(07.06)Number line with open circle on 9 and shading to the left. Which of the following inequalities best represents the graph above? x < 9 x > 9 x ≤ 9 x ≥ 9

The true statement for the given information is the y coordinate is negative

The correct answer is:

d. The y-coordinate is negative.

Let's break down the problem step by step:

1. Identify the Quadrants of the Endpoints: One endpoint lies in quadrant 2, and the other endpoint lies in quadrant 3.

2. Determine the Coordinates of the Endpoints:

  - For a point in quadrant 2, both the x-coordinate and y-coordinate are positive.

  - For a point in quadrant 3, the x-coordinate is negative, and the y-coordinate is negative.

3. Find the Midpoint Formula: The midpoint formula for a line segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:

  [tex]\[ \text{Midpoint} = \left(\frac{{x_1 + x_2}}{2}, \frac{{y_1 + y_2}}{2}\right) \][/tex]

Now, let's apply these steps to find the properties of the midpoint:

1. Identify the Quadrants of the Endpoints:

  - Endpoint 1: Quadrant 2

  - Endpoint 2: Quadrant 3

2. Determine the Coordinates of the Endpoints:

  - Endpoint 1 (Quadrant 2): Positive x-coordinate, Positive y-coordinate

  - Endpoint 2 (Quadrant 3): Negative x-coordinate, Negative y-coordinate

3. Find the Midpoint:

  - Since the x-coordinate of one endpoint is positive and the x-coordinate of the other endpoint is negative, the x-coordinate of the midpoint will be between these two values, but we cannot determine its sign from this information.

  - Since one y-coordinate is positive and the other is negative, the midpoint's y-coordinate will lie between these two values, but it will be negative.

Therefore, the correct answer is:

d. The y-coordinate is negative.

The midpoint's x-coordinate could be either positive or negative, depending on the specific values of the endpoints. However, the y-coordinate will always be negative because it lies between a positive y-coordinate and a negative y-coordinate. This is consistent with the fact that one endpoint lies in quadrant 2 (positive y) and the other lies in quadrant 3 (negative y).

Complete question:

one endpoint of the line segment lies on quadrant 2 while the other endpoint lies in quadrant 3 which statement is true about the segment's midpoint

a. the x coordinate is negative

b. the x coordinate is positive

c. the y coordinate is positive

d. the y coordinate is negative

Final answer:

The inequality representing Catherine's scenario is 8.5x + 20 < 54, and the number of tubes of paint she can buy is less than 4.

Explanation:

The inequality that best represents the scenario where Catherine has $54, plans to spend more than $20 on a painting canvas, and the rest on paint tubes that cost $8.50 each, is 8.5x + 20 < 54. This equation illustrates how much money Catherine will have left after purchasing the painting canvas for more than $20.

To determine the number of paint tubes Catherine can buy, we solve the inequality:

Subtract 20 from both sides: 8.5x < 54 - 20

Simplify the right side: 8.5x < 34

Divide both sides by 8.5 to isolate x: x < 34 / 8.5

Calculate x: x < 4

Therefore, the number of tubes of paint Catherine can buy is less than 4 (C. less than 4).

Kinsey walks a total of 148,400 feet to visit Carlito's house 112 times. This was calculated by multiplying the distance of a single trip (1,325 feet) by the number of trips (112).

To solve this problem, we simply need to multiply the distance that Kinsey walks to Carlito's house by the number of visits she makes. So, the calculation would be 1,325 feet * 112 visits.

After doing this multiplication, we find that the total distance Kinsey walks to Carlito's house in 112 visits is 148,400 feet.

This is a good example of how problems can be solved using simple multiplication in real-life situations, like calculating the total distance covered in multiple trips.

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Answer:  11.5 feet

Step-by-step explanation:

Given: The height of Fatim = 6 feet

At noon, he stands with the sun behind him casting a shadow. Also, Fatima is standing vertical to the ground such that a right triangle is formed.

Let the length of Fahim’s shadow be x.

By Pythagoras theorem , we have

[tex]13^2=x^2+6^2\\\\\Rightarrow169=x^2+36\\\\\Rightarrow\ x^2=169-36\\\\\Rightarrow\ x^2=133\\\\\Rightarrow x=\sqrt{133}=11.5325625947\approx11.5[/tex]

Hence, the  length of Fahim’s shadow =11.5 feet

After selling 6 out of 21 granola bars, the store has 15 left. Following a shipment of 42 granola bars, the store will have a total of 57 granola bars in stock.

To find out how many granola bars the store will have in stock after the shipment, we should first calculate how many granola bars are left after the sales by subtracting the number sold from the initial stock. They started with 21 granola bars and sold 6, so they have 21 - 6 = 15 granola bars left. Then, we add the number of granola bars in the shipment arriving tomorrow to the number they currently have in stock. They will receive 42 granola bars in the shipment, so the total will be 15 + 42 = 57 granola bars in stock after the shipment arrives.

To simplify the expression 4/7 * 5/9, the equivalent expression is 20/63.

To simplify the expression 4/7 * 5/9, we can multiply the numerators together to get the new numerator and multiply the denominators together to get the new denominator. So, the expression becomes 20/63. Therefore, none of the options listed are equivalent to 4/7 * 5/9.

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None of the options a, b or c are equivalent to the expression 4/7*5/9. The correct expression must simplify to 20/63.

The question is asking to find out which of the provided expressions is equivalent to the expression 4/7*5/9. The correct option should yield the same result as the original expression when calculated. The expression 4/7*5/9 simplifies to 20/63.

Let's check the provided options:

The provided information about relative frequencies is irrelevant for this question.

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