Solve similar triangles Solve for x x=?

Mathematics

1 answer:

lions [1.4K]2 years ago

6 0

Answer:

x/9 = 1/5

x = 9/5

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Choose Yes or No to tell whether the expressions are equivalent. 1. 4(5c + 3) and 9c + 7 yes or no 2. 10f – 10 and 2(8f – 5) yes

Juli2301 [7.4K]

Answer:

1) No

2) No

3)Yes

4)No

Step-by-step explanation:

Distributive property: a(b + c) =a*b + a*c

1) 4(5c + 3) = (4*5c) + 4*3

= 20c + 12

2) 2(8f - 5) = (2*8f) - (2*5)

= 16f - 10

3) 3(4g + 7) = (3*4g) + (3*7)

= 12g + 21

YES

4) 6(4j - 6) =(6 * 4j) - (6*6)

= 24j - 36

5 0

3 years ago

What is the supplementary angle to an angle that has 112 degrees?

olga55 [171]

Supplementary means they add up to 180°.
180-112= 68
The answer is 68°

7 0

3 years ago

Please Help! This is a trigonometry question.

liraira [26]

$\large\begin{array}{l} \textsf{From the picture, we get}\\\\ \mathsf{tan\,\theta=\dfrac{2}{3}}\\\\ \mathsf{\dfrac{sin\,\theta}{cos\,\theta}=\dfrac{2}{3}}\\\\ \mathsf{3\,sin\,\theta=2\,cos\,\theta}\qquad\mathsf{(i)} \end{array}$

$\large\begin{array}{l} \textsf{Square both sides of \mathsf{(i)} above:}\\\\ \mathsf{(3\,sin\,\theta)^2=(2\,cos\,\theta)^2}\\\\ \mathsf{9\,sin^2\,\theta=4\,cos^2\,\theta}\qquad\quad\textsf{(but }\mathsf{cos^2\theta=1-sin^2\,\theta}\textsf{)}\\\\ \mathsf{9\,sin^2\,\theta=4\cdot (1-sin^2\,\theta)}\\\\ \mathsf{9\,sin^2\,\theta=4-4\,sin^2\,\theta}\\\\ \mathsf{9\,sin^2\,\theta+4\,sin^2\,\theta=4} \end{array}$

$\large\begin{array}{l} \mathsf{13\,sin^2\,\theta=4}\\\\ \mathsf{sin^2\,\theta=\dfrac{4}{13}}\\\\ \mathsf{sin\,\theta=\sqrt{\dfrac{4}{13}}}\\\\ \textsf{(we must take the positive square root, because }\theta \textsf{ is an}\\\textsf{acute angle, so its sine is positive)}\\\\ \mathsf{sin\,\theta=\dfrac{2}{\sqrt{13}}} \end{array}$

________

$\large\begin{array}{l} \textsf{From (i), we find the value of }\mathsf{cos\,\theta:}\\\\ \mathsf{3\,sin\,\theta=2\,cos\,\theta}\\\\ \mathsf{cos\,\theta=\dfrac{3}{2}\,sin\,\theta}\\\\ \mathsf{cos\,\theta=\dfrac{3}{\diagup\!\!\!\! 2}\cdot \dfrac{\diagup\!\!\!\! 2}{\sqrt{13}}}\\\\ \mathsf{cos\,\theta=\dfrac{3}{\sqrt{13}}}\\\\ \end{array}$

________

$\large\begin{array}{l} \textsf{Since sine and cosecant functions are reciprocal, we have}\\\\ \mathsf{sin\,2\theta\cdot csc\,2\theta=1}\\\\ \mathsf{csc\,2\theta=\dfrac{1}{sin\,2\theta}\qquad\quad\textsf{(but }}\mathsf{sin\,2\theta=2\,sin\,\theta\,cos\,\theta}\textsf{)}\\\\ \mathsf{csc\,2\theta=\dfrac{1}{2\,sin\,\theta\,cos\,\theta}}\\\\ \mathsf{csc\,2\theta=\dfrac{1}{2\cdot \frac{2}{\sqrt{13}}\cdot \frac{3}{\sqrt{13}}}} \end{array}$

$\large\begin{array}{l} \mathsf{csc\,2\theta=\dfrac{~~~~1~~~~}{\frac{2\cdot 2\cdot 3}{(\sqrt{13})^2}}}\\\\ \mathsf{csc\,2\theta=\dfrac{~~1~~}{\frac{12}{13}}}\\\\ \boxed{\begin{array}{c}\mathsf{csc\,2\theta=\dfrac{13}{12}} \end{array}}\qquad\checkmark \end{array}$

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Tags: <em>trigonometry trig function cosecant csc double angle identity geometry</em>

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8 0

3 years ago

2. The electrical resistance R of a wire varies inversely with the square of its diameter d. If a wire with a

Mariulka [41]

Answer:

$0.225 \Omega =225 m\Omega$

Step-by-step explanation:

We know (Ohm second law) that $R= \frac{k}{d^2}$ where k inlcudes the rest of the parameters (material, lenght). In our situation we have k= $0.4\cdot9 \Omega mm^2$ . The moment the diameter becomes 8mm R becomes