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vladimir1956 [14]
2 years ago
13

How do you do this!?!

Mathematics
1 answer:
Andrei [34K]2 years ago
6 0

11x + y = 4

<u>x  |   y</u>

0  |   4

\frac{4}{11} |   0

<em>plot the y-intercept (0, 4) and the x-intercept (\frac{4}{11}, 0) </em>

or

11x + y = 4

<u>-11x      </u>  <u>-11x </u>

      y = -11x + 4      ⇒ m = \frac{-11}{1}, b = 4

<em>plot at point the y-intercept "b = 4" (0,4).  plot the next point using the slope "m = \frac{-11}{1}" from point (0,4), count down 11 and to the right 1 (1,-7).</em>

Using intercepts would not provide an accurate graph because you have to estimte where (\frac{4}{11}, 0) is, so it is best to use slope-intercept form.

***********************************************************************************************************

x + y = -2

<u>x  |   y</u>

0  |  -2

-2 |   0

<em>plot the y-intercept (0, -2) and the x-intercept (-2, 0)</em>

or

x + y = -2

<u>-x      </u>  <u> -x </u>

     y = -x - 2     ⇒ m = \frac{-1}{1}, b = -2

<em>plot at point the y-intercept "b = -2" (0,-2).  plot the next point using the slope "m = \frac{-1}{1}" from point (0,-2), count down 1 and to the right 1 (1,-3).</em>

Both methods are easy to use so either can be used.

**********************************************************************************************************

x - 2y = 18

<u>x  |   y</u>

0  |  -9

18 |   0

<em>plot the y-intercept (0, -9) and the x-intercept (18, 0)</em>

or

x - 2y = 18

<u>-x        </u>   <u> -x </u>

   -2y = -x + 18

    \frac{-2y}{-2} = \frac{-1}{-2}x + \frac{18}{-9}

       y = \frac{1}{2}x - 9

<em>plot at point the y-intercept "b = -9" (0,-9).  plot the next point using the slope "m = \frac{1}{2}" from point (0,-9), count up 1 and to the right 2 (2,-8).</em>

Using intercepts will make a large graph since you have to plot (18,0) so it is best to use the slope-intercept form.



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The focus of a parabola is (0, -3) and the directrix is y = 3. What is the equation of the parabola?
OleMash [197]

Answer:

The equation of the parabola is y = -12\cdot x^{2}.

Step-by-step explanation:

Since the directrix is of the form y = a, the parabola is vertical. The vertex of the parabola (V(x,y)) is the midpoint between the focus (F(x,y)) and a point of the directrix (P(x,y)), that is to say:

V(x,y) = \frac{1}{2}\cdot F(x,y) + \frac{1}{2}\cdot P(x,y) (1)

If we know that F(x,y) = (0, -3) and P(x,y) = (0, 3), then the coordinates of the vertex of the parabola:

V(x,y) = \frac{1}{2}\cdot (0, -3) + \frac{1}{2}\cdot (0, 3)

V(x,y) = (0, 0)

The vertex factor (p) is the distance of the focus with respect to the vertex:

p = \sqrt{[F(x,y)-V(x,y)]\,\bullet \,[F(x,y)-V(x,y)]} (2)

If we know that F(x,y) = (0, -3) and V(x,y) = (0, 0), then the vertex factor is:

p = \sqrt{0^{2}+(-3)^{2}}

p = -3

The equation of the parabola in the vertex form is described below:

y - k = 4\cdot p \cdot (x-h)^{2} (3)

Where:

x - Independent variable.

y - Dependent variable.

h, k - Coordinates of the vertex.

If we know that (h,k) = (0, 0) and p = -3, then the equation of the parabola is y = -12\cdot x^{2}.

6 0
2 years ago
–x – 7 = 16 please help me
atroni [7]
Move the -7 to the right, its sign will flip (do you know why?)
Negate both sides to change -x to x

-x = 16+7
-x = 23
x = -23
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3 years ago
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Step-by-step explanation:

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A student raises her grade average from a 75 to a 90. what was the percent of increase in the student's grade average? round you
Leona [35]
Here are some formulas...
percent increase = (new number - original number) / original number...* 100
percent decrease = (original number - new number) / original number...* 100
============
a student raises her grade from a 75 to a 90....since it is going from a smaller number to a larger number, u have an increase
percent increase = (90 - 75) / 70....* 100
                           =   15/70   * 100
                           = 0.2142 * 100
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-------------------------
36.50 on sale for 32.12...since it goes from a larger number to a smaller number, u have a decrease
percent decrease = (original number - new number) / original * 100
                             = (36.50 - 32.12) / 32.12...* 100
                             = 4.38 / 32.12...* 100
                             = 0.1363...* 100
                             = 13.63 rounds to 13.6% decrease
------------------------------
23.5 to 21.2......this is a decrease
percent decrease = (original number - new number) / original...* 100
                            = (23.5 - 21.2) / 23.5....* 100
                            = 2.3 / 23.5....* 100
                            = 0.0979 * 100
                            = 9.79 rounds to 9.8% decrease






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