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4 years ago

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Consider the system of equations. 5x – 2y = 6 –10x + 4y = –12 Check all the statements that are true. a)the lines coincide. b)Th

e system has no solution. c)The slopes are equal. d)The y-intercepts are equal. e)The system has an infinite number of solutions

1 answer:

QveST [7]4 years ago

5 0

Answer:

a) the lines coincide, c) the slopes are equal, d) the y-intercept are equal, e) the system has an infinite number of solutions.

Step-by-step explanation:

Each equation is a multiple of the other one. Thus, the system of equation has an infinite of solutions, reports same slopes and y-intercepts and coinciding lines.

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Mars2501 [29]

Answer:

-3/4

Step-by-step explanation:

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3 years ago

I need help please, I am so confused.

vazorg [7]

Answer:

$\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}$

4 0

2 years ago

section of a pipe's length and weight are in proportion. If 2.5 m of pipe weighs 10 kg, then A) 5 m of pipe weighs 30 kg. B) 5 m

motikmotik

We will proceed to resolve each case to determine the solution.

we know that

$2.5$ m of pipe weighs $10$ kg

so

by proportion

<u>Find the weighs of each case</u>

<u>case A)</u> $5$ m of pipe weighs $30$ kg

$\frac{10}{2.5}\frac{kg}{m}=\frac{x}{5}\frac{kg}{m}\\ \\2.5*x=5*10\\ \\x=50/2.5\\x=20\ kg$

$20\ kg\neq30\ kg$

therefore

The statement case A) is False

<u>case B)</u> $5$ m of pipe weighs $40$ kg

$\frac{10}{2.5}\frac{kg}{m}=\frac{x}{5}\frac{kg}{m}\\ \\2.5*x=5*10\\ \\x=50/2.5\\x=20\ kg$

$20\ kg\neq40\ kg$

therefore

The statement case B) is False

<u>case C)</u> $10$ m of pipe weighs $40$ kg

$\frac{10}{2.5}\frac{kg}{m}=\frac{x}{10}\frac{kg}{m}\\ \\2.5*x=10*10\\ \\x=100/2.5\\x=40\ kg$

$40\ kg=40\ kg$

therefore

The statement case C) is True

<u>case D)</u> $10$ m of pipe weighs $80$ kg

$\frac{10}{2.5}\frac{kg}{m}=\frac{x}{10}\frac{kg}{m}\\ \\2.5*x=10*10\\ \\x=100/2.5\\x=40\ kg$

$40\ kg\neq80\ kg$

therefore

The statement case D) is False

therefore

<u>the answer is</u>

$10$ m of pipe weighs $40$ kg

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