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What are the steps of factoring (5m-2)^2-(3m-4)^2 ?

Svetlanka [38]

We use the formula a^2 - b^2 = ( a - b )( a + b );
We have a = 5m - 2 and b = 3m - 4;
<span>(5m-2)^2-(3m-4)^2 = (5m - 2 -3m + 4) x (5m-2 + 3m - 4) = (2m + 2)(8m - 6) = 2(m +1) x 2(4m - 3) = 4(m+1)(4m-3);

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6 0

3 years ago

If the price of a business math text rose to $120 and this was 10% more than the original price what was the original selling pr

kolezko [41]

Step-by-step explanation:

120*10% =12

10% percent *120

= (10/100)*120

= (10*120)/100

= 1200/100 = 12

120 - 12 = 108.00 is original price of math text

5 0

2 years ago

The central angle of a minor arc is an acute angle.

Nostrana [21]

<span>The central angle in a minor arc is acute. In a minor arc, the angle must be less than 180˚. However, it doesn't have to be less than 90˚. So the central angle is sometimes acute.

hope this helps u leave a like if it does</span>

3 0

3 years ago

(4x-9)(2x^2+2x+1) (4x−9)(2x 2 +2x+1)

tia_tia [17]

Answer:

$(4x-9)^2*(2x^2+2x+1)^2$

Step-by-step explanation:

(((4x-9)•(((2•(x2))+2x)+1))•(4x-9))•((2x2+2x)+1)

] (((4x-9)•((2x2+2x)+1))•(4x-9))•(2x2+2x+1)

Trying to factor by splitting the middle term

Factoring 2x2+2x+1

The first term is, 2x2 its coefficient is 2 .

The middle term is, +2x its coefficient is 2 .

The last term, "the constant", is +1

Step-1 : Multiply the coefficient of the first term by the constant 2 • 1 = 2

Step-2 : Find two factors of 2 whose sum equals the coefficient of the middle term, which is 2 .

-2 + -1 = -3

-1 + -2 = -3

1 + 2 = 3

2 + 1 = 3

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

((4x-9)•(2x2+2x+1)•(4x-9))•(2x2+2x+1)

Multiplying Exponential Expressions:

4.1 Multiply (4x-9) by (4x-9)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (4x-9) and the exponents are :

1 , as (4x-9) is the same number as (4x-9)1

and 1 , as (4x-9) is the same number as (4x-9)1

The product is therefore, (4x-9)(1+1) = (4x-9)2

Trying to factor by splitting the middle term

5.1 Factoring 2x2+2x+1

The first term is, 2x2 its coefficient is 2 .

The middle term is, +2x its coefficient is 2 .

The last term, "the constant", is +1

Step-1 : Multiply the coefficient of the first term by the constant 2 • 1 = 2

Step-2 : Find two factors of 2 whose sum equals the coefficient of the middle term, which is 2 .

-2 + -1 = -3

-1 + -2 = -3

1 + 2 = 3

2 + 1 = 3

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Multiplying Exponential Expressions:

5.2 Multiply (2x2+2x+1) by (2x2+2x+1)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (2x2+2x+1) and the exponents are :

1 , as (2x2+2x+1) is the same number as (2x2+2x+1)1

and 1 , as (2x2+2x+1) is the same number as (2x2+2x+1)1

The product is therefore, (2x2+2x+1)(1+1) = (2x2+2x+1)2

Final result :

(4x - 9)2 • (2x2 + 2x + 1)2

6 0

2 years ago

A truck company charged $40 for one day truck rental +0.85 per mile formulate a linear equation to model the cost c(d) Of one da

liubo4ka [24]

For this case we have to:

d: Let the variable representing the number of miles traveled per day

Then, the cost will be given by the following equation:

$C (d) = 0.85d + 40$

If we have the cost $C (d) = 91$ , then the number of miles traveled is:

$91 = 0.85d + 40\\91-40 = 0.85d\\51 = 0.85d\\d = \frac {51} {0.85}\\d = 60$

Thus, the number of miles traveled is 60.

Answer:

$C (d) = 0.85d + 40$

For a $C (d) = 91$ , the number of miles traveled is 60

3 0

3 years ago

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