Solve for x in the equation 10.25(x−4.4)=69.7 .(1 point)

Question

Responses

63.85
63.85

6.8
6.8

11.2
11.2

2.4

Answer 1

To solve the equation $10.25(x-4.4)=69.7$, follow these steps:

1. Distribute $10.25$ on the left side: $$10.25x-10.25\times 4.4=69.7$$

   Calculating $10.25\times 4.4$: $$10.25\times 4.4=45.1$$

   So the equation is now: $$10.25x-45.1=69.7$$

2. Add $45.1$ to both sides: $$10.25x=69.7+45.1$$

   Calculating $69.7+45.1$: $$69.7+45.1=114.8$$

   Now, the equation is: $$10.25x=114.8$$

3. Divide both sides by $10.25$: $$x=\frac{114.8}{10.25}$$

   Calculating $\frac{114.8}{10.25}$: $$x\approx 11.2$$

Thus, the solution for $x$ is $\boxed{{\displaystyle 11.2}}$.

Answer 2

Solve for r in the equation 7/8(r−5/21)=3/2 .(1 point)
Responses

31/21
Start Fraction 31 over 21 End Fraction

41/21
Start Fraction 41 over 21 End Fraction

20/49
Start Fraction 20 over 49 End Fraction

521/336

Answer 3

To solve the equation

$$\frac{7}{8}(r-\frac{5}{21})=\frac{3}{2},$$

follow these steps:

1. Multiply both sides by 8 to eliminate the fraction on the left side:

$$7(r-\frac{5}{21})=8\cdot \frac{3}{2}.$$

Calculating the right side:

$$8\cdot \frac{3}{2}=4\cdot 3=12.$$

Now, the equation is:

$$7(r-\frac{5}{21})=12.$$

2. Divide both sides by 7:

$$r-\frac{5}{21}=\frac{12}{7}.$$

3. Add $\frac{5}{21}$ to both sides:

$$r=\frac{12}{7}+\frac{5}{21}.$$

4. To add the two fractions, find a common denominator. The common denominator for 7 and 21 is 21. Rewrite $\frac{12}{7}$ with a denominator of 21:

$$\frac{12}{7}=\frac{12\times 3}{7\times 3}=\frac{36}{21}.$$

Now we can add:

$$r=\frac{36}{21}+\frac{5}{21}=\frac{36+5}{21}=\frac{41}{21}.$$

Thus, the solution for $r$ is

$$\boxed{{\displaystyle \frac{41}{21}}}.$$

Answer 4

The supermarket is having a sale if you purchase 3 of an item. Maggie bought macaroni and cheese and ramen with this sale. In total, she spent $9. Each box of mac and cheese cost $1.25. Identify the equation that will determine the amount for each package of ramen.(1 point)
Responses

3x+1.25=9
3 x plus 1.25 equals 9

1.25(x+3)=9
1.25 Left Parenthesis x plus 3 Right Parenthesis equals 9

9(x+1.25)=3
9 Left Parenthesis x plus 1.25 Right Parenthesis equals 3

3(x+1.25)=9

Answer 5

To find the equation that determines the amount for each package of ramen, we need to consider the information provided:

1. Maggie bought macaroni and cheese and ramen, spending a total of $9.
2. She purchased 3 items, and each box of macaroni and cheese costs $1.25.

Let $x$ be the cost of each package of ramen.

Since there are 3 items purchased total, the total cost can be represented as:

$$\text{Total cost}=\text{Cost of macaroni and cheese}+\text{Cost of ramen}$$

If she bought 3 items and she spent $9 total, we need to account for both the mac and cheese (which is 1 box) and the ramen (2 boxes) if we assume she had 1 mac and cheese and 2 ramen.

The equation we want to construct is:

$$1.25+2x=9$$

Here, $1.25$ represents the cost of the macaroni and cheese, and $2x$ represents the cost of 2 packages of ramen.

However, none of the provided responses exactly match this equation. If we're assuming that Maggie bought 3 packages total and just one was mac and cheese, we might need to interpret that she bought either one mac and cheese and two ramen, forming the potential equations:

In that case:

$$1.25+2x=9⟹2x=9-1.25\to 2x=7.75\to x=\frac{7.75}{2}=3.875$$

From the provided options, it seems that the most appropriate corresponding option would be if she bought 3 ramen packages, equating the whole cost with respect to mac and cheese:

Thus the equation that provides the context when linking 3 items together with known costs would best align with $1.25(x+3)=9$ where $x+3$ includes some equal partition among mac and ramen.

This, however does not fully fit the description. The most pertinent conclusion ideally stands at finding the formula aligning to the balance of her total spend captured in a clearer definition.

In Logical Summary:

• The best-fitting response based on whether mac serves fully against the cost of ramen would land here: “3(x + 1.25) = 9”

Given the essence of reaching final sums fundamentally ruled under general assumptions.

Response:

$$3(x+1.25)=9$$

Answer 6

A farmer has a rectangular plot of land with an area of 300 square feet as shown in the diagram. Identify the equation to calculate the missing length based on the diagram shown.

(1 point)
Responses

15x=300
15 x equals 300

15(6+x)=300
15 Left Parenthesis 6 plus x Right Parenthesis equals 300

15(6)+x+15(4)=300
15 Left Parenthesis 6 Right Parenthesis plus x plus 15 Left Parenthesis 4 Right Parenthesis equals 300

15(x+10)=300

Answer 7

To determine the equation to calculate the missing length based on the information given (a rectangular plot of land with an area of 300 square feet), let's analyze the situation.

Assuming the dimensions of the plot are related as follows:

• One of the lengths of the rectangle is given as $15$ feet (which seems to be a side of the rectangle).
• The other side of the rectangle consists of $6+x$ feet, where $x$ is the unknown length we want to solve for.

The area $A$ of a rectangle is calculated as:

$$A=\text{length}\times \text{width}$$

In this case, the area is given as $300$ square feet, and we can recognize the following equation based on the area:

$$15\times (6+x)=300$$

This equation states that the fixed length (15 feet) multiplied by the unknown length (which is $6+x$) yields the total area of 300 square feet.

Therefore, the correct response is:

$$15(6+x)=300$$

Answer 8

Pick a different answer

Answer 9

Sure! Let's consider other options given your request to pick a different answer.

Since the area of the rectangular plot of land is $300$ square feet, and assuming that one dimension (length) is $15$ feet, we could derive $x$ based on:

1. If we simply look at the dimensions, $15x=300$ would solve for one dimension (where $x$ might represent the other side) but it doesn’t incorporate the $6$.

2. Other options presented include equations that combine dimensionality but process differently.

Given your request, let’s examine a suitable or alternative option considering the previously laid structure:

Consider: $$15(x+10)=300$$ This implies that:

• $x+10$ serves as the other dimension, giving a combined length setup.

Therefore, another option to understand here is:

$$15(x+10)=300$$

Please feel free to clarify further if there is a specific orientation towards scenarios or interpretations needed!

Answer 10

The product of 10 and the sum of a number and −1 is negative −40 . Find the number.(1 point)
Responses

5
5 - incorrect

−5
negative 5 - no response given

3
3 - no response given

−3

Answer 11

To solve the problem, we need to set up an equation based on the statement:

"The product of 10 and the sum of a number and -1 is negative -40."

Let's denote the number as $x$.

The equation can be set up as follows:

$$10(x+(-1))=-40$$

This simplifies to:

$$10(x-1)=-40$$

Now we can solve for $x$.

1. Divide both sides of the equation by 10:

$$x-1=-4$$

2. Now, add 1 to both sides:

$$x=-4+1$$

3. Finally, simplify:

$$x=-3$$

Thus, the number is $\boxed{{\displaystyle -3}}$.