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Question

Question
The equation 10x+13=−12
is solved as follows. Enter the correct numbers to complete the solution.(1 point)
10x+13=−12

10x=

Subtract 13 from both sides of the equation.

x=

Divide both sides of the equation by 10. If the answer is an improper fraction, enter the improper fraction.

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Answer 1

To solve the equation $10x+13=-12$, we can follow the steps provided.

1. Start with the original equation: $$10x+13=-12$$

2. Subtract 13 from both sides of the equation: $$10x=-12-13$$ $$10x=-25$$

3. Now, divide both sides of the equation by 10 to solve for $x$: $$x=\frac{-25}{10}$$ Simplifying this fraction gives: $$x=\frac{-5}{2}$$

So the numbers to fill in are:

• For $10x=$: $-25$
• For $x=$: $\frac{-5}{2}$

Thus, the complete solution is:

$$10x=-25$$ $$x=\frac{-5}{2}$$

Answer 2

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Question
It takes Julian 12
hour to walk 2 miles. He decides to start working in his spare time, but because he wants to make sure he has enough time to go a desired distance he created the data table. Determine the constant of proportionality, yx
.

(1 point)
The constant of proportionality is
miles per hour for this situation.
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Answer 3

To determine the constant of proportionality (which is the rate of speed in this context), we need to find Julian's speed in miles per hour.

Julian walks 2 miles in 12 hours. To find the speed in miles per hour, we can use the formula:

$$\text{Speed}=\frac{\text{Distance}}{\text{Time}}$$

Setting the distance to 2 miles and the time to 12 hours, we have:

$$\text{Speed}=\frac{2\text{ miles}}{12\text{ hours}}=\frac{2}{12}\text{ miles per hour}$$

This simplifies to:

$$\text{Speed}=\frac{1}{6}\text{ miles per hour}$$

Therefore, the constant of proportionality $yx$ is:

$$\frac{1}{6}\text{ miles per hour}$$

Finally, rounding off if needed, we can state the answer as:

The constant of proportionality is $\frac{1}{6}$ miles per hour for this situation.

Answer 4

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Question
A caterpillar can crawl 12
of an inch in 14
of a minute. How far can he crawl in 1 minute?(1 point)
The caterpillar can crawl
inch(es) in one minute.
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Answer 5

To find out how far the caterpillar can crawl in 1 minute, we start with the distance it crawls in $\frac{1}{4}$ of a minute, which is $\frac{12}{1}$ inches.

First, we find how far the caterpillar crawls in 1 minute. Since it crawls $\frac{12}{1}$ inches in $\frac{1}{4}$ of a minute, we can find the distance for a full minute by setting up a proportion:

$$\text{Distance in 1 minute}=\text{Distance in }\frac{1}{4}\text{ minute}\times \text{Number of }\frac{1}{4}\text{ minutes in 1 minute}$$

Since there are 4 quarters in a full minute:

$$\text{Distance in 1 minute}=\frac{12}{1}\text{ inches}\times 4$$

Let's calculate that:

$$\text{Distance in 1 minute}=12\times 4=48\text{ inches}$$

Therefore, the caterpillar can crawl 48 inches in one minute.

Answer 6

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Question
Determine the first step in simplifying this expression.

13−2(1−15)÷4

(1 point)
Responses

13−2
13 minus 2

2×1
2 times 1

1−15
1 minus 15

15÷4
15 divided by 4
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Answer 7

To determine the first step in simplifying the expression $13-2(1-15)÷4$, we should follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

The first step in this expression involves simplifying the expression inside the parentheses, $1-15$.

Therefore, the correct first step is:

1 − 15 (which simplifies to -14).

After this first step, the expression would proceed as follows, but for the purpose of the question, identifying the first step is sufficient.

So, the answer is: 1−15.

Answer 8

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Question 1
Correctly select the order of the steps to solve this equation.

13(6x−9)=−33

(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.
Step 1:
Step 2:
Step 3:
Question 2
Solve for x.

13(6x−9)=−33

(1 point)
Responses

x = -30
x = -30

x = -15
x = -15

x = -22
x = -22

x = -19
x = -19
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Answer 9

Let's solve the equation $13(6x-9)=-33$ step by step and determine the order of the steps.

Question 1: Order of Steps

To solve the equation, the steps are as follows:

1. Step 1: Distribute the 13. $$13\times 6x-13\times 9=-33\Rightarrow 78x-117=-33$$

2. Step 2: Add 117 to both sides. $$78x-117+117=-33+117\Rightarrow 78x=84$$

3. Step 3: Divide both sides by 78. $$x=\frac{84}{78}=\frac{14}{13}\text{(which simplifies to }x=\frac{14}{13}\text{ or approximately 1.08)}$$

However, it seems the choices you've provided for the value of $x$ are integers. Therefore, we should verify whether our result aligns with any of the options provided in Question 2.

Question 2: Solve for $x$

Let's go through the calculations again to ensure we can relate it to the options provided.

1. Start with: $$13(6x-9)=-33$$

2. Distribute 13: $$78x-117=-33$$

3. Add 117: $$78x=-33+117\Rightarrow 78x=84$$

4. Divide by 78: $$x=\frac{84}{78}$$

This can be simplified: $$x=\frac{14}{13}\text{(approximately 1.08)}$$

Since we have no matching options from the choices you provided, please verify the given options as none of them matches.

However, if you want to stick to the structured order, the correct sequence of steps is:

• Step 1: Distribute $13$
• Step 2: Add $117$ to both sides
• Step 3: Divide by $78$

Given this situation, it's possible that there was a miscommunication or misunderstanding of the correct answer, if this indeed relates to integers; hence you would need to review the context in which this equation was derived. Please check if there is a slight discrepancy in the equation or consider reevaluating the options provided.

Answer 10

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Question 1
A processing machine crushes 314
kilograms of dried fruits in 34
minute.

What process will you use to solve this problem?

(1 point)
Responses

34÷314
3 fourths divided by 3 1 fourth

314−34
3 and 1 fourth minus 3 fourths

314×34
3 and 1 fourth times 3 fourths

314÷34
3 and 1 fourth divided by 3 fourths
Question 2
(1 point)
Enter your solution as a mixed number.


kilograms per minute

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Answer 11

To determine the process for solving how many kilograms of dried fruits are crushed per minute by the machine, we need to calculate the rate of crushing. This can be found by dividing the total amount of fruit crushed by the time taken to crush it.

Question 1: Process Selection

The correct process to find the kilograms per minute is:

314 ÷ 34

This means you divide the total kilograms (314) by the total minutes (34) to find how many kilograms are processed per minute.

Question 2: Solution as a Mixed Number

Now, let's perform the division:

$$\frac{314}{34}\approx 9.235294117647059$$

To express it as a mixed number, we can first calculate how many whole times 34 fits into 314:

1. Perform the division: $$314÷34=9\text{(whole number part)}$$

2. Calculate the remainder: $$34\times 9=306$$ $$314-306=8\text{(remainder)}$$

3. Write as a mixed number: $$9\frac{8}{34}$$

4. Simplify the fraction $\frac{8}{34}$: $\frac{8}{34}$ simplifies to $\frac{4}{17}$ (dividing both by 2).

Thus, the final answer as a mixed number is:

$$9\frac{4}{17}\text{ kilograms per minute}$$

Summary of Answers:

• Question 1: 314 ÷ 34
• Question 2: $9\frac{4}{17}$ kilograms per minute