Vikas is the head of student council this year at his high school in London. He is responsible for planning the annual graduation trip to Canada's Wonderland. The students will spend one full day at the park and return late that evening. The school has rented a bus for transportation. The entry fee into the park is $50 and the bus costs $600. Write an equation to relate the cost, C, in dollars to the number of student, s, who participate in this fun trip. The total cost of the trip was $2750. How many students did Vikas recruit for this trip? Vikas receives a free trip if he is able to fill 90% of the bus. The bus has a seating capacity of 46 seats. Did Vikas receive his free trip? Show your work.

Answer:

1:3

Step-by-step explanation:

both divide by 60 so do 60 divided by 60 which is one

then 180 divided by 60 which is three

this gives you the answer

Answer:

1:3

Step-by-step explanation:

a ratio is basically the same as a fraction just in a different form. so it would be 60/180 simplified. both 60 and 180 can be divided by 60. so you would divide both numbers by 60 to get 1/3. this cannot be simplified any further. then to put it as a ratio it would just be 1:3

Answer: $70 per hour

Step-by-step explanation:

Hi, to answer this question we have to calculate the hourly fee.

To do this, we simply have to divide the 5 hour fee price (350) by the number of hours worked.(5):

Mathematically speaking:

350/5 = $70 per hour

So, since the work fee is proportional, for x hours, the expression is:

70x

Feel free to ask for more if needed or if you did not understand something.

Answer:

gradient = 9

Step-by-step explanation:

Note that [tex]\frac{dy}{dx}[/tex] is a measure of the gradient.

Differentiate y using the power rule

[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex]) = na[tex]x^{n-1}[/tex]

Given

y = x² + 5x - 3, then

[tex]\frac{dy}{dx}[/tex] = 2x + 5

x = 2 : [tex]\frac{dy}{dx}[/tex] = 2(2) + 5 = 4 + 5 = 9 ← gradient

Answer:

The number of different platters Selena can create by selecting two different vegetables is 60 different platters

Step-by-step explanation:

The information given are;

The number of different sizes of salad available = 4

The number of different vegetable to choose from = 6

The number of vegetables Selena ordered = 2

The number of ways Selena can choose 2 vegetables out of 6 = ₆C₂ = 15 ways

The number of different platters (choice of vegetable and size of platter) Selena can create = The number of different sizes of salad available × The number of ways Selena can choose the vegetables

The number of different platters (choice of vegetable and size of platter) Selena can create = 4 × 15 = 60 different platters.

Answer:

Option (2)

Step-by-step explanation:

Formula to get the distance between two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] is,

d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]

The given points are A(2, 7) and B(-4, -3)

Distance between these points will be,

AB = [tex]\sqrt{(2+4)^2+(7+3)^2[/tex]

     = [tex]\sqrt{6^2+10^2}[/tex]

     = [tex]\sqrt{136}[/tex]

     = 11.66

     ≈ 11.7 units

Therefore, distance between the points A and B is 11.7 units.

Option (2) will be the answer.

Answer:

For those with the square root answer its 2\sqrt(34)

Step-by-step explanation:

Answer:

the mean for the data set is 129.3

Answer:

a(4,3).  b( 2,3). c(4,-1). d(-2,-1/2).  e(5/2, 0).

Step-by-step explanation:

Hello , I can help you with that

the mid point is given by

Let

Point 1

[tex](x_{1},y_{1})[/tex]

Point 2

[tex](x_{2},y_{2})[/tex]

the midpoint is(m)

[tex]m=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} )[/tex]

all you have to do is to put those values into the equation

Step 1

P1(3,4)  and P2(5,2)

[tex]m=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} )\\m=(\frac{3+5}{2},\frac{4+2}{2} )\\m=(\frac{8}{2},\frac{6}{2} )\\m=(4,3)[/tex]

Step 2

P1(0,6) and P2(4,0)

[tex]m=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} )\\m=(\frac{0+4}{2},\frac{6+0}{2} )\\m=(\frac{4}{2},\frac{6}{2} )\\m=(2,3)[/tex]

Step 3

P1(4,2) and P2(4,-4)

[tex]m=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} )\\m=(\frac{4+4}{2},\frac{2-4}{2} )\\m=(\frac{8}{2},\frac{-2}{2} )\\m=(4,-1)[/tex]

Step 4

P1(-1,-5) and P2(-3,4)

[tex]m=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} )\\m=(\frac{-1-3}{2},\frac{-5+4}{2} )\\m=(\frac{-4}{2},\frac{-1}{2} )\\m=(-2,\frac{-1}{2} )[/tex]

Step 5

P1(-3,2) and P2(8,-2)

[tex]m=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} )\\m=(\frac{-3+8}{2},\frac{2-2}{2} )\\m=(\frac{5}{2},\frac{0}{2} )\\m=(\frac{5}{2} ,0)[/tex]

I really hope it helps you, have a nice day

Answer:

y = 4/3x + 5

Step-by-step explanation:

if the slope is -3/4 then the perpendicular slope is 4/3

y = mx + b

9 = 4/3(3) + b

9 = 4 + b

5 = b

y = 4/3x + 5

Answer:

Step-by-step explanation:

Exponential Growth:

1). The value of a home in a growing community every year.

2). The amount of money in a saving account that earns interest annually.

Exponential decay:

1). The monthly sale of albums of a band whose popularity is declining.

2). The amount of radioactive element remaining in a sample every decade.

3). The temperature of a hot cup of coffee left on the counter every minute.

Answer:

x=1/8

y=27/8

Step-by-step explanation:

First number=x

Second number=y

x+y=4x+3

x-y=2y-10

Hey there! :)

Answer:

m∠y = 55°.

Step-by-step explanation:

Begin by solving for x since y and x are supplementary angles.

Recall that all of the angles in a triangle must sum up to 180°. Therefore:

180 - 30 - 25 = 125°.

x = 125°, therefore:

180 - 125 = 55°.

m∠y = 55°.

Answer:

55 Degrees

Step-by-step explanation:

The remote interior angle theorem states that to find the value of and exterior angle (y) you need to add the two remote interior angles. (25&30)

Answer: 80

Step-by-step explanation:

[tex]5(9+7)\\\\Parenthesis\\\\5(16)\\\\Multiply\\\\80[/tex]

Hope it helps <3

Answer:

The average speed for his journey from York to Blackpool is 61.4 KM/H

Step-by-step explanation:

Answer:

Step-by-step explanation:

We khow that the radius of our circle is 6

Let A be the area of our cercle :

A= 6^2*Pi = 36 Pi = 113.09 sq.units

We khow that the mesure of our angle ABC is Pi over 2 wich is 90 degree

So this triangle ABC is a right one .

So I think that we must khow the area of this triangle to be able to khow the area of the sector .

We have a hint : ABC is 90 degree so it is the quarter of our cercle

We need to divide the area of the circle by 4

113.09 ÷4 = 28.27

Answer:

113

28

22

Step-by-step explanation:

Answer:

-3/2

Step-by-step explanation:

Let x be the missing number

Answer: (-2,1)

Step-by-step explanation:

y=x+3  

y=2x+5  substitute  the y value in the first equation into the second equation

x+3 = 2x+5  now solve for x

   -3        -3

x = 2x +2   subtract 2x from both sides

-2x   -2x

-1x = 2       Divide both sides by -1

x= -2  

The value of x is -2 to plot it into one of the equations to solve for y.

y= -2 + 3

y = 1  

(-2,1)

Answer: x = − 2  and y = 1

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

/| y-x-3 = 0| y-(2*x)-5 = 0

We try to solve the equation: y-x-3 = 0

y-x-3 = 0 // + -x-3

y = -(-x-3)

y = x+3

We insert the solution into one of the initial equations of our system of equations

We get a system of equations:

/| x-(2*x)-5+3 = 0| y = x+3

-x-2 = 0 // + 2

-x = 2 // * -1

x = -2

We insert the solution into one of the initial equations of our system of equations

For y = x+3:  

y = 3-2

y = 1

We get a system of equations:

/| y = 1| x = -2

Answer:

The answer would be letter B. This is because the problem wants you to find the equation that is not necessarily true. In this case G'G does not equal 8 units.

Answer: y = (5)(2)x-10

Step-by-step explanation:

Answer:

39600

Step-by-step explanation:

8! - 3!(5!)

Evaluate.

40320 - 6(120)

40320 - 720

= 39600

Answer: 39600

Step-by-step explanation:

8!=40320

3!=6

5!=120

40320 - 6(120)

120*6=720

40320 - 720

= 39600

Answer:

35%

Step-by-step explanation:

He pays 525 out of 1500 dollars.

525/1500 = 7/20

= 0.35

Marlon pays in rent 35% of his earnings.

Answer:

given,

base (b) = 2.25cm

height (h) = 1.5 cm

now,

area (a) = b×h

or, a=2.25cm×1.5cm

therefore the area of parallelogram is 3.375cm^2.

hope it helps..

Answer:3.375 cm²

Step-by-step explanation:

Find the area of the following

parallelogram:

1.5 cm

2.25 cm

Solution:

(1.5×2.25)cm²

= 3.375 cm²

Hope it helps

Answer:

All compositions are affected by the order in which they are performed

Step-by-step explanation:

We have the following transformations:

-translation

-reflection

-rotation

Each of them are affected by the order in which they are performed, for example:

If we rotate we have:

(x, y) -> (y, -x).

After the reflection:

(y, -x) -> (-y, -x).

If we translated by <2, 5> and reflected through the y-axis:

After the translation, (x, y) -> (x + 2, y + 5)

In other words, all compositions are affected by the order in which they are performed

Answer:

We have 6y² + 13y - 8. We can rewrite this as 6x² + 16x - 3x - 8. Grouping terms we get 2x(3x + 8) - (3x + 8) and since both terms have the common factor of (3x + 8) the answer is (3x + 8)(2x - 1).

Answer:

A = 4, B = 3, C = 7, D = 6

Step-by-step explanation:

A = 4 because A represents the number of people who didn't visit either place. This means that B + C + D = 20 - 4 = 16. To find C, which is the overlap we can do 10 + 13 - 16 = 7 so C = 7 which means B = 10 - 7 = 3 and D = 13 - 7 = 6.

Answer:

A = 4, B = 3, C = 7, D = 6

Step-by-step explanation:

Answer: PQT and TUV

Step-by-step explanation:

Answer:

NO

Step-by-step explanation:

IMAGE

Answer:  a) 110√2 meters

                b) 2.42 hectares

Step-by-step explanation:

a) Since it is a square, the diagonal cuts the square into two 45-45-90 triangles where the diagonal is the hypotenuse.  Therefore, the sides are length x and the diagonal is length x√2.

[tex]x\sqrt2=220\\\\\\x=\dfrac{220}{\sqrt2}\\\\\\x=\dfrac{220}{\sqrt2}\bigg(\dfrac{\sqrt2}{\sqrt2}\bigg)\\\\\\x=\large\boxed{110\sqrt2}[/tex]

b) Area of a square is side squared.    10,000 meters² = 1 hectare

   [tex]A=(110\sqrt2)^2\\\\.\quad =(110)^2(\sqrt2)^2\\\\.\quad =12100(2)\\\\.\quad =24200\ \text{meters}^2\\\\.\quad =\large\boxed{2.42\ \text{hectares}}[/tex]

Answer:

y = 2x + 7

Step-by-step explanation:

Step 1: Find slope

m = (9 - 3)/(1 + 2)

m = 2

y = 2x + b

Step 2: Find b

9 = 2(1) + b

9 = 2 + b

7 = b

Step 3: Rewrite equation

y = 2x + 7

Answer:

B) y - 9 = 2(x - 1)

Step-by-step explanation:

(-2, 3) ;(1,9)

[tex]Slope =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{9-3}{1-[-2]}\\\\=\frac{6}{1+2}\\\\=\frac{6}{3}\\\\=2[/tex]

(1, 9 ) ;  m = 2

Equation: [tex]y - y_{1}=m(x - x_{1})\\\\[/tex]

y - 9 = 2(x - 1)

y - 9 = 2x -2

      y = 2x - 2 + 9

      y = 2x + 7

Answer:

x= -2

Step-by-step explanation:

1.5(2x-4)=2(4x+2)

3x-6=8x+4

-5x=10

x= -2

Answer:

First find line DE using Pythagoras theorem

That's

DE² = 7² + 24²

DE = √ 49 + 576

DE = 25

The correct trigonometric ratio for triangle DEF is

Cos(E) = 24/25

Hope this helps

Answer:

Cos(E) = 24/25

Step-by-step explanation: