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2 years ago

Find the center and radius of the circle defined by the equation x^2+y^2-7x+3y-4=0

Mathematics

1 answer:

scoray [572]2 years ago

3 0

Answer:

C. center: (7/2, -3/2); radius: sqrt(74)/2

Step-by-step explanation:

x^2 + y^2 - 7x + 3y - 4 = 0

We can put the equation in standard form by completing the square in x and in y.

x^2 - 7x + ___ + y^2 + 3y + ___ = 4 + ___ + ___

x^2 - 7x + (7/2)^2 + y^2 + 3y + (3/2)^2 = 4 + (7/2)^2 + (3/2)^2

(x - 7/2)^2 + (y + 3/2)^2 = 16/4 + 49/4 + 9/4

(x - 7/2)^2 + (y + 3/2)^2 = 74/4

(x - 7/2)^2 + (y + 3/2)^2 = (sqrt(74)/2)^2

Answer: center: (7/2, -3/2); radius: sqrt(74)/2

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Please Solve this, it would be extremely helpful for me.

Sidana [21]

Answer:

Step-by-step explanation:

1) ΔCPD & ΔEPF

∠CPD = ∠EPF { Vertically opposite angles}

∠CDP = ∠PFE {CD║EF, FD is transversal, Alternate interior angles are equal}

ΔCPD ≈ΔEPF {AA criteria for similarity }

$\frac{DC}{EF} =\frac{PC}{EP}\\\\\\\frac{27}{EF}=\frac{15}{7.5}\\\\$

Cross multiply

EF * 15 = 27 * 7.5

$EF =\frac{27*7.5}{15}\\\\$

EF = 27 * 0.5

EF = 13.5 cm

ii) EF // AB, so Triangles ACB & ECF are similar triangles

$\frac{AB}{EF}=\frac{AC}{EC}\\\\\frac{22.5}{13.5}=\frac{AC}{22.5}$

$AC= \frac{22.5*22.5}{13.5}\\\\AC=37.5 cm$

AC = 37.5 cm

6 0

2 years ago

Type the slope-intercept equation

Zolol [24]

Answer: y=x-2

Step-by-step explanation:

P=(x1,y1), and Q=(x2,y2), we use this to find m because m=y2-y1/x2-x1, by using this you'll see that the slope equals one. So now we have our slope. To solve for b, you need to do b=y1-m*x1, or b=y2-m^x2, it doesn't matter which one you do because the results will be the same, but it is good to check over it. Now that you have your slope and y-intercept, you can put it into the equation y=mx+b, so the answer to the problem is y=x-2.

Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! As well as a great Valentines Day! :-)

- Cutiepatutie ☺❀❤

3 0

2 years ago

The area of the right triangle shown is 24 square feet. Which equations can be used to find the lengths of the legs of the trian

Gwar [14]

The equations to calculate the legs are 0.5(x)(x + 2) = 24, x^2 + 2x - 48 = 0 and x^2 + (x + 2)^2 = 100

<h3>How to determine the legs of the triangle?</h3>

The complete question is in the attached image

The given parameters are:

Area = 24

Legs = x and x + 2

The area of the triangle is calculated as:

Area = 0.5 * Base * Height

This gives

0.5 * x * (x + 2) = 24

So, we have:

0.5(x)(x + 2) = 24

Divide through by 0.5

(x)(x + 2) = 48

Expand

x^2 + 2x = 48

Subtract 48 from both side

x^2 + 2x - 48 = 0

Hence, the equations to calculate the legs are 0.5(x)(x + 2) = 24, x^2 + 2x - 48 = 0 and x^2 + (x + 2)^2 = 100