Answer:
The answer is below
Step-by-step explanation:
1. COST Mr. Rivera wants to purchase a riding lawn mower, which is on sale for 15% off the marked price. The store charges sales tax 6.5% on all sales. Write a function p(x) that represents the price after a 15% discount. Write a function t(x) that represents the total cost with sales tax. Write a composition of functions that represents the total cost of a riding lawn mower on sale. How much will Mr. Rivera pay for a riding lawn mower that has a marked price of $3000?
Solution:
a) Let x represent the marked price and p(x) represent the price after discount. Since a discount of 15% is given, the price would be:
p(x) = 
b) If x = discounted price and t(x) = total cost with sales tax, then:
t(x) = 
c) Let t(x) represents the total cost with sales tax
![t[p(x)] =p(x)+6.5\%\ of\ p(x) \\\\t[p(x)] = 0.85x+(0.065*0.85x)\\\\t[p(x)] =0.90525x\\\\for\ x=\$3000:\\\\t[p(3000)] = 0.90525*3000=\$2715.75](https://tex.z-dn.net/?f=t%5Bp%28x%29%5D%20%3Dp%28x%29%2B6.5%5C%25%5C%20of%5C%20p%28x%29%20%5C%5C%5C%5Ct%5Bp%28x%29%5D%20%3D%200.85x%2B%280.065%2A0.85x%29%5C%5C%5C%5Ct%5Bp%28x%29%5D%20%3D0.90525x%5C%5C%5C%5Cfor%5C%20x%3D%5C%243000%3A%5C%5C%5C%5Ct%5Bp%283000%29%5D%20%3D%200.90525%2A3000%3D%5C%242715.75)
Answer:
The area of the irregular object is 9 units.
Answer:
x = 14.4
Step-by-step explanation:
x is sin(angle 24/30)×24
how do we get the angle at 24/30 ?
by using the extended Pythagoras for baselines opposite other than 90 degrees.
c² = a² + b² - 2ab×cos(angle opposite of c)
in our example the angle 24/30 is opposite of the side 18.
so,
18² = 24² + 30² - 2×24×30×cos(angle 24/30)
324 = 576 + 900 - 1440×cos(angle 24/30)
324 = 1476 - 1440×cos(angle 24/30)
1440×cos(angle 24/30) = 1152
cos(angle 24/30) = 1152/1440 = 576/720 = 288/360 = 144/180 = 72/90 = 36/45 = 12/15 = 4/5
angle 24/30 = 36.9 degrees
x = sin(36.9) × 24 = 14.4
Answer:
1st question: y=1/3x-1
2nd question: y=-2/3x+9
Step-by-step explanation:
Y=mx+b form is what you are using
when a line in parallel to a line they have the same slop wich is m
when a line in perpendicular they have the opposite reciprocal
Examples: 2/5 opposite reciprocal would be -5/2
