Answer:
Step-by-step explanation:
<u>As per question we have:</u>
- p > 0, q > 0
- 31p/8q ≤ 5 ⇒ 31p ≤ 40q
Since 31 and 40 have no common factors, the minimum values of p and q are 40 and 31 respectively.
<u>So the minimum value of p + q is:</u>
Answer:
Option (3) is correct.
The zero of given function
is x= -1 and x= -3.
Step-by-step explanation:
Consider the given function ![f(x)=x^2+4x+3](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2%2B4x%2B3)
We need to find the zero of the above function. Put f(x)=0
then , ![f(x)=x^2+4x+3=0 \Rightarrow x^2+4x+3=0](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2%2B4x%2B3%3D0%20%5CRightarrow%20x%5E2%2B4x%2B3%3D0)
The above function represents a quadratic equation
We can solve the quadratic equation by splitting middle term method,
![\Rightarrow x^2+4x+3=0](https://tex.z-dn.net/?f=%5CRightarrow%20x%5E2%2B4x%2B3%3D0)
We can write 4x as x+ 3x ,
![\Rightarrow x^2+x+3x+3=0](https://tex.z-dn.net/?f=%5CRightarrow%20x%5E2%2Bx%2B3x%2B3%3D0)
![\Rightarrow x(x+1)+3(x+1)=0](https://tex.z-dn.net/?f=%5CRightarrow%20x%28x%2B1%29%2B3%28x%2B1%29%3D0)
![\Rightarrow (x+1)(x+3)=0](https://tex.z-dn.net/?f=%5CRightarrow%20%28x%2B1%29%28x%2B3%29%3D0)
or ![\Rightarrow (x+3)=0](https://tex.z-dn.net/?f=%5CRightarrow%20%28x%2B3%29%3D0)
or ![\Rightarrow x=-3](https://tex.z-dn.net/?f=%5CRightarrow%20x%3D-3)
Thus, the zero of given function
is x= -1 and x= -3.
Answer: B. No
Step-by-step explanation:
Direct variation has the following form:
![y=kx](https://tex.z-dn.net/?f=y%3Dkx)
Where the constant of variation is "k".
By definition, in direct variation, when the variable "x" changes, tha variable "y" changes in proportion to the variable "x".
As you can observe in the table, when the value of the variable "x" increase, the values of the variable "y" decrease, therefore we can conclude that it is not a direct variation.
Then the answer is the option B.
Okay i get it now
1) At 1.30 p.m. the barge has already traveled 4.5 X 10 = 45 miles.
To catch up it will take the train 25-10 = 15miles