By algebra properties we find the following relationships between each pair of algebraic expressions:
- First equation: Case 4
- Second equation: Case 1
- Third equation: Case 2
- Fourth equation: Case 5
- Fifth equation: Case 3
<h3>How to determine pairs of equivalent equations</h3>
In this we must determine the equivalent algebraic expression related to given expressions, this can be done by applying algebra properties on equations from the second column until equivalent expression is found. Now we proceed to find for each case:
First equation
(7 - 2 · x) + (3 · x - 11)
(7 - 11) + (- 2 · x + 3 · x)
- 4 + (- 2 + 3) · x
- 4 + (1) · x
- 4 + (5 - 4) · x
- 4 - 4 · x + 5 · x
- 4 · (x + 1) + 5 · x → Case 4
Second equation
- 7 + 6 · x - 4 · x + 3
(6 · x - 4 · x) + (- 7 + 3)
(6 - 4) · x - 4
2 · x - 4
2 · (x - 2) → Case 1
Third equation
9 · x - 2 · (3 · x - 3)
9 · x - 6 · x + 6
3 · x + 6
(2 + 1) · x + (14 - 8)
[1 - (- 2)] · x + (14 - 8)
(x + 14) - (8 - 2 · x) → Case 2
Fourth equation
- 3 · x + 6 + 4 · x
x + 6
(5 - 4) · x + (7 - 1)
(7 + 5 · x) + (- 4 · x - 1) → Case 5
Fifth equation
- 2 · x + 9 + 5 · x + 6
3 · x + 15
3 · (x + 5) → Case 3
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The greatest factor of 60 and 75 is 15.
Reasoning: I found the factors and prime factorization of 60 and 75. The biggest common factor number is the GCF number. So the greatest common factor 60 and 75 is 15.
Answer:
You must divide 
by 
Step-by-step explanation:
we have
Step 1
Solve for x
Step 2
Find the value of y
Substitute the value of x
therefore
You must divide by
C
If we drew a line of best fit, the gradient would be roughly equal to 1, and the y intercept would be at around -4
<h2>
Explanation:</h2>
In this exercise, we have the following functions:
And they are defined for all real numbers x. So we have to write the following expressions:
First expression:
That is, we subtract s(x) from r(x):
Second expression:
That is, we get the product of s(x) and r(x):
Third expression:
Here we need to evaluate:
First of all, we find the sum of functions r(x) and s(x):
Finally, substituting x = -2:
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