Examine the graph. Triangles S T U & X Y Z with these points: S (0, 0); T (0, 2); U (negative 10, 2); X (5, negative 1); Y (5, negative 2); & Z (10, negative 2). A line goes through U, S, X, & Z.

If you want to show that the slope of the line passing through points U, S, X, and Z is constant, why is it important to know if △STU and △XYZ are similar?

Select the answer that is completely correct.

1 It's important to know if △STU and △XYZ are similar because the corresponding sides of similar triangles are proportional. That means that the measure of SU¯¯¯¯¯¯¯ can be shown to be equal to the measure of XZ¯¯¯¯¯¯¯¯.
2 It's important to know if △STU and △XYZ are similar because the corresponding sides of similar triangles are proportional. That means that the slope of SU¯¯¯¯¯¯¯ can be shown to be equal to the slope of XZ¯¯¯¯¯¯¯¯.
3 It's important to know if △STU and △XYZ are similar because the corresponding sides of similar triangles are equal. That means that the measure of SU¯¯¯¯¯¯¯ can be shown to be equal to the measure of XZ¯¯¯¯¯¯¯¯.
4 It's important to know if △STU and △XYZ are similar because the corresponding sides of similar triangles are equal. That means that the slope of SU¯¯¯¯¯¯¯ can be shown to be equal to the slope of XZ¯¯¯¯¯¯¯¯.

area = length x width

length = 2 x width

32 = 2 x width x width

32 = 2 x width^2

36 = width ^2  

width = 6

length = 12

area is 32

perimeter = 2 x 12 + 2 x 6 = 24 + 12 = 36

step-by-step explanation:

just take the area of the square and then the area of the circle then subtract the circle area from the squares area

step-by-step explanation:

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true