Can someone help me solve this? i don't want the direct answer, just the way to solve it.
2 answers:
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Answer:
which agrees with option"B" of the possible answers listed
Step-by-step explanation:
Notice that in order to solve this problem (find angle JLF) , we need to find the value of the angle defined by JLG and subtract it from , since they are supplementary angles. So we focus on such, and start by drawing the radii that connects the center of the circle (point "O") to points G and H, in order to observe the central angles that are given to us as
and
. (see attached image)
We put our efforts into solving the right angle triangle denoted with green borders.
Notice as well, that the triangle JOH that is formed with the two radii and the segment that joins point J to point G, is an isosceles triangle, and therefore the two angles opposite to these equal radius sides, must be equal. We see that angle JOH can be calculated by :
Therefore, the two equal acute angles in the triangle JOH should add to:
resulting then in each small acute angle of measure
.
Now referring to the green sided right angle triangle we can find find angle JLG, using:
Finally, the requested measure of angle JLF is obtained via:
Answer:
a) number of tickets she could buy in a month with her allowance in 2008 = 4 tickets
b) number of tickets she could buy in a month with the same allowance in 2012 = 2 tickets
c) $5, an increase of 55.56%
d) $2, a 100% increase.
e) Hallie was able to buy more tickets in 2008 than in 2012.
f) $16
Step-by-step explanation:
The complete question is presented in the attached image to this answer.
a) Halie's allowance monthly = $9
Price of a ticket in 2008 = $2
number of tickets she could buy in a month with her allowance = (9/2) = 4.5 = 4 tickets (since there are no half tickets)
b) Halie's allowance monthly = $9
Price of a ticket in 2012 = $4
number of tickets she could buy in a month with her allowance = (9/4) = 2.25 = 2 tickets (since there are no quarter tickets)
c) In 2012, Hallie's allowance was $14.00 per month. How much did her monthly allowance increase between 2008 and 2012?
Her monthly allowance in 2008 = $9
Her monthly allowance in 2012 = $14
The increase = new allowance - old allowance = 14 - 9 = $5
In percentage terms,
% increase = 100% × (new - old)/(old)
% increase = 100% × (14 - 9)/9 = 55.56%
d) How much more did a carnival ticket cost in 2012 than it did in 2008?
Price of a ticket on 2008 = $2
Price of a ticket in 2012 = $4
Increase in price = 4 - 2 = $2
% increase = 100% × (4 - 2)/2 = 100%
e) Was Hallie able to buy more carnival tickets in 2008 or in 2012 with one month's allowance?
Hallie was able to buy more tickets in 2008 than in 2012.
f) What would Hallie's allowance need to be in 2012 in order for her to be able to buy as many carnival tickets as she could in 2008?
Hallie could buy 4 tickets in 2008.
Price of a ticket in 2012 = $4.
Price of 4 tickets in 2012 = 4 × $4 = $16
Hope this Helps!!!!
