Answer:
x = 6
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
Step-by-step explanation:
<u>Step 1: Define Equation</u>
3 - 2x = -1.5x
<u>Step 2: Solve for </u><em><u>x</u></em>
- Add 2x on both sides: 3 = 0.5x
- Divide 0.5 on both sides: 6 = x
- Rewrite: x = 6
<u>Step 3: Check</u>
<em>Plug in x into the original equation to verify it's a solution.</em>
- Substitute in<em> x</em>: 3 - 2(6) = -1.5(6)
- Multiply: 3 - 12 = -9
- Subtract: -9 = -9
Here we see that -9 does indeed equal -9.
∴ x = 6 is the solution to the equation.
Answers:
- Discrete
- Continuous
- Discrete
- Continuous
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Explanations:
- This is discrete because we can't have half a basketball, or any non-whole decimal value to represent the number of basketballs. We can only consider positive whole numbers {1,2,3,4,...}. A discrete set like this has gaps between items. In other words, the midpoint of 2 and 3 (the value 2.5) isn't a valid number of basketballs.
- This is continuous because time values are continuous. We can take any two different markers in time, and find a midpoint between them. For example, the midpoint of 5 minutes and 17 minutes is 11 minutes since (5+17)/2 = 22/2 = 11. Continuous sets like this do not have any gaps between items. We can consider this to be densely packed.
- This is the same as problem 1, so we have another discrete function. You either score a bullseye or you don't. We can't score half a bullseye. The only possible values are {1,2,3,4,...}
- This is similar to problem 2. This function is continuous. Pick any two different positive real numbers to represent the amount of gallons of water. You will always be able to find a midpoint between those values (eg: we can have half a gallon) and such a measurement makes sense.
So in short, always try to ask the question: Can I pick two different values, compute the midpoint, and have that midpoint make sense? If so, then you're dealing with a continuous variable. Otherwise, the data is discrete.
Answer:
Emily: 13, Peter: 9, Joshua: 18
Step-by-step explanation:
Emily = x
Peter = Emily - 4 = x - 4
Joshua = 2(Peter) = 2(x - 4)
Total = 40 = Emily + Peter + Joshua = (x) + (x - 4) + 2(x - 4)
40 = 2x - 4 + 2x -8
40 = 4x - 4 - 8
40 = 4x - 12
52 = 4x
x = 13
Emily = 13
Peter = 13 - 4 = 9
Joshua = 2(13 - 4) = 2(9) = 18
13 + 9 +18 = 40
Divide the amount she drove by the total amount she needs to drive, them multiply that answer by 100 to make it a percent. This will give you the percentage she drove. To find the percentage she has left,, subtract from 100%.
64 / 160 = 0.4
0.4 * 100 = 40% ( percent she has already driven)
100% - 40% = 60% left.
Answer:
x=0.5
y = 10.5
Step-by-step explanation:
y = 3x + 7
y = 5x + 8
3x + 7 = 5x + 8
3x - 5x= 8 - 7
2x = 1
x= 1/2
x=0.5
y = 5x + 8
y = 5(0.5) + 8
y = 2.5 + 8
y = 10.5