MATHEMATICS
MIDDLE SCHOOL

Answer: Divide $10 by $0.25 to determine the # of quarters:

$10

-------- = 40 (answer)

$0.25

$10

-------- = 40 (answer)

$0.25

Answer: There are 40 quarters in a roll

COLLEGE

A pharmacist has an 18% alcohol solution. How much of this solution and how much water must be mixed together to make 10 liters of a 12% alcohol solution? Answer:

We need a table to do this. 3 rows and 3 columns. Across the top the columns are number of liters, % alcohol, and total. We will label the first row stuff with alcohol, the second row stuff with water, and the third row will be the mix of alcohol and water. In the first column we will put an x for alcohol since we don't know how much alcohol we have in the mix. In the second column we will put the decimal equivalent of the percent alcohol, which is .18. In the total column we will put the product of those 2, which is .18x. Now for the second row, water. We will put a y in the first column since we don't know how much water we have in the mix. In the second column we will put a 0, since water doesn't have any alcohol in it. In the third column we will put the product of the 2 which will be 0. In the third row, the mix row, we put a 10 since we want 10 L of this mix. We will put the decimal equivalent of how much alcohol we want in this mix which is .12. In the total column we put the product of those 2 which is 1.2. Since we are adding the alcohol and the water, x and y, to get a total of 10, this is our first equation. x+y=10. In the total column we will add the percent alcohol in the alcohol and the water to get 1.2. .18x + 0 = 1.2, or just .18x = 1.2. Let's divide both sides by .18 to find the amount of alcohol is in this mix. We get 6 2/3 liters of alcohol. If there is a total of 10 L of this mix, 10 - 6 2/3 = water, and the amount of water then is 3 1/3 L.

HIGH SCHOOL

If line segment ab is defined by the endpoints a(4,2) and b(8,6) , write an equation of a line that is the perpendicualr bisector line segment ab

An equation of a line that is the perpendicular bisector line segment AB is y=-x+10.

What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

Given that, line segment AB is defined by the endpoints A(4,2) and B(8,6).

Midpoint of line AB is (x, y) =[(x₂+x₁)/2, (y₂+y₁)/2]

= [(8+4)/2, (6+2)/2]

= (6, 4)

Slope of line AB is (y₂-y₁)/(x₂-x₁)

= (6-2)/(8-4)

= 4/4

= 1

The slope of a line perpendicular to given line is m1=-1/m2

So, the slope of a line is -1

Now, substitute m=-1 and (x, y)=(6, 4) in y=mx+c, we get

4=-1(6)+c

c=10

Substitute m=-1 and c=10 in y=mx+c, we get

y=-x+10

Therefore, an equation of a line that is the perpendicular bisector line segment AB is y=-x+10.

To learn more about the equation of a line visit:

brainly.com/question/2564656.

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Slope of line ab = 6-2 / 8-4 = 4/4 = 1

So the slope of the perpendicular line is -1/1 = -1

This line passes through the midpoint of ab

The midpoint of ab = ( 8+4 / 2 , 2+6 / 2) = (6, 4)

Finding the equation of the perpendicular line:-

y - y1 = -1(x - x1) where x1 = 6 and y1 = 4:-

y - 6 = -1(x - 4)

y = -x + 10 is the answer

So the slope of the perpendicular line is -1/1 = -1

This line passes through the midpoint of ab

The midpoint of ab = ( 8+4 / 2 , 2+6 / 2) = (6, 4)

Finding the equation of the perpendicular line:-

y - y1 = -1(x - x1) where x1 = 6 and y1 = 4:-

y - 6 = -1(x - 4)

y = -x + 10 is the answer

MIDDLE SCHOOL

2z+ 1 = z

What value of z satisfies the equation above?

Answer:

z = -1

Step-by-step explanation:

2z + 1 = z .

To get the value of z that satisfies the equation, what we simply do is to rearrange the equation by moving the coefficients. Now, we move z to the left hand side of the equation and 1 to the right side of the equation.

We should note that their signs will change afterwards.

2z - z = -1

z = -1

MIDDLE SCHOOL

Round 5,294 to the nearest hundred

5,294 rounded to the nearest hundred is:

5, 300 because 9 is greater than 5.

Hope I Helped!!!

5, 300 because 9 is greater than 5.

Hope I Helped!!!

Round 5,294 to the nearest hundred

The answer to this question is 5,294 rounded to the nearest hundred is 5,300. That is the answer.

The answer to this question is 5,294 rounded to the nearest hundred is 5,300. That is the answer.