Answer:
65 pencils in all
Step-by-step explanation:
13 times 5 is 65, so 65 pencils in all.
Step-by-step explanation:
5. 56÷4 = 14
6. (2 × 27) - 3 × 5 - 8
54 - 15 - 8
39 - 8 = 31 ans.
Hope this answer helps you!
Answer:
![b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}](https://tex.z-dn.net/?f=b%20%3D%205%20%5Csqrt%7B3%7D%20%5C%20or%5C%20b%20%3D%20-5%20%5Csqrt%7B3%7D)
Step-by-step explanation:
Given
![f(b) = b^2 - 75](https://tex.z-dn.net/?f=f%28b%29%20%3D%20b%5E2%20-%2075)
Required
Determine the roots
To get the root of the function, then f(b) must be 0;
i.e. f(b) = 0
So, the expression becomes
![0 = b^2 - 75](https://tex.z-dn.net/?f=0%20%3D%20b%5E2%20-%2075)
Add 75 to both sides
![75 + 0 = b^2 - 75 + 75](https://tex.z-dn.net/?f=75%20%2B%200%20%3D%20b%5E2%20-%2075%20%2B%2075)
![75 = b^2](https://tex.z-dn.net/?f=75%20%3D%20b%5E2)
Take square roots of both sides
![\sqrt{75} = \sqrt{b^2}](https://tex.z-dn.net/?f=%5Csqrt%7B75%7D%20%3D%20%5Csqrt%7Bb%5E2%7D)
![\sqrt{75} = b](https://tex.z-dn.net/?f=%5Csqrt%7B75%7D%20%3D%20b)
Reorder
![b = \sqrt{75}](https://tex.z-dn.net/?f=b%20%3D%20%5Csqrt%7B75%7D)
Expand 75 as a product of 25 and 3
![b = \sqrt{25*3}](https://tex.z-dn.net/?f=b%20%3D%20%5Csqrt%7B25%2A3%7D)
Split the expression
![b = \sqrt{25} *\sqrt{3}](https://tex.z-dn.net/?f=b%20%3D%20%5Csqrt%7B25%7D%20%2A%5Csqrt%7B3%7D)
![b = \±5 *\sqrt{3}](https://tex.z-dn.net/?f=b%20%3D%20%5C%C2%B15%20%2A%5Csqrt%7B3%7D)
![b = \±5 \sqrt{3}](https://tex.z-dn.net/?f=b%20%3D%20%5C%C2%B15%20%5Csqrt%7B3%7D)
![b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}](https://tex.z-dn.net/?f=b%20%3D%205%20%5Csqrt%7B3%7D%20%5C%20or%5C%20b%20%3D%20-5%20%5Csqrt%7B3%7D)
The options are not clear enough; however the roots of the equation are ![b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}](https://tex.z-dn.net/?f=b%20%3D%205%20%5Csqrt%7B3%7D%20%5C%20or%5C%20b%20%3D%20-5%20%5Csqrt%7B3%7D)
Step-by-step explanation:
![\frac{(y - b)}{(x - a)} = m \\ y - b = m(x - a) \\ y - b = mx - am \\ mx = y - b + am \\ x = \frac{y - b + am}{m}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%28y%20-%20b%29%7D%7B%28x%20-%20a%29%7D%20%20%3D%20m%20%5C%5C%20y%20-%20b%20%3D%20m%28x%20-%20a%29%20%5C%5C%20y%20-%20b%20%3D%20mx%20-%20am%20%5C%5C%20mx%20%3D%20y%20-%20b%20%2B%20am%20%5C%5C%20x%20%3D%20%20%5Cfrac%7By%20-%20b%20%2B%20am%7D%7Bm%7D%20)