4 times a number is 44 less than 6 times the number. Find the number.

22

Step-by-step explanation:

4x = 6x-44

1. Set x as the number we want to find.

2. Multiply by four (this makes one side of the equation)

3. "Is" tells us that 4x will be set equal to another expression.

4. The expression "6 times the number" tells us that we need to multiply 6 by x: 6x.

5. We now must account for the "44 less than 6 times the number", less than indicates subtraction. We are told that 44 fewer units than 6x will define this function.

6. 6x-44

7. Now set 4x=6x-44 (this goes back to step 3)

8. Use algebra to solve, first we want to isolate x, so subtract 6x on both sides.

9. -2x=-44  Now divide by -2 on both sides.

10. You reach an answer of x=22.

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.