8. A school raffle sold 480 tickets. Students were charged $1/ticket and teachers $5/ticket. The total receipts were $560. How many of each ticket were sold? 9. An airplane travels 5432 km. On the outward trip it took 7 hours with the wind. On the return trip, it took 8 hours against the wind. What was the speed of the plane and the speed of the wind? (Remember: distance = speed x time)

Answers

Answer 1

Answer:

8. Number of student tickets = 460

Number of teacher tickets = 100

9. Speed of plane = 727.5 km/hr

Speed of wind = 48.5 km/hr

Step-by-step explanation:

8.

Let number of students' tickets = [tex]x[/tex]

Let number of teachers' tickets = [tex]y[/tex]

Total number of tickets = 480

[tex]x+y=480[/tex] ...... (1)

Price for one student's ticket = $1

Price for one teacher's ticket = $5

Total money collected by the tickets = $560

[tex]x +5y = 560[/tex] ...... (2)

Subtracting (1) from (2):

[tex]4y = 80\\\Rightarrow y = 20[/tex]

By equation (1):

[tex]x = 460[/tex]

Number of student tickets = 460

Number of teacher tickets = 100

9.

Let the speed of airplane in still air = [tex]u[/tex] km/hr

Let the speed of air = [tex]v[/tex] km/hr

Total distance = 5432 km

Time taken with the wind = 7 hours.

Speed with the wind = [tex]u+v[/tex] km/h

Time taken against the wind = 8 hours.

Speed with the wind = [tex]u-v[/tex] km/h

Using the formula:

Distance = Speed [tex]\times[/tex] Time

[tex]5432 = (u+v)\times 7\\\Rightarrow u +v = 776 .... (1)[/tex]

[tex]5432 = (u-v)\times 8\\\Rightarrow u - v = 679 .... (2)[/tex]

Adding (1) and (2):

[tex]2u = 1455\\\Rightarrow u = 727.5\ km/hr[/tex]

By equation (1):

[tex]v = 48.5\ km/hr[/tex]

Speed of plane = 727.5 km/hr

Speed of wind = 48.5 km/hr


Related Questions

New grass seeds grow rapidly. A grass seed has grown to 12 millimeters tall. Tomorrow it will
be 23 millimeters tall, the next day it will be 34 millimeters tall, and on the next day it will be
45 millimeters tall. Write a rule to represent the height of the bean plant as an arithmetic
sequence. How tall will the plant be in 15 days?

A(n) = 16 + (n – 1)11; 194 millimeters
A(n) = 12 + (n – 1)11; 166 millimeters
A(n) = 13n; 195 millimeters
A(n) = 12n; 180 millimeters

Answers

Answer:

The correct answer is;

A(n) = 12 + (n-1)11; 166 millimeters

Step-by-step explanation:

Here, we want to write a rule representing the growth

From the question, we can see that the rate of growth is ;

34-23 = 23-12 = 11

This means it grows at a rate of 11 mm per day

So on the 15th day, its height will be;

We can have an arithmetic progression here, with 12 as the first term and 11 as the common difference

The nth term An can be represented as;

An = a + (n-1)d

where a = 12 mm , n = 15 and d = 11 mm

Thus, we have

An = 12 + (15-1)11

An = 12 + 154

An = 166 mm

Please answer this question.

Answers

Answer:

C) 78

Step-by-step explanation:

its technically 77.5714... but rounds to 78, hope that helps

Answer:

It is 78 because when placed in numerical order it is in the middle

Does anyone know how to do this?

Answers

Answer:

y= Ix-3I    (that says absolute value btw)

Step-by-step explanation:

Answer:  y = |x-3|

This is the result of starting with y = |x|, then shifting it three units to the right. Replacing x with x-3 moves the xy axis three units to the left, giving the illusion the V shaped curve moved 3 spots to the right.

We don't shift up or down since the vertex is on the x axis.

We also don't vertically compress or stretch the graph either.

Side note: the vertex for this graph is (3,0) which is the lowest point of the curve.

*EASY* Solve with steps! *WILL MARK BRAINLIEST*

Answers

Answer:

OK I will If u need any math help just ask me!!

Step-by-step explanation:

Have a wonderful day!!!

Answer:

i can help you with math i have an A+ currently and i would love yo help you. have a good day!

Which reason is missing in step 2?
CPCTC
definition of supplementary angles
triangle parts relationship theorem
O triangle angle sum theorem

Answers

ΔHKJ and ΔLNP are similar triangle due to equal pair of corresponding angles .

What are Similar Triangles?

Similar triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.

Given,

m∠H = 30°

m∠J=50°

m∠P=50°

m∠N=100°

In triangle ΔHKJ

m∠H = 30°

m∠J=50°

m∠K= 180°- (m∠H+m∠J) = 180°-(30°+50°)

m∠K= 100°

In ΔHKJ and ΔLNP,

m∠J = m∠P= 50°

m∠K= m∠N= 100°

According to Angle-Angle (AA) rule, two triangles are said to be similar if two angles in one particular triangle are equal to two angles of another triangle.

Thus, ΔHKJ and ΔLNP are similar triangle due to equal pair of corresponding angles.

Hence, ΔHKJ ~ ΔLNP

learn more about similar triangle

https://brainly.com/question/25882965

Find the measure of each acute angle.

(3x + 2)∘ = and x∘ =

Answers

Answer:

The measure of one of the acute angles is 22 degrees, and the measure of the other acute angle is 68 degrees.

Step-by-step explanation:

The angles of a triangle add up to 180 degrees; we know this by the Sum of Angles of a Triangle Theorem.

Then one angle is marked as a right angle meaning it has a measure of 90 degrees.

Using this information and the labels on the diagram we can set up an equation:

x+3x+2+90=180

Now we can solve for x.

4x+92=180

4x=88

x=22 degrees

The measure of one of the acute angles is 22 degrees.

Now to solve for the measure of the other acute angle.

Subsitute the value of x first.

x=22

(3x+2)=?

3*22+2=68 degrees

The measure of the other acute angle is 68 degrees.

In the right-angled triangle given, the measure of each of the acute angles in the given diagram are:

[tex]\mathbf{22^{\circ}}\\\\\mathbf{68^{\circ}}[/tex]

The triangle given is a right triangle having an angle tat is 90 degrees and two other acute angles given as: x and (3x + 2)

Thus:

[tex]x + (3x + 2) + 90 = 180^{\circ}[/tex] (sum of triangle)

Solve for the value of x

[tex]x + 3x + 2 + 90 = 180[/tex]

Add like terms

[tex]4x + 92 = 180\\\\[/tex]

Subtract 92 from each side

[tex]4x = 180 - 92\\\\4x =88[/tex]

Divide both sides by 4

x = 22

Measure of one of the acute angles is 22 degrees.

To find the second acute angle measure, substitute the value of x

3x + 2 = 3(22) + 2 = 68 degrees

Therefore, in the right-angled triangle given, the measure of each of the acute angles in the given diagram are:

[tex]\mathbf{22^{\circ}}\\\\\mathbf{68^{\circ}}[/tex]

Learn more here:

https://brainly.com/question/347922

In a sale the price of a sofa is reduced by 70%. The price is £255 Work out the price before the sale

Answers

Answer:

850

Step-by-step explanation:

850*0.3=255

ok so tomorrow i have exams omg haha im so scareddd!!!!!

Answers

hopefully yu pass !

Answer:

Best of luck! I hope your exam goes well!!!

What function equation is represented by the graph?
f(x)=−4x−3
f(x)=1/4x−3
f(x)=−1/4x−3
f(x)=1/4x+3

Answers

Answer:

f(x)=1/4x-3

Step-by-step explanation:

y=mx+b

y-intercept is -3

-3=b

rise over round to find the slope

up 1 over 4

m=1/4

Three ballet dancers are positioned on stage. Greta is straight behind Bryan and directly left of Alice. If Bryan and Greta are 12 meters apart, and Alice and Bryan are 13 meters apart, what is the distance between Greta and Alice?

Answers

Answer:

12

Step-by-step explanation:

helpmepleasethankyou:)

Answers

Answer:

Step-by-step explanation:

If we take 1 cup of Original purple paint,

Ratio of blue and red paint = 2 : 3

Quantity of blue paint in 1 cup of the mixture = [tex]\frac{2\times (1)}{(2+3)}[/tex] = 0.4 cups

Similarly, ratio of blue and red paint in the New purple paint = 5 : 7

If we take 1 cup of New purple paint,

Amount of blue paint in 1 cup = [tex]\frac{5\times 1}{(5+7)}[/tex] = 0.42 cups

Therefore, shade of both the mixtures will not be same.

Since, blue color is more in quantity in New purple paint, it will be more blue than Original purple paint.

-4x -2y = -12
4x + 8y = -24

Answers

x= 6 and y= -6

Step-by-step explanation:

Answer:

x = 6, y = -6

Step-by-step explanation:

After adding the equations together, the 4x and -4x cancel each other out. This makes our new equation:

6y = -36

Divide both sides by 6

y = -6

Plug -6 into y in one of the equations

4x + 8y = -24   =

4x + 8(-6) = -24   =

4x - 48 = -24

Add 48 to both sides

4x = 24

Divide both sides by 4

x = 6

BRAINIST & 20 POINTS


*random answers will be reported*

Answers

Answer:

(0, 13)

Step-by-step explanation:

The midpoint is halfway between the line segment. First find the distance from the starting point to the midpoint.

2-1 = 1. So Since the midpoint is behind the start point, we are going backwards (moving to the left on the x axis).

So 1 space left from the midpoint is 1-1=0.

For y, the distance between the start and mid is 6 - -1 = 6+1 = 7 spaces. Then add 7 spaces to the midpoint value of 6, so 7+6 = 13. We moved upwards on the y axis.

please give thanks by clicking the heart button! :)

Erica sells magazine subscriptions and makes a flat rate of $5.35 for each subscription she sells. If Erica made $42.80 on Monday, $64.20 on Tuesday and $74.90 on Wednesday, how many subscriptions did she sell in the three days

Answers

to find the number of subscribtion sold we divide the money she made by the price of subscription

monday:

42.80/5.35=8 subscriptions sold

tuesday:

64.20/5.35=12 subscriptions sold

wednesday:

74.90/5.35=14 subscriptions sold

8+12+14=34 subscriptions sold in 3 days

Answer:

34 subscriptions she sold

Can anybody help with this?

Answers

Answer:

12

Step-by-step explanation:

Because < this means less than. So therefore 5 is less than 12

Circle theorems maths... Please help me!

Answers

Answer:

m = n = 14°

Step-by-step explanation:

The angle at the centre is twice the angle at the circumference subtended on the same arc.

angle at circumference = 0.5 × 98° = 49°, then

35° + m = 49° ( subtract 35° from both sides )

m = 14°

Angles subtended on the same arc are congruent.

m and n are 2 such angles, thus

n = m = 14°

The blue and orange lines represent a system. Use the sliders to manipulate the orange line to determine which equations would create a system that has no solution. Check all that apply. Hint: Convert to slope-intercept form.
2x + y = –5
y – 3 = 2x
x + y = –2
–2x = y
2x = 4 – y

Answers

Answer:

A) 2x + y = -5

D) -2x = y

E) 2d = 4 - y

Step-by-step explanation:

Answer:

The answers you are looking for is.... A) 2x + y = -5

D) -2x = y

E) 2d = 4 - y

Step-by-step explanation:

What are the coordinates of point F? On a coordinate plane, point F is 4 units to the right and 2.5 units down.

Answers

Answer:

(4,-2.5)

Step-by-step explanation:

because you move to the right it is a positive x-axis point and since you are moving down it is a negative y- axis point

Answer:

-3,-4.5

Step-by-step explanation:


Identify a pair of perpendicular lines in the given figure.



Question 1 options:

p and t


q and t


s and t


p and q

Answers

S and t most likely

Which graph represents the inequality? 2x+y>4

Answers

m=-2

b=4

Slope=-2x+4

y<-2x+4

The following is a list of heights for 6 six-year-olds.

50 inches, 47 inches, 36 inches, 42 inches, 47 inches, 45 inches

The median height for these children is 46 inches.

What would happen to the median height if the 50-inch measurement was changed to 47 inches?

A. The median would increase.
B. The median would decrease.
C. The median would stay the same.
D. The median would decrease, then increase.

Answers

Answer:

option b the median would decrease

Im really confused bc ive tried everything and i cant figure this out

-3 7/10 = -3/-4y
its a rational equation

Answers

Answer:

y = - [tex]\frac{15}{74}[/tex]

Step-by-step explanation:

Given

- 3 [tex]\frac{7}{10}[/tex] = [tex]\frac{-3}{-4}[/tex] y = [tex]\frac{3}{4}[/tex] y ( change the mixed number to an improper fraction )

- [tex]\frac{37}{10}[/tex] = [tex]\frac{3}{4}[/tex] y

Multiply through by 20 ( the LCM of 10 and 4 )

- 74 = 15y ( divide both sides by 15 )

- [tex]\frac{74}{15}[/tex] = y


What is the value of x?
A 42
В.50
C. 68
D. 70

Answers

The answer is C, because parallel means

Chris's age is 17 more than one-fourth of Brian's age. How old is Chris if Brian is 27?

Answers

Answer:

23.75

Step-by-step explanation:

Given that:

Brian's age = 27

Age of Chris is 17 more than one - fourth of Brian's age.

To find:

Age of Chris = ?

Solution:

Let age of Chris = [tex]x[/tex]

One - fourth of Brian's age =  [tex]\frac{27}{4}[/tex]

17 more than One - fourth of Brian's age = [tex]\frac{27}{4}[/tex] + 17

Therefore, we can write the equation as per question statement:

[tex]x = \frac{27}{4} + 17\\\Rightarrow x = 6.75+17\\\Rightarrow \bold{x = 23.75}[/tex]

Therefore, Chris is 23.75 years old if Brian is 27.

Which of the following equations Are a linear function.

Answers

Answer:A IS THE LINEAR FUNCTION

Step-by-step explanation: NO NEED FOR EXPLANATION

What is the value of b?

Answers

Answer:

128

Step-by-step explanation:

Add the two numbers then subtract from 360

First you add 150 and 82. Than subtract by 360.

could you answer this question cause i need it for math

Answers

Step-by-step explanation:

5p/7-18=-43

5p/7=-43+18

5p/7=-25

5p=-25×7

5p=-175

p=-175/5

p=-35

not sure lol

Answer:

5p/7 = -43+18

5p/7 = -25

5p= -25*7

p = -35

Step-by-step explanation:

Pls help I need to finish this

Answers

The answer is the last 2 ones

Answer:

Check box 4 and 5

Step-by-step explanation:

We know there can only be up to 2 solutions for a quadratic equation.

5x^2-2x-9=0 is your equation, make sure to move that 1 to the left

Now we can use the quadratic formula

a=5

b= -2

c= -9

x= −1.15647

x=1.55647

Thus I would select the last 2 boxes. Both of them are solutions.

I am thinking of a number, let's call it x . If I increase twice my number by 5, the result is the same as if I triple my number and subtract 1. Use the 4-step process to write and solve an equation to find my number. Make sure to answer in a sentence.

Answers

Answer: 6

Step-by-step explanation:

Let the number be x

If I increase twice my number by 5, the result is the same as if I triple my number and subtract 1. This can be formed into an equation as:

(2 × x) + 5 = (3 × x) - 1

2x + 5 = 3x - 1

5 + 1 = 3x - 2x

x = 6

The number you are thinking of is 6

A man is trying to fit a washing machine into a corner of a four-sided room. He knows that all the walls are perfectly straight, but he is not sure if the corner is an exact right angle. If the other three corners are all 90° angles, what is the measure of the missing corner?

Answers

I believe that it is just a square room, either that or he isn’t good at measuring
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