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Nora is writing statements as shown below to prove that if segment ST is parallel to segment RQ, then x = 45: Statement Reason
1. Segment ST is parallel to segment RQ. Given
2. Angle QRS is congruent to angle TSP. Corresponding angles formed by parallel lines and their transversal are congruent.
3. Angle SPT is congruent to angle RPQ. Reflexive property of angles
4. Triangle SPT is similar to triangle RPQ. Angle-Angle Similarity Postulate 5. ? Corresponding sides of similar triangles are in proportion.
Which equation can she use as statement 5?
60:x = 48:(48 + 36) 60 + x = 48 + 36 60 − x = 48 − 36 60:(60 + x) = 48:(48 + 36)

The value of x is 45

Step-by-step explanation:

Statement 1: Segment ST is parallel to segment RQ.      

Reason: Given

Statement 2: Angle QRS is congruent to angle TSP.

Reason : Corresponding angles formed by parallel lines and their transversal are congruent.

Statement 3: Angle SPT is congruent to angle RPQ.

Reason:  Reflexive property of angles

Statement 4: Triangle SPT is similar to triangle RPQ.

Reason: Angle-Angle Similarity Postulate

So, ΔSPT≈ΔRPQ

5. Corresponding sides of similar triangles are in proportion.

Hence The value of x is 45

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.