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2 years ago

Which of the following statements is NOT true about the graph of a system of

Mathematics

1 answer:

Trava [24]2 years ago

5 0

Answer:

The lines will have one positive y-intercept and one negative y-intercept is NOT true.

Step-by-step explanation:

If a graphed system has infinitely many solutions, that means that the two equations are the exact same. This means that they'll have the same slope, y-intercept, and will share all of the same points. Answer b is the only choice left.

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Find the equation of the line that passes through (-1,2) and is perpendicular to 2 y = 2 x − 1 . Leave your answer in the form y

Bogdan [553]

The equation in slope-intercept form of the line that passes through the point (-1, 2) and is perpendicular to the line equation, $2 y = 2 x - 1$ is: $y = -x + 1$

Recall:

Equation of a line in slope-intercept form is: $y = mx + c$ , where, slope = m, and y-intercept = c.

Point-slope form is: $y - b = m(x - a)$

The slope value of a line will be the negative reciprocal of the slope of the line it is perpendicular to. i.e. if the slope of a line is a, the slope of the line that it is perpendicular to will be -a.

Given:

The line passes through point (-1, 2)

Equation of line it is perpendicular to is: $2 y = 2 x - 1$

To write the equation of the line that passes through (-1, 2), we need to find the slope value.

First, rewrite $2 y = 2 x - 1$ and find its slope.

$\frac{2y}{2} = \frac{2x}{2} - \frac{1}{2} \\\\y = x - \frac{1}{2}$

The slope (m) of $2 y = 2 x - 1$ is therefore 1.

Thus, the slope (m) of the line that passes through (-1, 2) will be the negative reciprocal of 1 = -1.

Write the equation of the line by substituting (a, b) = (-1, 2) and m = -1 into $y - b = m(x - a)$ :

Thus:

$y - 2= -1(x - (-1))\\\\y - 2 = -1(x + 1)$

Rewrite this in the form of $y = m x + c$

Thus:

$y - 2 = -x - 1\\\\y = -x - 1 + 2\\\\y = -x + 1$

Therefore, the equation in slope-intercept form of the line that passes through the point (-1, 2) and is perpendicular to the line equation, $2 y = 2 x - 1$ is $y = -x + 1$

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6 0

2 years ago

Which is equivalent to 3i ( 2i6)?

Hatshy [7]

Answer:

2 * (i^6) * (3 * i) =

- 6 i

Step-by-step explanation:

3 0

2 years ago

How do you write 9.11 x 10 4 in standard form?

vitfil [10]

Answer:

9400.11

Step-by-step explanation:

7 0

3 years ago

A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 166 feet and a maximum height of 40 feet. Find

scoray [572]

Answer:

38.27775 feet

Step-by-step explanation:

The bridge has been shown in the figure.

Let the highest point of the parabolic bridge (i.e. vertex of the parabola) be at the origin, $O(0,0)$ in the cartesian coordinate system.

As the bridge have the shape of an inverted parabola, so the standard equation, which describes the shape of the bridge is

$x^2=4ay\;\cdots(i)$

where $a$ is an arbitrary constant (distance between focus and vertex of the parabola).

The span of the bridge = 166 feet and

Maximum height of the bridge= 40 feet.

The coordinate where the bridge meets the base is $A(83, -40)$ and $B(-83, -40).$

There is only one constant in the equation of the parabola, so, use either of one point to find the value of $a$ .

Putting $A(83,-40)$ in the equation (i) we have

$83^2=4a(-40)$

$\Rightarrow a=-43.05625$

So, on putting the value of $a$ in the equation (i), the equation of bridge is

$x^2=-172.225y$

From the figure, the distance from the center is measured along the x-axis, x coordinate at the distance of 10 feet is, $x=\pm 10$ feet, put this value in equation (i) to get the value of y.