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chubhunter [2.5K]
2 years ago
11

Explain why any of the four operations placed between two terms 5 and -3 sqrt (8) will result in an irrational number

Mathematics
1 answer:
Gnoma [55]2 years ago
7 0

Sum/difference:

Let

x = 5 + (-3\sqrt{8}) = 5-3\sqrt{8}

This means that

3\sqrt{8} = 5-x \iff \sqrt{8} = \dfrac{5-x}{3}

Now, assume that x is rational. The sum/difference of two rational numbers is still rational (so 5-x is rational), and the division by 3 doesn't change this. So, you have that the square root of 8 equals a rational number, which is false. The mistake must have been supposing that x was rational, which proves that the sum/difference of the two given terms was irrational

Multiplication/division:

The logic is actually the same: if we multiply the two terms we get

x = -15\sqrt{8}

if again we assume x to be rational, we have

\sqrt{8} = -\dfrac{x}{15}

But if x is rational, so is -x/15, and again we come to a contradiction: we have the square root of 8 on one side, which is irrational, and -x/15 on the other, which is rational. So, again, x must have been irrational. You can prove the same claim for the division in a totally similar fashion.

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The graph of a quadratic function contains (4,-64) and it's vertex is at the origin.write an equation for this function.
lesya692 [45]

Answer:

Step-by-step explanation:

Not sure what form you need this in, but it really doesn't matter, as you'll see in the final equation.  I used the vertex form and solved for a:

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

We are given the vertex (h, k) as the origin (0, 0), and we have a point that the graph goes through as (4, -64).  That's our x and y.  Plugging in what we have:

-64=a(4-0)^2+0 gives us

-64 = 16a and

a = -4.  That means that the quadratic equation is

y=-4x^2  which is both vertex form and standard form here, no difference.

5 0
3 years ago
Which of these describes the equation –18x + 9y = –416?
Minchanka [31]

Answer:

We conclude the equation is linear because it can be rewritten in the form y = mx + b.

Hence, option D is correct.

Step-by-step explanation:

The slope-intercept form of the line or linear equation

y = mx+b

where

  • m is the slope
  • b is the y-intercept

<u>Important Tip:</u>

The graph of a linear equation is always a straight line.

Convert the given equation in the slope-intercept form

18x + 9y = -416

subtract 18x from both sides

18x+9y-18x = - 18x-416

simplify

9y = -18x - 416

divide both sides by 9

y=-2x-\frac{416}{9}

Now, comparing the equation y=-2x-\frac{416}{9} with a slop-intercept form of linear equation

  • The slope m = -2
  • The y-intercept b = -416/9

Therefore, we conclude the equation is linear because it can be rewritten in the form y = mx + b.

From the attached graph, is also clear that the graph of the equation y=-2x-\frac{416}{9} is a straight line.

Hence, option D is correct.

3 0
2 years ago
Read 2 more answers
Find the vertex of this parabola:<br> y = -2x2 + 4x - 10
amm1812
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a is the same as the a coefficient in the standard form;
h is the x-coordinate of the parabola vertex; and.
k is the y-coordinate of the parabola vertex.
that’s how you find it
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Answer

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Assuming height of the pyramid = 20 in

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Volume of pyramid =\dfrac{hlw}{3}  

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