Let y be a function of x such that 2x-3y=6. What is the rate if change of y with respect to x?

Answers

Answer 1

Answer: 2x - 3y = 6
first, isolate y:
-3y = -2x + 6
y = (2/3)x - 2
This is a linear function in standard form, so we know that the slope (in this case the rate of change of y in respect to x) is 2/3

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A car rents for $45 per day plus 21 cents per mile. You are on a daily budget of $66. What mileage will allow you to stay within your budget?

Answers

Your budget = $66.

Car rental (for the car) = $45
Car rental (for each mile) = $0.21.

To work out the price you can afford, do 66 - 45 = $21.

Now do $21 ÷ $0.21 to find out the number of miles you can drive.

$21 ÷ $0.21 = 100 miles.

You can drive for 100 miles.

4. The admission fee at a play is $2.50 for each child and $4.00 for each adult. On opening night, the 1000 seat auditorium was sold out! When all the money was counted, they had $3400. How many adults attended the opening night's show? A.100

B.400

C.500

D.600

Answers

600 adults and 400 children attended the opening night's show

Let x represent the number of children and y represent the number of adult.

Since 1000 seat auditorium was sold out!, hence:

x + y = 1000 (1)

they had $3400. Hence:

2.5x + 4y = 3400 (2)

Solving equations 1 and 2 simultaneously gives:

x = 400, y = 600

600 adults and 400 children attended the opening night's show.

Find out more on equation at: brainly.com/question/2972832

Answer is D. 600 adults

Simplify a - {b - [c - (d - e) - f] - g}.

Answers

The key is to work from the middle.

c - (d - e) - f = c - d + e - f

b - (c - d + e - f) - g = b - c + d - e + f - g

a - (b - c + d - e + f - g) = a - b + c - d + e - f + g

Answer:
a - b + c - d + e - f + g

Which constants can be multiplied by the equations so one variable will be eliminated when the systems are added together?5x + 13y = 232
12x + 7y = 218
The first equation can be multiplied by –13 and the second equation by 7 to eliminate y.
The first equation can be multiplied by 7 and the second equation by 13 to eliminate y.
The first equation can be multiplied by –12 and the second equation by 5 to eliminate x.
The first equation can be multiplied by 5 and the second equation by 12 to eliminate x.

Answers

The THIRD sentence is correct.
The first equation can be multiplied by -12 and the second equation by 5, to eliminate x.
Let's do this:
(1st equation) 5*x + 13*y = 232 / *(-12)
(2nd equation) 12*x + 7*y = 218 / *(5)
---------------------------------
When multiplied, we get:
(1st equation) -60*x - 156*y = -2784
(2nd equation) 60*x + 35*y = 1090
---------------------------------
Further, first equation now will be obtained when ADDING 1st and 2nd equation together:
(1st equation) -60x+60x-156y+35y=-2784+1090
2nd equation we get from just writing any equation from the beginning, for example, the second one:
(2nd equation) 12*x + 7*y = 218
-----------------------------------------
(1st equation) 0*x - 121*y = -1694
(2nd equation) 12*x + 7*y = 218
------------------------------------------
(1st equation) -121*y = -1694 [x variable is in this step eliminated]
(2nd equation) 12*x + 7*y = 218
----------------------------------------------
(1st equation) y = 1694/121
(2nd equation) 12*x + 7*y = 218
----------------------------------------------
(1st equation) y = 14
(2nd equation) 12*x + 7*14 = 218
----------------------------------------------
(1st equation) y = 14
(2nd equation) 12*x + 98 = 218
----------------------------------------------
(1st equation) y = 14
(2nd equation) 12*x = 218 - 98
----------------------------------------------
(1st equation) y = 14
(2nd equation) 12*x = 120
----------------------------------------------
(1st equation) y = 14
(2nd equation) x = 120/12
----------------------------------------------
(1st equation) y = 14
(2nd equation) x = 10
----------------------------------------------
So, solution of the system of this two equations is obtained, and it is:
(x,y)=(10,14)

Answer:

The first equation can be multiplied by –12 and the second equation by 5 to eliminate x.

A square is _______ a rectangle

always
sometimes
never
inconclusive

Answers

A square is always a rectangle. Then the correct option is A.

What is a rectangle?

A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.

If all the sides of the rectangle become equal. Then the rectangle is known as a square.

A square is always a rectangle.

Thus, the correct option is A.

More about the rectangle link is given below.

brainly.com/question/10046743

#SPJ2

Always. A rectangle is a shape made of 2 sets of equal length parallel lines that forms 4 right angles. So all squares are rectangles and some rectangles are squares.

When solving for an unknown variable that has a number preceding it, you will divide both sides of the equation by this number, which is known as the ______________.

Answers

Answer: Coefficient

Step-by-step explanation:

When solving for an unknown variable that has a number preceding it, you will divide both sides of the equation by this number, which is known as the coefficient.

A coefficient is a number preceding any variable in a function for example, given the function 4x, the variable is 'x' and the number preceding it is 4. This number preceding the variable is what we call 'coefficient' of the variable 'x'

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