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Ksenya-84 [330]
3 years ago
15

A rectangle has a length of x and a width of 5x^3+4-x^2. What is the polynomial that models the perimeter of the rectangle

Mathematics
1 answer:
sveticcg [70]3 years ago
8 0

Answer:

L= x

And the width for this case is:

W= 5x^3 +4 -x^2

And we know that the perimeter is given by:

P= 2L +2W

And replacing we got:

P(x) = 2x +2(5x^3 +4 -x^2)= 2x +10x^3 +8 -2x^2

And symplifying we got:

P(x)= 10x^3 -2x^2 +2x+8

Step-by-step explanation:

For this problem we know that the lenght of the rectangle is given by:

L= x

And the width for this case is:

W= 5x^3 +4 -x^2

And we know that the perimeter is given by:

P= 2L +2W

And replacing we got:

P(x) = 2x +2(5x^3 +4 -x^2)= 2x +10x^3 +8 -2x^2

And symplifying we got:

P(x)= 10x^3 -2x^2 +2x+8

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Answer: 95

Step-by-step explanation:

That’s the same as 0.95 of 100. That’s because 0.95 represents 0.95 and 100 represents 100, the of is the same as x. You can switch the two numbers and you can still get the same answer. So, 0.95 of 100 is 95.

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Is 31/50 greater than 1/2
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Solving Rational Functions Hello I'm posting again because I really need help on this any help is appreciated!!​
Greeley [361]

Answer:

x = √17 and x = -√17

Step-by-step explanation:

We have the equation:

\frac{3}{x + 4}  - \frac{1}{x + 3}  = \frac{x + 9}{(x^2 + 7x + 12)}

To solve this we need to remove the denominators.

Then we can first multiply both sides by (x + 4) to get:

\frac{3*(x + 4)}{x + 4}  - \frac{(x + 4)}{x + 3}  = \frac{(x + 9)*(x + 4)}{(x^2 + 7x + 12)}

3  - \frac{(x + 4)}{x + 3}  = \frac{(x + 9)*(x + 4)}{(x^2 + 7x + 12)}

Now we can multiply both sides by (x + 3)

3*(x + 3)  - \frac{(x + 4)*(x+3)}{x + 3}  = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}

3*(x + 3)  - (x + 4)  = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}

(2*x + 5)  = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}

Now we can multiply both sides by (x^2 + 7*x + 12)

(2*x + 5)*(x^2 + 7x + 12)  = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}*(x^2 + 7x + 12)

(2*x + 5)*(x^2 + 7x + 12)  = (x + 9)*(x + 4)*(x+3)

Now we need to solve this:

we will get

2*x^3 + 19*x^2 + 59*x + 60 =  (x^2 + 13*x + 3)*(x + 3)

2*x^3 + 19*x^2 + 59*x + 60 =  x^3 + 16*x^2 + 42*x + 9

Then we get:

2*x^3 + 19*x^2 + 59*x + 60 - (  x^3 + 16*x^2 + 42*x + 9) = 0

x^3 + 3x^2 + 17*x + 51 = 0

So now we only need to solve this.

We can see that the constant is 51.

Then one root will be a factor of 51.

The factors of -51 are:

-3 and -17

Let's try -3

p( -3) = (-3)^3 + 3*(-3)^2 + +17*(-3) + 51 = 0

Then x = -3 is one solution of the equation.

But if we look at the original equation, x = -3 will lead to a zero in one denominator, then this solution can be ignored.

This means that we can take a factor (x + 3) out, so we can rewrite our equation as:

x^3 + 3x^2 + 17*x + 51 = (x + 3)*(x^2 + 17) = 0

The other two solutions are when the other term is equal to zero.

Then the other two solutions are given by:

x = ±√17

And neither of these have problems in the denominators, so we can conclude that the solutions are:

x = √17 and x = -√17

6 0
2 years ago
1. COST Mr. Rivera wants to purchase a riding lawn
antiseptic1488 [7]

Answer:

p(x) = 0.85x

t(x) = 1.065x

(t o p)(x) = 0.9x

$2700

Step-by-step explanation:

If the marked price is $x, then the function p(x) that gives the price of the riding lawn mower after 15% discount will be

p(x) = x(1 - \frac{15}{100}) = 0.85x

where x is the marked price.

Now, the function that gives the total cost with sales tax will be given by

t(x) = x(1 + \frac{6.5}{100}) = 1.065x

where x is the discounted price.

Therefore, the composite function that gives the total cost of the riding lawn mower on sale is given by

(t o p)(x) = 1.065(0.85x) = 0.9x ............ (1)

where x is the marked price.

If the marked price x = $3000, then Mr. Rivera has to pay for the riding lawn mower, from equation (1),

(t o p)(3000) = 0.9 × 3000 = 2700 dollars. (Answer)

8 0
3 years ago
IF XPOWER 3 =27,THEN X POWER 2=
kvv77 [185]

X²= 9

X POWER 3= 27

X³= 27

The number that can be multiplied three times to get 27 is 3

Therefore X POWER 2 (X²) can be calculated as follows

= 3²

= 3 × 3

= 9

Hence XPOWER 2 is 9

Read more here

brainly.com/question/27510248?referrer=searchResults

#SPJ1

8 0
1 year ago
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