The perimeter of the figure below is 54.9 in. Find the length of the missing side.
5.9 in
5.9 in
?
7-3 in
7.3 in
7.3 in
7.3 in
7.3 in
(Note: diagram is NOT to scale)

Answer:

Radius: [tex]r =\frac{\sqrt {21}}{6}[/tex]

[tex]Center = (-\frac{3}{2}, -\frac{2}{3})[/tex]

Step-by-step explanation:

Given

[tex]9x^2 + 9y^2 + 27x + 12y + 19 = 0[/tex]

Solving (a): The radius of the circle

First, we express the equation as:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

Where

[tex]r = radius[/tex]

[tex](h,k) =center[/tex]

So, we have:

[tex]9x^2 + 9y^2 + 27x + 12y + 19 = 0[/tex]

Divide through by 9

[tex]x^2 + y^2 + 3x + \frac{12}{9}y + \frac{19}{9} = 0[/tex]

Rewrite as:

[tex]x^2 + 3x + y^2+ \frac{12}{9}y =- \frac{19}{9}[/tex]

Group the expression into 2

[tex][x^2 + 3x] + [y^2+ \frac{12}{9}y] =- \frac{19}{9}[/tex]

[tex][x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}[/tex]

Next, we complete the square on each group.

For [tex][x^2 + 3x][/tex]

1: Divide the [tex]coefficient\ of\ x\ by\ 2[/tex]

2: Take the [tex]square\ of\ the\ division[/tex]

3: Add this [tex]square\ to\ both\ sides\ of\ the\ equation.[/tex]

So, we have:

[tex][x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}[/tex]

[tex][x^2 + 3x + (\frac{3}{2})^2] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2[/tex]

Factorize

[tex][x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2[/tex]

Apply the same to y

[tex][x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y +(\frac{4}{6})^2 ] =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2[/tex]

[tex][x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2[/tex]

[tex][x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ \frac{9}{4} +\frac{16}{36}[/tex]

Add the fractions

[tex][x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{-19 * 4 + 9 * 9 + 16 * 1}{36}[/tex]

[tex][x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{21}{36}[/tex]

[tex][x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{7}{12}[/tex]

[tex][x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}[/tex]

Recall that:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

By comparison:

[tex]r^2 =\frac{7}{12}[/tex]

Take square roots of both sides

[tex]r =\sqrt{\frac{7}{12}}[/tex]

Split

[tex]r =\frac{\sqrt 7}{\sqrt 12}[/tex]

Rationalize

[tex]r =\frac{\sqrt 7*\sqrt 12}{\sqrt 12*\sqrt 12}[/tex]

[tex]r =\frac{\sqrt {84}}{12}[/tex]

[tex]r =\frac{\sqrt {4*21}}{12}[/tex]

[tex]r =\frac{2\sqrt {21}}{12}[/tex]

[tex]r =\frac{\sqrt {21}}{6}[/tex]

Solving (b): The center

Recall that:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

Where

[tex]r = radius[/tex]

[tex](h,k) =center[/tex]

From:

[tex][x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}[/tex]

[tex]-h = \frac{3}{2}[/tex] and [tex]-k = \frac{2}{3}[/tex]

Solve for h and k

[tex]h = -\frac{3}{2}[/tex] and [tex]k = -\frac{2}{3}[/tex]

Hence, the center is:

[tex]Center = (-\frac{3}{2}, -\frac{2}{3})[/tex]

Answer:

Step-by-step explanation:

he volume of the topsoil is

28 ft by 21 ft by 5/15 ft = 245 cubic feet

There are 27 cubic feet in one cubic yard.

245/27 = 9.074074074.... = 9.074

Need 9.25 = 9 and 1/4 cubic yards

Answer:

1.86/2 = 0.93/2 = 0.465/2 = 0.2325

Step-by-step explanation:

Answer:

Long = 5√3

Step-by-step explanation:

Hypotenuse = 10

Short = 5

Long = ?

Apply Pythagorean theorem to find Long:

Long² = hyp² - short²

Long² = 10² - 5²

Long² = 100 - 25

Long² = 75

Long = √75

Long = √(25*3)

Long = 5√3

Answer:

D is one of them

Step-by-step explanation:

Answer:

6x-23+3m

6x+3m-27 we can't add them b/c they have d/t

variables so the answer is 6x+3m-27

Answer:

I'm think its parallel ||

Answer:

y=-2x-1

Step-by-step explanation:

Your goal from Standard form to slope intercept form is to have the x on the right side of the equal sign. All you have to do is subtract 2x from both sides and you end up with y= -2x-1

Answer:

I think it's false

Step-by-step explanation

Answer:

The 99% confidence interval for the mean consumption of meat among males over age 43 is between 2.9 pounds and 3.1 pounds.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.575\frac{1.3}{\sqrt{1384}} = 0.1[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 3 - 0.1 = 2.9 pounds

The upper end of the interval is the sample mean added to M. So it is 3 + 0.01 = 3.1 pounds

The 99% confidence interval for the mean consumption of meat among males over age 43 is between 2.9 pounds and 3.1 pounds.

Answer:

Yes.

10 > 9

Step-by-step explanation:

This inequality is true because 10 is greater than 9.

y > 2x + 7

10 > 2(1) + 7

10 > 2 +7

10 > 9

Answer:

The coordinates of point B are (-3,-3).

Step-by-step explanation:

Let [tex]A(x,y) = (6,-6)[/tex], [tex]C(x,y) = (-6,-2)[/tex] and [tex]\overrightarrow{AB} = \frac{3}{4}\cdot \overrightarrow{AC}[/tex], then we have the following formula by vectorial definition of a line segment:

[tex]\overrightarrow{AB} = \frac{3}{4}\cdot \overrightarrow{AC}[/tex]

[tex]B(x,y) -A(x,y) = \frac{3}{4}\cdot [C(x,y)-A(x,y)][/tex]

[tex]B(x,y) = \frac{3}{4}\cdot C(x,y) +\frac{1}{4}\cdot A(x,y)[/tex]

[tex]B(x,y) = \frac{3}{4}\cdot (-6,-2)+\frac{1}{4}\cdot (6,-6)[/tex]

[tex]B(x,y) = (-3, -3)[/tex]

Answer:

No, Andre is not correct.

Step-by-step explanation:

I believe Andre is not correct because each 1 on the left balances with a 1 on the right. So taking away the two 1s on the left only leaves the hanger balanced if two 1s are removed on the right. This leaves on the left and three 1s on the right, so x=3. This is like x+2=5 if you subtract 2 from the x side then you get x=3. Hope this helps!

Answer:

B

Step-by-step explanation:

Plug in 8 for y in each equation to see if it's true

6+5(8)=46

6+40=46 ✔️

Answer:

Yes.

Step-by-step explanation:

Well if the sum of the angles is equal to 180, then it's a triangle. Since [tex]52+18+110=180[/tex], a triangle with the measures 52°, 18°, and 110° is possible. Hope this helps!

Answer:

400

Step-by-step explanation:

V = a² * h/3

Plug in your values:

V = 10² * 12/3

Then solve:

100 * 4 = 400

Answer:B

Step-by-step explanation:

If d=4 and Danny has 7 more peices all you have to do is multiply. 7x4 and that equals 28

So the final answer is 28 which is choice B

Answer:

The answer to your problem is 1 5/6

Answer:

11/6

Step-by-step explanation:

First you need to get a common denomintor in order to add fractions.  Here you can multiply 6/3 by two to get 12/6.  Then you can just do 12/6-1/6 since adding a negative number is the same as subtracting, leaving you with 11/6, which cannot be reduced so that is your final answer.

Answer:

B

Step-by-step explanation:

The first probability is 10/24, and the second is 9/23. If you multiply these two fractoins you get 15/92. 15/92 is approximately equal to 16%.

the 1st, 2nd, and 3rd are correct

Answer:

-7/4

Step-by-step explanation:

Hi,

To find the slope of the line, get two points, and divide the change in y over the change in x. So, let's find two points.

(1,-3) and (-3,4)

Change in y: 4 - (-3) = 7 (Remember when you subtract a negative, you add)

Change in x: -3 - 1 = -4

7/-4 = -7/4

-7/4 is your slope.

I hope this helps :)

Answer:

it would take her 5 hours

Step-by-step explanation:

16 1/2 divided by 3.25 is 5

Brainliest plz

Answer:

18:45

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

(g o f) (-3) = g ( f(-3) )

First, let's find f(-3):

f(x)=2x²+6x+9

f(-3)=2(-3²)+6(-3)+9

f(-3)=18-18+9

f(-3)=9

Now that we know the value of f(-3), we can sub this into g(f(-3)):

g ( f(-3) ) = g(9)

Find g(9):

g(9)=3x-6

g(9)=3(9)-6

g(9)=27-6

g(9)=21

Answer:

25

Step-by-step explanation:

A = 70*M

B = 500 + 50*M

Costing the same means equal, so we have the equation:

70M = 500 + 50M

-50M           -50M

20M = 500

20M / 20 = 500 / 20

m- 25 months

Answer:

b/c

Step-by-step explanation:

Answer:

can you show the graph please?

Answer:

  7(1 +3x)

Step-by-step explanation:

The simplest monomial is a constant that is a prime number. That constant is a factor of the coefficient of the only other monomial in the expression, so it can factored from both terms.

  = 7 + 7·3x

  = 7(1 +3x)