6 is the slope and the y-intercepts is 2
<span>(5x+9)^2
= (5x)^2 + 2 (5x) (9) + 9^2
= 25x^2 + 90x + 81
hope it helps</span>
Answer:
9th Triangle
Step-by-step explanation:
Given the area of four triangles:![40 cm^2, 90 cm^2, 202.5 cm^2 \:and\: 455.6 cm^2](https://tex.z-dn.net/?f=40%20cm%5E2%2C%2090%20cm%5E2%2C%20202.5%20cm%5E2%20%5C%3Aand%5C%3A%20455.6%20cm%5E2)
If the Scale factor is 1.5.
This is a geometric sequence and the common ratio is 1.5 X 1.5.
Therefore, the area of any n triangle can be determined using the function:
![A(n)=40\cdot1.5^{2(n-1)}](https://tex.z-dn.net/?f=A%28n%29%3D40%5Ccdot1.5%5E%7B2%28n-1%29%7D)
We want to determine which triangle has an area greater than
.
When A(n)=15000
![40\cdot1.5^{2(n-1)}>15000\\1.5^{2(n-1)}>\frac{15000}{40} \\1.5^{2(n-1)}>375\\\text{Change to Logarithm form}\\2(n-1)>Log_{1.5}375\\\text{Applying logarithm change of base to base 10 law}\\2(n-1)>\frac{Log 375}{Log 1.5} \\2n-2>14.62\\2n>14.62+2=16.62\\n>8.31](https://tex.z-dn.net/?f=40%5Ccdot1.5%5E%7B2%28n-1%29%7D%3E15000%5C%5C1.5%5E%7B2%28n-1%29%7D%3E%5Cfrac%7B15000%7D%7B40%7D%20%5C%5C1.5%5E%7B2%28n-1%29%7D%3E375%5C%5C%5Ctext%7BChange%20to%20Logarithm%20form%7D%5C%5C2%28n-1%29%3ELog_%7B1.5%7D375%5C%5C%5Ctext%7BApplying%20logarithm%20change%20of%20base%20to%20base%2010%20law%7D%5C%5C2%28n-1%29%3E%5Cfrac%7BLog%20375%7D%7BLog%201.5%7D%20%5C%5C2n-2%3E14.62%5C%5C2n%3E14.62%2B2%3D16.62%5C%5Cn%3E8.31)
Therefore, the 9th triangle has an area greater than
.
Answer: 5 miles
Step-by-step explanation:
25 minutes is 25/60 hrs
If Kathryn is going 12 miles in one hour, she will go 12 x 25/60 = 5 miles in 25 minutes