He difference of 1/2 of one number and 2/3 of another number is equal to 2. if the first number were to decrease by 5/6 of it, and the second number were to increase by 1/6 of it, their sum would be equal to 59. find the two numbers.

Step-by-step explanation:

If we let x and y represent the first and second numbers, respectively, then the first sentence of the problem statement tells us ...

  (1/2)x - (2/3)y = 2

The second sentence of the problem statement tells us ...

  (1 -5/6)x +(1 +1/6)y = 59

Solution

Multiplying the first equation by 6 gives ...

  3x -4y = 12

Multiplying the second equation by 6 gives ...

  x + 7y = 354

Solving the second equation for x gives ...

  x = 354 -7y

Substituting that into the first equation gives ...

  3(354 -7y) -4y = 12

  1050 = 25y . . . . . . . . subtract 12-25y

  42 = y . . . . . . . . . . . .  divide by 25

Then we can find x using its equation ...

  x = 354 -7·42 = 60

The first number is 60; the second number is 42.

answer

see attachment

explanation

the given function is

this function has y-intercept at

-4 and a slope of 2.

note that, the graph has a positive slope.

the graph that represents this function is the straight line that moves upward from left to right.

the graph touches the y-axis at -4.

the correct choice is the graph shown in the attachment.

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.