In the triangle, the fact that wee are given 2AX = 3XD isn't enough to prove similarity.
<h3>How to explain the triangle?</h3>
a. In the question, we are given 2AX = 3XD. An arbitrary triangle AXB can be drawn where one extends AX and choose a point D on the extended line in order for 2AX = 3XD. Also, extend BX and choose a point C on the line so that 2BX = XC. Even though they both satisfy the condition, they're not similar.
b. We are given that AX/BX = DX/CX. When this is rearranged, we'll have AX/DX = BX/CX. In this case, let AX/DX = k. DX and AX will align upon rotation of 180°. The triangle can then be dilated by a factor of k. This brings about the mapping of triangle DXC to AXB. Therefore, the original triangle DXC is similar to AXB.
c. Lines AB and CD are parallel. Here, the dilation moves line CD onto line AB. Here, since the dilation moves D to a point on ray XA, D must move to A. Therefore, the rotation of triangle DXC is similar to AXB. Therefore, DXC is similar to AXB.
d. Here, angle XAB is congruent to angle XCD. This shows similarity and in this case, XCD is similar to XAB.
Learn more about triangles on:
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Total number of hours = 15
Let the hours spent tutoring french be x.
Therefore hours spent on scooping ice cream = (15 - x)
Amount: Tutoring french is $15 an hour, total for x hours = 15x
For scooping ice cream it is $10 an hour 10*(15 - x) = 150 - 10x
To make more than $180
15x + (150 - 10x) > 180
15x + 150 - 10x > 180
15x - 10x > 180 - 150
5x > 30
x > 30/5
Well if the gift card is worth $20 and your total expenses come to $30. That means you have to pay $10. No way around that sorry
