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Answers:</h3>
- ST = 23
- RU = 8
- SV = 5
- SU = 10
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Explanation:
Focus on triangles SVT and UVT.
They are congruent triangles due to the fact that SV = VU and VT = VT. From there we can use the LL (leg leg) theorem for right triangles to prove them congruent.
Since the triangles are the same, just mirrored, this means ST = UT = 23.
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Following similar reasoning as the previous section, we can prove triangle RVU = triangle RVS.
Therefore, RS = RU = 8
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SV = VU = 5 because RT bisects SU.
Bisect means to cut in half. The two smaller pieces are equal.
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SU = SV + VU = 5+5 = 10
Refer to the segment addition postulate.
Answer=92≤x
86+91+98+83+97+89+99+96=739
739/8=92.375
I'm assuming the scores are all whole numbers
92≤x
Hello from MrBillDoesMath!
Answer:
All real x
Discussion:
Take any real number, say, P. Then solve
f(x) = (x-2)2 + 2 = P => (subtract 2 from both sides)
(x-2)2 = P -2 => (divide both sides by 2)
(x-2) = (1/2) (P-2) => (add 2 to both sides)
x = (1/2)(P-2) + 2
Conclusion: for any real number range value, P, there is an x (given by the above formula) such that f(x) = P. In other words, the range of f is all real numbers x
Regards,
MrB
Answer:
313/7
Step-by-step explanation:
Here, we are interested in turning the wordings of the statement to numeric values.
We take it one at a time.
Sum of 35 and 1/5(35) = 35 + 7 = 42
This is added to 1/7(11 + 8)
= 1/7(19) = 19/7
So we have;
42 + 19/7 = (294 + 19)/7 = 313/7
Answer:
35,829,630 melodies
Step-by-step explanation:
There are 12 half-steps in an octave and therefore arrangements of 7 notes if there were no stipulations.
Using complimentary counting, subtract the inadmissible arrangements from to get the number of admissible arrangements.
can be any note, giving us 12 options. Whatever note we choose, must match it, yielding . For the remaining two white key notes, and , we have 11 options for each (they can be anything but the note we chose for the black keys).
There are three possible arrangements of white key groups and black key groups that are inadmissible:
White key notes can be different, so a distinct arrangement of them will be considered a distinct melody. With 11 notes to choose from per white key, the number of ways to inadmissibly arrange the white keys is .
Therefore, the number of admissible arrangements is: