## A student sees a newspaper ad for an apartment that has 1330 square feet (ft2 ) of floor space. how many square meters of area are there?

We know 1 meter = 3.28084 feet

So 1 square meter = 3.28084 × 3.28084 square feet.

Now to convert from square feet to square meters, we need to divide by 3.28084 × 3.28084.

The area given in the news paper advertisement is 1330 square feet.

So to convert to square meters we divide by 3.28084 × 3.28084

We get

1330 square feet =

**Hence 1330 square feet of area is equal to 123.56 square meters.**

## The angles in A triangle are such that one is 128° more than the smallest angle, while the third angle is two times as large as the smallest angle. Find the measure all three angles.

Let x degrees be the measure of the smallest angle. Then, since the 3 angles in a triangle add up to 180 degrees:-

x + x + 128 + 2x = 180

4x = 180 - 128 = 52

x = 13 degrees

The measure of the 3 angles is 13, 26 and 141 degrees (answer)

## What is half of the product of 8 1/7 and 7 4/5

First we must convert these mixed numbers to improper fractions:

So then we need the product of these two numbers. That means to multiply:

But then we need the value of half of this product. So then let's multiply by one-half:

Then we can convert this from an improper fraction to a mixed number:

And so this number is half of the product of the initial two numbers.

## PLEASE CORRECT THIS FOR ME THANKS****arrange the circles (represented by their equations in general form) in ascending order of their radius lengths.*****

Remark

I'm going to complete the square very quickly for all of these. You can fill in the missing steps.

**Top One**

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

(x - 1)^2 + (y + 1)^2 = 3

Radius = sqrt(3)

**Second One**

Divide by 4 to start with

x^2 + y^2 + 4x + 6y - 10 = 0

(x^2 + 4x + 4) + (y^2 + 6y + 9) = 10 + 4 + 9

(x + 2)^2 + (y + 3)^2 = 23

Radius = sqrt(23)

**Three**

(x^2 - 4x + 4) + (y^2 + 4y + 4) = 10 + 8

(x - 2)^2 + (y + 2)^2 = 18

Radius = sqrt(18) You would be wise not to reduce this even though the reducation is 3sqrt(2). The comparison will be easier.

**Four**

(x^2 - 8x + 16) + (y^2 - 6y + 9) = 20 + 16 + 9

(x - 4)^2 + (y - 4)^2 = 44

Radius = sqrt(44)

Again don't reduce this

**Five**

(x^2 - 12x + 36) + (y^2 - 2y + 1) = 9 + 36 + 1

(x -6)^2 + (y - 1)^2 = 46

radius = sqrt(46)

**Six**

Divide through by 5

x^2 + y^2 - 4x + 6y + 8 = 0

(x^2 - 4x + 4) + (y^2 + 6y + 9) = - 8 + 4 + 9 = 5

(x -2)^2 + (y + 3)^2 = 5

Radius = sqrt(5)

**Seven**

Divide through by 2

x^2 + y^2 - 14x - 32y - 4 = 0

(x^2 - 14x + 49) + (y^2 - 32y + 256) = 4 + 49 + 256

(x - 7)^2 + (y - 16)^2 = 309

The radius is sqrt(309)

**Comment**

The calculation order produces

One . . . . . sqrt(3)

Two . . . . . . sqrt(23)

Three . . . . .sqrt(18)

Four . . . . . .sqrt(44)

Five . . . . . .sqrt(46)

Six . . . . . . .sqrt(5)

Seven . . . . sqrt(309)

I leave the ordering part to you.

## A rectangular prism has a volume of 45 cubic inch length of a shape is 3 in what could be the width and the height of the shape

Possible combinations:

L = 3

H = 1

W = 15

L = 3

H = 2

W = 7.5

L = 3

H = 3

W = 5

L = 3

H = 4

W = 3.75

L = 3

H = 5

W = 3

L = 3

H = 6

W = 2.5

## The amount of time that American astronauts spent on space is about 13,507,804 minuets. What is the word form of that number

["Thirteen million, five hundred seven thousand, eight hundred four"]

## #18 Write the equation of the given circle. center (3, 3) radius of 2

Hello!

The center-radius form of the circle equation is written as: (x - h)² + (y - k)² = r², and in this equation, (h, k) is the center, and r is the radius. With the given values, the radius of two, and the center at (3, 3), we can find the equation of the circle.

(x - 3)² + (y - 3)² = 2²

(x -3)² + (y - 3)² = 4

Therefore, the equation of this circle is **(x - 3)² + (y - 3)² = 4**.

## Find the area of the composite figure

Look at the picture.

The area of the trapezoid:

The area of the rectangle:

The area of figure:

## #10 Write the equation of the given circle. center (-2, -2) radius of 6

h = -2

k = -2

r = 6

(x - (-2))^2 + (y - (-2))^2 = 6^2

(x + 2)^2 + (y + 2)^2 = 6^2

(x + 2)^2 + (y + 2)^2 = 36. your answer

hope this helped, blessings! :)

## 1. The beginning steps for determining the center and radius of a circle using the completing the square method are shown below: Step 1 [original equation]: x2 − 6x + y2 − 4y = 3 Step 2 [group like terms]: (x2 − 6x) + (y2 − 4y) = 3 Step 3 [complete the quadratics]: Which of the following is the correct equation for Step 3? (x2 − 6x + 6) + (y2 − 4y + 4) = 4 + (6 + 4) (x2 − 6x − 3) + (y2 − 4y − 2) = 4 + (−3 − 2) (x2 − 6x + 3) + (y2 − 4y + 2) = 4 + (3 + 2) (x2 − 6x + 9) + (y2 − 4y + 4) = 3 + (9 + 4) 2. Using the following equation, find the center and radius of the circle by completing the square. x2 + y2 + 6x − 6y + 2 = 0 center: (−3, 3), r = 4 center: (3, −3) r = 4 center: (3, −3), r = 16 center: (−3, 3), r = 16 3. The beginning steps for determining the center and radius of a circle using the completing the square method are shown below: Step 1 [original equation]: x2 + 8x + y2 − 6y = 11 Step 2 [group like terms]: (x2 + 8x) + (y2 − 6y) = 11 Step 3 [complete the quadratics]: (x2 + 8x + 16) + (y2 − 6y + 9) = 11 + (16 + 9) Step 4 [simplify the equation]: (x2 + 8x + 16) + (y2 − 6y + 9) = 36 Step 5 [factor each quadratic]: Which of the following is the correct equation for Step 5? (x + 4)2 + (y − 3)2 = 62 (x + 8)2 + (y − 6)2 = 62 (x − 4)2 + (y + 3)2 = 62 (x + 16)2 + (y + 9)2 = 62

**Answer : **

**Center is (-3,3) and radius = 4**

(1) Step 1:

Step 2:

In completing the square method we take coefficient of x and divide by 2 and the square it . Then add it on both sides

The coefficient of x is -6. = (-3)^2 = 9

The coefficient of y is -4. = (-2)^2 = 4

Step :

**(2)**

To find center and radius we write the equation in the form of

using completing the square form

Where (h,k) is the center and 'r' is the radius

In completing the square method we take coefficient of x and divide by 2 and the square it . Then add it on both sides

Here h= -3 and k=3 and so r= 4

**Center is (-3,3) and radius = 4**

(c) Step 1:

Step 2:

Step 3:

Step 4:

We factor out each quadratic

(x^2 + 8x + 16) = (x+4)(x+4) =

((y^2 - 6y + 9)) = (x-3)(x-3) =

**Step 5 :**