For any integer x,x2-x will always produce an even value
1 answer:
Consider expression First, you can factor it:
Since x is integer number, then you can see that x-1 is previous integer number (x-1 is 1 unit smaller than x).
Therefore, x-1 and x are two consecutive integers. When you have two consecutive integers, one of them is always even and one is always odd. Multiplying even integer number by odd integer number you always get even integer number.
Thus, is always even.
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Answer:
Step-by-step explanation:
Hi there!
<u>What we need to know:</u>
- Linear equations are typically organized in slope-intercept form:
where m is the slope of the line and b is the y-intercept (the value of y when the line crosses the y-axis)
- Parallel lines will always have the same slope but different y-intercepts.
<u>1) Determine the slope of the parallel line</u>
Organize 3x = 2y into slope-intercept form. Why? So we can easily identify the slope, m.
Switch the sides
Divide both sides by 2 to isolate y
Now that this equation is in slope-intercept form, we can easily identify that is in the place of m. Therefore, because parallel lines have the same slope, the parallel line we're solving for now will also have the slope
. Plug this into
:
<u>2) Determine the y-intercept</u>
Plug in the given point, (4,0)
Subtract both sides by 6
Therefore, -6 is the y-intercept of the line. Plug this into as b:
I hope this helps!
Answer:
The expression of h as function of x is h =
Step-by-step explanation:
Given as :
The distance of blimp (AB) = 5500 feet
The slanted distance to the pagoda (BC) = d feet
The horizontal distance (AC) = h
Let the angle made between slanted distance and horizontal distance be Ф
So , cos Ф = =
And sin Ф = =
∵, cos²Ф = 1 - sin²Ф
So, =
Or, =
Or, h² = d² - 5500²
∴ h =
Or, h =
Hence The expression of h as function of x is h = Answer