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2 years ago

At what root does the graph of f(x)=(x+4)^6(x+7)^5 cross the x axis?

Mathematics

1 answer:

xz_007 [3.2K]2 years ago

5 0

Answer:

f(x) crosses the x-axis, then

f(x)=(x+4)^6(x+7)^5 = 0

=> x+4 =0 or x+7=0

=> x =-4 or x = -7

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NO LINKS!! Use the method of substitution to solve the system. (If there's no solution, enter no solution). Part 11z

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Answer:

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Step-by-step explanation:

Given system of equations:

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To solve by the method of substitution, substitute the first equation into the second equation and rearrange so that the equation equals zero:

$\begin{aligned}x^2-9&=4x-4\\x^2-4x-9&=-4\\x^2-4x-5&=0\end{aligned}$

Factor the quadratic:

$\begin{aligned}x^2-4x-5&=0\\x^2-5x+x-5&=0\\x(x-5)+1(x-5)&=0\\(x+1)(x-5)&=0\end{aligned}$

Apply the zero-product property and solve for x:

$\implies x+1=0 \implies x=-1$

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Substitute the found values of x into the second equation and solve for y:

$\begin{aligned}x=-1 \implies y&=4(-1)-4\\y&=-4-4\\y&=-8\end{aligned}$

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Therefore, the solutions are:

$(x,y)=\left(\; \boxed{-1,-8} \; \right)\quad \textsf{(smaller $x$-value)}$

$(x,y)=\left(\; \boxed{5,16} \; \right)\quad \textsf{(larger $x$-value)}$

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