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Dvinal [7]
3 years ago
7

Sharon is decreasing the size of a diagram of a leaf that is 30 centimeters long by 10 centimeters wide, if the reduced diagram

is 4 centimeters wide how long will it be?
Mathematics
2 answers:
fiasKO [112]3 years ago
8 0
x-length\\\\From\ proportion:\\\\\frac{30}{10}=\frac{x}{4}\\\\10x=120\ \ \ \ \ \ |:10\\\\x=12\\\\It\ will\ be\ 12\ cm\ long
sertanlavr [38]3 years ago
7 0

Answer:

12 cm


Step-by-step explanation:

This is a proportionality/similarity problem.

10 cm turned to 4 cm. So by how much has it decreased? In other words, <em>10 multiplied by </em><em>WHAT</em><em> is 4?</em>

10*x=4\\x=\frac{4}{10}\\x=0.4

0.4 is also known as the scale factor from the large diagram to the small diagram.

So how much would 30 cm become?<em> It would be 30 multiplied by the scale factor, which is </em><em>0.4</em><em>.</em>

30*0.4=12

<u>Hence, the length of the reduced diagram would be </u><u>12 cm</u><u>.</u>

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3 years ago
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From a standard deck of cards, a 5-card hand is dealt. Calculate the number of hands that contain 4 diamonds and 1 black king
rjkz [21]

Answer:

1430

Step-by-step explanation:

Given that a standard deck of cards is 52 cards, we have 13 Diamonds and we need 4 diamonds.

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Hence, in this case, the correct answer to the question is 1430

7 0
3 years ago
Describe the two equations:<br> y=-3x + 2 and y = 2x - 3
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Find sinϴ and cosϴ if tanϴ=1/4 and sinϴ&gt;0
eduard
If you're using the app, try seeing this answer through your browser:  brainly.com/question/2787701

_______________


\mathsf{tan\,\theta=\dfrac{1}{4}\qquad\qquad(sin\,\theta\ \textgreater \ 0)}\\\\\\&#10;\mathsf{\dfrac{sin\,\theta}{cos\,\theta}=\dfrac{1}{4}}\\\\\\&#10;\mathsf{4\,sin\,\theta=cos\,\theta\qquad\quad(i)}


Square both sides:

\mathsf{(4\,sin\,\theta)^2=(cos\,\theta)^2}\\\\&#10;\mathsf{4^2\,sin^2\,\theta=cos^2\,\theta}\\\\&#10;\mathsf{16\,sin^2\,\theta=cos^2\,\theta\qquad\qquad(but,~cos^2\,\theta=1-sin^2\,\theta)}\\\\&#10;\mathsf{16\,sin^2\,\theta=1-sin^2\,\theta}

\mathsf{16\,sin^2\,\theta+sin^2\,\theta=1}\\\\&#10;\mathsf{17\,sin^2\,\theta=1}\\\\&#10;\mathsf{sin^2\,\theta=\dfrac{1}{17}}\\\\\\&#10;\mathsf{sin\,\theta=\pm\,\sqrt{\dfrac{1}{17}}}\\\\\\&#10;\mathsf{sin\,\theta=\pm\,\dfrac{1}{\sqrt{17}}}


Since \mathsf{sin\,\theta} is positive, you can discard the negative sign. So,

\mathsf{sin\,\theta=\dfrac{1}{\sqrt{17}}\qquad\quad\checkmark}


Substitute this value back into \mathsf{(i)} to find \mathsf{cos\,\theta:}

\mathsf{4\cdot \dfrac{1}{\sqrt{17}}=cos\,\theta}\\\\\\&#10;\mathsf{cos\,\theta=\dfrac{4}{\sqrt{17}}\qquad\quad\checkmark}


I hope this helps. =)


Tags:   <em>trigonometric identity relation trig sine cosine tangent sin cos tan trigonometry precalculus</em>

7 0
3 years ago
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