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3 years ago

Graph the circle which is centered at (-4,1) and which has the point (0,4) on it

Mathematics

1 answer:

Allushta [10]3 years ago

7 0

Answer:

see the attachment for the graph

Step-by-step explanation:

Since all you want is the graph, it is convenient to use a graphing program to produce it.

You will notice that the point on the circle is 4 units over and 3 units up from the center.* This tells you the square of the radius is 4²+3² = 25. You only need to know this if you're using a graphing calculator to plot the equation ...

(x +4)^2 +(y -1)^2 = 25

If you're graphing this by hand, you can set your compass to the distance between the plotted points, as we have done in our graphing program.

_____

* Hopefully, you recognize these (4 and 3) as the legs of a 3-4-5 right triangle, so you know immediately that the radius is 5. Even if you don't, you can figure it using the Pythagorean theorem, as we have done above.

The standard form equation of a circle with center (h, k) and radius r is ...

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

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Pick a expression that matches the written description Subtract a from the quotient of 6 and B

Luba_88 [7]

An expression that is equivalent to the statement Subtract a from the quotient of 6 and B is 6/b - a

<h3>How to write equivalent expression</h3>

Given statement

Subtract a from the quotient of 6 and B

The quotient of 6 and B can be written as 6/B

a subtracted from 6/B is written as

6/B - a

Therefore, the correct option equivalent to the statement is option A) 6/B - a

Learn more about equivalent expression:

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2 years ago

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A brace for a shelf has the shape of a right triangle. Its hypotenuse is 10 inches long and the two legs are equal in length. Ho

vagabundo [1.1K]

This is a classic example of a 45-45-90 triangle: it's a right triangle (one angle of 90) & two other sides of the same length, which means two angles of the same length (and 45 is the only number that will work). With a 45-45-90 triangle, the lengths of the legs are easy to determine:
45-45-90
1-1-sqrt2
Where the hypotenuse corresponds to sqrt2.
Now, your hypotenuse is 10.
To figure out what each leg is, divide 10/sqrt2 (because sqrt2/sqrt2 = 1, which is a leg length in the explanation above).
Problem: you can't divide by radicals. So, we'll have to rationalize the denominator:
(10•sqrt2)/(sqrt2•sqrt2)
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3 years ago

What is an equation of the line that passes through the point (-7, -6) and is parallel to the line x-y=7?

Alex_Xolod [135]

Answer:

Step-by-step explanation:

For two lines to be parallel their slopes must be equal. For two lines to be perpendicular their slopes must be the negative reciprocal of each other.

Step 1 Find the slope of the equation.

Put it into the slope-intercept form. y = mx + b.

For x-y = 7, move the x to the left; therefore subtract the x from both sides. this leaves you -y = -x + 7

Then, divide both sides by -1 to get a positive y. -y/-1 = (-x + 7)/-1

This leaves y = x - 7 The slope(m) for this equation is m = 1

The other equation must also have a slope of 1 or m=1 for the lines to be parallel.

Use the point given to you (-7, -6) and substitute for (x, y)

The slope-intercept form y = mx + b can once again be used.

x = -7, y =-6, and slope or m = 1

Therefore, y = mx + b substituted will be -6 = (1)(-7) + b; now, solve for b which is the y intercept

-6 = -7 + b add 7 to both sides -6 +7 = -7 + b +7 ; therefore, b = 1

Now you know the slope(m) which is equal to 1 and the y-intercept(b) which is equal to 1.

Finally, substitute the m and b in the slope-intercept form

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