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NeTakaya
3 years ago
6

Gracie is buying new jackets for her dance squad. She will pay $26.50 for each jacket

Mathematics
1 answer:
Mariana [72]3 years ago
4 0

Answer:

y=26.50x + 15.99

Step-by-step explanation:

Each jacket costs $26.50 so x is the variable to depict how many jackets she is buying because it does not tell us in the question. There is a one-time fee of $15.99 so that is added on to the total to find the total cost which is y.

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PLEASE HELP!!!!
Lunna [17]

NOTES:

Given a quadratic function in standard format (y = ax² + bx + c), the direction of the parabola is as follows:

  • if "a" is positive, then opens UP
  • if "a" is negative, then opens DOWN

Given a quadratic function in standard format (y = ax² + bx + c), the vertex can be found as follows:

  • the Axis Of Symmetry (x-value) is: x = \frac{-b}{2a}  
  • y-value is found by plugging in the AOS for "x" in the equation

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1) y = x² + 11x + 24

  • a = +1 so the parabola opens UP
  • x = \frac{-b}{2a} = \frac{-11}{2(1)}  = -\frac{11}{2}
  • y = (-\frac{11}{2})^{2} + 11(-\frac{11}{2} ) + 24 = -\frac{25}{4}
  • vertex (-\frac{11}{2}, -\frac{25}{4}) is in Quadrant 3 and is below the x-axis

This COULD be the graph of the rain gauge.

The graph should contain the vertex, x-intercepts (-3, 0) and (-8, 0), and y-intercept (0, 24)

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2) y = -x² - 6x - 8

  • a = -1 so the parabola opens DOWN
  • x = \frac{-b}{2a} = \frac{-(-6)}{2(-1)}  = \frac{6}{-2} = -3
  • y = -(-3)² - 6(-3) - 8 = -9 + 18 - 8 = 1
  • vertex (-3, 1) is in Quadrant 2 and is above the x-axis

This could NOT be the graph of the rain gauge.

The graph should contain the vertex, x-intercepts (-2, 0) and (-4, 0), and y-intercept (0, -8)

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3) y = x² - 2x + 3

  • a = 1 so the parabola opens UP
  • x = \frac{-b}{2a} = \frac{-(-2)}{2(1)}  = \frac{2}{2} = 1
  • y = (1)² - 2(1) + 3 = 1 - 2 + 3 = 2
  • vertex (1, 2) is in Quadrant 1 and is above the x-axis

This could NOT be the graph of the rain gauge.

The graph should contain the vertex, y-intercept (0, 3), and its mirror image (2, 3). <em>There are no x-intercepts</em>

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

4) y = x² + 4x + 4

  • a = 1 so the parabola opens UP
  • x = \frac{-b}{2a} = \frac{-4}{2(1)}  = -2
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This COULD be the graph of the rain gauge.

The graph should contain the vertex, y-intercept (0, 4), and its mirror image (-4, 4). <em>The x-intercept is the vertex.</em>

Compared to the other four graphs, this is most likely the equation for the rain gauge!

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

5) y = 3x² + 21x + 30

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This COULD be the graph of the rain gauge.

The graph should contain the vertex, x-intercepts (-2, 0) and (-5, 0), and y-intercept (0, 30)

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1 place to the left and 2 places down

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Answer:

the slope of line j is -1/8, the slope of lines m and n are both 8.

Explanation step by step:

Suppose j is the slope of line j, m the slope of line m and n the slope of line n. Since:

1. line j is perpendicular of line m, so j*m= -1

2. J is perpendicular of line n, so  j*n=-1

3. m and n and parallel so m=n

As we want to know the slope of j we clear the equations presented to us in order to find it.

(1) m* n* j = -8, since n=m we have  n^{2}* j = -8.

we clear j; n^{2} * j = -8 \\ j =\frac{-8}{n^{2} }

replacing in the equation n*j = -1 we get

n*(-8/n^2) = -1. Thus n = 8. Since j = -1/n = -1/8.

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3 years ago
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