Answer:
512 ft.
Step-by-step explanation:
From the parking lot at the Red Hill Shopping Center, the angle of sight (elevation) to the top of the hill is about 25. From the base of the hill you can also sight the top but at an angle of 55. The horizontal distance between sightings is 740 feet. How high is Red Hill? Show your subproblems.
Solution:
Let x be the distance from the base of the hill to the middle of the hill perpendicular to the height, let h be the height of the hill. Therefore:
tan 25 = h/(x + 740)
h = (x + 740)tan 25 (1)
tan 55 = h / x
h = x tan 55 (2)
Hence:
(x + 740)tan 25 = xtan 55
0.4663(x + 740) = 1.428x
0.4663x + 345.07 = 1.428x
0.9617x = 345.07
x = 359 ft.
h = xtan55 = 359 tan(55) = 512 ft.
three and twenty-seven thousand, five hundred twenty-five hundred-thousandths
C) (0.85 + x/100)(250+145) does not give the correct answer.
Explanation
A) works; adding the two costs together is 250+145=395. We multiply this by 0.85 because 100%-15%=85%=0.85. We also have x% tax, which is represented by x/100, added to 100% of the value, or 1.00. Altogether this gives us
395(0.85)(1+x/100) = 395(0.85 + (0.85x/100)) = 395(0.85) + 395(0.85x/100)
= 395(0.85) + 395(0.0085x)
B) works; we have 250+145 for the original price; we have 85% = 0.85 of the value; we also have 100% + x%, which is (100+x)/100.
C) does not work; (0.85+x/100)(395) does not take into consideration that you are finding the tax after taking the 85%. This will simplify out to
0.85*395 + (x/100)(395) = 335.75 + 395x/100 = 335.75 + 3.95x, which is too much.
D) works; simplifying the expression from A, we have 395(0.85) + 395(0.0085x) = 335.75 + 3.3575x.
Answer:
3.93939394
rounded it would be 3.934
Step-by-step explanation:
To write the equation of a line I need slope and y intercept (0,y)
I have y intercept (0,7) of +7 as written in the equation
The equation y=-5/4x + 11/4 has a slope of -5/4
To get perpendicular slope is negated reciprocal
so take -5/4 and flip it -4/5 and change the sign (in this case negative to positive) 4/5
so the new equation is y=4/5x +7 (third one)
