Answer:
16 is the answer
Step-by-step explanation:
add the numbers together
The statement which is true about the end behaviour of the graphed function is; As the x-values go to positive infinity, the function’s values go to positive infinity.
<h3>Which statement is true about the end behaviour of the graphed function?</h3>
The graph given according to the task content is described to have its first minimum at (-2,0), and then a maximum at; (-0.5, 5) and finally a minimum at; (1.05, -41).
Additionally, since the graph has 3 zeroes as given, it follows that the graph is that of a cubic function which takes the w-form.
Consequently, it can be inferred from the statements above that; As the x-values go to positive infinity, the function’s values go to positive infinity.
Read more on graph end behaviours;
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<h3>
Answer: The two factors are 5x+3 and x+1</h3>
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Explanation:
We could use the AC factoring method here. Multiply the first coefficient (10) with the last term (3) to get 10*3 = 30.
We need to find factors of 30 that add to 11
1+30 = 31
2+15 = 17
3+10 = 13
5+6 = 11
we have found the pair of factors that add to 11. So we'll break the 11x into 5x+6x and then use factor by grouping method
10x^2 + 11x + 3
10x^2 + 5x + 6x + 3
(10x^2 + 5x) + (6x + 3)
5x(2x + 1) + 3(2x + 1)
(5x+3)(2x+1)
We see the two factors are 5x+3 and 2x+1.
To check the answer, use either the box method, distribution, or FOIL rule to expand out (5x+3)(2x+1) and you should get 10x^2+11x+3 again.
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As an alternative, you can solve 10x^2+11x+3 = 0 through any method you prefer (graphing, completing the square, quadratic formula). The quadratic formula is the best option as it works for any quadratic. The two solutions you should get are x = -3/5 and x = -1/2
Using x = -3/5 and x = -1/2, we can do the following
- x = -3/5 becomes 5x = -3 after multiplying both sides by 5, then you add 3 to both sides to get 5x+3 = 0
- x = -1/2 becomes 2x = -1 after multiplying both sides by 2, and then turns into 2x+1 = 0 after adding 1 to both sides
Note how we have the 5x+3 and 2x+1 as found in the section above. At this point we can stop as we found the factors needed. I'm using the zero product property which says that if A*B = 0, then either A = 0 or B = 0.
