If a over 9 =b over 5 find the ratio of a over b
1 answer:
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Answer:
(1,4)
Step-by-step explanation:
Let's this of which is it's parent function.
How do we get to from there?
It has been reflected about the a-axis because of the - in front of the square root.
It has been shifted right 1 unit because of the -(1) in the square root.
It has been moved up 4 units because of the +4 outside the square root.
In general:
has the following transformations from the parent:
Moved right h units if h is positive.
Moved left h units if h is negative.
Moved up k units if k is positive.
Moved down k units if k is negative.
If is positive, it has not been reflected.
If is negative, it has been reflected about the x-axis.
also tells us about the stretching factor.
The parent function has a starting point at (0,0). Where does this point move on the new graph?
It new graphed was the parent function but reflected over x-axis and shifted right 1 unit and moved up 4 units.
So the new starting point is (0+1,0+4)=(1,4).
Answer:
d
Step-by-step explanation:
Using the Cosine rule to find ∠ A
cosA =
=
=
= , then
∠ A = (
) ≈ 84.9° ( to 1 dec. place )
Answer:
Step-by-step explanation:
Eqn. 1 ----> 4y = x
Eqn. 2 ----> 5x-10y = -50
(Simplifying eqn.2 further)
(Substituting the value of x from eqn. 1)
Now, substituting the value of y in eqn. 1 ,
Answer:
Step-by-step explanation:
Begin with the standard form of a circle as a conic:
For a circle, A and C will be the exact same, and B will equal 0. If B is non-zero, the equation represents a rotation of a conic, which is reserved for college-level courses. Shortening this, then:
is good enough for us for this. Start with the first point on the circle, (2, 31) and fill in the equation above with x and y:
which simplifies down to:
Do the same with the next point on the circle, (-15, 14):
which simplifies down to:
Do the same with the last point, (33, 0):
which simplifies down to:
Now we will add (1) and (2) to get (4):
2D + 31E + F = -965
-15D + 14E + F = -421
Multiply the top equatio by -1 to get rid of the F terms:
-2D - 31E - F = 965
-15D + 14E + F = -421
which simplifies to
(4): -17D - 17E = 544
Now add (2) and (3) to get (5):
-15D + 14E + F = -421
33D + F = -1089
Multiply the bottom equation by -1 to get rid of the F terms:
-15D + 14E + F = -421
-33D - F = 1089
which simplifies to
(5): -48D + 14E = 668
Now add (4) and (5) together and eliminate the E terms:
-17D - 17E = 544
-48D + 14E = 668
In order to eliminate the E terms, multiply the top equation by 14 and the bottom equation by 17 to solve for D:
-238D - 238E = 7616
-816D + 238E = 11356
Which gives you that
D = -18
Now plug the value for D into (4) to find E:
-17(-18) - 17E = 544 and
306 - 17E = 544 and
-17E = 238 so
E = -14
Now plug the values for both D and E into (1) to find F:
2(-18) + 31(-14) + F = -965 and
-36 - 434 + F = -965 and
-470 + F = -965 so
F = -495
Now we can fill in the standard form of the conic:
but we're not done til we complete the square on both the x terms and the y terms (and I am assuming you know how to complete the square):
which simplifies to
The second choice down matches that equation, but the center they have there is not correct. The center of that circle is (9, 7) and they have it as being (7, 10) with a radius of 5. The radius is 25. The center is wrong in the equation that represents the circle as is the radius. Maybe let someone know that...