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3 years ago

Which of the follow triangles is similar to APOR?

Mathematics

1 answer:

Paul [167]3 years ago

7 0

Answer:

Step-by-step explanation:

For each triangle, you are given two sides and the included angle (the one between those 2 sides). That's side-angle-side, so it is S-A-S.

The SAS Rule for Similar Triangles says that for 2 triangles X and Y, if you have the SAS of one and the SAS of the other, then X and Y are similar (same shape and proportions) if

(a) the angle in X is congruent (same) as the angle in Y

(b) the ratio between the two given sides in X is the same as the ratio between the two given sides in Y

For this particular problem, the ratio PR/PQ = 18/21 = 6/7 if you simplify by dividing both top and bottom by 3.

So we are looking for another triangle where we have the same ratio. (Put the smaller number on top, in the fraction.)

Answer A: 12/15 simplifies to 4/5, wrong answer

Answer B: 9/12 simplifies to 3/4, wrong answer

Answer C: 6/10 simplifies to 3/5, wrong answer

Answer D: 15/17.5 looks harder, because there is a decimal in it. But we know 17.5 is just 17 and a half, so I would first multiply top and bottom by 2

We get 30/35. That looks a lot better. Now it is easier to see we can divide both top and bottom by 5.

We get 6/7! That is the correct answer, so D is the triangle similar to PQR.

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36 is on 0.9% of what number help fast

Dmitriy789 [7]

The answer would be 4000

3 0

3 years ago

<img src="https://tex.z-dn.net/?f=prove%20that%5C%20%20%5Ctextless%20%5C%20br%20%2F%5C%20%20%5Ctextgreater%20%5C%20%5Cfrac%20%7B

inysia [295]

$\large \bigstar \frak{ } \large\underline{\sf{Solution-}}$

Consider, LHS

$\begin{gathered}\rm \: \dfrac { \tan \theta + \sec \theta - 1 } { \tan \theta - \sec \theta + 1 } \\ \end{gathered}$

We know,

$\begin{gathered}\boxed{\sf{ \:\rm \: {sec}^{2}x - {tan}^{2}x = 1 \: \: }} \\ \end{gathered} \\ \\ \text{So, using this identity, we get} \\ \\ \begin{gathered}\rm \: = \:\dfrac { \tan \theta + \sec \theta - ( {sec}^{2}\theta - {tan}^{2}\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered}$

We know,

$\begin{gathered}\boxed{\sf{ \:\rm \: {x}^{2} - {y}^{2} = (x + y)(x - y) \: \: }} \\ \end{gathered} \\$

So, using this identity, we get

$\begin{gathered}\rm \: = \:\dfrac { \tan \theta + \sec \theta - (sec\theta + tan\theta )(sec\theta - tan\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered}$

can be rewritten as

$\begin{gathered}\rm\:=\:\dfrac {(\sec \theta + tan\theta ) - (sec\theta + tan\theta )(sec\theta -tan\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac {(\sec \theta + tan\theta ) \: \cancel{(1 - sec\theta + tan\theta )}} { \cancel{ \tan \theta - \sec \theta + 1} } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:sec\theta + tan\theta \\\end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac{1}{cos\theta } + \dfrac{sin\theta }{cos\theta } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac{1 + sin\theta }{cos\theta } \\ \end{gathered}$

<h2>Hence,</h2>

$\begin{gathered} \\ \rm\implies \:\boxed{\sf{ \:\rm \: \dfrac { \tan \theta + \sec \theta - 1 } { \tan \theta - \sec \theta + 1 } = \:\dfrac{1 + sin\theta }{cos\theta } \: \: }} \\ \\ \end{gathered}$

$\rule{190pt}{2pt}$

5 0

3 years ago

What is the equation of the line that passes through the points (-1, 7) and (2, 10) in Standard Form?

Usimov [2.4K]

bearing in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

$\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{10}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{10-7}{2-(-1)}\implies \cfrac{3}{2+1}\implies \cfrac{3}{3}\implies 1$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-7=1[x-(-1)]\implies y-7=x+1 \\\\\\ y=x+8\implies \boxed{-x+y=8}\implies \stackrel{\textit{standard form}}{x-y=-8}$

just to point something out, is none of the options, however -x + y = 8, is one, though improper.

3 0

3 years ago

Explain how you would find the slope of the line y = 4.

Slav-nsk [51]

Answer:

The slope is 0.

Step-by-step explanation:

You could draw it on graphs paper . It will be a horizontal line passing through the point (0,4). y will always be 4 and x can be any value.

The slope of a horizontal line is 0.

4 0

3 years ago

What is the length of the hypotenuse? If necessary, round to the nearest tenth.

Diano4ka-milaya [45]

Answer:

The value of c is 2√2 or about 2.8.

Step-by-step explanation:

We can find the hypotenuse (c) with the help of Pythagoras Theorem.

=> c² = 2² + 2²
=> c² = 4 + 4
=> c² = 8
=> c = √8
=> c = √2 x 2 x 2
=> c = 2√2

If you want further simplification, seek for explanation below.

=> c = 2√2
=> c = 2 x √2
=> c = 2 x 1.414
=> c = 2.828 = 2.8 (Estimated)

Hence, the value of c is 2√2 or about 2.8.

Hoped this helped.

$BrainiacUser1357$

4 0

3 years ago

Read 2 more answers