Answer:

Step-by-step explanation:
Given: The ratio of cups of sparkling water to cups of grape juice concentrate is
in a recipe for fizzy grape juice.
To find: two more ratios of cups of sparkling water to cups of juice concentrate that would make a mixture that tastes the same as this recipe
Solution:
Equivalent ratios are the ratios that have the same value.
Find two ratios equivalent to 
Multiply both numerator and denominator of
by 2

Multiply both numerator and denominator of
by 3

So, two more ratios of cups of sparkling water to cups of juice concentrate that would make a mixture that tastes the same as this recipe are 
Answer:
x = 8, and y = 12
Step-by-step explanation:
There are 2 variables, so you need 2 equations to form a system of equations in two variables.
The upper left triangle has all angle measures given: 100, 2x + y, 5x + y. We know that the sum of the measures of the angles of a triangle is 180.
First equation:
100 + 2x + y + 5x + y = 180
Simplify:
7x + 2y = 80 (First equation)
Now we see that the upper and lower sides are parallel, so alternate interior angles are congruent. The angles measuring 2x + y and 5x - y are alternate interior angles and are congruent.
Second equation:
2x + y = 5x - y
Simplify:
3x - 2y = 0 (Second equation)
Now we use the first equation and the second equation as a system of simultaneous equations to solve for x and y.
7x + 2y = 80
3x - 2y = 0
Solve the second equation for 2x.
3x = 2y
Now replace 2y in the first equation with 3x.
7x + 3x = 80
10x = 80
x = 8
Replace x with 8 in the second equation.
3(8) - 2x = 0
24 = 2x
x = 12
Answer: x = 8, and y = 12
Given :
On a number line, suppose the coordinate of A is 0, and AR = 15.
To Find :
the possible coordinates of the midpoint of AR.
Solution :
Their can be two points R which is at a distance of 15 units from the A .
One is -15 and other is 15.
Now, mid-point of A(0) and R(-15) is M (-7/2).
Also, mid-point of A(0) and R(15) is M (7/2).
Therefore, possible coordinates of the midpoint of AR is 7/2 , -7/2.
Hence, this is the required solution.
---------------------------------------------------------------------------
Irina:
---------------------------------------------------------------------------
Irina takes 7 hours to paint the room.
In 1 hour, Irina can paint 1/7 of the room.
---------------------------------------------------------------------------
Paulo:
---------------------------------------------------------------------------
Paulo takes 6 hours to paint the room.
In 1 hour, Paulo can paint 1/6 of the room.
---------------------------------------------------------------------------
Both paint together:
---------------------------------------------------------------------------
In one hour they can paint (1/7 + 1/6) of the room.
1/7 + 1/6 = 13/42
So, it takes 13/42 of the room takes 1 hour.
---------------------------------------------------------------------------
Find the number of hours
---------------------------------------------------------------------------
13/42 of the room = 1 hour
Whole room = 1 ÷ 13/42
Whole room = 1 x 42/13
Whole room = 3.23 hours
---------------------------------------------------------------------------
Answer: They need 3.23 hours to paint the room.
---------------------------------------------------------------------------