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pav-90 [236]
3 years ago
10

An office building casts a 90 foot shadow. At the same time of day, a 5 foot woman standing near the building casts an 8 foot sh

adow. What is the approximate height of the building to the nearest foot?
Mathematics
1 answer:
professor190 [17]3 years ago
6 0
The answer is 56.25ft
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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

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

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)

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

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)

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

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
  • y = (-2)² + 4(-2) + 4 = 4 - 8 + 4 = 0
  • vertex (-2, 0) is in Quadrant 2 and is on the x-axis

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

  • a = +3 so the parabola opens UP
  • x = \frac{-b}{2a} = \frac{-21}{2(3)}  = -\frac{7}{2}
  • y = 3(-\frac{7}{2})^{2} + 21(-\frac{7}{2} ) + 30 = -\frac{27}{4}
  • vertex (-\frac{7}{2}, -\frac{27}{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 (-2, 0) and (-5, 0), and y-intercept (0, 30)

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

4 0
3 years ago
Read 2 more answers
The question is in the picture​
otez555 [7]

Answer:

x=27.8

Step-by-step explanation:

first, you need to find y. 2y-5=65. 65+5 is 60 and you are left with 2y=70. to get the 2 off of the y you divide everything by 2. 70/2 is 35 therefor y=35. Now you plug that into the other equation (2x+y) and get 2x+35 which is equal to segment 90.6 so 2x+35=90.6. subtract 35 on both sides and you have 2x=55.6. To get the 2 off the x, we divide everything by 2. all of that divided by 2 is x=27.8

5 0
2 years ago
A clearance rack is marked as 60% off the regular price to be taken at the register. If a jacket on the clearance rack is marked
dezoksy [38]

Answer:

$399.98

Step-by-step explanation:

Given

Mark down percent = 60%

Mark down price = $239.99

Required

Original price of the rack

Let x be the original price of the product. The equation to get x is as expressed below;

60% of x = 239.99

0.6x = 239.99

x = 239.99/0.6

x = 399.98

Hence the rack will ring up for $399.98 at the register

5 0
2 years ago
2) Cereal cost $7 / box. How many boxes<br> did Huong buy if she spent $21?
uysha [10]
Answer:3 boxes.
Explanation: $21 / $7=3 boxes
3 0
2 years ago
Read 2 more answers
Calculate the density of the steel in g/cm^3
faust18 [17]
The answer is 8 gram/cm^3
Hope this helps
6 0
2 years ago
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