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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.

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.