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aksik [14]
3 years ago
15

Recall the equation for a circle with center ( h , k ) (h,k) and radius r r. At what point in the first quadrant does the line w

ith equation y = 2.5 x + 2 y=2.5x+2 intersect the circle with radius 6 and center (0, 2)?
Mathematics
1 answer:
garri49 [273]3 years ago
7 0
Equation of this circle is
x^2 + (y - 2)^2 = 36
y = 2.5x + 2

Substitute for y in the equation of the circle:-

x^2 + (2.5x + 2 - 2)^2 = 36

x^2 + 6.25x^2 = 36

x^2 = 36 / 7.25  

x = +/-   6  /  2.693  =  +/- 2.228

when x = 2.228 y = 2.5(2.228) + 2 =  7.57    to nearest hundredth

when x = -2.228 y = 2.5(-2.228) + 2 =   -3.57

So they intersect at 2 points but the intersect in the first quadrant is at (2.23, 7,57)        to nearest hundredth.
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Hey there! I'm happy to help!

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Justine charges $25 to wash a dog. She washed 5 dogs on Saturday and then some more on Sunday. She made $325 for the weekend. Ho
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Answer

• A. Equation: 25(5 + x) = 325

,

• B. Answer: 8 dogs

Explanation

Given

• Charge to wash a dog: $25.

• She washed 5 dogs on Saturday and then some more on Sunday.

• She made $325 for the weekend.

Procedure

She charges $25 per wash, she made $325 for the weekend, and we know that on Saturday she washed 5 dogs, but we don't know how many she washed on Sunday. Thus, we have to build an equation in which the number of dogs washed on Sunday is represented by x (as we do not know the real number).

Considering that the total money made has to be equal to the multiplication of the charge times the dogs washed, the equation is:

25(5+x)=325

Then, we have to solve for x to know how many dogs did she wash on Sunday.

0. Multiplying the parenthesis

125+25x=325

<em>2. Subtracting 125 from both sides of the equation</em>

125-125+25x=325-12525x=200

<em>3. Dividing both sides of the equation against 25</em>

\frac{25x}{25}=\frac{200}{25}x=8

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