1. A circle with center (-5, 2) is tangent to the y-axis. What is the radius of the circle? What is the equation of the circle?

Mathematics

1 answer:

Bess [88]2 years ago

4 0

Answer:

Step-by-step explanation:

1) The center lies on the vertical line x = -5 and the the circle is tangent to (touches in one place only) the y-axis. Thus, the radius is 5.

2) Starting with (x - h)^2 + (y - k)^2 = r^2 and comparing this to the given

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

we see that h = 4, k = -3 and r = 6. The center is at (4, -3) and the radius is 6.

3) Notice that A and B have the same x-coordinate, x = 15. The center of the circle is thus (15, -2), where that -2 is the halfway point between the two given points in the vertical direction. Arbitrarily choose A(15, 4) as one point on the circle. Then the equation of this circle is

(x - 4)^2 + (y + 3)^2 = r^2 = 6^2, where the 6 is one half of the vertical distance between A(15, 4) and B(15, -8) (which is 12).

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Y=2x-1 y=1/2x+4 find the solution to the system equations

Evgesh-ka [11]

Answer:

x=10/3 y=17/3

Step-by-step explanation:

Use substitution to solve your equation. Plug in y=2x-1 into y=1/2x+4. This makes (2x-1)=1/2x+4. Simplify this to get 3/2x-1=4. Simplify it again to get 3/2x=5. No one likes fractions so multiply both sides by 2 to get 3x=10. Simplify this and get x=10/3. Plus 10/3 into one of the equations. You can pick anyone but I picked y=2x-1. Because you know x=10/3, you put y=2(10/3)-1. Simplify this and get y=20/3-1. Convert 1 into a fraction and get y=20/3-3/3. Simplify this and get y=17/3.

Therefore,

x=10/3 y=17/3

Hoped this helps you

7 0

3 years ago

Read 2 more answers

Jimmy was supposed to multiply a certain number by 43 but by mistake he multiplied that number by 34 as a result his answer was

vredina [299]

Answer:

345

Step-by-step explanation:

We can solve this problem by two equations. Our variables will be the following:

$x$ is the amount to be multiplied

and $y$ is the amount that should be obtained by multiplying by 43

Thus our first equation is:

$43x=y$

But the problem tells us that there was an error and the number $x$ was multiplied by 34, so the result failed by 3105, thus the second equation is as follows:

$34x=y-3105$