Answer:
He stepped back 59.71 feet.
Step-by-step explanation:
Start by making 2 triangles. One has 68 degrees as the acute angle at the base of the triangle and the other has 41 degrees as the acute angle at the base of the triangle. The side opposite of said angle on both triangles will be 80, the height of the tree. You're solving for the bottom (horizontal) side for both triangles.
For the triangle with an acute base angle of 68, the formula to solve for the horizontal side is tan(68) = 80/x.
Get x by itself to get 80/tan(68) = x
x = 32.32.
For the next triangle, the equation is the same but the angle is changed to 41.
tan(41) = 80/x
80/tan(41) = x
x = 92.03
Finally, subtract the smaller distance from the larger:
92.03 - 32.32 = 59.71 steps.
5x + 20 = 70
5x = 70 - 20
5x = 50
x = 50/5
x = 10
5(10) + 20 = 70
50 + 20 = 70
70 = 70
hope this helps :)
-5 maybe because it looks like it’s counting down.
Answer:
The transformation is " a horizontal translation 4 units to the right " ⇒ (d)
Step-by-step explanation:
Let us revise the translation of a function
- If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)
- If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)
- If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k
- If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) - k
Let us look at the graph and choose some points on the f(x) and find their images on y
∵ Point (1, 2) lies on f(x)
∵ Point (5, 2) lies on y
∵ Point (3, 8) lies on f(x)
∵ Point (7, 8) lies on y
→ There is no change in the y-coordinates of the points, the change
only in the x-coordinates
∴ The translation is horizontally
∵ 5 - 1 = 4 units ⇒ positive value means to right
∴ f(x) is translated 4 units to the right
∴ The answer is " a horizontal translation 4 units to the right " (d)
