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siniylev [52]
3 years ago
13

If you could please show all your steps that would be great.

Mathematics
1 answer:
bixtya [17]3 years ago
5 0

a. Angles ABC and CBD are supplementary, so you know that m\angle ABC=180^\circ-24^\circ=156^\circ

The interior angles of any triangle sum to 180 degrees in measure, so that m\angle ACB=180^\circ-156^\circ-16^\circ=8^\circ.

By the law of sines, we then have

\dfrac{\sin8^\circ}{7600\,\mathrm{ft}}=\dfrac{\sin16^\circ}{BC}\implies BC=\dfrac{(7600\,\mathrm{ft})\sin16^\circ}{\sin156^\circ}\approx15052\,\mathrm{ft}

b. In triangle BCD, we have

\sin24^\circ=\dfrac{CD}{BC}

and so

CD=\sin24^\circ\dfrac{(7600\,\mathrm{ft})\sin16^\circ}{\sin8^\circ}\approx6122\,\mathrm{ft}

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if a shape is a regular pentagon with five sides, which of the following must be true? Check all that apply
julsineya [31]

Answer:

A. It has reflectional symmetry

B. It is symmetrical

D. It has five lines of symmetry

Step-by-step explanation:

we know that

A regular pentagon has 5 sides and 5 lines of symmetry. The number of lines of symmetry in a regular polygon is equal to the number of sides

Every regular polygon has reflectional symmetry

Regular polygons are symmetrical

therefore

A. It has reflectional symmetry ------> Is true

B. It is symmetrical -----> Is true

C. It has exactly one line of symmetry ----> Is false

D. It has five lines of symmetry -----> Is true

4 0
3 years ago
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Consider the proof.
fiasKO [112]

Answer:

Correct choice is B

Step-by-step explanation:

In step 4 were proved that \triangle ABC\sim\triangle DEC.

By definition, similar triangles have proportional lengths of corresponding sides. To the side AB corresponds side ED, to the side AC corresponds side DC and to the side BC corresponds side EC. Thus,

\dfrac{AC}{DC}=\dfrac{BC}{EC}.

6 0
3 years ago
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Which number is both a rational number and an integer? A. B. 13/14 C. 194 D. 13.5
Misha Larkins [42]

Answer:

C. 194

Step-by-step explanation:

An integer can be a positive or negative whole number, but not a decimal. If this number is an integer, then it is also a rational number. So, 194 fits this description.

Maybe this image can help you.

7 0
3 years ago
Suppose cos(O) = 12/13, Quadrant I. Find sin(O).<br> A:13/12<br> B:5/13<br> C:13/5<br> D:5/12
noname [10]

Answer:

B: 5/13

Step-by-step explanation:

pythagoras theorem: a^2 + b^2 (sides) = c^2 (hypotenuse)

a^2 + 12^2 = 13^2

a^2 + 144 = 169

a^2 = 25

a = 5

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sin 5/13

Hope this helps

7 0
3 years ago
Drag and drop each pair of lines into the correct category to indicate whether the pair of lines are parallel, perpendicular, or
ANTONII [103]

Answer:

Step-by-step explanation:

<em>(1).</em> \frac{1}{7} x + y = 9 and y = - 7x <em>( Neither )</em> ; lines intersect.

<em>(2).</em> y = 3x - 3; 12x - 4y = 12 <em>( Neither ) </em>; Lines are overlapped or both equation are of the same line.

<em>(3).</em> 7y = 2x + 1; 14x + 4y = 12 <em>( Perpendicular )</em> ; m_{1} = \frac{2}{7} and m_{2} = - \frac{7}{2} , slopes are opposite reciprocals.

<em>(4).</em> x - 4y = 18; y = x + 4 <em>( Neither )</em> ; lines intersect.

<em>(5).</em> 3x - 4y = - 1; 3y = - 4x + 5 <em>( Perpendicular )</em> ; m_{1} = \frac{3}{4} and m_{2} = - \frac{4}{3} , slopes are opposite reciprocals.

7 0
2 years ago
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