Answer:
6 3/4
Step-by-step explanation:
y = abˣ
16 = ab¹
9 = ab⁵
ab⁵ / ab¹ = 9 / 16
b⁴ = 9/16
b² = 3/4
7th term: y = ab⁷ = ab⁵ x b² = 9 x 3/4 = 27/4 = 6 3/4
Answer:
y>-2
Step-by-step explanation:
her mistake was she did -22-6= -28 but the correct solution is -22+6= -16
Refer to the attached image.
Given the rectangle ABCD of length 'l' and height 'h'.
Therefore, CD=AB = 'l' and BC = AD = 'h'
We have to determine the area of triangle AEF.
Area of triangle AEF = Area of rectangle ABCD - Area of triangle ADF - Area of triangle ECF - Area of triangle ABE
Area of triangle ADF = ![\frac{1}{2}bh](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dbh)
= ![\frac{1}{2}(DF \times AD)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28DF%20%5Ctimes%20AD%29)
= ![\frac{1}{2}(\frac{l}{2} \times h)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28%5Cfrac%7Bl%7D%7B2%7D%20%5Ctimes%20h%29)
![=\frac{lh}{4}](https://tex.z-dn.net/?f=%3D%5Cfrac%7Blh%7D%7B4%7D)
Area of triangle ECF = ![\frac{1}{2}bh](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dbh)
= ![\frac{1}{2}(CF \times CE)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28CF%20%5Ctimes%20CE%29)
= ![\frac{1}{2}(\frac{l}{2} \times \frac{h}{2})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28%5Cfrac%7Bl%7D%7B2%7D%20%5Ctimes%20%5Cfrac%7Bh%7D%7B2%7D%29)
![=\frac{lh}{8}](https://tex.z-dn.net/?f=%3D%5Cfrac%7Blh%7D%7B8%7D)
Area of triangle ABE = ![\frac{1}{2}bh](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dbh)
= ![\frac{1}{2}(AB \times BE)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28AB%20%5Ctimes%20BE%29)
= ![\frac{1}{2}(l \times \frac{h}{2})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28l%20%5Ctimes%20%5Cfrac%7Bh%7D%7B2%7D%29)
![=\frac{lh}{4}](https://tex.z-dn.net/?f=%3D%5Cfrac%7Blh%7D%7B4%7D)
Now, area of triangle AEF =
Area of rectangle ABCD - Area of triangle ADF - Area of triangle ECF - Area of triangle ABE
= ![72 - (\frac{lh}{4} + \frac{lh}{8} + \frac{lh}{4})](https://tex.z-dn.net/?f=72%20-%20%28%5Cfrac%7Blh%7D%7B4%7D%20%2B%20%5Cfrac%7Blh%7D%7B8%7D%20%2B%20%5Cfrac%7Blh%7D%7B4%7D%29)
= ![72 - (\frac{2lh+lh+2lh}{8})](https://tex.z-dn.net/?f=72%20-%20%28%5Cfrac%7B2lh%2Blh%2B2lh%7D%7B8%7D%29)
=![72 - (\frac{5lh}{8})](https://tex.z-dn.net/?f=72%20-%20%28%5Cfrac%7B5lh%7D%7B8%7D%29)
=![72 - (\frac{5 \times 72}{8})](https://tex.z-dn.net/?f=72%20-%20%28%5Cfrac%7B5%20%5Ctimes%2072%7D%7B8%7D%29)
![=\frac{72 \times 8 - (5 \times 72)}{8}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B72%20%5Ctimes%208%20-%20%285%20%5Ctimes%2072%29%7D%7B8%7D)
= 27 units
Therefore, the area of triangle AEF is 27 units.
Answer:
6% growth
Step-by-step explanation:
The equation =
A = 2300(1.06)⁷
What does 0.06 represent in the equation?
The formula for Exponential growth =
y = a (1 +r)^t
Where
y = Size after time t
a = Initial size
r = Growth rate in Percentage
t = Time t
Equating both Equations together
y = a (1 +r)^t = A = 2300(1.06)⁷
1 + r = 1.06
r = 1.06 - 1
r = 0.06
Converting to percent
r = 0.06 × 100
r = 6% growth rate