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cluponka [151]
3 years ago
10

An integer, G, is rounded to give the value 10,000. There are many numbers that G could be.

Mathematics
1 answer:
marshall27 [118]3 years ago
8 0

Answer:

499

Step-by-step explanation:

9,999 would be the greatest value

9500 would be the smallest value

if you subtract them you'll get 499

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Can someone please help mee (20 points and i will give brainliest!!!)
FromTheMoon [43]

Answer:

a. y-intercept:(0,  -6), x-intercepts: (3, 0) and (-2, 0). vertex: (0.5, -6.25)

b. y-intercept: (0, 6), x-intercepts(3, 0) and (-2, 0). vertex: (0.5, 6.25)

Step-by-step explanation:

a:

 So finding the y-intercept is really easy and is simply when x=0. If you plug in 0 as x it makes y=(0)^2-0-6 which simplifies to -6, which is the y-intercept. As for the x-intercepts you can calculate that by using the quadratic equation x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\. In this case a=1, b=-1, c=-6. So plugging those values in you get x=\frac{-(-1)\pm\sqrt{(-1)^2-4(1)(-6)}}{2(1)}, which simplifies to x=\frac{1\pm5}{2}. This gives you the x-intercepts 6/2 and -4/2 which are 3 and -2. The vertex can be calculated by manipulating the equation so it's in the form of y=(x-h)^2+k where (h, k) is the vertex of the parabola. This is done by moving c to the other side and then completing the square and the isolating y. So the first step will be

Move c to the other side

y+6=x^2-x

Complete the square by adding (b/2)^2

y+6+0.25 = x^2-x+0.25

Rewrite as square binomial

y+6.25 = (x-0.5)^2

Isolate y

y=(x-0.50)^2-6.25

(h, k) = 0.50, -6.25 which is the vertex

b: To identify the y-intercept you plug in 0 as x which will only leave c which in this case is 6 which is the y-intercept. (0, 6). To identify the x-intercepts you can simplify plug in the values a, b, c into the quadratic equation which was stated in the previous answer. In this case a, b, c = -1, 1, 6. Plugging these values in gives the equation y=\frac{-(1)\pm\sqrt{1^2-4(-1)(6)}}{2(-1)}. which simplifies to x=\frac{-1\pm5}{-2} which gives the values -2 and 3. To find the vertex it's the same process as before

Factor out -1

y=-(x^2-x-6)

Add 6 to both sides (on the left side add -6 since -1 was factored out).

y-6=-(x^2-x)

Complete the square by adding (b/2)^2 to both sides (add -(b/2)^2 to left side since -1 was factored out)

y-6-0.25 = -(x^2-x+0.25)

Rewrite as square binomial

y-6.25=-(x-0.5)^2

Add 6.25 to both sides

y=(x-0.50)^2+6.25

(h, k) = (0.50, 6.25)

When you graph the parabolas you'll notice there just flipped relative to the x-axis. This can be deduced by simply looking at the two equations, since the two equations have the same absolute value coefficients, the signs are just different, and more specifically they're all opposite. If you took the first equation and multiplied the entire right side by -1 you would get the same equation. And since that equation really represents the value of y (since it's equal to y) you're reflecting it across the x-axis.

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Similar shapes are just shapes that have the same proportions and relative size. For example, a square that's 4 x 4 and a square that's 2 x 2. Although one's smaller, they are both the similar shapes.
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What is the period of y = 8 cos (5pie x + 3pie/2)-9<br> Give an exact value. Units
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\\ \rm\Rrightarrow y=Acos(Bx+C)+D

  • This is the general formula and the period is 2π/B

Now our given function

\\ \rm\Rrightarrow y=8cos\left(5\pi x+\dfrac{3\pi}{2}\right)-9

On comparing we get

  • A=8
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Period:-

\\ \rm\Rrightarrow \dfrac{2\pi}{B}

\\ \rm\Rrightarrow \dfrac{2\pi}{5\pi}

\\ \rm\Rrightarrow \dfrac{2}{5}

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