Answer:
60%
Step-by-step explanation:
To find the total pass = 65 * number of student that passed, let it be be represented by P and number of students that failed F
Total pass = 65p
And total fail = 35F
For the total pass and failure will be 53(P+F)
Equating to total pass and total fail
65P +35F = 53( P+ F)
65P+35F = 53P+ 53F
65P-53P =53F-35F
12P=18F
2P= 3F
Hence there are 3 passing scores for every 2 failure scores, hence there are a multiple of 5 scores and the same multiple of 3 passing scores.
3/5 * 100= 60%
Answer:
Sorry that is toooooooooooooooooooooo much
Step-by-step explanation:
<h2>
Answer:</h2>
<u>
</u>
<h2>
Step-by-step explanation:</h2>
In the question,
We have to find out the circumcentre of the circle passing through the triangle with the vertices (a₁, b₁), (a₂, b₂) and (a₃, c₃).
So,
The circle is passing through these points the equation of the circle is given by,
![x^{2}+y^{2}+ax+by+c=0](https://tex.z-dn.net/?f=x%5E%7B2%7D%2By%5E%7B2%7D%2Bax%2Bby%2Bc%3D0)
On putting the points in the circle we get,
![x^{2}+y^{2}+ax+by+c=0\\(a_{1})^{2}+(b_{1})^{2}+a(a_{1})+b(b_{1})+c=0\\and,\\(a_{2})^{2}+(b_{2})^{2}+a(a_{2})+b(b_{2})+c=0\\and,\\(a_{3})^{3}+(b_{3})^{3}+a(a_{3})+b(b_{3})+c=0\\](https://tex.z-dn.net/?f=x%5E%7B2%7D%2By%5E%7B2%7D%2Bax%2Bby%2Bc%3D0%5C%5C%28a_%7B1%7D%29%5E%7B2%7D%2B%28b_%7B1%7D%29%5E%7B2%7D%2Ba%28a_%7B1%7D%29%2Bb%28b_%7B1%7D%29%2Bc%3D0%5C%5Cand%2C%5C%5C%28a_%7B2%7D%29%5E%7B2%7D%2B%28b_%7B2%7D%29%5E%7B2%7D%2Ba%28a_%7B2%7D%29%2Bb%28b_%7B2%7D%29%2Bc%3D0%5C%5Cand%2C%5C%5C%28a_%7B3%7D%29%5E%7B3%7D%2B%28b_%7B3%7D%29%5E%7B3%7D%2Ba%28a_%7B3%7D%29%2Bb%28b_%7B3%7D%29%2Bc%3D0%5C%5C)
So,
![(a_{1})^{2}+(b_{1})^{2}+a(a_{1})+b(b_{1})+c=0\\a(a_{1})+b(b_{1})+c=-(a_{1})^{2}-(b_{1})^{2}\,.........(1)\\and,\\a(a_{2})+b(b_{2})+c=-(a_{2})^{2}-(b_{2})^{2}\,.........(2)\\and,\\a(a_{3})+b(b_{3})+c=-(a_{3})^{3}-(b_{3})^{3}\,.........(3)\\](https://tex.z-dn.net/?f=%28a_%7B1%7D%29%5E%7B2%7D%2B%28b_%7B1%7D%29%5E%7B2%7D%2Ba%28a_%7B1%7D%29%2Bb%28b_%7B1%7D%29%2Bc%3D0%5C%5Ca%28a_%7B1%7D%29%2Bb%28b_%7B1%7D%29%2Bc%3D-%28a_%7B1%7D%29%5E%7B2%7D-%28b_%7B1%7D%29%5E%7B2%7D%5C%2C.........%281%29%5C%5Cand%2C%5C%5Ca%28a_%7B2%7D%29%2Bb%28b_%7B2%7D%29%2Bc%3D-%28a_%7B2%7D%29%5E%7B2%7D-%28b_%7B2%7D%29%5E%7B2%7D%5C%2C.........%282%29%5C%5Cand%2C%5C%5Ca%28a_%7B3%7D%29%2Bb%28b_%7B3%7D%29%2Bc%3D-%28a_%7B3%7D%29%5E%7B3%7D-%28b_%7B3%7D%29%5E%7B3%7D%5C%2C.........%283%29%5C%5C)
On solving these equation using, <u>Matrix method we can get the required equation of the circle,</u>
<u>
</u>
<em><u>This is the required answer.</u></em>
Answer: 4x° = 80°, 60°, 2x° = 40°
Steps:
4x + 60 + 2x = 180
6x + 60 = 180
6x = 120
x = 20
4x
4(20) = 80
2x
2(20) = 40
Check:
80 + 40 + 60 = 180
180 = 180 ✅
Answer:
![x=-0.5,0.25,\frac{2}{3}](https://tex.z-dn.net/?f=x%3D-0.5%2C0.25%2C%5Cfrac%7B2%7D%7B3%7D)
Step-by-step explanation:
![f(x)=24x^3+10x^2-7x+2](https://tex.z-dn.net/?f=f%28x%29%3D24x%5E3%2B10x%5E2-7x%2B2)
For rational roots,
,so
![24x^3+10x^2-7x+2=0](https://tex.z-dn.net/?f=24x%5E3%2B10x%5E2-7x%2B2%3D0)
We can look at the factors for the constant term and the term multiplying the highest power to see if we can find candidates possible roots.
Factors of 2:
2, 1
Factors of 24:
24, 12, 6, 2, 4, 1, 2, 3, 8
We divide these factors of the constant term by the factors of the
term to give us possible factors.
This gives us a set of:
![\pm \{\frac{1}{12},\frac{1}{24}, \frac{3}{6}, \frac{1}{6}, 1, \frac{1}{2}, \frac{2}{3}, \frac{1}{3},\frac{1}{4},\frac{1}{8} \}](https://tex.z-dn.net/?f=%5Cpm%20%5C%7B%5Cfrac%7B1%7D%7B12%7D%2C%5Cfrac%7B1%7D%7B24%7D%2C%20%5Cfrac%7B3%7D%7B6%7D%2C%20%5Cfrac%7B1%7D%7B6%7D%2C%201%2C%20%5Cfrac%7B1%7D%7B2%7D%2C%20%5Cfrac%7B2%7D%7B3%7D%2C%20%5Cfrac%7B1%7D%7B3%7D%2C%5Cfrac%7B1%7D%7B4%7D%2C%5Cfrac%7B1%7D%7B8%7D%20%5C%7D)
We check all of these roots, by plugging them into the function to see if that will give us a result of 0.
We find the results that give us 0 are:
![x=-0.5,0.25,\frac{2}{3}](https://tex.z-dn.net/?f=x%3D-0.5%2C0.25%2C%5Cfrac%7B2%7D%7B3%7D)