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Ivan
2 years ago
6

The point P is the reflection of the point (-7, 5) in the line 5x - 3y = 18.

Mathematics
1 answer:
Sonbull [250]2 years ago
6 0

Answer:

(13,-7)

Step-by-step explanation:

5x-3y=18 \\ \\ -5x+3y=-18 \\ \\ 3y=5x-18 \\ \\ y=\frac{5}{3}x-6

The slope of the given line is 5/3. Perpendicular lines have slopes that are negative reciprocals of each other, so we need to find the line with slope -3/5 through P.

y-5=-\frac{3}{5}(x+7) \\ \\ y-5=-\frac{3}{5}x-\frac{21}{5} \\ \\ y=-\frac{3}{5}x+\frac{4}{5}

Finding where the lines intersect,

-\frac{3}{5}x+\frac{4}{5}=\frac{5}{3}x-6 \\ \\ -9x+12=25x-90 \\ \\ 34x=102 \\ \\ x=3 \implies y=-1

The point where the line of reflection and the perpendicular drawn to it through the point being reflected is the midpoint of the preimage and the image.

Let the coordinates of the image be (a,b). Then, by the midpoint formula,

\frac{-7+a}{2}=3 \implies -7+a=6 \implies a=13 \\ \\ \frac{5+b}{2}=-1 \implies 5+b=-2 \implies b=-7

Therefore, P has coordinates (13, -7).

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A new car is purchased for 15500 dollars. The value of the car depreciates at 7.5% per year. What will the value of the car be,
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Answer:

\$9,709.17  

Step-by-step explanation:

we know that

The  formula to calculate the depreciated value  is equal to  

V=P(1-r)^{x}  

where  

V is the depreciated value  

P is the original value  

r is the rate of depreciation  in decimal  

x  is Number of Time Periods  

in this problem we have  

P=\$15,500\\r=7.5\%=0.075\\x=6\ years

substitute

V=\$15,500(1-0.075)^{6}=\$9,709.17  

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3 years ago
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nikitadnepr [17]
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3 years ago
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When 4 times the number x is added to 12, the result is 8. What number results when 2 times x is added to 7 ?
Bumek [7]
<h2><u>Given </u><u>:</u><u>-</u></h2>

  • <u>\bf4 \: times \: a \: number \: x \: is \: added \: to \: 12 \\ \bf the \: result \: is \: 8</u> ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎
  • \bf⟹ \: 4x + 12 = 8

\large\bf{\underline{We\:have\:to\:find:-}}

  • \bf\:The \: number \: results \: when \: 2 \: times \: x  \\ \bf is \: added  \: to \: 7
  • \bf ⟹\: 2x + 7 =  ?

\large\bf{\underline{To \:find\:the\:value\:of\:x}}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎⟹4x + 12 = 8

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎⟹4x = 8 - 12

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎⟹4x =  - 4

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎⟹x =  \frac{ - 4}{4}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎⟹x =  - 1

\large\bf{\underline{Putting\:the\:value\:of\:x\:in\:2x+7}}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎=2x + 7

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎=2( - 1) + 7

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎= - 2 + 7

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎= 5

__________________________________________

\large\bf{\underline{Hence}}

\huge{2x + 7}

\huge{=5}

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Answer:

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Step-by-step explanation:

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Hope i helped :)

6 0
3 years ago
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