MATHEMATICS HIGH SCHOOL

Select the equation of the line that passes through the point (2, 6) and is perpendicular to the line x = 4.y = 4

y = 6

x = 6

x = 2

Answers

Answer 1
Answer: Hello,
All the perpendiculars of the line x=4 are parallele to the oy axis.

y=6
Answer B
Answer 2
Answer:

The equation of the perpendicular line is y = 6.

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A monster truck tire will travel will travel 12.56 ft in one revolution. What is the radius of the tire?

Answers

If it travels 12.56 ft in one revolution, then the circumference of the tire is 12.56 ft.
Circumference = 2 x π x radius
12.56=2 x 3.14 x radius
radius x 6.28=12.56

Radius= 2 ft

Hope this helps :)
1 revolution
the part that touches the ground makes 1 full circle
therefor 12.56 is the cirvmerncere
circumfrence=2pir
12.56=circumfrence
12.56=2pir
divide both sides by 2
6.28=pir
aprox pi to 3.14 and divide both sides by 3.14
2=r

radius=2 feet

A dog weighs two pounds less than three times the weight of a cat. The dog also weighs twenty-two pounds more than a cat. Write and solve an equation to find the weights of the dog and the cat.

Answers

Let's use algebra to represent the weights of the dog and the cat.

Let D represent the weight of the dog in pounds.

Let C represent the weight of the cat in pounds.

According to the information given:

1. The dog weighs two pounds less than three times the weight of a cat, so we can write this as an equation: D = 3C - 2.

2. The dog also weighs twenty-two pounds more than a cat, so we can write this as another equation: D = C + 22.

Now, we have a system of two equations:

1. D = 3C - 2

2. D = C + 22

To solve for the weights of the dog and the cat, we can set these two equations equal to each other since they both equal D:

3C - 2 = C + 22

Now, let's solve for C (the weight of the cat):

3C - C = 22 + 2

This simplifies to:

2C = 24

Now, divide both sides by 2 to find the value of C (the weight of the cat):

C = 24 / 2

C = 12

So, the weight of the cat is 12 pounds.

Now, we can find the weight of the dog using either of the two original equations. Let's use the second equation:

D = C + 22

D = 12 + 22

D = 34

So, the weight of the dog is 34 pounds.

Therefore, the dog weighs 34 pounds, and the cat weighs 12 pounds.

A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 16 ft, express the area A of the window as a function of the width x of the window.

Answers

This answer uses NMF for which, if needed, the syntax can be found in my profile. Please ignore the LaTeX (the image), I cannot remove it/change it, and it is incorrect. The answer is: f(x)={π{{x}^{2}}/{4}+x(16-{πx}/{2}-x)}/{2}

Final answer:

The area A of a Norman window in terms of its width x can be expressed as the function A(x) = 8x - x²/2 - πx²/8, deriving this equation involves isolating variables from the given perimeter equation.

Explanation:

A Norman window has the shape of a rectangle topped with a semicircle. If we take x as the width of the window and y as the height of the rectangle, then the perimeter of the window is given by P = 2y + x + πx/2 = 16 (since the perimeter is the sum of the rectangle's two sides, the width, and half the circumference of a circle with diameter x).

From this equation, we can express y as a function of x: y = 8 - x/2 - πx/4.

Then, the area A of the window is the sum of the area of the rectangle and the area of the semicircle, which equals A = xy + πx²/8 = x(8 - x/2 - πx/4) + πx²/8 = 8x - x²/2 - πx²/4 + πx²/8.

Therefore, the area A of the window as a function of the width x of the window is A(x) = 8x - x²/2 - πx²/8.

Learn more about Function of Window Area here:

brainly.com/question/32386293

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A car rental agency charges $120 per week plus $.12 per mile driven. How many miles did you drive if the total charge is $162?

Answers

\boxed{y=120+0.12x}\n \n y=162\n \n 120+0.12x=162\n \n 0.12x=162-120\n \n 0.12x=42\n \n x=(42)/(0.12)\n \n \boxed{\boxed{x=350 \ miles}}

The books in a private library are classified as fiction and nonfiction. There are 400 books in the library. There are 40 more fiction books than nonfiction books. Audrey randomly picks a book. A few minutes later, Ryan randomly picks one of the remaining books. What is the probability that both pick nonfiction books?

Answers

We must first solve the number of fiction and nonfiction books
if x is the number of fiction books and
y is the number of nonfinction books

Then,
x + y = 400
x = y + 40

Solving the system of equations:
x = 220
y = 180

Therefore, the probability that Audrey and Ryan will get both nonfiction books is
P = 180/400 + 179/399
P = 0.8986

Answer: The probability is P =  0.20

Step-by-step explanation:

The data that we have is:

Total books = 400

If the number of non fiction books is Nf and the number of fiction books is F, we have that:

F  = Nf  + 40

So here we have a system of equations:

Nf + F = 400

F = Nf + 40

we can replace the second equation in the first one, and solve it for Nf.

Nf + (Nf + 40) = 400

2*Nf + 40 = 400

2*Nf = 400 - 40 = 360

Nf = 180

So we have 180 non-fiction books.

We want to calculate the probability of picking at random two non-fiction books.

When Audrey picks one, the probabilty is equal to the number of non-fiction books divided the total number of books:

p1 = 180/400

for Ryan we have the same, but the number of books is 399 now (Because Audrey already took one), and the number of non-fiction books is 179.

p2 = 179/399

The probabiliy for both events to happen is:

P = p1*p2 = (180/400)*(179*399) = 0.20

K=m-n÷y (make y the subject)​

Answers

Answer:

y = (n)/(K - m)

Step-by-step explanation:

When doing problems like these, you should go through the process like using PEMDAS:

P - Parenthesis ()

E - Exponents x^(2)

M - Multiply x

D - Division ÷

A - Addition +

S - Subtraction -

1) Since there aren't any Parentheses, or exponents, we should then check for any use of Multiplication.

As shown, there are no shown methods of multiplying.

BUT there is Division, so we will do the opposite of division, which is multiplication.

K = m - n ÷ y

y(K = m - n ÷ y)y

^ Trying to multiply 'y' onto both sides, because when you do something to one side, you do to the other. ^

'y' then cancels out on one side, so you will be left with:

= m - n

But on the other side you will have:

Ky

So your problem will look like:

Ky = m - n

2) Since we are trying to get 'y' by itself, instead of multiplying now, we will be dividing, because:

K(y) = Ky  or you can also say K x y = Ky

Back to the problem, we will now divide 'K' to both sides, as stated before:

What you do to one side, you do to the other:

(Ky)/(K) = (m - n)/(K)

'K' will cancel out on one side:

(Ky)/(K) = y

Leaving you with:

'y'

While the other side, will be left as:

(m - n)/(K)

So your final answer will be:

y=(m - n)/(K)
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