the equation of a line β is 2x-3y=6
find the gradient of β

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!

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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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:

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:

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:

-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:

5.14

Step-by-step explanation

6/x = 42/36

42x= 216

x= 5.14

Answer:

1,607  volume

Step-by-step explanation:

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:

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:

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

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:

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: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:

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:

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:

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: 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:

-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: 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.

learn more about mathematics here

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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:

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:

  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:

B :)

Step-by-step explanation:

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!

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:

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:

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

Answer:

40

Step-by-step explanation:

add 21 + 20

hope this helps :)