The distributive properties applies every time you want to multiply a whole parenthesis by a number.
As the name suggests, you "distribute" the number to all terms in the parenthesis: you perform as many multiplication as many terms in the parenthesis.
So, for example, we begin with
So, we multiply -6 times both terms in the parenthesis, and sum the results:
And so on with the other terms:
Now sum all the pieces together:
Answer: a) 3 and -3 b) 4 and 2
c) 3.5 and 2.5 d) 5.5 and 0.5 e) This is due to the difference in the coefficient of (x-3)² and the value at the right side of each equation.
Step-by-step explanation:
a) 3x²-9 = 0
3x² = 0+9
3x² = 9
Dividing both sides by 3
x² = 9/3
x² = 3
x = √3
x = +3 and -3
b) (x-3)² = 1
Taking square root of both sides to remove the square,
√(x-3)² = √1
x-3 = √1
x-3 = 1 and x-3 = -1 (note that √1 is +1 and -1)
x = 4 and x = 2
c) 4(x-3)² = 1
Dividing both sides by 4 we have;
(x-3)² = 1/4
Taking the square root of both sides to eliminate the square.
√(x-3)² = √1/4
x-3 = √1/4
x-3 = +1/2 and x-3 = -1/2
x = 1/2+3 and x = -1/2+3
x = 3.5 and 2.5
d) 2(x-3)² = 12
Dividing both sides by 2 we have;
(x-3)² = 12/2
Taking the square root of both sides to eliminate the square.
√(x-3)² = √12/2
x-3 = √6
x-3 = 2.5 and x-3 = -2.5
x = 2.5+3 and x = -2.5+3
x = 5.5 and 0.5
e) The answers to questions 1 to 4 has different solutions due to the different value of the coefficient of (x-3)² and also the value at the right hand side of the equations also differs, hence, the reason for the difference in their answers.
Answer:
- The variation in the sample means makes it possible to make predictions about the population mean.
- The actual population mean is greater than 236.
- The actual population mean is less than 245.
Step-by-step explanation:
<u>Sample data</u>
- 1 2 3 4 5 6
- 240 236 245 243 238 242
<u>Mean = sum of sample data/sample frequency</u>
- (240+236+245+243+238+242)/6 = 240.67
Answer choices:
The variation in the sample means makes it possible to make predictions about the population mean.
The actual population mean is greater than 236.
The actual population mean is less than 245.
The actual population mean is greater than 245
The population mean is the average of the sample means.
No te parece que das muy poco puntos para una pregunta tan complicada eh
