<h3>Answer: QS is 37 units long</h3>
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Explanation:
PN = 24 and NR = 14 are pieces of the chord PR. The two pieces multiply to some value. At the same time, the other two pieces QN = 21 and NS = 2x-4 also multiply to that same value. In short, the chord pieces multiply to the same number. This is known as the intersecting chord theorem.
PN*NR = QN*NS
24*14 = 21*(2x-4)
336 = 42x-84
336+84 = 42x-84+84 .... add 84 to both sides
420 = 42x
42x = 420
42x/42 = 420/42 ...... divide both sides by 42
x = 10
We know that x = 10 so we can use it to find the length of NS
NS = 2x-4
NS = 2*10-4
NS = 20-4
NS = 16
Therefore,
QS = QN + NS
QS = 21 + 16
QS = 37
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note: as a check,
PN*NR = QN*NS
24*14 = 21*16
336 = 336
we get a true equation, so we have the proper values
20% decrease should be the answer
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--><span>For example, a credit card company might charge 1% interest each month; therefore, the APR would equal 12% (1% x 12 months = 12%). This differs from APY, which takes into account compound interest. The APY for a 1% rate of interest compounded monthly would be 12.68% [(1 + 0.01)^12 – 1= 12.68%] a year. If you only carry a balance on your credit card for one month's period you will be charged the equivalent yearly rate of 12%. However, if you carry that balance for the year, your effective interest rate becomes 12.68% as a result of compounding each month.</span>
If you solve for x the answer is x<-8
Answer:
<h3>11.8 feet</h3>
Step-by-step explanation:
Given
Length of the ladder = 12foot
angle of elevation = 80 degrees
Required
Height of the wall (opposite side)
The set up will form a right angled triangle where
length of the ladder is the hypotenuse
height of the wall is opposite;
Using SOH, CAH, TOA trig identity
According to SOH
sin 80 = opp/hyp
sin80 = opp/12
opp = 12sin80
opp = 11.82 feet
Hence the height of the wall is 11.8feet (to the nearest tenth)
