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Mnenie [13.5K]
1 year ago
6

Mr. Haley is leaning a ladder against the side of his house to repair the roof.

Mathematics
1 answer:
natima [27]1 year ago
5 0

Answer:

15 ft

Explanation:

We can represent the situation with the following figure

Therefore, the length of the ladder is the hypotenuse of the right triangle formed, where the legs are 12 ft and 9 ft. Using the Pythagorean theorem, we can calculate the length of the ladder as

\begin{gathered} Ladder=\sqrt{12^2+9^2} \\ Ladder=\sqrt{144+81} \\ Ladder=\sqrt{225} \\ Ladder=15 \end{gathered}

Therefore, the length of the ladder is 15 ft

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The 10th term of an a.p is -27 and the 5th term is -12 .find the first term?​
horsena [70]

Step-by-step explanation:

a_{10} = - 27... (Given) \\\\\therefore a + 9d = - 27...... (1)\\\\a_{5} = - 12... (Given) \\\\\therefore a + 4d = - 12.......(2)\\\\

Subtracting equation (2) from equation (1)

a + 9d-( a + 4d )= - 27-(-12)\\\\\therefore a +9d - a-4d = - 27+12\\\\\therefore 5d = - 15\\\\\therefore d = \frac {- 15}{5}\\\\\huge \orange {\boxed {\therefore d = -3}} \\\\

Substituting d = - 3 in equation (1), we find:

a + 9\times (-3)= - 27\\\\\therefore a - 27 = - 27\\\\\therefore a  = 27- 27\\\\\huge \red {\boxed {\therefore a  = 0}}\\\\

Hence, first term is zero.

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3 years ago
Triangle GHI is rotated 90Degrees clockwise and then reflected over the y-axis. Which congruency statement is true?
lesya [120]

The congruency statement which is true among the answer choices is;

  • On a coordinate plane, triangle G H I is rotated 90 degrees clockwise and then is reflected over the y-axis.
  • Triangle G H I is congruent to triangle G double-prime H double-prime I double-prime.

<h3>Which congruency statement is true?</h3>

According to the task content, the initial transformation is; Triangle GHI is rotated 90Degrees clockwise and then reflected over the y-axis.

On this note, the congruency which are true regarding the transformation are;

  • On a coordinate plane, triangle G H I is rotated 90 degrees clockwise and then is reflected over the y-axis.
  • Triangle G H I is congruent to triangle G double-prime H double-prime I double-prime.

This follows from the fact that the transformation.does not involved dilation by means of a scale factor and hence, size remains equal and all angle measures remain the same.

Read more on triangle congruence;

brainly.com/question/2102943

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Answer:

\large\boxed{100_{10}=1100100_2}

Step-by-step explanation:

100:2=50\qquad rest=0\\50:2=25\qquad rest=0\\25:2=12\qquad rest=1\\12:2=6\qquad rest=0\\6:2=3\qquad rest=0\\3:2=1\qquad rest=1\\1:2=0\qquad rest=1\\\\\text{We write from the bottom up}\\\\100_{10}=1100100_2

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Answer:

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Step-by-step explanation:

1 kilogram= about 2.2 pounds

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