Answer:
Step-by-step explanation:
sides of triangle are (4+3) and (2+3)
or 7,5
area of triangle=1/2×7×5=35/2=17.5 cm²
area of rectangle=3×2=6 cm²
area of shaded region=17.5-6=11.5 cm²
The length of the rectangle is 16.
Answer:
![{ \rm{y = - 3x + 5}}](https://tex.z-dn.net/?f=%7B%20%5Crm%7By%20%3D%20%20-%203x%20%2B%205%7D%7D)
Gradient = -3
• Parallel lines have the same gradient, therefore gradient, m is -3
![{ \rm{y = mx + c}}](https://tex.z-dn.net/?f=%7B%20%5Crm%7By%20%3D%20mx%20%2B%20c%7D%7D)
• At point (0, -4)
![{ \rm{ - 4 = ( - 3 \times 0) + c}} \\ \\ { \rm{c = - 4}}](https://tex.z-dn.net/?f=%7B%20%5Crm%7B%20-%204%20%3D%20%28%20-%203%20%5Ctimes%200%29%20%2B%20c%7D%7D%20%5C%5C%20%20%5C%5C%20%7B%20%5Crm%7Bc%20%3D%20%20-%204%7D%7D)
y intercept is -4
![{ \boxed{ \boxed{ \mathfrak{answer : }}{ \rm{\: \: y = - 3x - 4}}}}](https://tex.z-dn.net/?f=%7B%20%5Cboxed%7B%20%5Cboxed%7B%20%5Cmathfrak%7Banswer%20%3A%20%7D%7D%7B%20%5Crm%7B%5C%3A%20%20%5C%3A%20y%20%3D%20%20-%203x%20-%204%7D%7D%7D%7D)
Step-by-step explanation:
The function is as follows :
![f(x) = x^2 + 5x + 5](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E2%20%2B%205x%20%2B%205)
We need to find the zeroes of the function in the simplest radical form.The zero of the above function is given by :
![x=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%20%7D%7B2a%7D)
Here,
b = 5
a = 1
c = 5
So,
![x=\dfrac{-5\pm \sqrt{5^2-4\times 1\times 5} }{2(1)}\\\\x=\dfrac{-5\pm \sqrt{25-20} }{2(1)}\\\\x=\dfrac{-5\pm \sqrt{5} }{2}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B-5%5Cpm%20%5Csqrt%7B5%5E2-4%5Ctimes%201%5Ctimes%205%7D%20%7D%7B2%281%29%7D%5C%5C%5C%5Cx%3D%5Cdfrac%7B-5%5Cpm%20%5Csqrt%7B25-20%7D%20%7D%7B2%281%29%7D%5C%5C%5C%5Cx%3D%5Cdfrac%7B-5%5Cpm%20%5Csqrt%7B5%7D%20%7D%7B2%7D)
Hence, the correct option is (c).
1.; 3.; 5. are prime numbers.
All others are composite numbers.
Good luck!