Refer to the diagram attached.
TRIANGLE ABC
The height of the tree is the segment AB. The shadow of the tree is BC.
TRIANGLE DEC
Tanya's height is 5 feet 3 inches (since there are 12 inches in one foot that is (5)(12)+3 = 63 inches).
Tanya's shadow is EC
Since both triangles are right triangles (the both have a right angle) and they share the angle at C, they are similar triangles. That means that their corresponding angles are congruent and their corresponding sides are in proportion.
We can set up the following proportion:
(tree height / tree shadow) = (Tanya's height / Tanya's shadow)
BE is 2.5 times EC. This means that BE is (2.5)(EC). It also means that BC = 2.5EC + EC = 3.5EC
The shadow of the tree is 3.5 times Tanya's shadow. That means that the height of the tree must be 3.5 times Tanya's height.
The height of the tree is (3.5)(63) = 220.5 inches. If we divide this by 12 we get 18.375 which means 18 feet and some inches. (18)(12)=216 and the tree is 220.5. That means the tree is 18 feet and 4.5 inches.
I believe the answer is 2.
1) Yes, the relationship in the table is proportional. If, when you've been walking for 10 minutes, you are 1.5 miles away from home, and when you've been walking for 20 minutes, you are 1 mile away from home, and when you've been talking 30 minutes, you are 0.5 miles away from home, then we can see that there is a proportion that happens here. For every 10 minutes you walk, you get 0.5 miles closer to your home.
2) We know that you've been walking 10 minutes already at the start of this problem, and we know that you walk at a steady pace of 0.5 miles every 10 minutes, so we just need to add 0.5 miles to our starting point to get the distance from the school to home, which makes it 2 miles away.
3) An equation representing the distance between the distance from school and time walking could be something like this:
t = 20d
Where t is the amount of time it takes to get home (in this case, t = 40 minutes) and d is the distance you can walk in 10 minutes (in this case, 0.5 miles)
The equation is lame, but that's the best I could do :\
Hope that helped =)
Answer:
- <em>To solve these first swap x and y, solve for y and name it inverse function</em>
3. <u>y = -8x + 2</u>
- x = -8y + 2
- 8y = -x + 2
- y = -x/8 + 2/8
- y = -(18)x + 1/4
f⁻¹(x) = -(18)x + 1/4
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4.<u> y = (2/3)x - 5</u>
- x = (2/3)y - 5
- (2/3)y = x + 5
- y = (3/2)x + (3/2)5
- y = 1.5x + 7.5
f⁻¹(x) = 1.5x + 7.5
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5. <u>f(x) = 2x² - 6</u>
- x = 2y² - 6
- 2y² = x + 6
- y² = 1/2x + 3
- y =

f⁻¹(x) = 
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6. <u>y = (x - 3)²</u>
- x = (y - 3)²
= y - 3- y = 3 +

f⁻¹(x) = 3 + 