Answer:
The Length of JM is 20.
Step-by-step explanation:
Given,
JKLM is a kite in which JL and KM are the diagonals that intersect at point A.
Length of AK = 9
Length of JK = 15
Length of AM = 16
Solution,
Since JKLM is a kite. And JL and KM are the diagonals.
And we know that the diagonals of a kite perpendicularly bisects each other.
So, JL ⊥ KM.
Therefore ΔJAK is aright angled triangle.
Now according to Pythagoras Theorem which states that;
"The square of the hypotenuse is equal to the sum of the square of base and square of perpendicular".
On putting the values, we get;
On taking square root onboth side, we get;
Again By Pythagoras Theorem,
On putting the values, we get;
On taking square root onboth side, we get;
Hence The Length of JM is 20.
1) For each of these, keep in mind vertex form: f(x)=a(x-h)^2+k. With vertex form, a is the direction and width, h is the horizontal placement of the vertex, and k is the vertical placement. For the first one, notice that "a" is positive 1, so it faces up. This means that D, the one facing down, cannot be the answer. "h" is 1, so we will move the vertex to the right one unit (keep in mind (x-h), so if it were to be (h+3) you would move it to the left, not the right). "k" is -3, so we would move the vertex down 3 units. That said, the vertex should be at (1,-3) so the answer is C, or the one right below the first one.
2) The graph of f(x)=|2x| translated 5 units to the left means that h is equal to -5. When we plug -5 into vertex form, it should look like: g(x)=|2(x+5)|. The answer to this is A.
3) The equation for reflection on the x axis is f(x)=-a(x-h)+k. So, if the parent function f(x)=4|x| were to be reflected on the x axis, the function would look like this: g(x)=-4|x|. The answer to this should be B.
4) Since h=1 and k=0 in the function f(x)=-3|x-1|, the vertex will be (1,0).
5) This can also be written as g(x)=|x|-3. This means that k=-3, and will be a vertical translation of 3 units down.
9514 1404 393
Answer:
19 years
Step-by-step explanation:
The compound interest formula tells you the future value of principal P invested at annual rate r compounded n times per year for t years is ...
A = P(1 +r/n)^(nt)
Solving for t, we get ...
t = log(A/P)/(n·log(1 +r/n))
Using the given values, we find t to be ...
t = log(2.13022)/(4·log(1 +0.04/4)) ≈ 19.000
The investment will be worth $213,022 after 19 years.
Answer:
2. (-2)(4)
Step-by-step explanation:
The fraction form would be 21/4. The decimal form would be 5.25.
