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Maslowich
3 years ago
13

Should the quotient of an integer divided by a nonzero integer always be a rational number? Why or Why not?

Mathematics
1 answer:
lubasha [3.4K]3 years ago
8 0
Yes, it will always be a rational number. I'll expound on this by defining what a rational number is. It is any number that can be expressed as a fraction. Otherwise, it is called an irrational number with a non-terminating decimal expansion. So, although 1/3 has a non-terminating decimal expansion because it is equal to 0.33333333...., it is still a rational number because it can be expressed into a fraction.
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which shapes best model the surface areas of the object? What is the surface are of each object, based on it’s model?
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I need help with math algebra homework
lesya [120]

Answer:

1. Slope: -3/4

2. Point-slope: y+4=-3/4(x+4)

3. Slope-intercept: y=-3/4x-7

4. Standard form: 3x+4y=-28

Step-by-step explanation:

1. To find the slope, use the slope formula, which is: y2-y1/x2-x1.

Plug the y-coordinates into the top part of the equation and the x-coordinates into the bottom part.

2--4/-4-4

2+4/-8 = 6/-8, or 3/-4

2. Use the slope and one of the x and  y coordinates to put the equation into point-slope form. Recall that point-slope form is: y-y1=m(x-x1). Let's use the coordinates (4,-4).

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

3. To put the point-slope equation into slope-intercept form (y=mx+b), you need to distribute -3/4 to x+4 and subtract 4 from both sides.

When you distribute, the equation becomes:

y+4=-3/4x-3

Finally, when you subtract 4, the equation becomes:

y=-3/4x-7

4. Standard form is written as x+y= #.

To convert y=mx+b to standard form, first subtract -3/4x from both sides.

-3/4x + y = -7

Multiply everything by 4

3x + 4y = -28

3 0
3 years ago
HELP PLEASE! Write a quadratic function that passes through the point (-1,9), has an axis of symmetry of x=-3 and a minimum valu
xxTIMURxx [149]

Answer:

y = \frac{1}{2}x^{2} - 3x + 11.5

Step-by-step explanation:

Vertex form of a quadratic equation;

y = a( x - h )^{2} + k

Vertex of the parabolas (h, k)

The vertex of the parabola is either the minimum or maximum of the parabola. The axis of symmetry goes through the x-coordinate of the vertex, hence h = -3. The minimum of the parabola is the y-coordinate of the vertex, so k= 7. Now substitute it into the formula;

y = a ( x + 3 ) ^{2} + 7

Now substitute in the given point; ( -1, 9) and solve for a;

9 = a( (-1 ) + 3)^2 + 7\\9 = a (2)^{2} + 7\\9 = 4a + 7\\-7           -7\\2 = 4a\\\frac{1}{2} = a\\

Hence the equation in vertex form is;

y = \frac{1}{2}(x - 3)^{2} + 7

In standard form it is;

y = \frac{1}{2}x^{2} - 3x + 11.5

7 0
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