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2 years ago

7. What type of lines does the system y=3x+2 and 3x-y=-2 form?

Mathematics

1 answer:

Aleks [24]2 years ago

3 0

Answer: The system forms the same line.

Step-by-step explanation:

3x - y = -2

-y = -3x - 2 (subtract 3x from both sides)

y = 3x + 2 (divide both sides by -1)

First equation: y = 3x +2

Second equation: y = 3x +2

THEY ARE THE SAME LINE —> there are infinitely many solutions.

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Write an equation for a circle with center at (5,-2) and diameter of 8 centimeters.

mars1129 [50]

Answer:

$(x-5)^2+(y+2)^2=16$

Step-by-step explanation:

lol brainlessly...

General Circle function: $(x-h)^2+(y-k)^2=r^2$ , where h is the x-coordinate of the center, k is the y-coordinate of the center, and r is the radius.

The radius of the circle is half the diameter so: 8 / 2 = 4

The x-coordinate of the circle is 5

The y-coordinate of the circle is -2

Plug in.

$(x-5)^2+(y-(-2))^2=4^2$

$(x-5)^2+(y+2)^2=16$

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3 years ago

What is the equation of the line in the graph

iren [92.7K]

Always, ALWAYS remeber this format: y = mx + b

In this equation, 'm' is the slope, and 'b' is the y-intercept

When you're trying to find a slope, remember that the equation is $\frac{rise}{run}$

When finding the rise and run, look at two points that are on the graph AND on the line as well. Essentially, make sure the points you're using are integers.

In this, case, the rise is -3, and the run is 2. This means that the slope is $\frac{-3}{2}$

Now we have the first part of our equation:

y = - $\frac{3}{2}$ + b

But wait! How do we find b?

Sometimes you have to input x in order to find it, but only when you're not supplied with a graph. In this case, all you have to do is look!

The point of the line that is on the y-axis is called the y-intercept.

In this graph, the y-intercept is -1

Now we have our complete equation!

y = - $\frac{3}{2}$ - 1

Good luck!

3 0

2 years ago

Find the domain of f(x)=x-9/x squared-81

vagabundo [1.1K]

$f(x)=\dfrac{x-9}{x^2-81}\\\\\text{The domain:}\\\\x^2-81\neq0\qquad\text{add 81 to both sides}\\\\x^2\neq81\to x\neq\pm\sqrt{81}\\\\x\neq-9\ \wedge\ x\neq9\\\\Answer:\ \boxed{\text{All real numbers except -9 and 9}}\to\boxed{x\in\mathbb{R}-\{-9,\ 9\}}$

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3 years ago

How do I simplify the n^-6*n^3 topic "Negative and Zero Exponents"

Alchen [17]

Since you’re multiplying n^-6 and n^3, you can add the exponents: -6+3 = -3

n^-6 * n^3 = n^-3

If you need to finish without having a negative exponent in your answer, then remember a negative exponent means that factor is on the wrong side of the fraction.

n^-3 = n^-3 / 1 = 1/n^3

when the factor moves to the other side of the fraction, the side of the exponent changes.

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2 years ago

Which graph represents a system of equations with no solutions?

VladimirAG [237]

The last graph represents a system with no solutions. The solution to a system of equations is the point at which both lines intersect. Because the equations in the last graph don't intersect and are parallel, it has no solutions. Hope this helps :))

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2 years ago