The Pythagorean theorem is the idea that the sum of the two legs which are both squared is equal to the hypotenuse's length squared.
*<em>look at the image I attached for a better explanation</em>
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By looking at the picture, we are missing the leg's length, and by using the Pythagorean theorem, we get the equation
![?^2+9^2 = 16^2\\?^2 + 81 = 256\\?^2 = 175\\? = 13.2](https://tex.z-dn.net/?f=%3F%5E2%2B9%5E2%20%3D%2016%5E2%5C%5C%3F%5E2%20%2B%2081%20%3D%20256%5C%5C%3F%5E2%20%3D%20175%5C%5C%3F%20%3D%2013.2)
Thus the <u>missing side length is 13.2 cm</u>
Hope that helps!
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Using polynomial long division, we get
3x^3+6x^2+11x
_____________
(x+2) | 3x^4-x^2+cx-2
-(3x^4+6x^3)
____________
6x^3-x^2+cx-2
- (6x^3+12x^2)
_____________
11x^2+cx-2
-(11x^2+22x)
__________
(22+c)x-2.
If you're wondering how I did the long division, what I essentially did was get the first value (at the start, it was 3x^4) and divided it by the first value of the divisor (which in x+2 was x) to get 3x^3 in our example. I then subtracted the polynomial by the whole divisor multiplied by, for example, 3x^3 and repeated the process.
For this to be a perfect factor, (x+2)*something must be equal to (22+c)x-2. Focusing on how to cancel out the 2, we have to add 2 to it. To add 2 to it, we have to multiply (x+2) by 1. However, there's a catch, which is that we subtract whatever we multiply (x+2) by, so we have to multiply it by -1 instead. We still need to cross out (22+c)x. Multiplying (x+2) by -1, we get
(-x-2) but by subtracting the whole thing from something means that we have to add -(-x-2)=x+2 to something to get 0. x+2-x-2=0, xo (22+c)x-2 must equal -x-2, meaning that (22+c)=-1 and c=-23
Answer:
y = 2x - 10
Step-by-step explanation:
y2 - y1/ x2 - x1
0 - 2 / 5 - 6
= 2
y = 2x + b
2 = 2(6) +b
2 = 12 + b
-10 = b
The equation is y = 2x - 10
Answer:
I think the answer would be C or B
Step-by-step explanation:
Q 5) No. of boys = 20
Answer:
Q 6) Total time taken to answer both the quizzes = 90 minutes
Step-by-step explanation:
Q 5.
Let the number of boys = x
Therefore, number of girls = x - 5
Since,
No. of boys + No. of girls = 35
hence,
x + x- 5 = 35
2x-5 = 35
2x = 35 + 5
2x = 40
x = 40/2
x = 20
Hence 20 boys participated in the activity.
Let the time taken to answer history quiz= x min
Therefore, time taken to answer geography quiz = (x + 30) min
According to the given information:
x = 1/2(x + 30)
2x = x + 30
2x - x = 30
x = 30 min
Hence, x + 30 = 30 + 30 = 60 min
Total time taken to answer both the quizzes = 30 + 60 = 90 minutes