Answer:
7) 13 in. Because the hypotenuse is the longest length than opposite and adjacent.
8) 12 in. Because it has 90° angle.
9) 12 in
10) 5 in
Answer:
Helena gave the answer as (7y²z + 6yz²- 5 - 3yz² + 2) which is equivalent to (7y²z + 3yz² - 3).
Step-by-step explanation:
Misha's group was asked to write an expression equivalent to
7y²z + 3yz² - 3
When Mr. Chen checked their answers, he found only one to be correct.
And she was Helena.
Helena gave the answer as (7y²z + 6yz²- 5 - 3yz² + 2) which is equivalent to (7y²z + 3yz² - 3).
Because, (7y²z + 6yz²- 5 - 3yz² + 2)
= 7y²z + (6yz² - 3yz²) - (5 - 2)
= 7y²z + 3yz² - 3 (Answer)
Yuto is correct because he isolated the variable correctly and reversed the inequality symbol.
x < 3
Answer:
-![\sqrt{5}](https://tex.z-dn.net/?f=%5Csqrt%7B5%7D)
Step-by-step explanation:
A root with square root or under root is only obtained when we take the square root of both sides. Remember that when we take a square root, there are two possible answers:
- One answer with positive square root
- One answer with negative square root
For example, for the equation:
![x^{2}=3](https://tex.z-dn.net/?f=x%5E%7B2%7D%3D3)
If we take the square root of both sides, the answers will be:
![x=\sqrt{3} \text{ or } x= -\sqrt{3}](https://tex.z-dn.net/?f=x%3D%5Csqrt%7B3%7D%20%5Ctext%7B%20or%20%7D%20x%3D%20-%5Csqrt%7B3%7D)
Only getting one solution with square root is not possible. Solutions with square root always occur in pairs.
For given case, the roots are 6 and
. Therefore, the 3rd root of the polynomial function f(x) had to be -![\sqrt{5}](https://tex.z-dn.net/?f=%5Csqrt%7B5%7D)
It seems you made error while writing option B, it should be - square root of 5.
Answer: A. 85.7
Step-by-step explanation:
Given : Two sections of a class took the same quiz.
Section A had 15 students who had a mean score of 80, and Section B had 20 students who had a mean score of 90.
We know that , ![\text{Mean}=\dfrac{\text{Sum of observations}}{\text{No. of observations}}](https://tex.z-dn.net/?f=%5Ctext%7BMean%7D%3D%5Cdfrac%7B%5Ctext%7BSum%20of%20observations%7D%7D%7B%5Ctext%7BNo.%20of%20observations%7D%7D)
Then , for section A :
![\text{Mean score }=\dfrac{\text{Sum of scores in sec A}}{\text{No. of students}}](https://tex.z-dn.net/?f=%5Ctext%7BMean%20score%20%7D%3D%5Cdfrac%7B%5Ctext%7BSum%20of%20scores%20in%20sec%20A%7D%7D%7B%5Ctext%7BNo.%20of%20students%7D%7D)
![\Rightarrow\ 80=\dfrac{\text{Sum of scores in sec A}}{15}\\\\\Rightarrow\ \text{Sum of scores in sec A}=80\times15=1200](https://tex.z-dn.net/?f=%5CRightarrow%5C%2080%3D%5Cdfrac%7B%5Ctext%7BSum%20of%20scores%20in%20sec%20A%7D%7D%7B15%7D%5C%5C%5C%5C%5CRightarrow%5C%20%5Ctext%7BSum%20of%20scores%20in%20sec%20A%7D%3D80%5Ctimes15%3D1200)
Similarly in Section B, ![\text{Sum of scores in sec B}=90\times20=1800](https://tex.z-dn.net/?f=%5Ctext%7BSum%20of%20scores%20in%20sec%20B%7D%3D90%5Ctimes20%3D1800)
Total scores = Sum of scores in sec A+Sum of scores in sec B
=1200+1800=3000
Total students = Students in sec A +Students in sec B
=15+20=35
Now , the mean score for all of the students on the quiz =![\dfrac{\text{Total score}}{\text{Total students}}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctext%7BTotal%20score%7D%7D%7B%5Ctext%7BTotal%20students%7D%7D)
![=\dfrac{3000}{35}=85.7142857143\approx85.7](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B3000%7D%7B35%7D%3D85.7142857143%5Capprox85.7)
Hence, the approximate mean score for all of the students on the quiz = 85.7
Thus , the correct answer is option A. 85.7.