Answer:
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Step-by-step explanation:
Answer:
3. r = -8
4. x = -5
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>
2(-5r + 2) = 84
<u>Step 2: Solve for </u><em><u>r</u></em>
- Divide 2 on both sides: -5r + 2 = 42
- Subtract 2 on both sides: -5r = 40
- Divide -5 on both sides: r = -8
<u>Step 3: Check</u>
<em>Plug in r into the original equation to verify it's a solution.</em>
- Substitute in <em>r</em>: 2(-5(-8) + 2) = 84
- Multiply: 2(40 + 2) = 84
- Add: 2(42) = 84
- Multiply: 84 = 84
Here we see that 84 does indeed equal 84.
∴ r = -8 is a solution of the equation.
<u>Step 4: Define equation</u>
264 = -8(-8 + 5x)
<u>Step 5: Solve for </u><em><u>x</u></em>
- Divide both sides by -8: -33 = -8 + 5x
- Add 8 to both sides: -25 = 5x
- Divide 5 on both sides: -5 = x
- Rewrite: x = -5
<u>Step 6: Check</u>
<em>Plug in x into the original equation to verify it's a solution.</em>
- Substitute in<em> x</em>: 264 = -8(-8 + 5(-5))
- Multiply: 264 = -8(-8 - 25)
- Subtract: 264 = -8(-33)
- Multiply: 264 = 264
Here we see that 264 does indeed equal 264.
∴ x = -5 is a solution of the equation.
In a parallelogram the two angles on the same side need to equal 180 degrees. So in the picture angle F and angle G need to equal 180:
Add them together:
7x -5 + 3x-15 = 180
Simplify by combining like terms:
10x -20 = 180
Add 20 to both sides:
10x = 200
Divide both sides by 10:
X = 20
Now you know x, replace x in the angle for g and solve:
G= 7x-5 = 7(20) -5 = 140-5 = 135
G = 135 degrees.
In a parallelogram the top and bottom are the same length, so set the two to equal each other and solve for y:
3y = y + 8
Subtract y from both sides:
2y = 8
Divide both sides by 2:
Y = 4
Now replace y and solve for EF:
EF = 3y = 3(4) = 12
EF = 12
Answer:
A prison administration wants to know whether the prisoners think the guards treat them fairly. The explanation, of each component could be used to produce biased and unbiased results, is as follow
A) Component 2:
- If the prison guards ask the questions from the prisoners directly by themselves then it is highly like to get the biased results.
- If the person are hired outside from the staff then it will minimize the probability of biased results rather it will allow to get the best results.
B) Component 4:
- The question asked from prisoner would be biased if it is like "You don't have any complaints about how you are treated, do you?"
- The same question can be unbiased if asked in such a way "We are interested in your opinion about your treatment by the guards. Do you think you are fairly or unfairly treated by them?"
The correct answer is c . E
