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GrogVix [38]
2 years ago
5

class="latex-formula">

Show Work!

Solve by factoring, please!
Mathematics
1 answer:
melamori03 [73]2 years ago
5 0

Answer:

x=-\frac{3}{2},-1

Step-by-step explanation:

2x^2+5x+3=0

Split the second term (5x) into two terms. Multiply the coefficient of the first term (2) by the constant term (3):

2*3=6

Find which two numbers add up to 5 and multiply into 6:

3+2=5\\3*2=6\\3,2

Split 5x as the sum of 3x and 2x:

2x^2+3x+2x+3

Now factor out a common term for the first 2 terms:

2x^2+3x\\x(2x+3)

And do the same for the last 2 terms:

2x+3\\1(2x+3)

Re-insert:

x(2x+3)+1(2x+3)=0

Factor out the common term 2x+3 and insert the values in front of the parentheses (x and 1):

(2x+3)(x+1)=0

Separate the parentheses and equal them to 0. Solve for x:

2x+3=0\\2x+3-3=0-3\\2x=-3\\\\\frac{2x}{2}=\frac{-3}{2}\\\\  x=-\frac{3}{2}

and

x+1=0\\x+1-1=0-1\\x=-1

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\dbinom{20}2=\dfrac{20!}{2!(20-2)!}=190

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We want the word to start with T, and we'll allow any arrangement of the other 4 letters, so that the total number of words is

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Keep in mind that this means words like TRIES and TIRES are treated as different.

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2 years ago
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Step-by-step explanation:

Since we have given that

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Third year is given by

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it becomes geometric progression, as there is exponential decline.

so,

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Sum of terms will be given by

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We'll put this value in this formula,

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Step-by-step explanation:

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2 years ago
A car dealership pays a wholesome price of $12,000 to purchase a vehicle. The car dealership wants to make a 32% profit. The car
cestrela7 [59]

Answer:

$102.96

Step-by-step explanation:

Lets take this one part at a time.

the dealership pays 12000 for the car, so they start at -12000 for how much money they have.

The dealership wants to make a 32% profit.  This means they want to make back the 12000 plus 32% of that.  what is 32% of 12000?  just multiply 12000 bty .32  In the end it works out that the price they sell it for is 15840

I do want to mention that there is a chance the 32% might also be accounting the bonus.  So in other words the dealership spent 12000 for the car then however much in paying the bonus, and they want to make a 32% profit on both of these combined.  I do not think that is what it is asking for, but I wanted to mention it.

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Now the question says the salesperson offers a 10 percent discount.  This changes the sales price (by 10%) and the bonus they earn.  let's calculate both.

First 10% discount of the sales price is .9*15840 = 14,256

Then 6.5% of that is .065*14256 = 926.64 So this is the new bonus.

The question wants the difference of the two bonuses, and difference is subtraction.  so 1029.60 - 926.64 = 102.96 So if the salesperson offers a 10% discount they lose $102.96

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