28.02.2023

Choose the inequality that represents the following graph. Choose 1 answer

. 12

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Mathematics
Step-by-step answer
P Answered by PhD

A

Step-by-step explanation:

b<3

Mathematics
Step-by-step answer
P Answered by PhD

A

Step-by-step explanation:

b<3

StudenGPT
Step-by-step answer
P Answered by Studen AI
To find the solution for the given system of inequalities, we need to graph each inequality and identify the region that satisfies both inequalities. Let's solve this step by step: 1. Start with the first inequality: \(y < \frac{2}{3}x + 2\) To graph this inequality, we need to plot the line \(y = \frac{2}{3}x + 2\). To plot the line, we can start by identifying two points on the line. Let's choose x = 0 and x = 3 to find the respective y-values. For x = 0: \(y = \frac{2}{3}(0) + 2 = 2\) For x = 3: \(y = \frac{2}{3}(3) + 2 = 4\) Plotting these two points, we have the line that goes through (0, 2) and (3, 4). 2. Now, let's examine the second inequality: \(y > -\frac{4}{3}x + 1\) To graph this inequality, we need to plot the line \(y = -\frac{4}{3}x + 1\). Again, let's choose x = 0 and x = 3 to find the respective y-values. For x = 0: \(y = -\frac{4}{3}(0) + 1 = 1\) For x = 3: \(y = -\frac{4}{3}(3) + 1 = -3\) Plotting these two points, we have the line that goes through (0, 1) and (3, -3). 3. Now, let's analyze the shaded regions for each inequality. For the first inequality \(y < \frac{2}{3}x + 2\), the shaded region is below the line. For the second inequality \(y > -\frac{4}{3}x + 1\), the shaded region is above the line. 4. Finally, we need to consider the overlapping region of the shaded regions from both inequalities. This overlapping region is the solution to the system of inequalities. Comparing the descriptions provided for each choice, we can determine that the correct answer is Choice A. So, the graph that represents the system of inequalities is a coordinate plane with a graphed system of inequalities. The x- and y-axes both scale by one. There is a solid line representing an inequality that goes through the points (-3, 0) and (0, 2). The shaded region for this inequality is below the line. There is a dashed line representing the second inequality that goes through the points (0, 1) and (3, -3). The shaded region for this inequality is above the line.
Mathematics
Step-by-step answer
P Answered by PhD

Given that “The amount of money in my wallet is more than $10, but less than $20 " can be written in inequality form as

10 < w <  20   where  " w"  is the amount in the wallet .

1 ) Puzzle : -

Ryan  is eating cookies . His mother ask how many cookies did he have .

He said number of cookies he ate is more than 19 and less than 41 .

We can write it in equality form as  19 < x < 41 where  ' x ' is number of cookies Ryan have .  

2) Puzzle :-

Number of steps a child take in an hour is more than 19 and less than 41 .

Write the situation in inequality form .

19 < p < 41 where  " p " is the number of steps a child take in an hour .

3) Puzzle :-

Mother said to his child : " the number of  coins in your piggy bank is more than 19 and less than 41 .

19 < c < 41  where " c " is number of coins in piggy bank .

Step-by-step explanation:

Mathematics
Step-by-step answer
P Answered by PhD

1. C

2. D

3. C

Explanation:

1. Girls = 12 plus twice the number of boys, so  C. y = 12 + 2x.

2. You have to see which point has the second value being greater than the first value:

 A) -1 > -2 is not true

 B) 0 > 1 is not true

 C) 2 > 3 is not true

 D) 8 > 4 is true, so it's D

3. Add the two values and see if it's less than 5

 A) -1-4 < 5 is true

 B) 0 + 4 < 5 is true

 C) 1 + 7 < 5 is not true, so this is the answer

 D) 2 + 2 < 5 is true

Mathematics
Step-by-step answer
P Answered by PhD

1. C

2. D

3. C

Explanation:

1. Girls = 12 plus twice the number of boys, so  C. y = 12 + 2x.

2. You have to see which point has the second value being greater than the first value:

 A) -1 > -2 is not true

 B) 0 > 1 is not true

 C) 2 > 3 is not true

 D) 8 > 4 is true, so it's D

3. Add the two values and see if it's less than 5

 A) -1-4 < 5 is true

 B) 0 + 4 < 5 is true

 C) 1 + 7 < 5 is not true, so this is the answer

 D) 2 + 2 < 5 is true

StudenGPT
Step-by-step answer
P Answered by Studen AI
The task requires us to find the number of tickets (let's denote it as 't') the committee needs to sell to have money left over after they pay for the dance.

Let's start with what we know:

1. The dance committee already has $72 from a bake sale.
2. They will earn $4 from each ticket they sell.
3. The dance will cost $400.

The inequality to determine the number of tickets the committee could sell to have money left over after they pay for the dance is:

4t + 72 > 400

The 4t term represents the income from selling t tickets, and 72 is the income from the bake sale. The total income should be greater than the dance cost (which is $400) for there to be money left over.

Now let's solve the inequality:

Step 1: Reorganize the inequality:
4t > 400 - 72

Step 2: Simplify the right-hand side:
4t > 328

Step 3: Divide through by 4 to solve for 't':
t > 82

We can review our steps to ensure we didn't overlook anything. Step 1 involved basic arithmetic operations. Step 2 was subtraction, where we combined like terms, and the result checks out. Step 3 was a simple division operation.

Our final answer is:
t > 82

So, the dance committee needs to sell more than 82 tickets to have money left after they pay for the dance. This means the solution set of the inequality is (Choice C) t > 82.

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