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Valentin [98]
2 years ago
7

Find the equation of the circle whose center and radius are given. center (5,6), radius = 3

Mathematics
1 answer:
MArishka [77]2 years ago
4 0

Answer:

(x - 5)² + (y - 6)² = 9

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = (5, 6) and r = 3, thus

(x - 5)² + (y - 6)² = 9 ← equation of circle

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Determine the next step for solving the quadratic equation by completing the square
GaryK [48]

Answer:

  • The two solutions are:           x=\frac{1}{2}+/-\frac{\sqrt{7} }{2}

  • The next and every step are below.

Explanation:

1. -3=-2x^2+2x    : Given (addition property / add - 3 to both sides)

2. -3 = - 2(x^2-x)    : Given (commom factor - 2)

3. -3-1/2=-2(x^2-x+1/4)

    To obtain the perfect square it was added the square of half of the coefficient of x: (1/2)² = 1/4, inside the parenthesis.

Since, the terms inside the parentthesis are multiplied by - 2, you have to add - 2 (1/4) = - 1/2 to the left side of the equation.

4. Now, you have that the trinomial x² - x + 1/4 is a square perfect trinomial which is factored as (x - 1/2)² and get the expression:

-7/2=-2(x-1/2)^2

5. Divide both sides by - 2 to get the next expression:

-7/4=(x-1/2)^2

6. The last step is to extract squere root from both sides of the equality:

(x-1/2)=+/-\sqrt{\frac{7}{4}}\\ \\ x-1/2=+/-\frac{\sqrt{7} }{2}\\ \\ x=\frac{1}{2}+/-\frac{\sqrt{7} }{2}

8 0
2 years ago
Write the equation of a straight line passing through the point (1,8) and perpendicular to y=3x+2
Neko [114]
Hello there!

The first thing you must do is to find the slope of the line. To do this, find the negative reciprocal of your current equation. Since your current slope is 3, the negative reciprocal of that would be -1/3, which would be your slope.

Now that you have your slope, plug it into the slope intercept equation as well as your known points:
(1,8)  m(slope)=-1/3
8=1(-1/3)+b

Now, solve for b:
8=1(-1/3)+b
8=-1/3+b
b=25/3

Now that you have the slope and the b value, you can conclude that your equation would be:
y=-1/3x+25/3
5 0
3 years ago
Please help! I’ve been trying to find the answer to this problem and couldn’t & I can’t find the answers anywhere!
Kryger [21]
The answer is if you tilt it a little bit it looks like a kite and if you look on the web a rhombus kinda looks like a kite and plz mark me brainiest because you know you looked for answers on the web
6 0
2 years ago
What is the volume of a box with a width 2 1/2 inches, length 1 3/4 inches, and height 3 1/4 inches?
enot [183]

Answer:

The volume of the box is 41.21 inches cube.

Step-by-step explanation:

Given,

Width of the box 2\frac{1}{2} inches

                           =\frac{5}{2} inches  

Length of the box 1\frac{3}{4}inches

                           =\frac{7}{4} inches

Height of the box 3\frac{1}{4} inches

                            = \frac{13}{4} inches

The box is in cuboid form.

The volume of cuboid is given by (length × breadth × height ).

So,

volume of the box is  ( \frac{5}{2}  × \frac{7}{4} × \frac{13}{4} )

                                    = ( \frac{455}{32} )

                                    = 14.21 inches cube

 The volume of the box is 41.21 inches cube.

8 0
3 years ago
What numbers are less than -0.625
Ivanshal [37]

Answer:

-8/5 = -1.6 (the smallest number here)

-5/8 = -0.625

your answer is A :)

7 0
2 years ago
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