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Bess [88]
2 years ago
7

A school system is reducing the amount of dumpster loads of trash removed each week. In week 5, there were 45 dumpster loads of

waste removed. In week 10, there were 30 dumpster loads removed. Assume that the reduction in the amount of waste each week is linear. Write an equation in function form to show the amount of trash removed each week.
f(x) = −3x + 45
f(x) = 3x + 45
f(x) = −3x + 60
f(x) = 3x + 60
Mathematics
1 answer:
Mice21 [21]2 years ago
5 0

Answer:

f(x) = -3x+60

Step-by-step explanation:

For the slope of the function:

  • Comparing week 5 to week 10: we know that as time goes on, the number of dumpster loads decreases from 45 to 30. This means the slope has to be negative.

For the intercept of the function:

  • Since it's a negative-sloped linear function, we know that the y-intercept has to be bigger than the y-value at week 5. This means it has to be 60.

Therefore:

f(x) = -3x+60

You might be interested in
What does -3(n+5)=12 equal
Reil [10]

Answer:

n= -9

Step-by-step explanation:

-3 ( n+5 ) = 12

-3n - 15 = 12

-3n = 12+15

-3n = 27

n = -27/3

n = -9

6 0
3 years ago
Solve the system of equations. 8x – 3y = 1 –2x + 3y = 11 A. (–1, –3) B. (–1, 3) C. (2, 5) D. (5, 2)
Makovka662 [10]

Answer:

C. (2, 5)

Step-by-step explanation:

Looking at the answer choices, you can see that solving for y will tell you which choice is correct. We can eliminate x from the equations by adding 4 times the second equation to the first:

(8x -3y) +4(-2x +3y) = (1) +4(11) . . . . . adding the equations to eliminate x

9y = 45 . . . simplified; next we divide by 9

y = 5 . . . . . matches choice C

_____

Check

8(2) -3(5) = 16 -15 = 1

-2(2) +3(5) = -4 +15 = 11 . . . . the answer checks OK in both equations

4 0
3 years ago
Solve system of equations 2x + 2y + 5z = 7 6x + 8y + 5z = 9 2x + 3y + 5z = 6
svet-max [94.6K]

Answer:

the values of x, y and z are x= 2, y =-1 and z=1

Step-by-step explanation:

We need to solve the following system of equations.

We will use elimination method to solve these equations and find the values of x, y and z.

2x + 2y + 5z = 7     eq(1)

6x + 8y + 5z = 9     eq(2)

2x + 3y + 5z = 6     eq(3)

Subtracting eq(1) and eq(3)

2x + 2y + 5z = 7

2x + 3y + 5z = 6

-    -       -        -

_____________

0 -y + 0 = 1

-y = 1

=> y = -1

Subtracting eq(2) and eq(3)

6x + 8y + 5z = 9    

2x + 3y + 5z = 6    

-     -      -          -

______________

4x + 5y +0z = 3    

4x + 5y = 3      eq(4)

Putting value of y = -1 in equation 4

4x + 5y = 3

4x + 5(-1) = 3

4x -5 = 3

4x = 3+5

4x = 8

x= 8/4

x = 2

Putting value of x=2 and y=-1 in eq(1)

2x + 2y + 5z = 7

2(2) + 2(-1) + 5z = 7

4 -2 + 5z = 7

2 + 5z = 7

5z = 7 -2

5z = 5

z = 5/5

z = 1

So, the values of x, y and z are x= 2, y =-1 and z=1

5 0
3 years ago
-3x+2<8 answer this equation
icang [17]

Answer:

x>-2

Step-by-step explanation:

-3x+2<8

Subtract 2 from each side

-3x+2-2<8 -2

-3x < 6

Divide each side by -3. remembering to flip the inequality

-3x/-3 >6/-3

x>-2

7 0
3 years ago
Read 2 more answers
2x-4y=8 and 7x-3y=61 solve by substitution
Ratling [72]

Answer:

(10, 3)

Step-by-step explanation:

Solve by Substitution

2x − 4y = 8 and 7x − 3y = 61

Solve for x in the first equation.

x = 4 + 2y 7x − 3y = 61

Replace all occurrences of x with 4 + 2y in each e quation.

Replace all occurrences of x in 7x − 3y = 61 with 4 + 2y. 7 (4 + 2y) − 3y = 61

x = 4 + 2y

Simplify 7 (4 + 2y) − 3y.

28 + 11y = 61

x = 4 + 2y

Solve for y in the first equation.

Move all terms not containing y to the right side of the equation.

11y = 33

x = 4 + 2y

 Divide each term by 11 and simplify.

y = 3

x = 4 + 2y

 

Replace all occurrences of y with 3 in each equation.

Replace all occurrences of y in x = 4 + 2y with 3. x = 4 + 2 (3)

y = 3

Simplify 4 + 2 (3).

x = 10

y = 3

The solution to the system is the complete set of ordered pairs that are valid solutions.

(10, 3)

The result can be shown in multiple forms.

Point Form:

(10, 3)

Equation Form:

x = 10, y = 3

4 0
3 years ago
Read 2 more answers
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