Mathematics Mastery: Equations, Ratios, and Analytical Skills Quiz

1) Solve for x: 29 + -1x = 13

X = 2

X = 10

X = -14

First, move all terms containing x to the left side and all other terms to the right side. Then, simplify the equation by combining like terms. Finally, divide each side by -1 to solve for x. The correct solution is x = 16.

Explanation

First, move all terms containing x to the left side and all other terms to the right side. Then, simplify the equation by combining like terms. Finally, divide each side by -1 to solve for x. The correct solution is x = 16.

2) How to simplify ratios?

(b) 15:20 - 3:4

(c) 12:18:24 - 2:3:4

(1) 2:10:2.- - 1:5:1(2) 5:10:15- - 1:2:3(3) 28:12- - 7:3

(a) 3:9:2 - 1:3:6

Ratios can be simplified by finding the greatest common factor (GCF) between the numbers in the ratio and dividing all the numbers by the GCF. This will result in a simplified ratio that represents the same proportional relationship.

Explanation

Ratios can be simplified by finding the greatest common factor (GCF) between the numbers in the ratio and dividing all the numbers by the GCF. This will result in a simplified ratio that represents the same proportional relationship.

3) Solving equations.

X = 13. Remember to divide by 3 on both sides.

X = -3. Remember to multiply by 3 on both sides.

X + 3 = 10 What's the value of x? Remember to subtract 3 from both sides.

X = 5. Remember to add 3 to both sides.

In the given equation x + 3 = 10, the correct solution is x = 7 obtained by subtracting 3 from both sides.

Explanation

In the given equation x + 3 = 10, the correct solution is x = 7 obtained by subtracting 3 from both sides.

4) How can you find the area of compound shapes?

Draw a line through the center of the shape and measure the diameter.

Count the number of vertices on the shape and use that to determine the area.

Calculate the perimeter of the shape and divide it by the number of sides to find average side length.

Divide the shape into squares and rectangles, find their individual areas and then add them together.

When dealing with compound shapes, it is important to break them down into simpler shapes like squares and rectangles to find the total area. By finding the individual areas of these simpler shapes and then adding them together, you can accurately calculate the area of the compound shape.

Explanation

When dealing with compound shapes, it is important to break them down into simpler shapes like squares and rectangles to find the total area. By finding the individual areas of these simpler shapes and then adding them together, you can accurately calculate the area of the compound shape.