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2 years ago

Which of the following equations will produce the graph shown below?

Mathematics

1 answer:

Gnesinka [82]2 years ago

6 0

The equation that produces the circle in the given graph is; x² + y² = 16. The correct answer is option B.

The complete graph is attached with the answer below.

<h3>How to interpret the equation of a Circle?</h3>

A circle is a two-dimensional geometry on the plane having a centre point and the circular line is drawn equidistant from the centre point.

The general form of the equation of a circle is;

(x - h)² + (y - k)² = r²

where;

h, k are coordinates of the circle centre r is the radius

From the graph, we can see that the coordinates of the centre are; (0, 0).

Also, the radius is;

r = √(4² - 0²)

r = √16

Thus, our equation of the circle in the graph is;

(x - 0)² + (y - 0)² = (√16)²

⇒ x² + y² = 16

Therefore the equation that produces the circle in the given graph is; x² + y² = 16. The correct answer is option B.

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What is the slope of the line?<br> A. -2<br> B. -1/2<br> C. 1/2<br> D. 2

Alexxandr [17]

To find the slope, you can either use the slope equation:
(y2-y1) / (x2-x1)
{I would recommend you remember this because you'll need to know this in the future}

or,

Just count. A slope is rise over run, so you see how far up the slope goes from one point to the other, (1), and then you see how far sideways the slope goes (2).
Going right, the slope is naturally declining downwards, so it's a negative.

The answer is B. -1/2.

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3 years ago

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4 years ago

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Which equations represent the line that is parallel to 3x – 4y = 7 and passes through the point (-4,-2)? Select two

seropon [69]

Answer:

4y = 3x + 4

3x-4y = -4 is correct

Step-by-step explanation:

This is what we do.

We first express the first equation in the form;

y = mx + c

where m represents the slope of the line

Thus we have;

4y = 3x -7

divide through by 4

y = 3/4x -7/4

Thus the slope here is the coefficient of x which is 3/4

Now, since the lines are parallel, it means that their slopes are equal

So the slope of the other line too is 3/4

We now use the point slope form to find the equation of this other line

Mathematically, that would be;

y-y1 = m(x-x1)

where (x1,y1) = (-4,-2)

Substituting this into the point slope equation, we have;

y-(-2) = 3/4(x-(-4))

y + 2 = 3/4(x + 4)

Cross multiply

4y + 8 = 3x + 12

4y = 3x + 12-8

4y = 3x + 4

5 0

4 years ago

A force of 8 lb is required to hold a spring stretched 8 in. beyond its natural length. How much work W is done in stretching it

-BARSIC- [3]

Answer:

The work done in stretching it from its natural length to 14 in. beyond its natural length is W=8.17 ft-lb.

Step-by-step explanation:

We know that a force of 8 lb is required to hold a spring stretched 8 in. beyond its natural length.

This let us calculate the spring constant k as:

$F=kx\\\\k=F/x=(8 \;lb)/(8\;in)=1\;lb/in$

We know that work is, in an scalar form, the product of force and distance.

The force F is equal to the spring constant multiplied by the distance from the natural length.

Then, as the force changes with the distance from the natural length, we have to calculate integrating:

$W=\int_0^{14}F\,dx=\int_0^{14}kx\,dx\\\\\\W=\dfrac{1}{2}kx^2\left|^{14}_0=\dfrac{1}{2}(1\,lb/in)(14 \,in)^2-\dfrac{1}{2}(1\,lb/in)(0 \,in)^2$

$W=98lb\cdot in-0lb-in\\\\W=98(lb\cdot in)\cdot \dfrac{1 \,ft}{12\,in}=8.17\;lb\cdot ft$

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3 years ago

Add Linear Expression. (8x + 9 ) + (- 6x -2 )

BartSMP [9]

Answer:

2x+7 is the answer......

8 0

3 years ago

Read 2 more answers