Matthew sold 528 sets of dinnerware in a year.If each set contained 14 pieces.How many pieces were sold in all?

A circle has a diameter with endpoints at (6, 5) and (8, 5). Write the equation for the circle.

mario62 [17]

Answer:

$(x-7)^2+(y-5)^2=1$

Step-by-step explanation:

The two things that are required to formulate the equation of the circle is the center coordinate and the radius of the circle!

Center of the circle:

The center of the circle always lies at the midpoint of the endpoints of its diameter: Let's call the endpoints A(6,5) and B(8,5).

Using the midpoint formula we'll get:

$(x_m, y_m) = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

$(x_m, y_m) = \left(\dfrac{6+8}{2},\dfrac{5+5}{2}\right)$

$(x_m, y_m) = (7,5)$

This is the center coordinate of our circle.

Radius:

The radius of the circle is the distance from the center of the circle to any of the endpoints of the diameter (A or B)

We can use the distance formula:

$r = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$r = \sqrt{(x_1-x_m)^2+(y_1-y_m)^2}$

$r = \sqrt{(6-7)^2+(5-5)^2}$

$r = \sqrt{1^2}$

$r = 1$

Equation of the circle:

The equation is written as:

$(x-a)^2+(y-b)^2=r^2$

here, (a,b) are the center points of the circle

in our case this is $(a,b)=(x_m,y_m)=(7,5)$

and r = 1

$(x-7)^2+(y-5)^2=1^2$

$(x-7)^2+(y-5)^2=1$

This is the equation of the circle!

3 0

2 years ago

Given that AXB is complementary to both CYD and FZE, and mAXB = 36°, what is mCYD + mFZE?

anyanavicka [17]

Complementary angles always equal 90°
So here is how to find what mCYD + mFZE equal
mCYD + mFZE + mAXB
mCYD + mFZE + 36° = 90°
Subtract
mCYD + mFZE = 54°

7 0

2 years ago

PART 1:Using the scale 1 cm : 5 meters, Tamara calculated the length of her old gym to be 45 meters and the width to be 20 meter

statuscvo [17]

Answer:

Step-by-step explanation:

40 meters and 2 times

7 0

3 years ago

Read 2 more answers

1, 5, 17, 53, ... Use inductive reasoning to create a general rule for the sequence. A. Multiply by 3, then add 2. B. Multiply b

Basile [38]

The answer to this problem is the letter "A" which is "Multiply by 3, then add 2"
and can be written a N = 3n + 2
At first, we have initial value such n = 1
Then the second value is:
N = 3*1 + 2
N = 5
The third value is:
N = 3*5 + 2
N=17
The next values are:
N = 3*17 + 2
N= 53
The letter "A" is the inductive reasoning to the given sequence.

6 0

2 years ago

(-6x3-4x2-8)+(x3-x2-9x+4) add together and simply

Aleksandr [31]

Answer:

-5x³ -5x² -9x - 4

Step-by-step explanation:

(-6x³-4x²-8)+(x³-x²-9x+4)

Add the like terms.

-6x³ and x³ are like terms. -6x³ + x³ = -5x³

-4x² and -x² are like terms. -4x² - x² = -5x²

-8 and 4 are like terms. -8 + 4 = -4

-6x³-4x²-8 +x³-x²-9x+4 = -5x³ -5x² -9x - 4

6 0

2 years ago

Matthew sold 528 sets of dinnerware in a year.If each set contained 14 pieces.How many pieces were sold in all?​

Matthew sold 528 sets of dinnerware in a year.If each set contained 14 pieces.How many pieces were sold in all?