Both triangles that are given (with right angles) lie in plane m, proving that AC is perpendicular to plane m. As angle acd is from a triangle that shares the common perpendicular, it too is a right angle
Answer:
y = -1/2x + 2
Step-by-step explanation:
A line in slope-intercept form in y = mx + b
"m" is the slope
"b" is the y-intercept
x and y represent points on the graph
To write an equation, you need "m" and "b".
We already know m = -1/2
The point (0, 2) is the y-intercept. The y-intercept occurs when x = 0.
Points are in the form (x , y), so x = 0 and y = 2.
Therefore b = 2.
Substitute m = -1/2 and b = 2 into the equation:
y = mx + b
y = -1/2x + 2
The answer is B) it shifts up and to the right
Answer:
14,850
Step-by-step explanation:
You need the sum of
3 + 6 + 9 + 12 + ... + 294 + 297
Factor out a 3 from the sum
3 + 6 + 9 + 12 + ... + 294 + 297 = 3(1 + 2 + 3 + 4 + ... + 98 + 99)
You need to add all integers from 1 to 99 and multiply by 3.
The sum of all consecutive integers from 1 to n is:
[n(n + 1)]/2
The sum of all consecutive integers from 1 to 99 is
[99(99 + 1)]/2
The sum you need is 3 * [99(99 + 1)]/2
3 + 6 + 9 + 12 + ... + 294 + 297 =
= 3 * [99(99 + 1)]/2
= 3 * [99(100)]/2
= 3 * 9900/2
= 14,850
