 3W + 1. This will be our substitute for the length.

The perimeter of a rectangle is 2 times the length plus the width P = 2(L + W). By substituting these variables from what we now know we can find out the dimensions of the rectangle.

42 = 2(3W + 1 + W)
42 = 6W + 2 + 2W Multiply everything in parenthesis by 2.
42 = 8W + 2 Add the like terms.
40 = 8W Subtract 2 on both sides to get the variable (W) by itself.
5 = W Divide 8 from 40 to get what W equals.

The width is equal to 5. We can now plug in this answer to the original equation (P = 2(L + W)) or the length equation we made earlier (L = 3W + 1) to find the length.

42 = 2(L + 5)
42 = 2L + 10 Multiply everything in parenthesis by 2.
32 = 2L Subtract 10 from both sides to get the variable (L) by itself.
16 = L Divide 2 from 32 to get what L equals.
Or
L = 3(5) + 1 Replace the variable (W) with 5.
L = 15 + 1 Multiply 3 by 5 to get 15.
L = 16 Add the remaining terms!

So the dimensions of the rectangle are 5 and 16, where 5 is the width and 16 is the length. I hope this answer made sense and that you can solve these on your own in the future!

4 0

4 years ago

Property for the equation 5x23x2

Vesnalui [34]

Go on a calculator and txt that and might get it

5 0

4 years ago

Read 2 more answers

PLZ FIND THE AREA FOR THE CIRCLE, plz show me how you got ur ANWSER thx

pishuonlain [190]

Answer:

i got 78.54 as my answer