MATHEMATICS MIDDLE SCHOOL

Write the equation of the circle with center (3, 2) and with (9, 3) being a point on the circle. A) (x − 3)2 + (y − 2)2 = 13 Eliminate B) (x − 3)2 + (y − 2)2 = 18 C) (x − 3)2 + (y − 2)2 = 25 D) (x − 3)2 + (y − 2)2 = 37

Answers

Answer 1

Answer:

Answer:

D) (x - 3)^2 + (y - 2)^2 = 37

Step-by-step explanation:

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

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

We are given the center (3, 2), so we have h = 3, and k = 2.

The equation is now:

(x - 3)^2 + (y - 2)^2 = r^2

We need to find the radius.

The radius of a circle is the distance from the center of the circle to any point on the circle. We know the center, (3, 2), and we know a point on the circle, (9, 3). We can use the distance formula to find the distance between the center and that point which is the radius of the circle.

d = sqrt[(x2 - x1)^2 + (y2 - y1)^2]

d = sqrt[(9 - 3)^2 + (3 - 2)^1]

d = sqrt(6^2 + 1^2)

d = sqrt(37)

Now that we have the radius, we apply it to the equation of the circle.

(x - 3)^2 + (y - 2)^2 = (sqrt(37))^2

(x - 3)^2 + (y - 2)^2 = 37

Answer: D) (x - 3)^2 + (y - 2)^2 = 37

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The sales tax on a new camera is $5.60, which is 8% of the total priceWhat is the price of the camera?

Answers

The total price is 6.05 because 8 percent of 5.60 is .45 so 5.60+.45 is 6.05

Hope this helps!

8% of the total price is .45 because $6.05 is the total price and 8% of that is .45

Find the average rate of change for f(x)=x+6 over the interval [4,8]

Answers

Solve for f(x) using both 4 and 8:

f(x) = 4+6 = 10

f(x) = 8+6 = 14

Find the difference between the answers:

The difference between the two answers is 14-10 = 4

Find the difference between the interval:

The difference between 4 and 8 is: 8-4 = 4

The rate of change is the change in the answers over the difference in the interval:

The rate of change is 4/4 = 1

Answer:

The Average rate of change for f(x) = x+6 over the interval (4,8) is 1

Solution:

We define the Average rate of function f(x) over the interval (a, b) as

$(f(b)-f(a))/(b-a)$ --- eqn 1

From question, given that

f(x) =x+6 --- eqn 2

The interval is (4,8) .hence we say a = 4 and b = 8

The average rate of change for f(x) = x + 6 is given by using eqn 1

$(f(8)-f(4))/(8-4)$ --- eqn 3

Where, by using eqn 2 , we get f(8) = 8+6 =14 and f(4) = 4+6 =10

Such that the required value would be f(8)-f(4) = 14-10 = 4

By substituting the values of f(8) and f(4) in eqn 3 ,the average rate of change for the given expression is

$=(14-10)/(8-4)=(4)/(4)=1$

Hence the Average rate of change for f(x) = x+6 over the interval (4,8) is 1

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Answers

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an aquarium holds 33.75 gallons of water. it has a length of 2 feet and a height of 1.5 feet what is the width of the aquarium

Answers

The correct answer is Width = 11.25feet

What is cube?

It is a symmetrical three dimensionalshape containing 6 equal squares

How to solve the problem?

This problem can be solved by following steps
The volume of the aquarium given is 33.75 gallons
The length of the aquarium given is 2 feet
The height of the aquarium given is 1.5 feet
We need to find the width of the aquarium

As we know that aquarium is made of cube shape

So , The volume of a cube = length*width*height

Let the width be x

Therefore ,

33.75=2*x*1.5

33.75 = 3x

Therefore , x = 11.25 feet

Hence the width is 11.25 feet

Learn more about volume of cube here

brainly.com/question/1972490

#SPJ2

33.75 = 2*1.5*x
33.75 = 3x
x = 11.25 feet

The sector shows the area of a lawn that will be watered by a sprinkler. What is the area, rounded to the nearest tenth? Use 3.14 for

Answers

The area of the sector which representsthe lawn irrigated by the sprinkler is: $\mathbf{ 95.5 $ ft^2}$

Recall:

Area of sector = $(\theta)/(360) * \pi r^2$

Length of arc = $(\theta)/(360) * 2 \pi r$

Given:

$\theta = 30^(\circ)$

length of arc = 10 feet

First, find the radius using the length of arc formula.

$(\theta)/(360) * 2 \pi r$

Substitute

$10 = (30)/(360) * 2 * 3.14 * r\n\n10 = 0.52r\n\nr = (10)/(0.52) \n\nr = 19.2$

radius = 19.2 ft

Find the area of the sector:

Area of sector = $(\theta)/(360) * \pi r^2$

Substitute

$= (30)/(360) * * 3.14 * 19.2^2\n\n\mathbf{= 95.5 $ ft^2}$

The area of the sector which representsthe lawn irrigated by the sprinkler is: $\mathbf{ 95.5 $ ft^2}$

Learn more here:

brainly.com/question/14117642

Answer:

$95.5\ ft^2$

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

A circumference of the circle subtends a central angle of 360 degrees

using proportion

$(2\pi r )/(360^o)=(10)/(30^o) \n\nr=(360(10))/(2(3.14)(30))\n\nr= 19.1\ ft$

step 2

Find the area of sector

we know that

The area of the circle subtends a central angle of 360 degrees

so using proportion

Let

x ----> the area of the sector

$(\pi r^(2))/(360^o)=(x)/(30^o)\n\nx=(3.14(19.1^2)(30))/(360)\n\nx=95.5\ ft^2$

Susan's math teacher assigned x homework problems on Monday. On Tuesday, she assigned 12 more problems. Over the two days, a total of 20 homework problems were assigned. Which equation could be used to find x, the number of problems assigned on Monday?A.
x - 12 = 20
B.
20 + x = 12
C.
12x = 20
D.
x + 12 = 20

Answers

D. lets see what you know, you have 20 problems in 2 days, they did not say the amount of problems were equal on both days, so she had x amount on monday and on tuesday she had 12 more to find the total just add 12 + x = 20
hope I helped

the answer is D because you are trying to find Mondays and yoyu know tuesday and the total already.

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