This is the theory of exponential growth. Given that the an athlete is training to run marathon and she plans to run 2 miles in the first week and increase the distance by 8%. The function modeling how far she will run the nth week will be given by
nth=ae^(bx)
nth=2e^(0.08x)
where x is the nth time.
Answer:
reflection
Step-by-step explanation:
from 1 to 2 it is reflection across the y-axis and from 2 to three it is reflection across the x-axis then 3 to 4 it is reflected across the y-axis again and then from 4 to 5 it is reflected across the x-axis.
Answer:
70% of the juice boxes are left.
Step-by-step explanation:
10 is the total number of juice boxes which means that 10 is 100%
If there are 10 total juice boxes and Sam drank 3, there are 7 juice boxes left. Sam drank 30% of the juice boxes which means that there is 70% of the juice boxes left.
Hope this helps!
Answer:
x=0
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
2x+5=−2x+5
Step 2: Add 2x to both sides.
2x+5+2x=−2x+5+2x
Step 3: Subtract 5 from both sides.
4x+5−5=5−5
4x=0
Step 4: Divide both sides by 4.
4x/4=0/4
X=0
Angle D is 180° -75° -45° = 60°. Drawing altitude MX to segment DN divides the triangle into ΔMDX, a 30°-60°-90° triangle, and ΔMNX, a 45°-45°-90° triangle. We know the side ratios of such triangles (shortest-to-longest) are ...
... 30-60-90: 1 : √3 : 2
... 45-45-90: 1 : 1 : √2
The long side of ΔMDX is 10√3, so the other two sides are
... MX = MD(√3/2) = 15
... DX = MD(1/2) = 5√3
The short side of ΔMNX is MX = 15, so the other two sides are
... NX = MX(1) = 15
... MN = MX(√2) = 15√2
Then the perimeter of ΔDMN is ...
... P = DM + MN + NX + XD
... P = 10√3 +15√2 + 15 + 5√3
... P = 15√3 +15√2 +15 . . . . perimeter of ΔDMN
