In the parallelogram ABCD, diagonals AC and BD intersect at point E.
According to the definition of parallelogram, opposite sides are equal and parallel to each other. That means, AB = DC
Now as AB and DC are parallel, so according to the property of Alternate Interior Angles, we will get:
∠EAB = ∠ECD and ∠EBA = ∠EDC
Thus , in two triangles ΔABE and ΔDCE, two angles and one side are equal. So, ΔABE and ΔDCE are congruent to each other.
That means, AE = CE and BE = DE
So, AE is congruent to CE and BE is congruent to DE
Answer:
$12,500
Step-by-step explanation:
Using the compound interest formula Accrued Amount = P (1 + r)^n
where Accrued amount = $18000
P = principal; we need to generate it
r = 20% = 0.2
n = 2
Therefore
P = Accrued amount/ (1 + r)^n
= 18000/(1+0.2)^2
= 18000/1.44
= 12,500
hence $12,500 needs to be invested
Answer:
4.41 x 10^3 hope this helps
Answer:
(7/3) x^3 ln x - (7/9) x^3 + c.
Step-by-step explanation:
∫udv = uv - ∫vdu
u = ln x and dv = 7x^2dx so,
du = 1/x and v = 7x^3/3 so:
∫7x^2 ln x = (7x^3/3) ln x - 7 ∫x^3/3 * 1/x dx
= 7/3 x^3 ln x - 7 ∫x^2/3 dx
= 7/3 x^3 ln x - 7/x^3/2 * 1/3 dx
= 7/3 x^3 ln x - 7/9 x^3 + c.
Answer: x=-4
Step-by-step explanation:
Add 12 to both sides
x/2=-14+12
Simplify
x/2=-2
Multiply
x=-2*2
Simplify
x=-4
