Equations with Independent and Dependent Variables
Common Core Standard: Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.
Dependent variable – is a variable that changes because of the other variable or depends on the other variable
Independent variable –is a variable that is not impacted by other variables
Dependent and independent variables are very common in the real world
Example: Most coaches will say that the longer a player practices a sport the better the player will be at the sport.
o The dependent variable is the player’s ability, as it relies on the length of a practice
o The independent variable is the number of hours the player practices, because the player’s ability does not
impact the amount of time the player practice
Answer:
the right answer is
"A store had 500 apples to be placed in bags with an equal number of apples in each bag. If n is the number of bags to be used, then 500n is the number of apples in each bag"
Answer:
28-24x
Step-by-step explanation:
4(7-6x)= 28-24x
choices:
28-6x
-24x+28
-24x+28
28-24x
Answer:
<h2><em><u>
A to C = 25
</u></em></h2><h2><em><u>
A to B = 13
</u></em></h2><h2><em><u>
C to B = 37
</u></em></h2><h2><em><u>
</u></em></h2>
Step-by-Step Explanation:
<em><u>Perimeter</u></em> = 75
<em><u>Sides:</u></em>
2x + 3
3x + 4
2x - 9
<h2 /><h2><em><u>
1. Equal the sides added together to the perimeter</u></em></h2>
75 = 2x + 3 + 3x + 4 + 2x - 9
<h2><em><u>
2. Simplify Like terms</u></em></h2>
2x + 3 + 3x + 4 + 2x - 9 = 7x - 2
<h2><em><u>
3. Place the equation back together</u></em></h2>
75 = 7x - 2
<h2><em><u>
4. Isolate the variables and numbers</u></em></h2>
75 = 7x - 2
+2 +2
77 = 7x
<h2><em><u>
5. Simplify the equation</u></em></h2>
77 = 7x
/7 /7
<h2><em><u>
11 = x
</u></em></h2>
<h2><em><u>
6. Substitute the value of x into the side lengths.</u></em></h2>
2x + 3 = 2(11) + 3 = 22 + 3 = <em><u>25</u></em>
3x + 4 = 3(11) + 4 = 33 + 4 = <em><u>37</u></em>
2x - 9 = 2(11) - 9 = 22 - 9 = <em><u>13</u></em>
Answer:
a. 59.73_3 ft²/h
b. 5.093 h
c. $149.95
Step-by-step explanation:
a. The specified unit rate is ...
... (square ft)/(hour) = (10.5 ft)(12.8 ft)/(2.25 h) = 134.4 ft²/2.25 h = 59.73_3 ft²/h
b. The wall area is the product of the perimeter of the room and its height:
... A = (2(l+w))h = 2(10.2 ft + 6.7 ft)·(9 ft) = 304.2 ft²
At the above rate, the time required is ...
... (304.2 ft²)/(59.73_3 ft²/h) ≈ 5.093 h
c. If the charge is proportional to the time required, the charge for painting the basement walls will be ...
... $66.25/(2.25 h) = charge/(5.093 h)
... (5.093 h)/(2.25 h)×$66.25 = charge ≈ $149.95
_____
Note that the number 5.093 shown here is a representation of the number 5.09263392857 used in the calculations. Only the final numbers are rounded in each case.
The underbar in 59.73_3 is a text representation of the overbar usually used to signify the repeating digits in a repeating decimal:
... 
