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Natali [406]
3 years ago
13

Lisa tied a piece of rope to a tree branch. She is standing 5 feet away from the base of the tree, and the branch is 12 feet off

the ground. The length of the rope from the tree branch to Lisa’s feet is r feet long.
Mathematics
1 answer:
Ksenya-84 [330]3 years ago
8 0
When you draw this out, what you have is a right triangle problem.  The height of the rope from the ground is 12 (a side), the distance she is from the base of the tree is 5 (a side), and the length of the rope is the hypotenuse.  Use Pythagorean's Theorem to find the length of the hypotenuse: 5^2+12^2 = c^2 or
25+144 = c^2 and c^2 = 169, which makes the length of the rope come out to be 13 feet long.
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Answer:

The answer for the value of x is, x=20

4 0
2 years ago
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PLEASE HELP!!!!
Lunna [17]

NOTES:

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  • 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>

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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
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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!

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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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4 0
3 years ago
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In ABC, the interior angle at A is 51° and the exterior angle at B is 119º. The interior angle at C measures
erastova [34]

Answer:

68 degrees

Step-by-step explanation:

To get the interior angle, we use an important triangle principle

The principle is that the sum of the opposite interior angles equal the exterior angle

Let the second interior angle be x

x + 51 = 119

x = 119-51

x = 68

7 0
3 years ago
2. Four less than six times a number is 32. Write and solve an equation.
zhenek [66]

Answer:

6x - 4 = 32. The variable (times a number) is equal to 6.

Step-by-step explanation:

So this equation is basically asking you to formulate an equation using only the words given. For this equation, let's use a variable in place of the part where it says "times a number." When a question says that phrase, that means that they are telling you to use a variable in place of a mystery number. A variable is a letter in place of a mystery number. Knowing this, let's now solve the equation. We will use the variable x in place of our mystery number.

Four less than 6 times a number: 6x - 4 _ __.

Now we can add the equal sign and the 32: 6x - 4 = 32.

We can now solve. Add 4 to both sides of the equation to cancel out the -4:

6x - 4 = 32

    <u>+4   + 4</u>

6x  =    36

Now we divide 6 into both sides of the equation to single out the x.

<u>6x = 36</u>

6      6

36/6 = 6, so:

x = 6

I hope that this helps.

8 0
2 years ago
two weeks ago i bought 2 cupcakes last week i bought 7 today id like to follow this pattern how many cupcakes do i want
monitta

Answer:

12

Step-by-step explanation:

2+5=7

7+5=12

Pattern of +5

5 0
3 years ago
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