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Answer:
Isosceles triangles have two sides with the same length, and one side that ... Similarly, if two angles of a triangle have equal measure, then the sides ... (2) Set up an equation and solve for x. ... x = 60/2 x = 30. Each base angle of triangle ABC measures 30 degrees. ... In isosceles triangle RST, angle S is the vertex angle.
Step-by-step explanation:
Mean = Sum of all the observations/ Number of observations = (87+46+90+78+89)/5 = 78
Variance = SD^2 ------ SD = Standard deviation
It means that with Variance, square root is never taken.
Therefore,
Variance = Summation of square of differences between observation and the mean divided by the number of observations.
That is,
Variance = {(87-78)^2 + (46-78)^2 + (90-78)^2 + (78-78)^2 + (89-78)^2}/5 = 274
a)
If the triangles are similar, the corresponding sides vary on the same proportion, so the ratios between the corresponding sides are equal.
For
![\frac{x}{20}=\frac{12}{16}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B20%7D%3D%5Cfrac%7B12%7D%7B16%7D)
To solve for x you have to multiply both sides of the expression by 20
![\begin{gathered} \frac{20x}{20}=(\frac{12}{16})\cdot20 \\ x=(\frac{3}{4})\cdot20 \\ x=15 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B20x%7D%7B20%7D%3D%28%5Cfrac%7B12%7D%7B16%7D%29%5Ccdot20%20%5C%5C%20x%3D%28%5Cfrac%7B3%7D%7B4%7D%29%5Ccdot20%20%5C%5C%20x%3D15%20%5Cend%7Bgathered%7D)
b)
Following the same logic, the ratio between x and 20 is the same as the ratio between 6 and 8
![\frac{x}{20}=\frac{6}{8}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B20%7D%3D%5Cfrac%7B6%7D%7B8%7D)
6/8 can be simplifies as 3/4. Then multiply both sides by 20 to determine the value of x.
![\begin{gathered} \frac{x}{20}=\frac{6}{8} \\ 20\cdot\frac{x}{20}=(\frac{3}{4})\cdot20 \\ x=15 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7Bx%7D%7B20%7D%3D%5Cfrac%7B6%7D%7B8%7D%20%5C%5C%2020%5Ccdot%5Cfrac%7Bx%7D%7B20%7D%3D%28%5Cfrac%7B3%7D%7B4%7D%29%5Ccdot20%20%5C%5C%20x%3D15%20%5Cend%7Bgathered%7D)
As mentioned above, when two triangles are similar, the corresponding sides are always in the same ratio, that is why the results in a and b are the same.
B * 3 < 140
B being the number of books Frank owns. Because tripling the amount of books he owns is still less than the amount of book Emily owns, b*3 has to be less than 140