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Sergeeva-Olga [200]
2 years ago
6

Write the coordinate rule to describe The translasion​

Mathematics
1 answer:
sergejj [24]2 years ago
6 0

Answer:

The coordinates are:

A ( 4,7 )

B ( 8,10 )

c ( 7,7 )

Step-by-step explanation:

You could take the original coordinates and add the x value with 3 and y value with 6. Like for example...

The original coordinates of C is ( 4,1 ). Hence you could add the x value with 3 and y value with 6. 4 + 3 and 1 + 6 giving you the coordinates after translation = ( 7,7 )

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Answer:

16. Angle C is approximately 13.0 degrees.

17. The length of segment BC is approximately 45.0.

18. Angle B is approximately 26.0 degrees.

15. The length of segment DF "e" is approximately 12.9.

Step-by-step explanation:

<h3>16</h3>

By the law of sine, the sine of interior angles of a triangle are proportional to the length of the side opposite to that angle.

For triangle ABC:

  • \sin{A} = \sin{103\textdegree{}},
  • The opposite side of angle A a = BC = 26,
  • The angle C is to be found, and
  • The length of the side opposite to angle C c = AB = 6.

\displaystyle \frac{\sin{C}}{\sin{A}} = \frac{c}{a}.

\displaystyle \sin{C} = \frac{c}{a}\cdot \sin{A} = \frac{6}{26}\times \sin{103\textdegree}.

\displaystyle C = \sin^{-1}{(\sin{C}}) = \sin^{-1}{\left(\frac{c}{a}\cdot \sin{A}\right)} = \sin^{-1}{\left(\frac{6}{26}\times \sin{103\textdegree}}\right)} = 13.0\textdegree{}.

Note that the inverse sine function here \sin^{-1}() is also known as arcsin.

<h3>17</h3>

By the law of cosine,

c^{2} = a^{2} + b^{2} - 2\;a\cdot b\cdot \cos{C},

where

  • a, b, and c are the lengths of sides of triangle ABC, and
  • \cos{C} is the cosine of angle C.

For triangle ABC:

  • b = 21,
  • c = 30,
  • The length of a (segment BC) is to be found, and
  • The cosine of angle A is \cos{123\textdegree}.

Therefore, replace C in the equation with A, and the law of cosine will become:

a^{2} = b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}.

\displaystyle \begin{aligned}a &= \sqrt{b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}}\\&=\sqrt{21^{2} + 30^{2} - 2\times 21\times 30 \times \cos{123\textdegree}}\\&=45.0 \end{aligned}.

<h3>18</h3>

For triangle ABC:

  • a = 14,
  • b = 9,
  • c = 6, and
  • Angle B is to be found.

Start by finding the cosine of angle B. Apply the law of cosine.

b^{2} = a^{2} + c^{2} - 2\;a\cdot c\cdot \cos{B}.

\displaystyle \cos{B} = \frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}.

\displaystyle B = \cos^{-1}{\left(\frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}\right)} = \cos^{-1}{\left(\frac{14^{2} + 6^{2} - 9^{2}}{2\times 14\times 6}\right)} = 26.0\textdegree.

<h3>15</h3>

For triangle DEF:

  • The length of segment DF is to be found,
  • The length of segment EF is 9,
  • The sine of angle E is \sin{64\textdegree}}, and
  • The sine of angle D is \sin{39\textdegree}.

Apply the law of sine:

\displaystyle \frac{DF}{EF} = \frac{\sin{E}}{\sin{D}}

\displaystyle DF = \frac{\sin{E}}{\sin{D}}\cdot EF = \frac{\sin{64\textdegree}}{39\textdegree} \times 9 = 12.9.

7 0
3 years ago
Find the median for the scores 91, 69, 71, 82, 71, 95, 87, 74, 71, 89, 89, 95, 72, 75
AnnyKZ [126]

\huge\text{Hey there!}

\huge\textbf{What does \boxed{median} mean in math?}}

\boxed{\text{Median}}\rightarrow\textsf{ is the number in the middle.}

\huge\textbf{How do you find the \boxed{median}?}

\text{You can found it by putting the numbers from \bf least to greatest.}

\huge\textbf{Question reads....}

\text{Find the median for the scores 91, 69, 71, 82, 71, 95, 87, 74, 71, 89, 89, 95,}\\\text{72, 75}

\huge\textbf{Equation:}

\text{91, 69, 71, 82, 71, 95, 87, 74, 71, 89, 89, 95, 72, 75}

\huge\textbf{Rearrange the problems to:}

\text{69,71,71,71,72,74,75,82,87, 89,89,91,95,95}

\huge\textbf{The expression:}

\mathsf{\dfrac{75 + 82}{2} = median}

\huge\textbf{Simplify it:}

\mathsf{\dfrac{75 + 82}{2} = median}

\mathsf{\dfrac{157}{2} = median}

\mathsf{257\div2 = median}

\mathsf{78.5 = median}

\huge\textbf{Therefore, your answer should be:}

\huge\boxed{\mathsf{78.5}}\huge\checkmark

\huge\text{Good luck on your assignment \& enjoy your day!}

<h3>~\frak{Amphitrite1040:)}</h3>
8 0
1 year ago
What would the answer be to this
Vladimir79 [104]

Answer:

265.2

Step-by-step explanation:

3(6*13)=234

2*15.6=31.2

234+31.2=265.2

6 0
3 years ago
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