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Arturiano [62]
3 years ago
8

okay so for some reason my mind went completely blank and forgot how to do pathagoream theorem. so like could you tell me the st

eps please​

Mathematics
2 answers:
ira [324]3 years ago
8 0
The formula for the pythagorean theorem is a^2 + b^2 = c^2, or in this case, leg^2 + leg^2 = hypotenuse^2. After inserting the values into the equation, you get x^2 + 9^2 = 15^2. The next step is to find the value of x, and to do so, you must evaluate the powers (9^2 = 81, 15^2 = 225) and subtract 81 from both sides of the equation. Lastly, take the square root of both sides, and you get the final answer of 12.
Hope this helps! Have a good day!
Nookie1986 [14]3 years ago
3 0

Answer:

12

Step-by-step explanation:

Pythag Theorem is Leg² + Leg²= Hypotenuse²

So I set it up as: x² + 9²=15²

Then solved and got: x² + 81 =225

Then I subtracted 81 on both sides and got: x² = 144

Then squareroot each side to undo the x² and got x=12

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3 years ago
Which of the following statements are true about the graph of f(x) = 6(x + 1)2 -9?
Sphinxa [80]

Answer:

Step-by-step explanation:

a. The vertex is (1, -9).  False.  The vertex is (-1, -9).

b. The graph opens upward.  True.  That coefficient '6' is positive.

c. The graph is obtained by shifting the graph of f(x) = 6(x + 1)2 up 9 units.  False.  It's DOWN 9 units.

d. The graph is steeper than the graph of f(x) = x^2.  True.  The given function increases 6 times faster than does x^2.

e. The graph is the same as the graph of f(x) = 6x2 + 12x - 3.

Let's put f(x) = 6(x + 1)^2 -9 into standard form.  Expanding the first term, we get f(x) = 6(x^2 + 2x + 1) - 9, or f(x) = 6x^2 + 12x + 6 - 9.  YES, TRUE

3 0
2 years ago
Dont really understand how to do this
bija089 [108]

Answers:

t_{10} = -22 \ \text{ and } S_{10} = -85

========================================================

Explanation:

t_1 = \text{first term} = 5\\t_2 = \text{first term}-3 = t_1 - 3 = 5-3 = 2

Note we subtract 3 off the previous term (t1) to get the next term (t2). Each new successive term is found this way

t_3 = t_2 - 3 = 2-3 = -1\\t_4 = t_3 - 3 = -1-3 = -4

and so on. This process may take a while to reach t_{10}

There's a shortcut. The nth term of any arithmetic sequence is

t_n = t_1+d(n-1)

We plug in t_1 = 5 \text{ and } d = -3 and simplify

t_n = t_1+d(n-1)\\t_n = 5+(-3)(n-1)\\t_n = 5-3n+3\\t_n = -3n+8

Then we can plug in various positive whole numbers for n to find the corresponding t_n value. For example, plug in n = 2

t_n = -3n+8\\t_2 = -3*2+8\\t_2 = -6+8\\t_2 = 2

which matches with the second term we found earlier. And,

tn = -3n+8\\t_{10} = -3*10+8\\t_{10} = -30+8\\t_{10} = \boldsymbol{-22} \ \textbf{ is the tenth term}

---------------------

The notation S_{10} refers to the sum of the first ten terms t_1, t_2, \ldots, t_9, t_{10}

We could use either the long way or the shortcut above to find all t_1 through t_{10}. Then add those values up. Or we can take this shortcut below.

Sn = \text{sum of the first n terms of an arithmetic sequence}\\S_n = (n/2)*(t_1+t_n)\\S_{10} = (10/2)*(t_1+t_{10})\\S_{10} = (10/2)*(5-22)\\S_{10} = 5*(-17)\\\boldsymbol{S_{10} = -85}

The sum of the first ten terms is -85

-----------------------

As a check for S_{10}, here are the first ten terms:

  • t1 = 5
  • t2 = 2
  • t3 = -1
  • t4 = -4
  • t5 = -7
  • t6 = -10
  • t7 = -13
  • t8 = -16
  • t9 = -19
  • t10 = -22

Then adding said terms gets us...

5 + 2 + (-1) + (-4) + (-7) + (-10) + (-13) + (-16) + (-19) + (-22) = -85

This confirms that S_{10} = -85 is correct.

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Answer:

Triangle ABC is similar but not congruent to Triangle XYZ

Step-by-step explanation:

When you dilate the size changes but the angles are the same with makes them similar and since the size of the triangles are different they cannot be congruent.

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