Evaluate –6(x – 2y) when x = –3 and y = –5



–42

80

–80


–16

Answer:

8 miles per hour

Step-by-step explanation:

Given that a person runs a distance of  1/ 4 of a mile in 1/ 32 of an hour.

We have to compute the unit rate by setting up a complex fraction and simplifying

Let us find distance travelled in one hour.

[tex]\frac{1}{32} hour  .... \frac{1}{4} miles\\1 hour                  ... \frac{1}{4} /\frac{1}{32}\\=\frac{32}{4} =8mph[/tex]

i.e. unit rate is he travels in one hour 8 miles.

Unit rate is normally for a single unit and other unit is left correspondingly

Here hour or time is made as unit i.e. one hour and distance travelled in one hour is calculated as 8 miles per hour.

Final answer:

To find out how many 1-cup servings can be made from 4 gallons of cider, convert gallons to cups. Since 1 gallon equals 16 cups, 4 gallons equal 64 cups. Therefore, 64 children can be served 1 cup each.

Explanation:

To determine how many children can be served 1 cup of cider from a total of 4 gallons of cider, we need to first convert gallons to cups.

There are 4 quarts in a gallon.

Each quart consists of 4 cups.

Therefore, 1 gallon equals 4 quarts, which equals 16 cups (since 4 quarts x 4 cups/quart = 16 cups).

Now, to find out how many cups are in 4 gallons, we multiply the number of cups in one gallon by 4:

16 cups/gallon x 4 gallons = 64 cups

So, from 4 gallons of cider, 64 children can each have a 1 cup serving.

The equation 7(y-8)=7y+42 results in an implausible mathematical statement, meaning it has no valid solutions.

To begin, we isolate variable y in the given equation 7(y-8)=7y+42. First, expand the product on the left-hand side, which will be 7y - 56. This provides the simplified form 7y - 56 = 7y + 42. From this equation, we realize that this is an equation that has no solutions because it results in an implausible statement: -56 is not equal to 42. If we try to solve such an equation, we reduce it to a statement that does not hold true in mathematics, leaving us with no valid solutions for variable y. Therefore, this equation has no solutions.

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Alex had 24 video games originally, using deductive reasoning and simple algebra we concluded that the 6 games given by Hector represented a quarter of Alex's total games.

To solve the problem, we need to find out the total number of video games Alex had at the start. We know that Alex ended up with 16 games after making several transactions. He sold 3 games and gave 2 games to his brother, which means he had 16 + 3 + 2 = 21 video games after Hector gave him 6 games. As the given problem mentions that Hector received one fourth of Alex's total video games, that means these 6 games are one fourth of the total number of games Alex originally had. Hence, we can denote the total number of video games Alex initially had as X. Thus, 1/4 * X = 6. Solving this equation for X gives us X = 4 * 6 which is 24 video games.

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Answer:

18

Step-by-step explanation:

6 times 3 equals 18

Both trains will leave the station together again in B. 36 minutes.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers.

We have been given that "A" train leaves a subway station every 12 minutes. An "E" train leaves every 9 minutes.

If both trains just left the station on parallel tracks, then both leave the station together again;

We will solving for the LCM (Least Common Multiple),

The LCM of 12 and 9

12 = 2 x 3 x 4 x 6 x 12

9 = 3x 1 x 9

The LCM of 12 and 9 is 36

Hence, Both trains will leave the station together again in B. 36 minutes.

Learn more about multiplications;

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Answer:

1) true

2) false

Step-by-step explanation:

1) 4/2=2

-4/-2=2

2)-4/2 = -2≠2

4/-2 = -2 ≠2

Using a system of linear equations, the problem is solved to find that 407 adult tickets and 839 student tickets were sold to attain a total sale of $2,874 from 1,246 tickets.

The student's question involves solving a system of linear equations which is a topic in Mathematics, typically covered at the high school level. The system to solve is based on the following two equations derived from the information given:

The total amount of money collected from selling adult and student tickets is $2,874.

The total number of tickets sold, which is 1,246.

We assign variables to represent the quantity of each type of ticket sold. Let A represent the number of adult tickets and S represent the number of student tickets. Thus, we have these two equations:

5A + 1S = 2874 (This equation represents the total money collected.)

A + S = 1246 (This equation represents the total number of tickets.)

To solve the system, we can use the method of substitution or elimination. We'll use elimination:

Multiply the second equation by 5 to have the same coefficient for A as in the first equation: 5A + 5S = 6230

Subtract the first equation from this new equation to eliminate A: (5A + 5S) - (5A + 1S) = 6230 - 2874, simplifying to 4S = 3356

Divide by 4 to solve for S: S = 839

Substitute the value of S back into the second original equation: A + 839 = 1246

Solve for A: A = 1246 - 839, so A = 407

So, 407 adult tickets and 839 student tickets were sold.

Answer:

3.71

Step-by-step explanation:

We are asked to divide 70.49 by 19.

We know that 19 times 3 is equal to 57 and 19 times 4 is 76, so 19 will go in 70 for 3 times and give a remainder of 13.

9)70.49( 3

  57

    13

Now, we will bring down 4. To do so we need to put a decimal in quotient as:

9)70.49( 3.71

  57

    134

   133

        19

       19

          0

Therefore, 70.49 divided by 19 is equal to 3.71.

Answer:

The rate for this situation is  $7 saved per weeks

Step-by-step explanation:

We get a rate when we compare two measurements with different units. In this case ,  we must compare the amount saved with time (each week).  If we have $28 saved in 4 weeks,  we can divide;

$28 saved / 4 weeks =$ 7 saved / weeks

Answer:

CircularPendicular

Step-by-step explanation:

The length of the page inside the margin is 5 3/4 inches.

The length of the page inside of the margin can be found by subtracting the top margin and bottom margin from the total length of the page. In this case, the top margin is 1/2 inch and the bottom margin is 3/4 inch. The length of the page inside of the margin is:

Length of page inside margin = Total length of page - Top margin - Bottom margin
Length of page inside margin = 10 inches - 1/2 inch - 3/4 inch

First, let's convert the fractions to a common denominator which is 4:

Length of page inside margin = 10 inches - 2/4 inch - 3/4 inch

Now, we can subtract the fractions to get a single fraction:

Length of page inside margin = 10 inches - 5/4 inch

Next, let's convert the mixed number to an improper fraction:

Length of page inside margin = 10 inches - 1 1/4 inches
Length of page inside margin = 10 inches - 4/4 inches - 1/4 inches
Length of page inside margin = 10 inches - 4 1/4 inches

Finally, subtracting gives us the length of the page inside of the margin:

Length of page inside margin = 10 - 4 1/4
inches = 5 3/4 inches

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Answer:

1

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