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2 years ago

Which shows one way to determine the factors of 12x3 – 2x2 + 18x – 3 by grouping?

Mathematics

2 answers:

Debora [2.8K]2 years ago

6 0

Option A

$2x^2(6x-1) + 3(6x-1)$ is one way to determine the factors of $12x^3-2x^2+18x-3$ by grouping

Solution:

Factoring by grouping means that you will group terms with common factors before factoring

Given expression is:

$12x^3-2x^2+18x-3$

Group the first two terms together and then the last two terms together.

$(12x^3-2x^2)+(18x-3)$

We can see that $2x^2$ is common in first two terms

And 3 is common in last two terms

Factor them out

$(12x^3-2x^2)+(18x-3) = 2x^2(6x-1) + 3(6x-1)$

$2x^2(6x-1) + 3(6x-1)$

Thus option A is correct

Scorpion4ik [409]2 years ago

5 0

Answer:

is one way to determine the factors of by grouping

Solution:

Factoring by grouping means that you will group terms with common factors before factoring

Given expression is:

Group the first two terms together and then the last two terms together.

We can see that is common in first two terms

And 3 is common in last two terms

Factor them out

Step-by-step explanation:

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That means we need to add 10 miles to the given distance.

So new distance = 423.4 + 10 = 433.4 miles

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2 years ago

Frank started out in his car travelling 45 mph. When Frank was 1 3 miles away, Daniel started out from the same point at 50 mph

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Answer:

It will take 2.6 hours by Daniel to catch up with Frank.

Step-by-step explanation:

Let Daniel will catch up with Frank after t hours.

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So, the distance traveled by Frank in (t + 0.228) hours with 45 mph speed will be equal to the distance traveled by Daniel in t hours with 50 mph speed.

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Therefore, it will take 2.6 hours by Daniel to catch up with Frank. (Answer)

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2 years ago

Tonyas dog walking service charges a flat rate of $20 per month, plus $3 per mile that each dog is walked. beth does not charge

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Answer:

Step-by-step explanation:

given that tonya charges 20$ monthly fee and 3$ per mile of her dog-walking service.

and beth does not charge any monthly fee but charges 5$ per mile of the dog walked in.

let x be the number of miles dog has walked in a month.

the amount tonya will charge on x miles = fixed monthly fee + number of miles * charge per mile = 20+3x

and the amount beth will charge on x miles = 0+ 5*x = 5x.

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2 years ago

A person is standing 50 ft from a statue. The person looks up at an angle of elevation of 16o when staring at the top of the sta

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Answer:

The height of the statue is 21.4 feet

Step-by-step explanation:

We are given

A person is standing 50 ft from a statue

The person looks up at an angle of elevation of 16 degree when staring at the top of the statue

hen the person looks down at an angle of depression of 8 degree when staring at the base of the statue

Firstly, we will draw diagram

In triangle ABF:

FC=50

we can use trig formula

$tan(16)=\frac{y}{50}$

$y=50tan(16)$

$y=14.33727ft$

now, we can find x

In triangle DEF:

we can use trig formula

$tan(8)=\frac{x}{50}$

$x=50tan(8)$

$x=7.0270ft$

we can see that

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so, the height of statue is

$=14.33727+7.0270$

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2 years ago

Bill buys and sells laptops. Last month Bill bought 50 laptops. He paid £400 for each laptop. He sold 40 of these laptops at a p

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Answer:

As Bill's sales is £25400, which is greater than £25000, he achieved his target.

Step-by-step explanation:

Cost of each laptop = £400

lets calculate for 40 laptops first

Given, he sold 40 of these at 30% profit

30% of cost price = 30% of £400 = 30/100 * 400 = 120

Therefore, selling price of these laptops = £400 + £120 = £520

Total sales generated from selling 40 of these laptop = 40*£520

= £520 =£20,800

lets calculate for 10 laptops now

Given, he sold 10 of these at 15% profit

15% of cost price = 15% of £400 = 15/100 * 400 = 60

Therefore, selling price of these laptops = £400 + £60 = £460

Total sales generated from selling 10 of these laptop = 10*£460

= £4600

Total sales generated from selling all the 50 laptop =

Total sales generated from selling 40 of these laptop + Total, sales generated from selling 10 of these laptop = £20,800 + £4600 = £25,400

Target for Bill = £25000

As his sales is £25400, which is greater than £25000, he achieved his target.

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2 years ago