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06.05.2020

Lmc of x^2-4 and x^2-5x-14

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09.07.2023, solved by verified expert

Rajat Thapa

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Mathematics, DAV Post Graduate College

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Mathematics

Lmc of x^2-4 and x^2-5x-14

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P Answered by Specialist

$\left(x+2\right)\cdot \left(x-2\right)\cdot \left(x-7\right)$

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$\mathrm{Find\:Least\:Common\:Multiplier\:of\:}x^2-4,\:x^2-5x-14$

$\mathrm{The\:LCM\:of\:}a,\:b\:\mathrm{is\:the\:smallest\:multiplier\:that\:is\:divisible\:by\:both\:}a\mathrm{\:and\:}b$

x^2-4

$\mathrm{Rewrite\:}4\mathrm{\:as\:}2^2$

=x^2-2^2

$x^2-2^2=\left(x+2\right)\left(x-2\right)$

$=\left(x+2\right)\left(x-2\right)$

x^2-5x-14

$=\left(x^2+2x\right)+\left(-7x-14\right)$

$=x\left(x+2\right)-7\left(x+2\right)$

$=\left(x+2\right)\left(x-7\right)$

$\mathrm{Multiply\:each\:factor\:with\:the\:highest\:power:}$

$\left(x+2\right)\cdot \left(x-2\right)\cdot \left(x-7\right)$

Mathematics

Neil places £2000 in a bank account that pays 1.5% simple interest per year. How much interest will he earn in 6 years?

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P Answered by PhD

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

Mathematics

You can buy jars of the same jam in 2 sizes large jar:440g for £1.54 small jar:340g for £1.26 By considering the price per gram, work out which jar is the best value for money. Working must be shown

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P Answered by PhD

Answer: 440 grams for 1.54 is the better value
Explanation:
Take the price and divide by the number of grams
1.54 / 440 =0.0035 per gram
1.26 / 340 =0.003705882 per gram
0.0035 per gram < 0.003705882 per gram

Mathematics

The last time Robert filled up his car with gas, he paid $24.50 for 7 gallons. This time, he needs 15 gallons. If the price is the same, how much will he pay?

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P Answered by PhD

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

Mathematics

Anthony received $150 for his birthday this year. This was $10 less than half the amount he received last year. How much money did Anthony receive for his birthday last year?

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P Answered by PhD

The answer is in the image

Mathematics

A new school randomly assigns a six-character student code to every prospective student. The school uses the characters 1, 2, 3, 4, 5, X, Y, and Z. If none of the student codes contain a repeated character, what is the total number of codes that can be randomly assigned?

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P Answered by PhD

The total nom of code that can be used is equal to 5+3 = 8

Mathematics

An online media service offers video and music downloads. Each download of a song costs $1. Each download of a video costs 5 times as much as the song download. You have a credit of $70. How many songs can you purchase after buying 12 videos?

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P Answered by PhD

The answer is in the image

Mathematics

Which number is the smallest? 4.4 ⋅ 10−5, 3.99 ⋅ 10−6, 2.6 ⋅ 102, 1.85 ⋅ 103

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P Answered by PhD

The answer is in the image

Mathematics

If a salesperson makes 6% commission, how much would they make from a $1,800 sale?

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P Answered by PhD

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

Mathematics

Thomas got a haircut from the barber. If the haircut costs $32 and he wants to leave a 18% tip, how much will he pay in total?

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P Answered by PhD

Here,

tip=18%of $32

tip=(18/100)*32

=0.18*32

=$5.76

Total payment=32+5.76=$37.76

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