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3 years ago

In the diagram shown, m>1 = x + 16 and m<2 = 3x - 24 Find the value of x

Mathematics

2 answers:

Oksanka [162]3 years ago

7 0

X + 16 = 3x - 24
30 = 2x
x = 15

Eduardwww [97]3 years ago

5 0

$x + 16 = 3x - 24 \\ x = 20$

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Answer:

Therefore, the solutions of the quadratic equations are:

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The graph is also attached.

Step-by-step explanation:

The solution of the graph could be obtained by finding the x-intercept.

$y=\left(x-\:4\right)^2-1$

Finding the x-intercept by substituting the value y = 0

$y=\left(x-\:4\right)^2-1$

$\:0\:=\:\left(x\:-\:4\right)^2\:-\:1$ ∵ y = 0

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$\left(x-4\right)^2=1$

$\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}$

$\mathrm{Solve\:}\:x-4=\sqrt{1}$

$\mathrm{Apply\:rule}\:\sqrt{1}=1$

$x-4=1$

$x=5$

$\mathrm{Solve\:}\:x-4=-\sqrt{1}$

$\mathrm{Apply\:rule}\:\sqrt{1}=1$

$x-4=-1$

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So, when y = 0, then x values are 3, and 5.

Therefore, the solutions of the quadratic equations are:

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The graph is also attached. As the graph is a Parabola. It is visible from the graph that the values of y = 0 at x = 5 and x = 3. As the graph is a Parabola.

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