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Whitepunk [10]
3 years ago
7

Let x represent each number. write an equation and solve for the variable.

Mathematics
1 answer:
GaryK [48]3 years ago
6 0

Answer:

Hi there!

Your answer is;

1) x= 13

2) x= 5

Step-by-step explanation:

x-5 = 8

3x+2= 17

x-5=8

+5

x= 13

3x+2 = 17

-2

3x= 15

/3

x= 5

Hope this helps

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\begin{tabular}{| c | c | c |}\cline{1-3} Equation & x-intercepts & x-coordinate of vertex\\\cline{1-3} $y=x(x-2)$ & $x=0, x=2$ & $x=1$\\\cline{1-3} $y=(x-4)(x+5)$ & $x=-5, x=4$ & $x=-0.5$\\\cline{1-3} $y=-5x(x-3)$ & $x=0, x=3$ & $x=1.5$\\\cline{1-3} \end{tabular}

Step-by-step explanation:

x-intercepts are when the curve intercepts the x-axis, so when y =0.

Therefore, to find the x-intercepts, substitute y = 0 and solve for x.

The vertex is the turning point:  the minimum point of a parabola that opens upward, and the maximum point of the parabola that opens downward.  As a parabola is symmetrical, the x-coordinate of the vertex is the midpoint of the x-intercepts.

Equation:  y=x(x-2)

\implies x(x-2)=0

\implies x=0

\implies (x-2)=0 \implies x=2

Therefore, the x-intercepts are x = 0 and x = 2

The midpoint of the x-intercepts is x = 1, so the x-coordinate of the vertex is x = 1

Equation: y=(x-4)(x+5)

\implies (x-4)(x+5)=0

\implies (x-4)=0 \implies  x=4

\implies (x+5)=0 \implies x=-5

Therefore, the x-intercepts are x = -5 and x = 4

The midpoint of the x-intercepts is x = -0.5, so the x-coordinate of the vertex is x = -0.5

Equation: y=-5x(3-x)

\implies -5x(3-x)=0

\implies -5x=0 \implies x=0

\implies (3-x)=0 \implies x=3

Therefore, the x-intercepts are x = 0 and x = 3

The midpoint of the x-intercepts is x = 1.5, so the x-coordinate of the vertex is x = 1.5

\begin{tabular}{| c | c | c |}\cline{1-3} Equation & x-intercepts & x-coordinate of vertex\\\cline{1-3} $y=x(x-2)$ & $x=0, x=2$ & $x=1$\\\cline{1-3} $y=(x-4)(x+5)$ & $x=-5, x=4$ & $x=-0.5$\\\cline{1-3} $y=-5x(x-3)$ & $x=0, x=3$ & $x=1.5$\\\cline{1-3} \end{tabular}

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