Answer:
2 cm
Step-by-step explanation:
Figure RSTU and Figure XWZY are the same meaning it has the same side lengths and angles. Also, if you reflect the shape the angle will be on the same side. The side lengths are not shown on Figure XWZY but they are the same.
<span>Part A
</span>Chorus:
Expontential growth = b*a^x
b = 15
a = 1.12 (a= r+1), r = 12%
Which gives a function of f(x) = 15*1.12^x
Band
Linear growth = ax+b
a = 2
b = 30
Which gives a function of g(x)=2x+30
<span>Part B:
</span>f(9) = 15*1.12^9 = 41.59
g(9) = 2*9+30 = 48
<span>Part C:
</span>This is probably problem solving, where you're allowed to use calculators and other softwares.
Therefore you can use different softwares, and make f(x) = g(x).
I did this, and got it to 10.95427141
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<span> Ambitious </span>
Let the sides of the polygon (which is a triangle, by the way) be x, y and z. The sum of x, y and z is the perimeter of the original poly, and this equals 18 cm.
Letting f be the scale factor, f(18 cm) = 12 cm. Then f=2/3.
The dilation reduces the size of the polygon by a factor of 1/3, producing a similar polygon which is 2/3 the size of the original one.
In each case we have 3 side lengths but no angles. We can use Heron's formula to obtain the area in each case. Look up Heron's formula. In one version of this formula, p is half the actual perimeter, meaning that p is 18 cm / 2 for the first triangle and 12 cm / 2 for the second.
The area of the first triangle would be
A18 = sqrt( 9(9-x)(9-y)(9-z) )
whereas
A12 = sqrt( 6(6-x*a)(6-y*a)(6-z*a) ), where a represents the dilation factor 2/3.
Then the ratio of the areas of the 2 triangles is
sqrt( 6(6-x*a)(6-y*a)(6-z*a) )
---------------------------------------
sqrt( 9(9-x)(9-y)(9-z) )
Outliers should be excluded when producing a trend line, regardless of the method used.
The student got a score of 100 with no sleep.
This data pair was a rare event.
If the outlier was included, it would cause the trend line to misrepresent the typical data relationship.
