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.

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297,060 ÷ 0.0004839 =

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

Histogram titled Items Sold with Price Range on the x axis and Number of Items Sold on the y axis. Bar 1 is 0 to 2 dollars and 50 cents and has a height of 2. Bar 2 is 2 dollars and 51 cents to 5 dollars and has a height of 4. Bar 3 is 5 dollars and 1 cent to 7 dollars and 50 cents and has a height of 0. Bar 4 is 7 dollars and 51 cents to 10 dollars and has a height of 1.

Which of the following data sets is represented in the histogram?

{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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The blueprint for Audrey's new room has a
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A train travels at 100 miles per hour. Write an equation that compares the time (t) with the distance (d).

t = 100d

d = 100t

d = t + 100

t = d + 100

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

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Click on the graph to draw a trapezoid with right angles at (0, -7) and (8,−7), another vertex at (8,0), and a vertical base of 16 units

7. A fundraising group charges $0.25 per cookie and has a daily expense of $18. Which of the
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Your help will be much appreciated because i am losing my sanity doing this math

What is the distance from the point (-6, 2) to the point (2, 17)
19.21 units
15.13 units
17.00 units
19.10 units
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Find the radius of the circle.
3(x – 5)^2 + 3(y + 9)^2 = 48
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6 is 15% of what number

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f(x)=8x-5 when x=-1, x=2, and x=3
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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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