Answer:
43.407 years
Step-by-step explanation:
Zoe invest $600 in college savings account. The account earns 5.7% interest compounded quarterly. How many years will it take for Zoe's account to reach $7,000?
We are asked to find time t in a compound interest formula
The formula is given as:
t = log(A/P) / n[log(1 + r/n)]
A = Total amount = $7000
P = Principal = $600
n = number of times interest is compounded = Quarterly =4
r = Interest rate = 5.7% = 0.057
Hence,
t = log(7000/600) /4[log (1 + 0.057/4)]
t = 43.407 years
Since the discriminant is positive, this means we have two distinct real solutions.
If a, b, and c are rational numbers, then a discriminant of D = 40 indicates the two solutions are not rational. We would need D to be a perfect square to get two rational solutions.
Answer:
Δ MLP ~ Δ HKG
By S-A-S similarity Postulate.
Step-by-step explanation:
Given:
In Δ MLP
MP = 20 ,
LP = 15
∠ P = 42°
In Δ HKG
HG = 16 ,
KG = 12
∠G = 42°
To Prove:
Δ MLP ~Δ HKG
Proof:
In Δ MLP and Δ HKG
..........( 1 )
..............( 2 )
∴ 
...From 1 and 2
∠P ≅ ∠ G = 42° ...............Given
∴ Δ MLP ~Δ HKG ......{ By S-A-S similarity test}............Proved
For a cyclic quadrilateral
The opposite angles are supplementary (meaning they sum up to 180 °)
I.e (x +20) ° + 3x ° =180 °
20 + 4x = 180
4x=180 - 20
4x = 160
Divide through by 4
x = 40 °
Angle at point A
(2x + 38) = (2(40) + 38) = 118 °
Angle at point B
3x = 3(40) = 120 °
Angle at point D
x + 20 = 40 + 20 = 60 °
Angle at point C
The total angle in a quadrilateral is 360 °
I.e 118 + 120 + 298 +
Answer:
Step-by-step explanation:
V = volume
r = rate
t = time
Use formula 
connecting volume, rate and time.
In your case,
cup of water
hours
r is unknown.
Substitute all data into the formula:
![\dfrac{1}{4}=r\cdot 1\dfrac{1}{2}\\ \\\dfrac{1}{4}=r\cdot \dfrac{3}{2}\\ \\2\cdot \dfrac{1}{4}=3r\ [\text{Multipled by 2}]\\ \\3r=\dfrac{1}{2}\\ \\r=\dfrac{\frac{1}{2}}{3}\ [\text{Divided by 3}]\\ \\r=\dfrac{1}{6}\ \text{cups per hour}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B4%7D%3Dr%5Ccdot%201%5Cdfrac%7B1%7D%7B2%7D%5C%5C%20%5C%5C%5Cdfrac%7B1%7D%7B4%7D%3Dr%5Ccdot%20%5Cdfrac%7B3%7D%7B2%7D%5C%5C%20%5C%5C2%5Ccdot%20%5Cdfrac%7B1%7D%7B4%7D%3D3r%5C%20%5B%5Ctext%7BMultipled%20by%202%7D%5D%5C%5C%20%5C%5C3r%3D%5Cdfrac%7B1%7D%7B2%7D%5C%5C%20%5C%5Cr%3D%5Cdfrac%7B%5Cfrac%7B1%7D%7B2%7D%7D%7B3%7D%5C%20%5B%5Ctext%7BDivided%20by%203%7D%5D%5C%5C%20%5C%5Cr%3D%5Cdfrac%7B1%7D%7B6%7D%5C%20%5Ctext%7Bcups%20per%20hour%7D)
