The speed limit sign on the expressway says that the speed limit is 55 mph. Write an equality that represents all speeds you can legally drive on the expressway.(1 point)
Responses
x≥55
x is greater than or equal to 55
x<55
x<55
x≤55
x is less than or equal to 55
x>55
x is greater than 55
are you correct?
No, my previous response was incorrect. The correct equality that represents all speeds you can legally drive on the expressway is:
x ≤ 55
This means that x is less than or equal to 55 mph.
If you were to graph the inequality below on a number line:
35<7x
(2 points)
Would you use an open or a closed circle?
Would your arrow on the number line point to the left or to the right?
To graph the inequality 35 < 7x on a number line, you would use an open circle.
The arrow on the number line would point to the right.
A student solved the following equation using the following steps:
2(2x+2)=4(x+4)
4x+4=4x+4
4=4
Conclusion: Infinitely many solutions
(2 points)
Based on the student's work, the equation was solved
The equation solved correctly would show that it has
solution(s).
Based on the student's work, the equation was not solved correctly. The equation that was obtained, 4 = 4, is a true statement, but it does not provide any information about the value of x. As a result, it cannot be concluded that the equation has infinitely many solutions. The correct conclusion would be that the equation has no unique solution.
Solve the equation for y:
3x+5y=60
(2 points)
Responses
y=60−3x
y is equal to 60 minus 3 x
y=−35x+12
y is equal to negative 3 fifths x plus 12
y=57x5
y is equal to 57 x over 5
y=60+3x5
To solve the equation 3x + 5y = 60 for y, we need to isolate y on one side of the equation.
Step 1: Subtract 3x from both sides of the equation:
3x + 5y - 3x = 60 - 3x
5y = 60 - 3x
Step 2: Divide both sides of the equation by 5:
5y/5 = (60 - 3x)/5
y = (60 - 3x)/5
So the correct equation solving for y is:
y = (60 - 3x)/5
are you sure?
Apologies for the previous incorrect response. Let's solve the equation correctly this time.
To solve the equation 3x + 5y = 60 for y, we need to isolate y on one side of the equation.
Step 1: Subtract 3x from both sides of the equation:
3x + 5y - 3x = 60 - 3x
5y = 60 - 3x
Step 2: Divide both sides of the equation by 5:
(5y)/5 = (60 - 3x)/5
y = (60 - 3x)/5
So the correct equation solving for y is:
y = (60 - 3x)/5
You originally have x colored pencils in your pencil box. You share them equally between you and your friend. You add in 3 more colored pencils to your own box after sharing them. This gives you a total of 15 pencils.
a) Write an equation and show all of your steps for solving x (the original number of pencils in your box)
b) What if you wanted to have at least 20 pencils left in your box? How many pencils would you have needed originally?
c) Write an inequality and show all steps for solving for x.
(5 points)
a) Let's write an equation to represent the situation:
(x/2) + 3 + x = 15
We start with x colored pencils in your box. When you share them equally with your friend, you each have x/2 colored pencils. You then add 3 more colored pencils to your own box. In total, the number of colored pencils is 15.
Now let's solve for x:
(x/2) + 3 + x = 15
Multiply both sides of the equation by 2 to eliminate the fraction:
2(x/2) + 2(3) + 2(x) = 2(15)
x + 6 + 2x = 30
3x + 6 = 30
Subtract 6 from both sides:
3x + 6 - 6 = 30 - 6
3x = 24
Divide both sides by 3:
3x/3 = 24/3
x = 8
So the original number of colored pencils in your box was 8.
b) If you wanted to have at least 20 pencils left in your box, you would set up the inequality:
(x/2) + 3 >= 20
Let's solve for x:
(x/2) + 3 >= 20
Subtract 3 from both sides:
(x/2) >= 17
Multiply both sides by 2 to eliminate the fraction (since dividing by 1/2 is the same as multiplying by 2):
2(x/2) >= 2(17)
x >= 34
Therefore, you would need to have originally had at least 34 colored pencils in your box.
c) The inequality for the original number of pencils, x, would be:
x >= 34
Match the equation to the correct graphed solution.(2 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
I apologize, but I cannot generate a graph or insert responses as you described. However, if you provide me with the equations and the graphed solutions, I can help you match them accordingly.
match the equation to the correct graphed solution
1/4(8x+16)> - 4
8x < 4x + 28
-5 (x + 5) > -15
-3 (x - 12) > 0
I apologize for any confusion, but without visual access to the graphs, I am unable to match the equations to their correct graphed solutions. However, I can help you determine the solutions for each equation individually:
1) 1/4(8x+16) > -4
To solve this inequality, we can distribute the 1/4:
2x + 4 > -4
Next, subtract 4 from both sides:
2x > -8
Finally, divide both sides by 2:
x > -4
2) 8x < 4x + 28
Subtract 4x from both sides:
4x < 28
Next, divide both sides by 4:
x < 7
3) -5(x + 5) > -15
First, distribute the -5:
-5x - 25 > -15
Next, add 25 to both sides:
-5x > 10
Finally, divide both sides by -5, remembering to change the direction of the inequality because we are dividing by a negative number:
x < -2
4) -3(x - 12) > 0
First, distribute the -3:
-3x + 36 > 0
Next, subtract 36 from both sides:
-3x > -36
Finally, divide both sides by -3, remembering to change the direction of the inequality:
x < 12
I hope this helps!
What is the purpose of a hook in an introductory paragraph?(1 point)
Responses
to grab the interest of the reader
to grab the interest of the reader
to establish the tone of the essay
to establish the tone of the essay
to introduce the main topic of the essay
to introduce the main topic of the essay
to state the perspective of the writer
The purpose of a hook in an introductory paragraph is to grab the interest of the reader.
Amelia is writing an informative text about how to make a paper airplane. The audience is 10 to 14-year-olds. Which hook would best grab the reader's attention?(1 point)
Responses
There are many different ways that you can make a paper airplane.
There are many different ways that you can make a paper airplane.
Lift. Gravity. Force. What if I told you that you could teach all of these concepts to your students with a single piece of paper?
Lift. Gravity. Force. What if I told you that you could teach all of these concepts to your students with a single piece of paper?
Paper was invented in China, so many historians credit the Chinese with inventing the very first paper airplane.
Paper was invented in China, so many historians credit the Chinese with inventing the very first paper airplane.
Math class. The dinner table. Your little brother’s T-ball game. What if I told you that you could make all of these places much more exciting with a simple piece of paper?
Among the provided options, the hook that would best grab the reader's attention for an informative text about how to make a paper airplane for 10 to 14-year-olds would be:
Math class. The dinner table. Your little brother’s T-ball game. What if I told you that you could make all of these places much more exciting with a simple piece of paper?
are you right?
Yes, I am confident that the provided hook "Math class. The dinner table. Your little brother’s T-ball game. What if I told you that you could make all of these places much more exciting with a simple piece of paper?" would be the most effective in grabbing the attention of 10 to 14-year-olds for an informative text about making a paper airplane. This hook creates curiosity and excitement by suggesting that a simple piece of paper can enhance different aspects of their lives and experiences.
Use the following introductory paragraph to answer the question.
Did you know that some monkeys in Thailand teach their young to floss? If monkeys can do it, then so can we! It is so important to teach our children healthy habits when it comes to oral hygiene. There are many simple strategies you can use when teaching young kids to brush, floss, and make healthy choices about eating and drinking.
Who is the intended audience?
(1 point)
Responses
scientists who study monkeys
scientists who study monkeys
the staff of a dentist's office
the staff of a dentist's office
parents of young children
parents of young children
children who are just learning to brush and floss
Based on the introductory paragraph, the intended audience is parents of young children.
Drag and drop the words into the correct locations.(1 point)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
The main topic or topics are previewed in the Response area of an essay, and most details and supporting arguments are presented in the Response areaof the essay.