Consider the equation as shown:
(x-a)(y-b) = (x-2a)(y- b/2)

x(x + 1/2b) + y(y + a/2) -2xy = 5+(x-y)²

On comparing the coefficient, a student says these pairs of equations is consistent. Is he/she correct? Which of these explains why?
(a) Yes; because they are parallel lines.
(b) No; because they are interesting lines.
(c) Yes; because they are parallel lines.
(d) No; because they are interesting lines.​

[tex]\large\underline{\sf{Solution-}}[/tex]

First equation is

[tex]\rm \longmapsto\:(x - a)(y - b) = (x - 2a)\bigg(y -\dfrac{b}{2}\bigg) [/tex]

can be further simplified to

[tex]\rm \longmapsto\:xy - bx - ay + ab = xy - \dfrac{bx}{2} - 2ay + ab[/tex]

[tex]\rm \longmapsto\: - bx - ay = - \dfrac{bx}{2} - 2ay [/tex]

[tex]\rm \longmapsto\: - bx + \dfrac{bx}{2} = - 2ay + ay[/tex]

[tex]\rm \longmapsto\: - \dfrac{bx}{2} = - ay[/tex]

[tex]\rm \longmapsto\: \dfrac{bx}{2} = ay[/tex]

[tex]\rm \longmapsto\:bx = 2ay[/tex]

[tex]\rm:\longmapsto \:\boxed{\tt{ bx - 2ay = 0}} - - - - (1)[/tex]

Second equation is

[tex]\rm \longmapsto\:x\bigg(x + \dfrac{1}{2b} \bigg) + y \bigg(y + \dfrac{a}{2}\bigg) - 2xy = 5 + {(x - y)}^{2} [/tex]

[tex]\rm \longmapsto\: {x}^{2} + \dfrac{x}{2b} + {y}^{2} + \dfrac{ay}{2} - 2xy = 5 + {x}^{2} + {y}^{2} - 2xy[/tex]

[tex]\rm \longmapsto\: \dfrac{x}{2b} + \dfrac{ay}{2} = 5[/tex]

[tex]\rm \longmapsto\: \dfrac{x + aby}{2b} = 5[/tex]

[tex]\rm :\longmapsto\:\boxed{\tt{ x + aby = 10b}} - - - (2)[/tex]

So, we have two equations in simplest form as

[tex]\rm \longmapsto\:bx - 2ay = 0 [/tex]

and

[tex]\rm \longmapsto\:x + aby = 10b[/tex]

Now, Consider

[tex]\rm \longmapsto\:\dfrac{a_1}{a_2} = \dfrac{b}{1} = b[/tex]

[tex]\rm \longmapsto\:\dfrac{b_1}{b_2} = \dfrac{ - 2a}{ab} = - \dfrac{2}{b} [/tex]

[tex]\bf\implies \:\dfrac{a_1}{a_2} \: \ne \: \dfrac{b_1}{b_2} [/tex]

This implies, System of equations is consistent having unique solution.

So, The student is correct as lines are intersecting.

So, option (b) is correct.

NO LINKS!!! Part 2:

[tex]y = \sqrt{x} [/tex]
Shape:
Domain:
Range:​

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Allowance method entries

The following transactions were completed by Wild Trout Gallery during the current fiscal year ended December 31:

Jan. 19. Reinstated the account of Arlene Gurley, which had been written off in the preceding year as uncollectible. Journalized the receipt of $2,560 cash in full payment of Arlene’s account.
Apr. 3. Wrote off the $14,670 balance owed by Premier GS Co., which is bankrupt.
July 16. Received 25% of the $26,300 balance owed by Hayden Co., a bankrupt business, and wrote off the remainder as uncollectible.
Nov. 23. Reinstated the account of Harry Carr, which had been written off two years earlier as uncollectible. Recorded the receipt of $4,175 cash in full payment.
Dec. 31. Wrote off the following accounts as uncollectible (compound entry): Cavey Co., $11,035 ; Fogle Co., $3,275 ; Lake Furniture, $ 8,420 ; Melinda Shryer, $2,380.
Dec. 31. Based on an analysis of the $1,299,500 of accounts receivable, it was estimated that $56,500 will be uncollectible. Journalized the adjusting entry.
Required:

1. Record the January 1 credit balance of $53,800 in a T account presented below in requirement 2b for Allowance for Doubtful Accounts.

2. a. Journalize the transactions. If an amount box does not require an entry, leave it blank. Note: For the December 31 adjusting entry, assume the $1,299,500 balance in accounts receivable reflects the adjustments made during the year.
2. b. Post each entry that affects the following T accounts and determine the new balances:
3. Determine the expected net realizable value of the accounts receivable as of December 31 (after all of the adjustments and the adjusting entry).
$fill in the blank 73711efa1fe301a_1
2,290,000

4. Assuming that instead of basing the provision for uncollectible accounts on an analysis of receivables, the adjusting entry on December 31 had been based on an estimated expense of ½ of 1% of the sales of $8,020,000 for the year, determine the following:

a. Bad debt expense for the year.
b. Balance in the allowance account after the adjustment of December 31.

c. Expected net realizable value of the accounts receivable as of December 31 (after all of the adjustments and the adjusting entry).

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he following histogram shows the number of items sold at a grocery store at various prices:

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{0.50, 2.00, 2.52, 3.37, 4.53, 5.00, 8.99}
{2, 4, 0, 1}
{2.50, 2.51, 5.00, 5.01, 7.50, 9.00, 10.00}
{0.50, 2.50, 2.50, 5.00, 5.00, 5.00, 7.51}

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