MATHEMATICS HIGH SCHOOL

In Becky's class, there are 22 students. 5/11 of the students are girls. How many of the students in her class are girls?5 students
10 students(correct answer)?
12 students
16 students

Answers

Answer 1
Answer: 10 students

Working
5/11 * 22 =10 
Answer 2
Answer:

Answer: 10 students

Step-by-step explanation:

half 22 is 11 - 1 = 10

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A prism with a volume of 360 yd³ is scaled down to a volume of 45 yd³.What is the scale factor?

Enter your answer, as a decimal or a fraction in simplest form, in the box.

Answers

Answer: The scale factor is 0.125.

Step-by-step explanation:

Given: The volume of the prism=360\ yd^3

The scaled volume of the prism=45\ yd^3

We know that when we scaled a shape by a scale factor k, then we multiply k to the dimension of the original shape.

So, to find the scale factor k, we need to the divide the scaled volume  by the volume of prism , we get

k=\frac{\text{scaled volume of the prism}}{\text{volume of the prism}}=(45)/(360)=(1)/(8)=0.125

Hence, the scale factor k = 0.125
45/360 and reduce
45/360 =15/120 = 5/40 = 1/8

The scale factor is 1/8

Given the Vertices of ΔABC are A (2, -5,) B (-4, 6) and C (3, 1), find the vertices following each of the transformations FROM THE ORIGINAL vertices :(I honestly have no idea what to do and I really need help with this one)

Answers

Answer:

I. A' =  (5,-5), B' = (-1,6), C' = (6,1)

II. A' =  (5,-11), B' = (-1,0), C' = (6,-5)

III. A' = (-5,-2), B = (6,4), C' = (1,-3)

Step-by-step explanation:

We are given the vertices of ΔABC as A = (2,-5), B = (-4,6) and C = (3,1).

I. It is required to 'reflect the triangle about the line x= 3'.

This rule changes (x,y) to (x+3,y).

So, the new vertices are given by,

A' = (2+3,-5) = (5,-5)

B' = (-4+3,6) = (-1,6)

C' = (3+3,1) = (6,1)

II. It is required to 'translate the triangle 3 units to the right and 6 units down'.

This rule changes (x,y) to (x+3,y-6).

So, the new vertices are given by,

A' = (2+3,-5-6) = (5,-11)

B' = (-4+3,6-6) = (-1,0)

C' = (3+3,1-6) = (6,-5)

III. It is required to 'rotate the triangle by 90° about the origin counter-clockwise'.

This rule changes (x,y) to (y,-x).

So, the new vertices are given by,

A = (2,-5) implies A' = (-5,-2)

B = (-4,6) implies B = (6,4)

C = (3,1) implies C' = (1,-3)

The town of gettysburg, PA, plans to shoot a live cannon as part of their annual Gettysburg Civil War Battle Reenactment. The organizers want to make sure that when they fire the cannon, it lands in a location that does not injure any participants or spectators. The slope of the field they are firing into can be represented by the equation y=0.15x. Let x represent horizontal distance, and y represents vertical distance.. if the cannon fires the cannon ball at an arc denoted by the equation y=-0.5x^2+2.5x+1, at what distance will the cannonball land. -I know i'm supposed to set -0.5x^2+2.5x+1=.15x and use distance formula BUT I KEEP GETTING DIFFERENT ANSWERS.

Answers

Answer:

The cannonball lands at approximately 5.093 unit distance from the point of fire

Step-by-step explanation:

The given parameters are;

The arc denoting the equation of motion of the cannon is y₁ = -0.5·x² + 2.5·x + 1

The slope of the field where in the direction the cannon is fired is y₂ = 1.5·x

The points where the cannonball land on the slopping field is given as rightly pointed by equating the two equations, the cannonball path path and the field path as follows;

At the point of contact of the cannonball and the field, the y-values of both equation will be equal

y₁ = y₂

∴ -0.5·x² + 2.5·x + 1 = 0.15·x

Which gives;

-0.5·x² + 2.5·x - 0.15·x + 1 = 0

-0.5·x² + 2.35·x + 1 = 0

-(-0.5·x² + 2.35·x + 1) = 0.5·x² - 2.35·x - 1 = 0

0.5·x² - 2.35·x - 1 = 0

The above equation is in the general form of a quadratic equation, which is given as follows;

a·x² + b·x + c = 0

By the quadratic equation, we have;

x = \frac{-b\pm \sqrt{b^(2)-4\cdot a\cdot c}}{2\cdot a}

Plugging in the values, gives;

x = \frac{2.35\pm \sqrt{(2.35)^(2)-4\cdot (0.5)* (-1)}}{2\cdot (0.5)} = (2.35\pm √(7.5225))/(1) =2.35 \pm √(7.5225)

∴ x ≈ 5.093 or x ≈ -0.393

Therefore, the cannonball will takeoff at x ≈ -0.393 and land at x ≈ 5.093

The height from which they fire the cannon is given by the substituting the value of x ≈ -0.393 into the equation for the path of the cannonball, to give;

y_((initial)) = -0.5·(-0.393)² + 2.5·(-0.393) + 1 = -0.0597

y_((initial)) ≈ -0.0597.

However, the actual initial height from which the cannonball is fired given by placing x = 0, which gives y = 1, which is the reason for the other (negative) value for x. Please see the attached graph created with Microsoft Excel.

Pieter wrote and solved an equation that models the number of hours it takes to dig a well to a level of 72 feet below sea level. 7h – 5(3h – 8) = –72Which statement is true about Pieter’s solution?
1. It cannot be a fraction or decimal because the depth of the well is a whole number.
2.It must be a positive number since it represents a number of hours.
3. It must be a negative number because the depth is below sea level.
4.It cannot be greater than –72 because that is the depth of the well.

Answers

Answer:

Option B is correct

It must be a positive number since it represents a number of hours.

Step-by-step explanation:

As per the statement:

Pieter wrote and solved an equation that models the number of hours it takes to dig a well to a level of 72 feet below sea level.

Given the equation as:

7h-5(3h-8) = -72

Using distributive property, a\cdot (b+c) = a\cdot b+ a\cdot c

7h-15h+40 = -72

Combine like terms;

-8h+40 = -72

Subtract 40 from both sides we have;

-8h= -112

Divide both sides by -8 we have;

h = 14 hours

Therefore, the statement is true about Pieter’s solution is, It must be a positive number since it represents a number of hours.

the answer is B It must be a positive number since it represents a number of hours.

Complete the two column proof.Given: m
Prove: x = 15


m
m
5x + 7x = 180 a. ____________________

12x = 180 b. ____________________

x = 15 c. ____________________

Answers

I think the answers to the second column are as follows:

1. definition of a supplementary angle
 
2. Addition property of equality

3. division property of equality

I hope my answer has come to your help. God bless and have a nice day ahead!

Answer:

2016

Step-by-step explanation:

wow ita been 4 years and i needed this and its wrong

Express 5×-4y=20 in the form a×+by+c=0and write the value of a,band c

​

Answers

Answer:

a = 5

b = -4

c = -20

Step-by-step explanation:

Here, we want to express the given equation in the following form;

So we can have this as;

5x-4y-20 = 0

That means we have;

a as 5

b as -4

and c as -20

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