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Dominik [7]
2 years ago
10

Find two integers whose sum is -12 and product is 35

Mathematics
1 answer:
qwelly [4]2 years ago
7 0

Answer:

-5;-7

Step-by-step explanation:

Start with the product. 35 is either 35x1, 7x5, or the product of their opposites. 35 and 1 doesn't work for the sum, neither does 7 and 5. Let's go negative. -35 and -1 gives -36, so it has to be -7 and -5, which is indeed, correct.

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Find the range, median, and mode for each data set
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4 years ago
What is the y-value of the vertex of the function f(x)=-(x-3)(x+11)
lutik1710 [3]

so, this is a quadratic equation, meaning two solutions, and we have a factored form of it, meaning you can get the solutions by simply zeroing out the f(x).

\bf \stackrel{f(x)}{0}=-(x-3)(x+11)\implies 0=(x-3)(x+11)\implies x= \begin{cases} 3\\ -11 \end{cases} \\\\\\ \boxed{-11}\stackrel{\textit{\large 7 units}}{\rule[0.35em]{10em}{0.25pt}}-4\stackrel{\textit{\large 7 units}}{\rule[0.35em]{10em}{0.25pt}}\boxed{3}

so the zeros/solutions are at x = 3 and x = -11, now, bearing in mind the vertex will be half-way between those two, checking the number line, that midpoint will be at x = -4, so the vertex is right there, well, what's f(x) when x = -4?

\bf f(-4)=-(-4-3)(-4+11)\implies f(-4)=7(7)\implies f(-4)=49 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{vertex}{(-4~~,~~49)}~\hfill

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3 years ago
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