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jok3333 [9.3K]
3 years ago
13

Write the equation 5x − 2y = 10 in the form y = mx + b. y equals start fraction five over two end fraction x minus 10 y equals s

tart fraction five over two end fraction x minus five y equals start fraction five over two end fraction x plus five y equals negative start fraction five over two end fraction x minus five
Mathematics
1 answer:
vaieri [72.5K]3 years ago
6 0

Answer:

y = 5/2x - 5

Step-by-step explanation:

You have to rearrange the equation so that it is equal to y.

5x - 2y = 10

(5x - 2y) - 5x = -5x + 10

-2y = -5x + 10

(-2y)/-2 = (-5x)/-2 + (10)/-2

y = 5/2x - 5

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Please help and thank you!
Lynna [10]

Since polar coordinates are made up in this way

(r, \theta )

we need to solve for r and then find the angle. In our rectangular coordinate given,

(-4,-4\sqrt{3})

x = -4 and y=-4\sqrt{3}

We will use this fact to first find the angle then r, which might seem backwards but I am going to do it in this order. The formula to find the angle measure uses the tangent identity

tan\theta=\frac{y}{x}.

Filling in our y and x from the rectangular coordinate we have

tan\theta=\frac{-4\sqrt{3}}{-4} or

tan\theta =\frac{\sqrt{3}}{1}.

The tangent identity is the side opposite the reference angle (theta) over the side adjacent to it. Since in our rectangular coordinate both x and y are negative, we will be in QIII where x and y are negative. The side across from the reference angle is the square root of 3, which should tell us at this point in our math careers that the reference angle is a 60 degree angle. But in the third quadrant, the angle is 180+60 which is 240 degrees. Converting that to radians we get \frac{4\pi}{3}. That's our angle. In order to solve for r now, we will need the cosine of that angle. In our 30-60-90 right triangle we can solve for the length of the missing side which is the hypotenuse. If our Pythagorean triple is

(x, x\sqrt{3},2x)

and x = -4, then the length of the hypotenuse is 2(-4) which is -8 but since a hypotenuse is never negative, it's just 8. That's also the value for r! That means that the polar coordinates that are the same as the rectangular ones we were given are

(8,\frac{4\pi}{3})

first choice above.

6 0
3 years ago
Classify each number as rational or irrational. Drag the choices into the boxes to correctly complete the table.
Alex17521 [72]

Answer:

3 = irrational

-1/16 = rational

0 = rational

2 =irrational

7 0
3 years ago
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Which of the following is equivalent to
sineoko [7]

Answer:

It's the first one

Step-by-step explanation:

7 0
3 years ago
Three fishermen caught 74 fish. They divide them equally. How many are left over ?
otez555 [7]

Answer:

2 left

Step-by-step explanation:

74/3 = 24.

24*3 = 72

74-72 = 2

8 0
3 years ago
Which pairs of polygons are congruent?
Ronch [10]

The <em><u>correct answer</u></em> is:

pairs 2, 3, and 4

Explanation:

Congruent polygons are polygons that have the same size and the same shape.  We can see from the diagram that the figure in pair 2 has been rotated to form the second figure in the pair.  Since the shape and size were not changed, they are congruent.

The figure in pair 3 has also been rotated; this again preserves size and shape, so the figures are congruent.

The figure in pair 4 sees to have been reflected.  This did not change the size or shape of the figure, so the pair is congruent.

5 0
4 years ago
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