Use the Pythagorean Theorem to determine the lengths of QT and RS Show your work

How many gallons of a 50% antifreeze solution must be mixed with 60 gallons of 30% antifreeze to get a mixture that is 40% antif

Mariulka [41]

I don't know what the "six-step method" is supposed to be, so I'll just demonstrate the typical method for this problem.

Let x be the amount (in gal) of the 50% antifreeze solution that is required. The new solution will then have a total volume of (x + 60) gal.

Each gal of the 50% solution used contributes 0.5 gal of antifreeze. Similarly, each gal of the 30% solution contributes 0.3 gal of antifreeze. So the new solution will contain (0.5 x + 0.3 * 60) gal = (0.5 x + 18) gal of antifreeze.

We want the concentration of antifreeze to be 40% in the new solution, so we need to have

(0.5 x + 18) / (x + 60) = 0.4

Solve for x :

0.5 x + 18 = 0.4 (x + 60)

0.5 x + 18 = 0.4 x + 24

0.5 x - 0.4 x = 24 - 18

0.1 x = 6

x = 6/0.1 = 60 gal

6 0

3 years ago

In the figure above, quadrilateral ABCD is a parallelogram. Let x represent the measure of angle GBF, y represent the measure of

ira [324]

Answers:
measure angle x = 40°
measure angle y = 35°
measure angle z = 55°

Explanation:
Part (a): getting angle x:
In triangle BED, we have:
measure angle BED = 90°
measure angle BDE = 50°
Therefore:
measure angle DBE = 180 - (90+50) = 40°
Now, we have angle DBE and angle GBF vertically opposite angles.
This means that they are both equal. Therefore angle GBF = 40°
Since angle GBF is x, therefore:
x = 40°

Part (b): getting angle y:
We know that the sum of measures of angles on a straight line is 180.
This means that:
angle GBF + angle GBC + angle CBE = 180
We have:
angle GBF = 40°
angle GBC = 105°
angle CBE = y
Therefore:
40 + 105 + y = 180
y = 35°

Part (c): getting angle z:
In triangle BCE, we have:
measure angle BCE = z
measure angle BEC = 90°
measure angle CBE = 35°
Therefore:
z + 90 + 35 = 180
z = 55°

Hope this helps :)

8 0

3 years ago

I don’t understand this problem can someone explain it and give the answe

Feliz [49]

Answer:

Explanation:

4x + 2x = 180 degree
6x = 180
x = 180/6
x = 30

Therefore, x = 30 degree

6 0

4 years ago

Write an expression that is equivalent to -0.5(20f – 16).

pashok25 [27]

Answer:

- 10f + 8

Step-by-step explanation:

Given expression:

- 0.5(20f - 16)

Distribute and simplify:

-0.5(20f) - 0.5(- 16) =
- 10f + 8

6 0

3 years ago

Read 2 more answers

What are symbols of inclusion

Kipish [7]

Answer:

Symbols of inclusion are symbols used in mathematical expressions that group terms or factors together. They indicate that when we are simplifying expressions, we are to perform what's inside the symbols first. The three types of symbols of inclusion are parentheses, brackets, and braces.

5 0

3 years ago