In the equation x^2+10x+24=(x+a)(x+b), b is an integer. Find algebraically all possible values of b
1 answer:
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Answer:
We have the function,
On simplifying, we get,
i.e.
Thus, the standard form of the function is .
Now, the factors of the given functions are (x+1) and (x+5).
<em>Since, the intercept form of the function is the factored form of the function.</em>
So, we have, intercept form of the function is .
Now, we know that,
Value of x-coordinate of the vertex is i.e.
i.e.
i.e. x= -3
Then, i.e.
i.e. f(-3)=-4
So, the vertex of the function is (-3,-4).
Further, we know that,<em> 'the y-intercept of a function is the point where the function crosses y-axis'.</em>
So, when x=0, we have, i.e. f(0) = 5
Thus, the y-intercept is (0,5)
Also, <em>'the x-intercept of a function is the point where the function crossese x-axis'.</em>
Then, for f(x)=0, we have i.e.
i.e. x= -1 and x= -5
Thus, the x-intercept are (-1,0) and (-5,0).
Answer:
Check Explanation
Step-by-step explanation:
The complete question plus diagram is presented in the attached image to this solution.
From the attached image, the dimensions of the playground drawn will be a bit variable now as zooming and some editing might have tampered with the original intended dimensions to be measured.
But still, let us assume that on measuring the rectangular playground shown, we obtain approximately that the length is 4.5 cm and the breadth is 2 cm.
The scale to convert to real life is 1;500 indicating that
1 cm on the drawing = 500 cm lenght units of the real playground.
So,
4.5 cm on the drawing = 4.5 × 500 = 2250 cm of the playground
2 cm on the drawing = 2 × 500 = 1000 cm of the playground.
Hence, the real life dimensions of the playground is 2250 cm by 1000 cm.
In meters, that is 2.25 m by 1 m
The perimeter of a rectangular figure is given as
Perimeter = 2(Length + Breadth)
= 2(2.25 + 1)
= 6.5 m
Hope this Helps!!!
