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3 years ago

In the equation 0.5x - 8 = 1.5, the decimal coefficient is

Mathematics

1 answer:

Keith_Richards [23]3 years ago

4 0

We have been given an equation $0.5x - 8 = 1.5$ . We are asked to find the decimal coefficient of the equation.

We know that coefficient of an equation is the number multiplied by variable.

We can see that $-8$ and 1.5 are constants for our given equation.

We can see that variable of our given equation is $x$ . We can also see that $x$ is being multiplied by 0.5, therefore, 0.5 would be the decimal coefficient of our given equation.

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The Hendersons went on a driving vacation. They decided to travel 1/3 of the distance on the first day. Owing to bad weather, th

Sloan [31]

Answer:

$\displaystyle \frac{1}{12}$

$\displaystyle \frac{3}{5}$

$\displaystyle \frac{17}{24}$

Step-by-step explanation:

Part A)

The Hendersons were traveling 1/3 of the distance on the first day.

However, they had to stop, having only traveled 1/4 of the 1/3 distance.

So, we can multiply the two fractions together.

Therefore, the fraction of the total distance they traveled is given by:

$\displaystyle \frac{1}{4}\times\frac{1}{3}=\frac{1}{12}$

The Hendersons traveled 1/12 of the total distance.

Part B)

We are assuming the bottle of milk was full at the beginning.

So, at the beginning, there were 1/1 bottle of milk left.

Howie fed a piglet 1/5 of the bottle. So, there is now:

$\displaystyle 1-\frac{1}{5}$

Of the bottle left.

Making common denominators and subtracting yields:

$\displaystyle =\frac{5}{5}-\frac{1}{5}=\frac{4}{5}$

So, after feeding the piglet, 4/5 of the bottle of milk was still there.

3/4 of the remainder was fed to a calf.

So, the amount that was fed to the calf is 3/4 times 4/5. Therefore:

$\displaystyle \frac{3}{4}\times\frac{4}{5}$

Multiply:

$\displaystyle =\frac{12}{20}=\frac{3}{5}$

So, the calf drank 3/5 of the bottle of milk.

Part C)

Nathan used 2 (5/6) loaves of bread to make 4 sandwiches.

First, convert 2 (5/6) to an improper fraction. So:

$\displaystyle 2\frac{5}{6}=\frac{12+5}{6}=\frac{17}{6}$

Nathan made 4 sandwiches using this. So, we will divide this by 4. Note that this is the same as multiplying by 1/4. Therefore:

$\displaystyle \frac{17}{6}\times\frac{1}{4}=\frac{17}{24}$

So, Nathan used 17/24 loaves of bread per sandwich.

4 0

3 years ago

Adam plans to choose a video game from a section of the store where everything is 75% off. He writes the expression −0.75 to fin

Salsk061 [2.6K]

Answer:

Step-by-step explanation:

Adam plans to choose a video game from a section of the store where everything is 75% off.

The expression written by him for this situation is d - 0.75d.

Here, the part d represents the sale price before discount and the part 0.75d is the discount amount.

The expression written by Rena is 0.25d.

Here, the part 0.25d is the price after discount. Since 75% is the discount, the rate after disount is 25% and 25% of d is 0.25d.

6 0

3 years ago

Ester's choir wants to learn a new song for the school concert in 7 weeks. The song has 3016 lines. The choir learns an equal nu

andriy [413]

Hello!

We are asked to find the number of lines the choir has to learn in time for a concert.

We're given that the concert is in 7 weeks, but they learn new lines each day, so we have to convert it to days. We know that there is 7 days in a week, we would multiply 7 weeks by 7 days, which is 49 days.

Now, we would take the total number of lines, which is 3016, and divide that by 49 days.

3016 lines / 49 days ≈ 61.55 lines/day

Since this is a real-world situation, we should round our answer is to nearest whole number, which would be 62 lines/day.

Therefore, Ester's choir needs to learn about 62 lines per day in time for the concert.

3 0

3 years ago

At the hairdresser, Jenny had 27 centimeters cut off her hair. How many decimeters of hair did Jenny have cut off?

lions [1.4K]

1 centimetre=0.1 decimetre
therefore the answer is 2.5 decimetres.

3 0

4 years ago

Read 2 more answers

What is the solution to this system of equations?

Basile [38]

Answer:

C. x = 3, y = -6

Step-by-step explanation:

You can divide the second equation by 2. Then you have ...

x +2y = -9

This gives you a couple of choices for solution. The x-coefficients match, so subtracting one equation from the other eliminates x:

(x +2y) -(x -2y) = (-9) -(15)

4y = -24 ⇒ y = -6

Adding the two equations eliminates y:

(x -2y) +(x +2y) = (15) +(-9)

2x = 6 ⇒ x = 3

The solution is (x, y) = (3, -6).

_____

Additional comment

I find it quick and easy to use a graphing calculator to find the solution. Many graphing calculators also make it simple to solve systems of equations in matrix form. Either way, you can obtain a solution in little more than the time it takes to enter the equations (or their coefficients).

5 0

3 years ago