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1. D. 2x + y = 4

2. A

Step-by-step explanation:

Problem 1:

To find the equation in standard form, first find the equation of the graph in slope-intercept form, y = mx + b.

Where, m = slope and b = y-intercept.

Slope (m) = ∆y/∆x

Using two points on the line, (0, 4) and (2, 0):

Slope (m) = (0 - 4)/(2 - 0) = -4/2 = -2

m = -2

y-intercept is the y-coordinate of the point where the line intercepts the y-axis = 4.

Thus,

b = 4

Substitute m = -2, and b = 4 into y = mx + b:

y = -2x + 4

Rewrite in standard form:

2x + y = 4

Problem 2:

The funtion y = ½(x) + 2 is given in the slope-intercept form y = mx + b.

m = slope = ½

b = y-intercept = 2

Therefore, the graph that has a slope value of ½ and y-intercept value of 2 would be the graph that represents the given function.

Thus, the graph in option A, has a y-intercept (b) value of 2 (the line intercepts the y-axis at y = 2).

Also, the slope of graph A = ½.

Therefore, the answer is option A.

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet