Answer: ΔRST ≅ ΔBAC
Step-by-step explanation:
We know that To rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y).
Thus, The coordinates of Δ RST becomes
R (1,1) → R'(-1,-1)
S (3,4) → S'(-3,-4)
T(-5,0) → T'(5,0)
Also ΔRST after rotation is translated up 3 units. , so we apply the rule (x,y)→(x,y+3)
R'(-1,-1)→R"(-1,-1+3)=R"(-1,2)→ B
S'(-3,-4) → S"(-3,-4+3) = R"(-3,-1) → A
C'(-5,0) → C"(-5,0+3) → C"(-5,3) → C
As rotation and translation both are rigid transformation that maps only congruent figures.
Therefore, ΔRST ≅ Δ BAC
That funky circle in the middle is the composition of the function. It asks you to take a function as an input and to yield an output that's another function. It's one of the five function operations, along with adding, subtracting, multiplying, and dividing.
When you compose, you might find the notation w(u(x)) easier to understand. It's saying evaluate u then evaluate w.
For our functions, the compositions are:
u(w(x)) = u(2x²) = -(2x²) - 2 = -2x² - 2
w(u(x)) = w(-x - 2) = 2(-x - 2)² = 2(x² + 4x + 4) = =2x²+ 8x +8
Now we evaluate each composition at 4.
u(w(4)) = -2(4²) - 2 = -2(16) - 2 = -32 -2 = -34
w(u(4)) = -2(2²) +8(2) + 8 = -2(4) + 16 + 8 = -8 + 16 + 8 = 16.
Thus, u(w(4)) = -34 and w(u(4)) = 16.
405 because 120+50+65=405
See the attached figure.
<span>ad is a diameter of the circle with center p
</span>
∵ pd = radius = 7 ⇒⇒⇒ ∴ ad = 2 * radius = 2 * 7 = 14
∵ ae = 4 ⇒⇒⇒ ∴ ed = ad - ae = 14 - 4 = 10
∵ ad is a diameter
Δ acd is a triangle drawn in a half circle
∴ Δ acd is a right triangle at c
∵ bc ⊥ ad at point e
By applying euclid's theorem inside Δ acd
∴ ce² = ae * ed
∴ ce² = 4 * 10 = 40
∴ ce = √40 = 2√10 ≈ 6.325
Answer:
7√(x) = 14
Step-by-step explanation: