Solving Equations and Ratios

This video tutorial covers a quiz review on various mathematical concepts. It begins with calculating the ratio of height to length, followed by solving equations using the cross product property. The tutorial then explores triangle similarity through angle-angle, side-angle-side, and side-side-side methods. Real-world problems involving proportions are addressed, and the video concludes with discussions on polygon similarity and scale model ratios.

What is the simplified ratio of the height to the length of an object if the height is 23 feet and the length is 69 feet?

• 69:23

• 1:3

• 3:1

• 23:69

How can the ratio 1:3 be expressed as a fraction?

• 23/69

• 69/23

• 3/1

• 1/3

What is the value of x if x^2 = 50?

• ±5√2

• 5

• ±10

• 10

Which of the following is a prime factorization of 50?

• 1 x 50

• 2 x 25

• 10 x 5

• 5 x 5 x 2

What is the solution for x in the equation 80 = 7(x + 3)?

• x = 10

• x = 59/7

• x = 11

• x = 8.43

If 24 = 5x, what is the value of x?

• 5

• 4.8

• 5/24

• 24/5

Which method can be used to determine if two triangles are similar?

• Side-Angle

• Angle-Angle

• Side-Side

• Angle-Side

What is the similarity ratio if the corresponding sides of two similar triangles are 8 and 5?

• 8:5

• 5:8

• 1.6

• 0.625

If a meter stick casts a shadow of 2 meters, how tall is a building that casts a shadow of 120 meters?

• 60 meters

• 120 meters

• 240 meters

• 30 meters

What is the distance between two cities on a map if 2 inches represents 70 kilometers and the map distance is 1.5 inches?

• 52.5 km

• 35 km

• 70 km

• 105 km