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1 year ago

Pleaseee help, question what is the sum of 4x^2 + 2x - 5 and 7x^2 - 5x + 2

Mathematics

2 answers:

Nataliya [291]1 year ago

6 0

Simplification of polynomials.

Polynomials <em>are</em> mathematical expressions made up of many terms.<em>To</em> simplify a polynomial <em>the most, you must collect all</em><em> </em>like terms <em>and rearrange them from highest to lowest power.</em>

<h3>4x² + 2x -5 + 7x² - 5x+2</h3><h3>4x² + 2x -3 + 7x² - 5x+2</h3><h3>11x² + 2x - 3 - 5x</h3><h3>11x² - 3x - 3 ====> Option "A"</h3>

AlladinOne [14]1 year ago

3 0

Answer:

Add the expressions.

11x2−3x−3

Step-by-step explanation:

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A Norman window has the shape of a rectangle surmounted by a semicircle. Suppose the outer perimeter of such a window must

Feliz [49]

The base length that will maximize the area for such a window is 168.03 cm. The exact largest value of x when this occurs is 233.39 cm

Suppose we make an assumption that:

(x) should be the width of the rectangle base;
(h) should be the height of the rectangle

Also, provided that the diameter of the semi-circle appears to be the base of the rectangle, then;

the radius $\mathbf{r = \dfrac{x}{2}}$

and, the perimeter of the window can now be expressed as:

$\mathbf{x + 2h + \pi r = x + 2h + \dfrac{\pi x }{2}}$

$\mathbf{= \Big ( 1 + \dfrac{\pi}{2}\Big) x + 2h}$

Given that the perimeter = 600 cm

∴

$\mathbf{ \Big ( 1 + \dfrac{\pi}{2}\Big) x + 2h= 600}$

$\mathbf{ h = 300 - \Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) x}$

Since h > 0, then:

$\mathbf{ h = 300 - \Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) x>0}$

By rearrangement and using the inverse rule:

$\mathbf{ x< \dfrac{ 300}{\Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) } }$

$\mathbf{ x= \dfrac{ 1200}{\Big( 2 +\pi \Big) } }$

$\mathbf{ x= 233.39 \ cm }$

Thus, the largest length x = 233.39 cm

However, the area of the window is given as:

$\mathbf{A(x) = xh + \dfrac{1}{2} \pi r^2}$

$\mathbf{A = x \Big [ 300 - \Big ( \dfrac{1}{2}+\dfrac{1}{4} \Big) x \Big ] +\dfrac{1}{2}\pi \Big(\dfrac{x}{2} \Big )^2}$

$\mathbf{A (x) = 300x - \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) x^2 \ cm^2}$

Now, at maximum, when the area A = 0. Taking the differentiation, we have:

$\mathbf{\dfrac{d}{dx} 300x - \dfrac{d}{dx} \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) x^2 \ =0}$

$\mathbf{ 300 - 2x \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) \ =0}$

Making x the subject of the formula, we have:

$\mathbf{x = \dfrac{1200}{4 +\pi}}$

x = 168.03 cm

Taking the second derivative:

$\mathbf{\dfrac{d}{dx} \Big [300 -2x \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) \Big]}$

$\mathbf{= -2 \Big( \dfrac{1}{2}+\dfrac{\pi}{8}\Big )$

Therefore, we can conclude that the maximum area that exists for such a window is 168.03 cm

Learn more about derivative here:

brainly.com/question/9964510?referrer=searchResults

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3 years ago

Hellen has a bag with 14 red block, 9 blue blocks, 10 purple blocks, 25 green blocks, 12

stiks02 [169]

Answer:

0.10

Step-by-step explanation:

14 red block

9 blue blocks

10 purple blocks

25 green blocks

12 yellow blocks

18 orange blocks

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88 total number of blocks

9 blue blocks

p(blue) = 9/88 = 0.10

4 0

11 months ago

What is the mean of the values below{48,59,70,27,61}

hram777 [196]

Answer:

Step-by-step explanation:

Mean=Average

To find it, add al the numbers and divide by how many there are.

48+59+70+27+61=265

265/5=53

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3 years ago

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25 POINTS GUYS PLEASE HELP ME WITH THIS QUESTION<br><br>WHAT IS 1+1

kirza4 [7]

Answer:

Step-by-step explanation:

1 + 1 = 2

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3 years ago

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What is the coefficient of the term of degree 8 in the polynomial below?

Nesterboy [21]

The correct answer is: [D]: "5 (five)" .
______________________________________________________
<u>Note</u>: The term of "degree 8" is the term with a variable with
an exponent of "8" ; which in this case is " + 5x⁸ ".

The "coefficient" is "5" (five).
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3 years ago