There are rational numbers that are integers / true or false

A chemistry teacher needs to mix a 20% salt solution with a 80% salt solution to make 25 qt of a 44% salt solution. How many qua

NNADVOKAT [17]

Let there be x quarts of the 20% salt solution, and (25 - x) quarts of the 80% salt solution.
Then the total amount of salt in the 20% portion would be 0.2x, while that from the 80% portion would be (0.8)(25 - x). This would have to total up to (0.44)(25) in the final solution, so the equation is:
0.2x + 0.8(25 - x) = (0.44)(25)
-0.6x + 20 = 11
x = 15 quarts of the 20% salt solution
25 - x = 10 quarts of the 80% salt solution

5 0

3 years ago

Parallelogram MNPQ was dilated to create parallelogram M'N'P'Q'. On a coordinate plane, 2 parallelograms are shown. Parallelogra

Naddika [18.5K]

Answer:

The answer is below

Step-by-step explanation:

Which statements are true about the parallelograms? Check all that apply.

The length of side MN is 2 units.

The length of side M'N' is 5 units.

The image is smaller than the pre-image.

Sides MQ and M'Q' both have the same slope, 1.

The scale factor is 2/5

a) The length of side MN is determined using the formula:

$|MN|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(4-2)^2+(-2-(-2))^2}=\sqrt{2^2}=2\\ \\ |MN|=2$

The first option is correct

b) The length of side M'N' is determined using the formula:

$|M'N'|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(10-5)^2+(-5-(-5))^2}=\sqrt{5^2}=2\\ \\ |M'N'|=5$

The second option is correct

c) From the coordinates of parallelogram MNPQ and M'N'P'Q', we can see that parallelogram MNPQ is dilated by a factor of 5/2 to produce parallelogram M'N'P'Q' , hence parallelogram M'N'P'Q' is bigger that parallelogram MNPQ. This means that The image is bigger than the pre-image.

The third option is wrong

d) The slopes are given as:

$Slope\ of\ MQ=\frac{Change\ in\ y}{Change\ in\ x}=\frac{1-2}{-3-(-2)} =1\\ \\Slope\ of\ M'Q'=\frac{Change\ in\ y}{Change\ in\ x}=\frac{3-5}{-7-(-5)} =1\\$

Option four is correct

e) From the coordinates of parallelogram MNPQ and M'N'P'Q', we can see that parallelogram MNPQ is dilated by a factor of 5/2 to produce parallelogram M'N'P'Q', hence the scale factor is 5/2

Option 5 is wrong

6 0

3 years ago

Read 2 more answers

!!!!PLEASE HELP!!!! I will mark you brainliest and you get 15 points

vfiekz [6]

Answer:

(none, it's a word problem)

Step-by-step explanation:

they all have the same denominator.

3 0

3 years ago