The intersection of three altitudes of a triangle is called the orthocenter, while altitude is the line drawn from one of the vertex of a triangle and extends it in such a way that it cuts perpendicularly the opposite side of the same triangle.
<span> For obtuse triangle, the orthocenter always lies outside of the triangle. So option “C” is correct. </span>
<span>An image of obtuse triangle along with orthocenter is attached herewith.</span>
<span> </span>
The equation is
This case asking the end result in the form of a slope-intercept.
<u>Step-1: find out the gradient. </u>
10x + 2y = -2
We isolate the y variable on the left side. Subtract both sides by 10x, we get:
2y = - 10x - 2
Divide both sides by two
y = -5x -1
The slope-intercept form is , with the coefficient m as a gradient. Therefore, the gradient is m = -5.
If you want a shortcut to find a gradient from the standard form, implement this:
10x + 2y = −2 ⇒ a = 10, b = 2
<u>Step-2:</u> the conditions of the two parallel lines
The gradient of parallel lines is the same . So
<u>Final step:</u> figure out the equation, in slope-intercept form, of the parallel line to the given line and passes through the point (0, 12)
We use the point-slope form.
Given that
y - 12 = - 5(x - 0)
y - 12 = - 5x
After adding both sides by 12, the results is
<u>Alternative steps </u>
Substitutes m = -5 and (0, 12) to slope-intercept form
12 = -5(0) + c
Constant c is 12 then arrange the slope-intercept form.
Similar results as above, i.e.
<u>Note: </u>
Keywords: given line, the equation, slope-intercept form, standard form, point-slope, gradien, parallel, perpendicular, passes, through the point, constant
Answer:
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Step-by-step explanation:
Given
---x = 0, in 2012
-- x = 5, in 2017
Required
Select all possible equations
Because there is a reduction in the population, as time increases; the rate must be less than 1.
An exponential function is represented as:
Where
rate > 1 in options (a) and (b) i.e. 1.03
This implies that (a) and (b) cannot be true
For option (c), we have:
Set x = 0
Set x = 5
<em>This is true because the calculated values of f(0) and f(5) correspond to the given values</em>
For option (d), we have:
Set x = 0
<em>This is false because the calculated value of f(0) does not correspond to the given value</em>
For option (e), we have:
Set x = 0
undefined
<em>This is false because the f(x) is not undefined at x = 0</em>
For option (f), we have:
Set x = 0
<em>This is false because the calculated value of f(0) does not correspond to the given value</em>
<em>From the computations above, only (c) </em><em> is true</em>