For which value of x is the figure a rectangle? a. x = 1 b. x = 2.5 c. x equals 6 and two-thirds d. x = 10

We know that the diagonals of rectangle are congruent and bisect each other. So it means the given measurements would be equal to each other. We can set them equal asn solve for x.

8x + 3 = 4x + 7

Subtracting 3 from both sides;

8x + 3 - 3 = 4x + 7 - 3

8x = 4x + 4

Subtracting 4x from both sides;

8x - 4x = 4x + 4 - 4x

4x = 4

Dividing by 4 on both sides;

4x/4 = 4/4

x = 1

Hence, option A is correct i.e. x = 1.

y= 2x+7

changed to y= 5x +7

as slope is increased from 2 to 5

therefore it would be less steeper

so, option d) is correct