I used to shovel snow for $5 an hour.
If ' t ' was the number of hours I spent shoveling somebody's driveway,
then ' 5t ' was the number of dollars he owed me for the job.
' t ' didn't even have to be a whole number. It worked fine with any number.
Assign x to adult tickets and y to student tickets, then set up the system
5x+y=2465 and
x+y=1077
You can subtract the second equation from the first to get
4x=1388
=> x=347
Then to find y do 1077-347 to find
y=730
Final answer:
347 adult tickets and 730 student tickets were sold.
Hope I helped :)
Complete the square
first isolate x terms
y=(x^2-4x)-9
complete square inside (take 1/2 of square of b )
-4/2=-2, (-2)^2=4
add 4-4 inside
y=(x^2-4x+4-4)-9
complete the square
y=((x-2)^2-4)-9
y=(x-2)^2-4-9
y=(x-2)^2-13
The equation for cosine is <span><span><span>cos<span>(x)</span></span>=<span>Adjacent/Hypotenuse
</span></span></span>The inside trig function is <span><span>arccos<span>(<span>3/5</span>)</span></span></span>, which means <span><span><span>cos<span>(x)</span></span>=<span>3/5</span></span></span>. Comparing <span><span><span>cos<span>(x)</span></span>=<span>Adjacent/Hypotenuse</span></span></span> with <span><span><span>cos<span>(x)</span></span>=<span>3/5
</span></span></span>
Find <span><span>Adjacent=3</span></span> and <span><span>Hypotenuse=5.
</span></span>Then, using the Pythagorean theorem, find <span><span>Opposite=?
</span></span>a² = c² - b²
a² = 5² - 3² = 25 - 9 = 16
a = √16 = 4
<span><span>Adjacent=3</span></span><span><span>Opposite=4</span></span><span><span>Hypotenuse=5
</span></span><span>
Plug in the value for sin(x) = opposite/hypotenuse
sin(x) = 4/5 </span>
In linear models there is a constant additve rate of change. For example, in the equation y = mx + b, m is the constanta additivie rate of change.
In exponential models there is a constant multiplicative rate of change.
The function of the graph seems of the exponential type, so we can expect a constant multiplicative exponential rate.
We can test that using several pair of points.
The multiplicative rate of change is calcualted in this way:
[f(a) / f(b) ] / (a - b)
Use the points given in the graph: (2, 12.5) , (1, 5) , (0, 2) , (-1, 0.8)
[12.5 / 5] / (2 - 1) = 2.5
[5 / 2] / (1 - 0) = 2.5
[2 / 0.8] / (0 - (-1) ) = 2.5
Then, do doubt, the answer is 2.5
