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3 years ago

Write the equation in standard form for the circle passing through (7, 1) centered at the origin

Mathematics

1 answer:

Alenkinab [10]3 years ago

4 0

Step-by-step explanation:

the standard form of a circle equation is

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle, and r is the radius.

since the center of this circle is the origin (0, 0), we have the simplified version

x² + y² = r²

to get r² we simply use the given point

7² + 1² = r²

49 + 1 = r²

r² = 50

our equation in standard form is therefore

x² + y² = 50

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Write the equation of a quadratic function who has the vertex of (4,-7)

timama [110]

Given:

The vertex of a quadratic function is (4,-7).

To find:

The equation of the quadratic function.

Solution:

The vertex form of a quadratic function is:

$y=a(x-h)^2+k$ ...(i)

Where a is a constant and (h,k) is vertex.

The vertex is at point (4,-7).

Putting h=4 and k=-7 in (i), we get

$y=a(x-4)^2+(-7)$

$y=a(x-4)^2-7$

The required equation of the quadratic function is $y=a(x-4)^2-7$ where, a is a constant.

Putting a=1, we get

$y=(1)(x-4)^2-7$

$y=(x^2-8x+16)-7$ $[\because (a-b)^2=a^2-2ab+b^2]$

$y=x^2-8x+9$

Therefore, the required quadratic function is $y=x^2-8x+9$ .

6 0

2 years ago

what would be the equation of a line that passes through (3,-4) with slope 2/3

Len [333]

Answer:

y = 2/3x - 6

Step-by-step explanation:

Use the slope intercept equation, y = mx + b

Plug in the slope and given point, then solve for b

y = mx + b

-4 = 2/3(3) + b

-4 = 2 + b

-6 = b

Plug in the slope and b into the equation

y = 2/3x - 6

So, the equation of the line is y = 2/3x - 6

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3 years ago

There are 20 sixth graders and 25 seventh graders. If each group has the greatest possible number of club members, how many grou

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5 groups of 7th graders

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3 years ago

A 56-foot piece of siding is cut into three pieces so that the second piece is twice as long as the first piece and the third pi

ELEN [110]

The lengths of the first, second and third piece are respectively 8 ft, 16 ft and 32 ft

<h3>How to solve Algebra word Problems?</h3>

Let the length of the first piece be x.

Let the length of the second piece be 2x

Let the length of the thrid piece be 4x

Since the total length of the piece is 56 ft, then we can say that;

x + 2x + 4x = 56

7x = 56

x = 56/7

x = 8 ft

Thus, length of first piece = 8 ft

Length of second piece = 2 * 8 = 16 ft

Length of third piece = 4 * 8 = 32 ft

Thus, the lengths of the first, second and third piece are respectively 8 ft, 16 ft and 32 ft

Read more about Algebra Word Problems at; brainly.com/question/13818690

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2 years ago