Answer:
C. Triangle BAC is congruent to triangle FDE by AAS
Step-by-step explanation:
BAC names the vertices in the order longest-side, shortest-side. That same order is FDE in the other triangle, eliminating choiced B and D. The triangles are not right triangles, eliminating choice A.
The only viable answer choice is C.
No specific sides are shown as being congruent, but two angles are, so we could claim congruence by ASA or AAS. Answer choice C uses the latter.
Answer:
a) cos(α+β) ≈ 0.8784
b) sin(β -α) ≈ -0.2724
Step-by-step explanation:
There are a couple of ways to go at these. One is to use the sum and difference formulas for the cosine and sine functions. To do that, you need to find the sine for the angle whose cosine is given, and vice versa.
Another approach is to use the inverse trig functions to find the angles α and β, then combine those angles and find find the desired function of the combination.
For the first problem, we'll do it the first way:
sin(α) = √(1 -cos²(α)) = √(1 -.926²) = √0.142524 ≈ 0.377524
cos(β) = √(1 -sin²(β)) = √(1 -.111²) ≈ 0.993820
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a) cos(α+β) = cos(α)cos(β) -sin(α)sin(β)
= 0.926×0.993820 -0.377524×0.111
cos(α+β) ≈ 0.8784
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b) sin(β -α) = sin(arcsin(0.111) -arccos(0.926)) ≈ sin(6.3730° -22.1804°)
= sin(-15.8074°)
sin(β -α) ≈ -0.2724
Answer: C. (-7x+9)(x-2)
Step-by-step explanation:
1. Factor out the negative sign.
−(7x^2+5x−18)
2. Split the second term in 7x2+5x−18 into two terms.
−(7x^2+14x−9x−18)
3, Factor out common terms in the first two terms, then in the last two terms.
−(7x(x+2)−9(x+2))
4. Factor out the common term x+2x+2x+2.
−(x+2)(7x−9) or (-7x+9)(x-2)
Answer:
144π
Step-by-step explanation:
we need the radisu
circumference formula: 2πr
2πr=24π
12=r
area formula:
πr²
12²π= 144π
The pattern grows by 2, because if you count each cube you can see.
There will be 1 cube in Figure 0, because if it grows by 2 then you take away 2 cubes.
