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2 years ago

Find GH. What does GH equal?

Mathematics

2 answers:

KATRIN_1 [288]2 years ago

5 0

Answer: GH = HJ = 4.6

igor_vitrenko [27]2 years ago

4 0

Answer: GH = HJ = 4.6

Step-by-step explanation:

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Find+the+positive+value+for+α+if+the+radius+of+the+circle+3x^2+3y-6αx+12y-3α=0+is+4

Alik [6]

Answer:

$\alpha=3$

Step-by-step explanation:

<u>Equation of a Circle</u>

A circle of radius r and centered on the point (h,k) can be expressed by the equation

$(x-h)^2+(y-k)^2=r^2$

We are given the equation of a circle as

$3x^2+3y^2-6\alpha x+12y-3\alpha=0$

Note we have corrected it by adding the square to the y. Simplify by 3

$x^2+y^2-2\alpha x+4y-\alpha=0$

Complete squares and rearrange:

$x^2-2\alpha x+y^2+4y=\alpha$

$x^2-2\alpha x+\alpha^2+y^2+4y+4=\alpha+\alpha^2+4$

$(x-\alpha)^2+(y+2)^2=r^2$

We can see that, if r=4, then

$\alpha+\alpha^2+4=16$

Or, equivalently

$\alpha^2+\alpha-12=0$

There are two solutions for $\alpha$ :

$\alpha=-4,\ \alpha=3$

Keeping the positive solution, as required:

$\boxed{\alpha=3}$

8 0

3 years ago

M² + 18m - 81 help me please

Marina CMI [18]

The question is incomplete

7 0

2 years ago

It this pattern a net for the three-dimensional figure?

elena-s [515]

Answer:

yes it is because the second triangle is the base and the other three triangles are the sides of the three dimensional shape

3 0

2 years ago

The vertex angle of an isosceles triangle measures 40°. What is the measure of a base angle?

disa [49]

<span>Triangle is 180 degrees, so you will subtract 50 from 180 which will give you 130.</span>

8 0

2 years ago

If 3x-8=-2 fins the value of x-6

adell [148]

Steps to solve:

3x - 8 = -2; x - 6

~Substitute

3(x - 6) = -2

~Distribute left side

3x - 18 = -2

~Add 18 to both sides

3x = 16

~Divide 3 to both sides

x = 16/3

Best of Luck!

7 0

3 years ago