Mathematics, 06.05.2021 18:30 lea5261

What are the domain and range of the function y = x^2 - 2x - 1?

Answers: 2

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Answer from: Quest

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

Answer from: Quest

step-by-step explanation:

Answer from: Quest

$\begin {array}{c|c}\underline {\quad x\quad}& \underline{\quad y\quad}\\ -2& 4\\-1& 2\\0& 0\\1& 2\\ 2& 4\\\end{array}$

step-by-step explanation:

y = | -2(-2) | → y = | 4 | → y = 4 ⇒ (-2, 4)

y = | -2(-1) | → y = | 2 | → y = 2 ⇒ (-1, 2)

y = | -2(0) | → y = | 0 | → y = 0 ⇒ (0, 0)

y = | -2(1) | c → y = | -2 | → y = 2 ⇒ (1, 2)

y = | -2(2) | → y = | - 4 | → y = 4 ⇒ (2, 4)

Answer from: Quest

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

$ab^2+ac^2=bc^2$

$ab^2+ac^2=x^2$ )

triangle abd and cba are similar,

$\frac{ab}{bc}=\frac{bd}{ab}$

$ab^2=bc\cdot bd$

$25=bc\cdot bd$ (2)

triangle cad and cba are similar,

$\frac{ac}{bc}=\frac{cd}{ac}$

$ac^2=bc\cdot dc$

$7\times 7=bc\cdot dc$

$49=bc\cdot dc$ )

using (1), (2) and (3), we get

$25+49=x^2$

$74=x^2$

hence proved.

therefore option 2 is correct.

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