Answer:
- ΔHJK shows G as the orthocenter
- Show A.F is the median of BC
- 18
Step-by-step explanation:
1) This is a vocabulary question. The <em>orthocenter</em> is the point where the altitudes intersect. Of course, each altitude is a segment from a vertex that is perpendicular to the opposite side of the triangle.
Perhaps it could be useful to remember the prefix ortho- means perpendicular, as in <em>orthogonal</em>. Each altitude is perpendicular to one of the sides of the triangle.
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2) To do this proof, you would find midpoints of segments AB and AC, write the equations of the lines through them from the opposite vertex, then solve those equations to find point G. You would then write the equation for line AG and find its intersection point with segment BC (point F). The last step is to show that point F is the midpoint of BC. (It might be easier to show that midpoint F is on line AG.)
The closest answer choice, though poorly worded, is the last one: show A.F is the median of BC.
(Strictly speaking, a line segment (A.F) is not a median of a line segment (BC), but can be a median of a <em>triangle</em>, or a <em>bisector</em> of a line segment.)
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3) The centroid divides the median into parts with the ratio 2:1. That is, the shorter part differs from the longer one by 2-1 = 1 ratio unit. If those parts differ in length by 6 measurement units, then one ratio unit must be 6 measurement units. The total length of the median is 2+1 = 3 ratio units, or 3×6 measurement units = 18 measurement units.
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<em>Comment on A.F</em>
Brainly thinks the name of the segment starting with A and ending with F is a "bad word" so won't let it be posted.
Answer: -7/-3.
Step-by-step explanation: In this problem we're asked to find the slope of the line that passes through the points (4,3) and (1,-4).
Using our slope formula, we take the second y minus the first y which in this case is -4 - 3 over our second x minus our first x which in this case is 1 - 4.
-4 - 3 is -7 and 1 - 4 is -3.
So the slope of this line is -7/-3.
Answer:
26 times
Step-by-step explanation:
The question has missing details. However, the given parameters are
Given
Without Coupon
Bus Fare = $2.00
With Coupon
Coupon = $39.00
Bus Fare = $0.50
Represent the number of fares with x
Without Coupon, cost of fares is
Cost = 2x
i.e.
f(x) = 2x
With Coupon, cost of fares is
Cost = 39 + 0.5x
i.e.
g(x) = 39 + 0.5x
To calculate when both fares will be equal, we must have:
f(x) = g(x)
2x = 39 + 0.5x
Collect like terms
2x - 0.5x = 39
1.5x = 39
Solve for x
x = 39/1.5
x = 26
This implies that, for both cost to be equal, the person must go 26 times
Answer:
False! However all equilateral triangles are acute
