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melamori03 [73]
3 years ago
10

Factor the expression 6x^2 + 5x + 1

Mathematics
2 answers:
Ivahew [28]3 years ago
8 0

Answer:

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

Step-by-step explanation:

Given

6x² + 5x + 1

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 6 × 1 = 6 and sum = + 5

The factors are + 3 and + 2

Use these factors to split the x0 term

6x² + 3x + 2x + 1 ( factor the first/second and third/fourth terms )

= 3x(2x + 1) + 1 (2x + 1) ← factor out (2x + 1) from each term

= (2x + 1)(3x + 1) ← in factored form

Brilliant_brown [7]3 years ago
4 0

Answer:

The factors are (3x+1)(2x+1)

Step-by-step explanation:

The expression is:

6x^2 + 5x + 1

We have to break the middle term to find its factors. For this first we have to multiply the coefficient of 1st terms with the constant term:

6*1 = 6

Now we have to find any two numbers whose product is 6 and whose sum is the middle term:

3*2=6

3+2=5

Now break the middle term by these two numbers.

6x^2 + 5x + 1

6x^2+3x+2x+1

Group the first two terms and last two terms:

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

Now take out common factor from each term:

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

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

Therefore the factors are (3x+1)(2x+1)....

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4 0
3 years ago
From 1990 to 2000, the population of Florida increased by 2.13% per year. The population (in millions) in the year 1990 was 16 E
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Answer:

19 million

Step-by-step explanation:

So generally whenever we express a exponential function, it's in the form: y=a(b)^x

where a=initial value aka when x=0

in this case, b can be expressed as: 1+r, where r is the growth rate, which in this case is 2.13%, and expressing that as a decimal (divide by 100), r=0.0213, thus b=1.0213

This gives us the following equation: y=16(1.0213)^x

To kind of give you a intuitive reason as to why this makes sense, think of that 1.0213 wrapping around the previous value.

So when x=0, it's actually just 16, since any number (besides 0) to the power of 0, equals 1.

When x=1, we get: 1.0213(16), which can be expressed as a 2.13% increase from year 0

When x=2, we get: 1.0213(1.0213(16)), which can be expressed as a 2.13% increase from year 1

when x=3, we get: 1.0213(1.0213(1.0213(16))), which can be expressed as a 2.13% increase from year 2.

In other words, each year we're getting another 1.0213 to multiply by (very definition of an exponent).

So to calculate the population in 1997, we put in x=7, since it's 7 years after 1990

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2 years ago
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Answer: There were 40 euros in the drawer at the beginning.

Step-by-step explanation:

When we subtract 6 from 16, we get 10 more ice-creams were sold.

Similarly, we subtract 70 from 120, we get 50 euros was the total selling price of 10 ice-creams.

i.e. Selling price of 1 ice-cream = (50)÷10 =5 euros

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Money in the drawer at the beginning = 70-30 = 40 euros

Hence, there were 40 euros in the drawer at the beginning.

7 0
3 years ago
What is the equation to this?
Fiesta28 [93]
THE EQUATION TO THIS PROBLEM IS y=2x+12
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3 years ago
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