Determine the center and radius of the following circle equation:

22 + y2 – 10x + 18y + 42 = 0

Answer:

26 gallons of juice

Step-by-step explanation:

156/12 = 13

13x2=26

Answer: 26 gallons

Step-by-step explanation:

2 gallons for every 12 people so you want to do 156 divided by 12 which would be 13. That shows that there are 13 times more people than there were before. You would then multiply 2 by 13 which would give you 26 gallons of juice.

Answer:

The right answer is, -420

Step-by-step explanation:

Because we use common factor:

60 (x - 15)

We multiply for each term:

60 (x) - 60 (15)

60 (8) - 60 (15)

We solve:

480 - 900 = -420

Answer:13.9

Step-by-step explanation:

Using the compound interest formula, it will take approximately 14.9 years for an account with a $3,200 initial deposit and an 8.25% annual interest rate to grow to $9,600.

To find out how long it will take for an account with an initial value of $3,200 and an annual interest rate of 8.25% to grow to $9,600, we can use the future value formula for compound interest:

The formula is FV = PV (1 + r)^n, where:

To find n when FV is $9,600, we rearrange our formula to solve for n:

n = log(FV / PV) / log(1 + r)

Now, plug in the values:

n = log(9600 / 3200) / log(1 + 0.0825)
n = log(3) / log(1.0825)
n ≈ 14.9 years

So, it will take approximately 14.9 years for the account value to reach $9,600.

Answer: D

Step-by-step explanation: yes, because with each simulation, as the number of trials increase, the experimental probability gets closer and closer to the theoretical probability of

1/4.

The answer is D

Step-by-step explanation:

because with each simulation, as the number of trials increase, the experimental probability gets closer and closer to the theoretical probability of

1

4

. The law of large numbers indicates that if an event of probability p is observed repeatedly during independent repetitions, the ratio of the observed frequency of that event to the total number of repetitions approaches p as the number of repetitions becomes arbitrarily large.

Answer:

y = 6x − 11

Step-by-step explanation:

x = t + (1/t), y = t² + (1/t²)

If we square x:

x² = t² + 2 + (1/t²)

x² = y + 2

When x = 3, y = 7.

Taking derivative with respect to time:

2x = dy/dx

dy/dx = 6

So the equation of the tangent line is:

y − 7 = 6 (x − 3)

y − 7 = 6x − 18

y = 6x − 11

Answer:

55m

Step-by-step explanation:

a²+b²=c²

19 x 19 = 361

52 x 52 = 2704

2704 + 361= 3065

the square root of 3065 is 55.4 so round that to 55.

Step-by-step explanation:

[tex]y = 6x[/tex]

[tex]2x + 3y = -20[/tex]

To solve this system of equations, let's multiply the first equation by [tex]-3[/tex] to get a [tex]3y[/tex] term in each equation:

[tex]-3y = -18x[/tex]

Now, let's add the two equations together:

[tex](2x + 3y) + (-3y) = -20 + (-18x)[/tex]

[tex]2x = -20 - 18x[/tex]

[tex]20x = -20[/tex]

[tex]x = -1[/tex]

Now, we can plug in this value of [tex]x[/tex] into either equation to solve for [tex]y[/tex]:

[tex]y = 6x[/tex]

[tex]y = 6(-1)[/tex]

[tex]y = -6[/tex]

or

[tex]2x + 3y = -20[/tex]

[tex]2(-1) + 3y = -20[/tex]

[tex]-2 + 3y = -20[/tex]

[tex]3y = -18[/tex]

[tex]y = -6[/tex]

Therefore, the solution to this system of equations is [tex](-1, -6)[/tex].

Answer:

x = -1

y = -6

Step-by-step explanation:

y = 6x

2x + 3y = -20

Substitute the first expression into the second one

We have

2x + 3y = -20

2x + 3(6x) = -20

2x + 18x = -20

20x = -20

Divide both sides by 20 to isolate x

20x/20 = -20/20

x = -1

Remember the first expression

y = 6x

Therefore

y = 6(-1)

y = 6 x -1

y = -6

Check

2(-1) + 3(-6) = -20

-2 + -18 = -20

-2 - 18 = -20

-20 = -20

So our answer is correct

Answer:

-0.125

Step-by-step explanation:

To find the decimal version of the fraction, divide using a calculator or long division.

-1 / 8 = -0.125

Best of Luck!

Question 1: Option B: [tex]\frac{10}{14}=\frac{5}{7}[/tex]

Question 2: Option C: [tex]\frac{12}{18}=\frac{4}{6}[/tex]

Solution:

Question 1:

Given ratio is [tex]\frac{10}{14}[/tex].

To find the equivalent ratio of [tex]\frac{10}{14}[/tex].

10 and 14 have the common factor 2.

So divide both numerator and denominator by the common factor 2.

[tex]$\frac{10}{14}=\frac{10\div2}{14\div 2}[/tex]

    [tex]$=\frac{5}{7}[/tex]

[tex]$\frac{10}{14}=\frac{5}{7}[/tex]

Hence option B is the correct answer.

Question 2:

Given ratio is [tex]\frac{10}{14}[/tex].

To find the equivalent ratio of [tex]\frac{12}{18}[/tex].

12 and 18 have the common factor 3.

So divide both numerator and denominator by the common factor 3.

[tex]$\frac{12}{18}=\frac{12\div3}{18\div 3}[/tex]

    [tex]$=\frac{4}{6}[/tex]

[tex]$\frac{12}{18}=\frac{4}{6}[/tex]

Hence option C is the correct answer.

Answer:

Eli has to run for 2.25 minutes at this pace to win the bet.

Step-by-step explanation:

At his last track meet, Eli ran the 400-meter dash in 54 seconds.

So, the speed of Eli's run is [tex]\frac{400}{54} \times 60 = 444.44[/tex] meters per minute.

Now, if Eli is determined to run a whole kilometer with the same speed, then it will take Eli to run 1 kilometer within [tex]\frac{1000}{444.44} = 2.25[/tex] minutes.

Hence, Eli has to run for 2.25 minutes at this pace to win the bet. (Answer)

Answer:

18

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

The volume of the lid is approximately 113.8 cubic inches.

The volume of the lid can be found by multiplying the area of the triangular base by the height of the lid. The area of a triangle can be found by using the formula: Area = (base x height) / 2. In this case, the base is 6 1/2 inches and the height is 3 1/2 inches. Plugging these values into the formula, we get: Area = (6.5 x 3.5) / 2 = 11.375 square inches. Now, to find the volume of the lid, we multiply the area by the height: Volume = 11.375 x 10 = 113.75 cubic inches. Rounding to the nearest tenth, the volume of the lid is 113.8 cubic inches.

The volume of the lid is 113.8 cubic inches.

To determine the volume of the lid of the jewelry box, we need to use the formula for the volume of a triangular prism, which is V = (1/2 * base * height of triangular base) * height of the prism.

First, calculate the area of the triangular base:

Next, multiply the area of the triangular base by the height of the prism:

Therefore, the volume of the lid to the nearest tenth is 113.8 cubic inches.

Answer:

x = 10

Step-by-step explanation:

3x + 55 = 9x - 5  (add 5 to both sides)

3x + 55 + 5 = 9x - 5 + 5

3x + 60 = 9x  (subtract 3x from both sides)

60 = 9x - 3x

60 = 6x (rearrange)

6x = 60   (divide both sides by 6)

x = 60/6

x = 10

Answer:

x=10

Step-by-step explanation:

[tex]\mathrm{Subtract\:}55\mathrm{\:from\:both\:sides}\\3x+55-55=9x-5-55[/tex]

[tex]\mathrm{Simplify}\\3x=9x-60[/tex]

[tex]\mathrm{Subtract\:}9x\mathrm{\:from\:both\:sides}\\3x-9x=9x-60-9x[/tex]

[tex]\mathrm{Simplify\:}again\\-6x=-60[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-6\\\frac{-6x}{-6}=\frac{-60}{-6}[/tex]

[tex]\mathrm{\:Simplify\:one\:more\:time}\\x=10[/tex]

I hope this helps you out!

Have a wonderful afternoon!

Answer:

B :)

Step-by-step explanation:

Answer:

5.14

Step-by-step explanation

6/x = 42/36

42x= 216

x= 5.14

Answer:

1,607  volume

Step-by-step explanation:

Answer:

  6

Step-by-step explanation:

The center of the circle is the midpoint of the diameter. The midpoint can be found by averaging the coordinates of the end points:

  ((-4, 2) +(12, 10))/2 = ((-4+12)/2, (2+10)/2) = (4, 6)

The y-coordinate of the center is 6.

The center of the circle has a y-coordinate of 6, determined by averaging the y-coordinates (2+10)/2 of the diameter's endpoints (-4,2) and (12,10).

The y-coordinate for the center of a circle can be determined by finding the midpoint of the y-coordinates of the diameter's endpoints. Given the endpoints (-4,2) and (12,10), the midpoint can be found by averaging the y-coordinates: (2 + 10) / 2 = 12 / 2 = 6. Therefore, the y-coordinate of the center of the circle is 6.

Answer:

The distance between (-4, 3) and (4, 3) is 8

Step-by-step explanation:

Distance formula:  [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2)}[/tex]

Distance:  [tex]\sqrt{(4 - (-4)^2 + (3 - 3)^2}[/tex]

Distance:  [tex]\sqrt{(4 + 4)^2 + (0)^2}[/tex]

Distance:  [tex]\sqrt{8^2} \\[/tex]

Distance:  8

Answer:  The distance between (-4, 3) and (4, 3) is 8

The app uses 2^28 bytes.

Step-by-step explanation:

⇒ 4^4 × 2^20 = (2²)^4 × 2^20 = 2^8 × 2^20

                       = 2^8+20

                       = 2^28 bytes (using the law of exponents a^m × a^n = a^m+n)

A.12 grapes, 23 plums

Step-by-step explanation:

1. solve all the equations by multiplying each number by how much each item is worth

2. A: 290 =(12× 5)+(10×23)

B: 100 =(10×5)+(5×10)

C:125 =(5×5)+(10×10)

D:235 =(23×5)+(12×10)

Answer:  8^3,  Eight to the third power,  Eight times eight times eight.

To calculate the volume of a cube with a side length of 8 inches, you write the calculation in exponential form as V = 8^3, which is read as '8 cubed' or '8 to the third power', resulting in a volume of 512 cubic inches.

To calculate the volume of a cube using a side length of 8 inches, you can write the calculation in exponential form as V = 8^3. This represents the volume (V) as the length of a side of the cube (8 inches) raised to the power of 3. In exponential form, 8^3 is 8 cubed or 8 to the third power, both of which mean 8 multiplied by itself twice more (8 x 8 x 8).

Therefore, the volume of the cube would be 512 cubic inches because 8 x 8 x 8 equals 512.

Answer:

Step-by-step explanation:

We need to analyze the surface

Look at the L shape, it has a mirror image at the back, which is symmetrical to the front side

Then,

area of rectangle = length × breadth

The L shape can be divided into two plane shape

1. A rectangle of length 10in and breadth 6in,

Then, A=l×b=10×6 = 60in²

2. To a square of side a=4in

Then, A=s²=4²=16in²

Then, the total area of one side of the L shape is

A=60+16=76in²

Also, the total area of the two L shape is =2×76

A=152in²

Then, let look at the back side of the solid and the front side, they are also symmetrical.

It forms a rectangle of length 10in and breadth 6in

Then, A= l×b=10×6=60in²

Area of the two sides is =60×2

A=120in²

The total are of the front and back side is 120in²

A=120in²

Let take a look at the top and bottom, they are also symmetrical and has a dimension of length 10in and breadth 6in

Then, A=l×b=10×6=60in²

So, total area =2×60 =120in²

The total area of the shape is the total area of top+ total are of the sides + total area of the L shape

Total area=152+120+120=392in²

A(total)=392in²

Then, the total area of the solid shape is 392in²

The first option is correct

Answer:

40

Step-by-step explanation:

add 21 + 20

hope this helps :)

Answer:

-12

Step-by-step explanation:

we know that

(fºg)(x)=f(g(x))

To find out the composite function f(g(x)) substitute the variable x in the function f(x) by the function g(x)

we have

[tex]f(x)=-3x-9[/tex]

[tex]g(x)=x+7[/tex]

so

[tex]f(g(x))=-3(x+7)-9[/tex]

For x=-6

substitute

[tex]f(g(-6))=-3(-6+7)-9[/tex]

[tex]f(g(-6))=-3(1)-9[/tex]

[tex]f(g(-6))=-12[/tex]

Answer:

I believe it would be true

Answer:

17. 50

18. 150

19. 240

20. 20

21. 60

22. 240

23. 150

24. -240

25. 222

26. 75

27. 300

28. 340

29. 175

30. 265

31. 298

32. 118

Step-by-step explanation:

How you find co-terminal is by adding or subtracting 360 degrees to the value you are given.

If it is a positive number like #18. all you do is subtract 510 - 360 = 150 until you get to a value between 0 degrees and 360 degrees.

The same thing applies to negative numbers. Like #21. You will add 360 + (-660) until you get to a number between 0 degrees and 360 degrees.

-660 + 360 = -300 (this is not a value in between 0 and 360 so we must add 360 again)

-300 + 360 = 60 (this is a value in between 0 and 360) (this is the co-terminal angle)

That is the idea of finding co-terminal angles.

Answer:

2/3

Step-by-step explanation:

Rewrite the equation into the form of y=mx+c

m is the gradient of the line.

2x-3y=6

3y= 2x-6 (bring y terms to one side, the rest to the other)

y= 2/3x -2 (÷3 throughout)

Thus the gradient is 2/3.

IS THERE AN OPTION TO SAY THEY ARE EQUAL IF THERE IS THEN THAT IS THE ANSWER :}

Answer:

Option A, V = π(7)^2h

Step-by-step explanation:

The formula for the volume of a cylinder:  V = πr^2h

Step 1:  Since the give us diameter we need to find radius

radius = diameter/2

radius = 14/2

radius = 7

Answer:  Option A, V = π(7)^2h

Answer:

A

Step-by-step explanation:

Volume of a cylinder = pi r2 h

Where pi = 3.14

Radius r = diameter/2

Diameter given is 14,

So radius = 24/2 = 7

Height h

Volume = pi(7)^2 h

Answer:

6.4cm

Step-by-step explanation:

The radius of a circle with a diameter of 12.8 cm is 6.4 cm.

The diameter of a circle is twice the length of its radius, so to find the radius of a circle given its diameter, you simply divide the diameter by 2.

In this case, the diameter is 12.8 cm, so the radius would be 12.8 cm / 2 = 6.4 cm.

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