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4.
The equation of the circle C is[tex] {x}^{2} + {y}^{2} - 6x + ky - 108 = 0[/tex]
where k is a constant. If the area of C is
[tex]121\pi [/tex]
find the centre of C
​

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:

False, since x values cannot have more than one y value.

Step-by-step explanation:

Because if you were to plot the points on a graph, and do the vertical line test, there will be points that cross one another making it not a function.

Hope I Helped

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:

  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:

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

Answer:

Step-by-step explanation:

(a+1)+(b-2)i=6+7i

⇔

a + 1 = 6

and

b - 2 = 7

⇔

a = 5

and

b = 9

Answer: 14

Step-by-step explanation:

The number of fraternity members taking physics but not mathematics is 27, calculated using inclusion-exclusion principle: 18 members take math, 5 take both math and physics, and 8 take neither.

Let's use the principle of inclusion-exclusion to solve this problem.

Total fraternity members (n) = 40

Members taking mathematics (M) = 18

Members taking both mathematics and physics (B) = 5

Members taking neither mathematics nor physics (N) = 8

To find the number of members taking physics but not mathematics (P).

We can start by using the formula for the number of elements in the union of two sets:

n(M ∪ P) = n(M) + n(P) - n(B)

Since the total members are 40, the equation becomes:

18 + n(P) - 5 = 40

Solving for n(P):

n(P) = 40 - 18 + 5

n(P) = 27

Therefore, 27 members take physics but not mathematics.

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Answer:

5.14

Step-by-step explanation

6/x = 42/36

42x= 216

x= 5.14

Answer:Let x be the number of miles driven on 60 gallons of gas. By setting up and solving a proportion involving x, find the value of x for the car that you have chosen. State the type of car, the mileage, and show both the set up of the proportion and the steps

Step-by-step explanation:

Answer:

147 miles

Step-by-step explanation:

Let x be the number of miles travelled on 7 gallons, then proportion is of the form

[tex]\frac{miles}{gallons}[/tex], thus

[tex]\frac{63}{3}[/tex] = [tex]\frac{x}{7}[/tex] ( cross- multiply )

3x = 63 × 7 = 441 ( divide both sides by 3 )

x = 147

Thus the car can travel 147 miles on 7 gallons

The calculated length of the arc MPN is 79/9π units

Finding the length of arc MPN

From the question, we have the following parameters that can be used in our computation:

Central angle = 360 - 44 = 316 degrees

Radius = 5 units

Using the above as a guide, we have the following:

arc MPN = central angle/180 * π * Radius

Substitute the known values in the above equation, so, we have the following representation

arc MPN = 316/180 * π * 5

Evaluate

arc MPN = 79/9π

Hence, the length of the arc is 79/9π units

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.

Area of the square = side x side = side ^2

therefore to find a length of one side = Square root of the 441

sqrt of 441 = 21 cm

so the perimeter of a square is 21 x 4 = 84 cm

Answer:

1/4

Step-by-step explanation:

9 Chocolate cupcakes, 9/12

3 Cupcakes are the remaining cupcakes, over 12 it's 3/12

Then Simplify, 3/12

by dividing

3 divided by 3 equals 1

12 divided by 3 equals 4

then use the simplified version 1/4

To check:

add 3/12 + 9/12

and it equals all 12 cupcakes

Final answer:

There are 3 cupcakes with vanilla frosting out of 12 total, resulting in the fraction 3/12, which simplifies to 1/4 for the cupcakes with vanilla frosting.

Explanation:

The student's question is asking us to find what fraction of the cupcakes have vanilla frosting. Mindy buys 12 cupcakes in total and 9 of them have chocolate frosting. To find how many have vanilla frosting, we subtract the chocolate frosted cupcakes from the total:

12 cupcakes - 9 chocolate frosted cupcakes = 3 vanilla frosted cupcakes

To express this as a fraction, we take the number of vanilla frosted cupcakes (which is 3) over the total number of cupcakes (which is 12).

Therefore, the fraction of cupcakes that have vanilla frosting is 3/12, which can be simplified to 1/4.

Answer:

3/10 probability as it is the same as getting 2gm +1rm =3m

Step-by-step explanation:

You add up the numbers 7+2+1=10m

The cost of each raffle ticket was $5.

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

Now it is given that,

Amount donated by Aldon = $40

Number of tickets sold by Aldon = 12

Amount denoted by Jamal = $25

Number of tickets sold by Jamal = 15

Let x be the cost of each raffle ticket.

So, Cost of tickets sold by Aldon = 12x

Cost of tickets sold by Jamal = 15x

So, Total amount raised by Aldon = 12x + 40

Total amount raised by Jamal = 15x + 25

∵ Aldon and Jamal raised the same amount of money for the school fundraiser

⇒ 12x + 40 = 15x + 25

Taking aliketerms together we get,

15x - 12x = 40 - 25

⇒ 3x = 15

Dividing both side by 3 we get,

x = $5

which is the required cost of each raffle ticket.

Thus, the cost of each raffle ticket was $5.

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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

Answer:

B :)

Step-by-step explanation:

Answer: B, [tex]\sqrt{\frac{1}{6} }[/tex]

Step-by-step explanation:

Using half-angle identities

Using half angle identities, we know that

[tex]sin\frac{x}{2} = +/- \sqrt{\frac{1-cosx}{2} }[/tex]

Plug in 2/3 for cosx

[tex]sin\frac{x}{2} = +/- \sqrt{\frac{1-2/3}{2} }[/tex]

[tex]sin\frac{x}{2} = +/- \sqrt{\frac{1/3}{2} }[/tex]

[tex]sin\frac{x}{2} = +/- \sqrt{\frac{1}{6} }[/tex]

Determining sign

Since the angle x is in quadrant 4 from 270 to 360 degrees, if we divide the angle by 2, the angle x should be somewhere from 135 to 180 degrees, which would all fall in quadrant 2

all sin values in quadrant 2 are positive

Final answer

[tex]sinx = \sqrt{\frac{1}{6} }[/tex]

If cos x=2/3 and x is in quadrant 4 then value of sin x/2 is  -√(1/6), option C is correct.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

To find sin(x/2), we can use the half-angle formula for sine:

sin(x/2) = ±√[(1 - cos x)/2]

Since x is in quadrant 4, cosine is positive and sine is negative. We are given that cos x = 2/3

so we can substitute this value into the formula:

sin(x/2) = -√[(1 - 2/3)/2]

sin(x/2) = -√(1/6)

Hence, if cos x=2/3 and x is in quadrant 4 then sin x/2 is  -√(1/6)

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Answer:

A) y= -8/5x -3

Step-by-step explanation:

This is your current equation: y= -8/5x + b. I would plug in your point to the equation. It should look like this: 5= -8/5(-5)+b. Multiply -8/5 by -5 to get 8. This is what you should have: 5=8+b. Subtract 8 from both sides to get -3=b. So, this is your final answer: y= -8/5x -3. So, A is the correct answer. Hope this helped!

Answer:

4t^2-32t+64=4(t^2-8x+16)

Step-by-step explanation:

f(x)=4x^2-8x+4

f(t-3)=4(t-3)^2 - 8(t-3)+4=

4(t^2-2*t*3+9)-8t+24+4=

4(t^2-6t+9)-8t+28=

4t^2-24t+36-8t+28=

4t^2-32t+64=4(t^2-8x+16)

Answer:

87/4

Step-by-step explanation:

Step 1:  Convert 21 3/4 into an improper fraction

21 3/4 is same as 21 * 4/4 + 3/4

21 * 4/4 = 84/4

Step 2:  Add them up

84/4 + 3/4

87/4

Answer:  87/4

Answer: 87/4

Step-by-step explanation:

Multiply:

21*4=84

Add:

84+3=87

Your answer should be: 87/4

The denominator stays the same

Answer:

-6/7

Step-by-step explanation:

So the question basically is asking, 6x7/15+x=8/7 so find the value of X.

We multiply 7/15 by six because the question says 6 7/15 and we multiply 8 by 1/7 to get 8/7. Hope that was useful!

Answer:

164 adult tickets

Step-by-step explanation:

164×3 = 492 tickets

Really hope this helped! :)

Final answer:

A total of 123 adult tickets were sold for the school play, with the total number of tickets sold being 492 and student tickets being three times the number of adult tickets.

Explanation:

To solve the problem of how many adult tickets were sold at the school play when a total of 492 tickets were sold and the number of student tickets was three times the number of adult tickets, we set up a system of equations. Let A be the number of adult tickets and S be the number of student tickets sold.

Steps to solve this question:

The total number of tickets sold was 492: A + S = 492

The number of student tickets was three times the number of adult tickets: S = 3A

We can substitute the second equation into the first to find the number of adult tickets:

A + 3A = 492

4A = 492

A = 492 / 4

A = 123

Therefore, 123 adult tickets were sold for the school play.

Answer:

12

Step-by-step explanation:

Percent means out of 100

We have 3/25

Multiply the top and bottom by 4

12/100

The percent is 12

Final answer:

Based on the estimate provided, 12% of men are left-handed, which is calculated by dividing 3 by 25 and then multiplying the result by 100.

Explanation:

To calculate the percentage of men who are left-handed based on the estimate that 3 out of every 25 men are left-handed, you can use the following steps:

Therefore, based on the given estimate, 12% of men are left-handed.

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:

the square root of -25 is 5i

Answer:

5i

Step-by-step explanation

All negative roots have i, which is an imaginary number.

i^2=-1.

Following this, the square root of -25 is 5i.

To double check:

5i*5i=5*5*i*i

25*-1=-25

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: 5 units

Step-by-step explanation:

Answer:

40 Miles Per Hour

Step-by-step explanation:

If this is traveling 100 Miles in 2.5 hours...

100/2.5 = 40

You would have to go 40 Miles Per Hour.

Answer:40

Step-by-step explanation: