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Nimfa-mama [501]
2 years ago
8

What is the y-intercept of the function f(x)=4 - 5x? (Hint: use the commutative property)

Mathematics
1 answer:
Tom [10]2 years ago
7 0

Answer:

Therefore the y-intercept of the function is 4.

Step-by-step explanation:

Intercepts:

The line which intersect on x-axis and y-axis are called intercepts.

y-intercept: The line or function which intersect at y-axis. So when the line intersect at y-axis, X coordinate is zero.

So in the given Function Put x = 0 we will get the y-intercept

f(x)= 4-5x

Put x =0

f(0)= 4-5\times 0

f(0)= 4-0=4

Therefore the y-intercept of the function is 4.

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3 \times  {7}^{4}
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In a school of 2100 students, the ratio of teachers to students is 1:14. Some teachers join the school and the ratio changes to
mrs_skeptik [129]

Answer:

50 Teachers

Step-by-step explanation:

To solve this problem, we first need to find the number of teachers <em>before </em>the new teachers were added. To do so, I created Model 1. On the bottom of the ratios, we have students. On the top, is teachers. The X is the number of teachers we are trying to find. Following the model, I multiplied 2,100 x 1 (2,100) and divided it by 14 to get 150 teachers. Then, I set up a similar model with the new student-teacher ratio (Model 2). From there, I multiplied 2,100 x 2 (4,200) and divided it by 21 to get 200 teachers. Now I have the original number of teachers and the new number of teachers. Subtract the new by the original to find the teachers added and you get the answer of 50 teachers added.

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A forest ranger is in a forest 2 miles from a straight road. A car is located c miles down the road. The forest ranger can walk
Tcecarenko [31]

Answer:

  • T(x) = (√(4+x^2))/2 +(c -x)/4
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Step-by-step explanation:

The straight line distance from the starting point to the point x on the road is given by the Pythagorean theorem:

  d1 = √(2²+x²)

The time required to walk that distance in the woods (at 2 miles per hour) is ...

  time = distance / speed

  t1 = √(4+x²)/2

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and the corresponding time at 4 mph is ...

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__

(a) The value of x that minimizes total time is the one that makes the derivative zero.

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  0 = (2x -√(4+x²))/(4√(4+x²))

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  4/3 = x² . . . . . . . . . subtract x², divide by 3

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__

(b) For c < (2/3)√3, the shortest travel time will be along the straight-line path to the car.

If c = 1/2 mile, x = 1/2 mile.

8 0
2 years ago
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