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DochEvi [55]
3 years ago
9

If f(x) = 16x – 30 and g(x) = 14x – 6, for which value of x does (f – g)(x) = 0?

Mathematics
1 answer:
Kay [80]3 years ago
6 0

(f – g)(x) = 0

16x-30 -(14x-6) =0

distribute

16x-30 -14x+6 = 0

combine like terms

2x-24=0

add 24 to each side

2x=24

divide by 2

x=12

Answer: x=12


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Part A: Marguerite rented a truck at $125 for 2 days. If she rents the same truck for 5 days, she has to pay a total rent of $27
SOVA2 [1]
Part A: To get an equation into standard form to represent the total amount  rented (y) that Marguerite has to pay for renting the truck for x amount of days, we use the formula for the equation of a straight line.

Remember that the equation of a straight line passing through points is ( x_{1} , y_{1} ) and the points ( x_{2} , y_{2} ) is given by
y - y_{1} / x - x_{1} = y - y_{2} / x - x_{2}

Knowing that Marguerite rented a truck at $125 for 2 days, we know if she rents the exact same truck for 5 days, she has to pay a total of $275 for the rent.
<span>
This means that the line modeling this situation crosses points at (2, 125) and (5, 275).
</span>
The equation modeling <span>the total rent (y) that Marguerite has to pay for renting the truck for x days is given by
</span><span>
y - 125 / x - 2 = 275 - 125 / 5 - 2 = 150 / 3 = 50
</span>
But if you are writing the equation in standard form it would be <span>
</span><span>
50x - y = -25


Part B:
When writing the function using function notation it means you are making y the subject of the formula and then replacing the y with f(x).
</span>
If you remember that from part A, we have that the equation for the total rent which is y that Marguerite has to pay for renting the truck for x amount of days is given by
y = 50x + 25.<span>
</span><span>
Writing the equation using the function notation would give us this
f(x) = 50x + 25


Part C:
To graph the function, we name the x-axis the number of days and name the y-axis total rent. The x-axis is numbered using the intervals of 1 while the y-axis is numbered using the intervals of 50.
The points of </span>(2,125) and of (5,275) are marked on the coordinate axis and a straight line is drawn to pass through these two points.
6 0
3 years ago
9000 is 10 times as much as?
Zanzabum

Answer:

900

Step-by-step explanation:

4 0
3 years ago
x^2+2x+7=21 the approximate value of the greatest solutoon to the equation, rounded to the nearest hundreth​
daser333 [38]

9514 1404 393

Answer:

  x ≈ 2.87

Step-by-step explanation:

We  can subtract 6 to put the equation into a form easily solved.

  x^2 +2x +1 = 15

  (x +1)^2 = 15

  x +1 = √15 . . . . . for the greatest solution, we only need the positive root

  x = √15 -1 ≈ 2.87

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2 years ago
Give the domain and range.
alexgriva [62]

Answer:

c. domain: {-2, 0, 2}, range: {-1, 1, 3}

Step-by-step explanation:

Given:

There are three points on the graph.

Locate the x and y values of the points on the graph.

The points are (-2,-1),(0,1),\textrm{ and }(2,3)

Domain is the set of all possible x values. Here, the x values are -2, 0 and 2.

So, domain is: {-2, 0, 2}.

Range is set of all possible y values. Here, the y values are -1, 1 and 3.

So, range is: {-1, 1, 3}

7 0
3 years ago
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