Select the locations on the number line to plot the points 4 1/ 3 and −1 1/3 .

The locations of given number are shown on the below number line.

Step-by-step explanation:

The given numbers are

We need to plot these points on the given number line.

In the given number write the integers -4,-3,-2,-1,0,1,2,3,4 on points indicated and two sub point between two consecutive points divides the line in three equal parts.

It means lies next to 4 on right side.

It means lies next to -1 on left side.

Therefore, the locations of given number are shown on the below number line.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.