The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1. On a coordinate plane, a parabola, labeled f of x, opens up. I

Answer:

The correct selection is 1.

Step-by-step explanation:

The histogram indicates that

In the 5-10 age group, there are 7 students.

In the 11-13 age group, 5 students are represented.

In the 14-18 age category, 4 students are included.

This implies that the ages of 7 students fall within the 5-10 range, 5 students within the 11-13 range, and 4 students within the 14-18 range.

The total count in the dataset is

In options 3 and 4, the counts in the datasets are fewer than 16. Hence, options 3 and 4 are invalid.

Option 2 exclusively contains data within the 5-10 range, making it incorrect as well.

In option 1,

Class intervals      elements           frequency

5-10                    5,6,7,8,9,10,10           7

11-13                  11,11,12,12,13            5

14-18                    14,14,15,16              4

Based on the above table, we can determine that data set 1 is represented in the provided histogram.

Thus, the answer is option 1.

Answer:

1. Both directions

2. Only in one direction

Step-by-step explanation:

    The reason Statement 1 can occur both ways is that if Bo and Mel are connected, it holds true forward and backward.

The reasoning for Statement 2 being one-directional is that if the sprinklers are operating, then the grass is wet will be valid since it's stating ONLY that the sprinklers are on. If it were to reverse and the grass is wet ONLY because of the sprinklers, then it's incorrect as rain could also cause the grass to be wet. Thus, there are numerous possibilities for the grass being wet, which explains the answers.

Response:

Step-by-step explanation:

A line is defined as a one-dimensional entity that lacks thickness and stretches infinitely in both directions.

A line segment contains two endpoints, while a ray consists of a single endpoint.

The equation given is .

Objective: to identify a line completely within the set designated by this equation.

Solution:

Consider .

Verification:

.

Thus, fulfills the criteria of the given equation.

Answer:

The diameter of the circular path is 120√2 m.      

Step-by-step explanation:

The information provided indicates:

When Luis walked one-fourth of the distance around the circular path, the magnitude of his displacement measured 120 m.

Displacement = 120 m

The two radius lengths along with the displacement form a right-angle triangle.

Using the Pythagorean theorem:

where r represents the radius of the circular path.

Thus, the diameter of the circular path can be expressed as:

Therefore, the diameter of the path is 120√2 m.

The accompanying image depicts the circular path.