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iragen [17]
3 years ago
5

The equations of the two circles can also be written as follows: (x-1)²+(y+2)²=16 and (x+2)²+(y+1)²=14. Graph the circles and th

e line joining their points of intersection.

Mathematics
1 answer:
Semenov [28]3 years ago
8 0

Answer:(x,y)=(-0.0464,-0.86) & (-2.15,-5.45)

Step-by-step explanation:

Given

circle

\left ( x-1\right )^2+\left ( y+2\right )^2=16

center of circle is (1,-2)

second circle

\left ( x+2\right )^2+\left ( y+1\right )^2=14

center of circle is (-2,-1)

Solving Two circles we get

y=3x+1 Put it any circle

(x,y)=(-0.0464,-0.86) & (-2.15,-5.45)

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6 0
3 years ago
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by th
Naddika [18.5K]

Answer:

The rocket will hit the ground after about 8.20 seconds.

Step-by-step explanation:

The height of the rocket <em>y</em>, in feet, <em>x</em> seconds after launch is modeled by the equation:

y=-16x^2+121x+83

We want to find the time at which the rocket will hit the ground.

If it hits the ground, the height of the rocket <em>y</em> will be 0. Thus:

0=-16x^2+121x+83

We can solve for <em>x</em>. Factoring (if possible at all) or completing the square can be tedious, so we can use the quadratic formula:

\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

In this case, <em>a</em> = -16, <em>b</em> = 121, and <em>c </em>= 83. Substitute:

\displaystyle x=\frac{-(121)\pm\sqrt{(121)^2-4(-16)(83)}}{2(-16)}

Simplify:

\displaystyle x=\frac{-121\pm\sqrt{19953}}{-32}

Divide everything by -1 and simplify the square root. The plus/minus will remain unchanged:

\displaystyle x=\frac{121\pm3\sqrt{2217}}{32}

Therefore, our two solutions are:

\displaystyle x=\frac{121+3\sqrt{2217}}{32}\approx 8.20\text{ or } x=\frac{121-3\sqrt{2217}}{32}\approx -0.63

Since time cannot be negative, we can ignore the second solution.

Therefore, the rocket will hit the ground after about 8.20 seconds.

7 0
3 years ago
$120 is shared among 3 friends Ava, Ben, and Carlos. If Ava receives $20 less than
kenny6666 [7]

Answer:$20

Step-by-step explanation:

If Carlos had $20

Ben would have $60

And Ava would have $40

8 0
3 years ago
(1.6x + 3.25) + (0.3x + 0.5)
STatiana [176]

(1.6x + 3.25) + (0.3x + 0.5)

combine like terms

1.6x+.3x +3.25 +.5

Result:

1.9 x + 3.75

7 0
3 years ago
What is greater 30% or 0.03
Orlov [11]
30 percent is greater because o0.03 is actually 3 Percent
5 0
3 years ago
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