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2 years ago

Which graph shows the solution to the system of linear inequalities below?

Mathematics

2 answers:

hodyreva [135]2 years ago

7 0

Answer:

Option B

The solution in the attached figure

Step-by-step explanation:

we have

<em>Inequality A</em>

$y > -\frac{1}{3}x+1$

we know that

The solution of the inequality A is the shaded area above the dashed line

The equation of the dashed line is $y=-\frac{1}{3}x+1$

The slope of the dashed line is negative $m=-\frac{1}{3}$

<em>Inequality B</em>

$y > 2x-1$

we know that

The solution of the inequality B is the shaded area above the dashed line

The equation of the dashed line is $y=2x-1$

The slope of the dashed line is positive $m=2$

therefore

The solution in the attached figure

Vikentia [17]2 years ago

6 0

<h2>Answer:</h2>

The correct graph is:

Graph B

<h2>Step-by-step explanation:</h2>

First inequality is given by:

$y>\dfrac{-1}{3}x+1$

The inequality is a straight line that passes through (0,1) and (3,0) and also the line is dotted since the inequality is strict.

The shaded region is away from the origin since the inequality does not pass the zero point test.

Second inequality is given by:

$y>2x-1$

The graph of this inequality is a dotted line (since the inequality is strict) and passes through (0,-1) and (1/2,0) and the shaded region is towards the origin

( since the line passes the zero point test )

Graph B represents the system of inequality.

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The center of a circle lies on the line y = 4x + 1 and is tangent to the x-axis at (−3,0) . What is the equation of the circle i

Hunter-Best [27]

Answer:

$(x+3)^2+(y+11)^2=121$

Step-by-step explanation:

Consider a sketch of the problem as shown in the picture, where:

Blue line is given by y = 4x + 1.
Point B is the center of the circle.
Point A is (-3, 0).

Since the center of the circle lies on the line y = 4x +1 and is tangent to the x-axis at point A, then its radius BA is perpendicular to the x-axis. To find the coordinates of point B, we must replace x = -3 into the blue line equation: y = 4x(-3) + 1 = -11.

So, we know that the center of the circle is at B=(-3, -11). And furthermore, the radius BA is of length r=11.

Since the <em>general equation of the circle</em> of radius lenght r centered at (h, k) is given by

$(x-h)^2+(y-k)^2=r^2$