Initially, the ratio of Alex’s toy cars to Pete’s toy cars was 7:3. After Alex gave 20 toy cars to Pete, they had each an equal

The choice is the first one (positive)

Answer:

1) (2.2, -1.4)

2) (1.33, 1)

Detailed solution:

Question 1)

We are provided with two linear equations representing lines, and we need to find the intersection point that solves the system.

The lines given are:

Line 1 equation:

This line passes through points (0, 2.5) and (2.2, -1.4).

Line 2 equation:

The second line goes through (0, -3) and (2.2, -1.4).

According to the graph and data, the solution to the system is the coordinate where both lines intersect.

The solution to a system of linear equations is the coordinate pair common to both lines, i.e., the intersection point.

Here, both lines share the point (2.2, -1.4), indicating it is their intersection and the solution.

Therefore, the solution for question 1 is (2.2, -1.4).

Question 2)

The equations given are:

y = 1.5x - 1               Equation 1

y = 1                           Equation 2

The method of substitution can be used to find the solution.

Replacing y from Equation 2 into Equation 1 gives:

1 = 1.5x - 1

Add 1 to both sides:

2 = 1.5x

Dividing both sides by 1.5 yields:

x = 2/1.5

x = 1.33

y = 1

Thus, the solution of the system is (1.33, 1).

This equation can be solved with two solutions, corresponding to and .

Answer:

Step-by-step explanation:

Given

Solving for (a): n

To find n;

We will utilize

Substituting values for XY and XZ

Dividing by -6

Solving for (b) XY

Substituting 3 for n

Solving for (c): XZ

A dilation represents a transformation , centered at point O with a scale factor of k, which cannot be zero. This transformation keeps O fixed while transforming any other point P into its image P'. Points O, P, and P' are collinear.

In a dilation of , the scale factor maps the original figure to its transformed image in such a way that the distances from O to points of the image are half the distances from O to the original figure. Consequently, the image's size is also half that of the original figure.

Thus, <span>If represents the dilation of △ABC, then the properties of the image △A'B'C'</span> are:

<span>AB is parallel to A'B'.



The distance from A' to the origin is half that from A to the origin.</span>