9514 1404 393
Answer:
-7/4 < x < 8
Step-by-step explanation:
The value of y can be determined from the sum of the angles, so you know each of the angles exactly. That means you know the ratio of side lengths exactly, which lets you solve for x exactly.
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Setting that aside, we observe that angle C is greater than angle A, so side AB will be longer than side BC.
3x +15 > 4x +7
8 > x . . . . . . . . . . subtract 3x+7
We also know that the lengths of these sides must be positive. Since BC is the shorter side, we require ...
4x +7 > 0
4x > -7
x > -7/4
So, the allowable values of x are ...
-7/4 < x < 8
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<em>More complete solution</em>
If we read the figure correctly, the sum of angles is ...
(2y +12) +(4y +12) +(y -18) = 180
7y +6 = 180
y = (180 -6)/7 = 24 6/7°
Then (in degrees) ...
∠A = 2(24 6/7) +12 = 61 5/7, and ∠C = 4(24 6/7) +12 = 111 3/7
The Law of Sines tells us ...
AB/sin(C) = BC/sin(A)
sin(A)(3x +15) = sin(C)(4x+7)
x(4sin(C) -3sin(A)) = 15sin(A) -7sin(C)
x = (15sin(A) -7sin(C))/(4sin(C) -3sin(A))
x ≈ 6.1872652
You do 14 divided by 16 which is 0.875 times by 100
which is 87.5 so that means 14/16 in a percentage is 87.5 %
Answer:
C
Step-by-step explanation:
given a function f(x) then
f(x) + c ← denotes a vertical translation of f(x)
• If c > 0 then shift vertically up
• If c < 0 then shift vertically down
Here the vertex of f(x) is at the origin and the vertex of g(x) is (0, 3 ), that is 3 units vertically up
Hence g(x) = x² + 3 → C
Unusual question. 4/5 = 0.8, which is NOT a repeating decimal; it's a rational fraction.
