Two sides of a triangle have lengths 10 and 15. What must be true about the length of the third side?

Final answer:

The given equation can be rewritten into the form of an equation for a circle with center (h,k) and radius r. After completing the squares for x and y coefficients, we determine the center as (2, -5/2) and radius as 1.

Explanation:

The provided equation is 2x2 + 2y2 - 8x + 10y + 2 = 0.Let's rewrite it in the form of an equation for a circle, which is (x-h)^2 + (y-k)^2 = r^2, where (h,k) represents the center of the circle and r represents the radius:

First, we group the terms related to x and y separately like this: 2(x2- 4x) + 2(y2 + 5y) +2 = 0.

Now, re-arrange the terms to complete the square: 2[(x-2)^2 - 4] + 2[(y+5/2)^2 - (5/2)^2] + 2 = 0.

Re-arrange again, this time to make it equate to zero: (x-2)^2 + (y+5/2)^2 = 1. Hence, the circle's center (h,k) is at (2, -5/2) and the radius (r) is the square root of 1, which is 1.

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Answer:

first group x's with x's and y's with y's

then complete the squra with x's and y's

2x^2-8x+2y^2+10y+2=0

2(x^2-4x)+2(y^2+5y)+2=0

take 1/2 of linear coeficient and square

-4/2=-2, (-2)^2=4

5/2=2.5, 2.5^2=6.25

add that and negative inside

2(x^2-4x+4-4)+2(y^2+5y+6.25-6.25)+2=0

factor perfect squares

2((x-2)^2-4)+2((y+2.5)^2-6.25)+2=0

distribute

2(x-2)^2-8+2(y+2.5)^2-12.5+2=0

2(x-2)^2+2(y+2.5)^2-18.5=0

add 18.5 both sides

2(x-2)^2+2(y+2.5)^2=18.5

divide both sides by 2

(x-2)^2+(y+2.5)^2=9.25

that is a circle center (2,-2.5) with radius √9.25

Answer:

Step-by-step explanation:

the function -16t^2 + 64t + 192 give the height S, in ft, of a model water rocket launched with a velocity of 64 ft/second from a hill that is 192 ft high. a) determine how long it will take the rocket to reach the ground, b) find the interval on which the height of the rocket is greater than 240 ft.

Answer:The answer is A

Answer:

Option second!!!!!!!