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3 years ago

3x + 2x – x + 2x² + 4

Mathematics

1 answer:

Ivenika [448]3 years ago

3 0

Answer:

Step-by-step explanation:

Combine like terms, in this case there is only x

$3x+2x-x+2x^2+4\\4x+2x^2+4\\2x^2+4x+4\\2(x^2+2x+2)$

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Y^2 - 12y + 27 / y^2 - 6y - 27 <br> simply the rational equation.

Ulleksa [173]

The simplified rational expression is (y - 3)/(y + 3). Where y ≠ -3.

<h3>How to simplify a rational expression?</h3>

A rational expression is in the p/q form. Where p and q are polynomial functions.

To simplify this rational equation,

Factorize the polynomials in both numerator and denomiantor.
Cancel out common factors if any.
If the denominator and the numerator have no common factors except 1, then that is said to be the simplest form of the given rational expression.

<h3>Calculation:</h3>

The given rational equation is

$\frac{y^2 - 12y + 27 }{y^2 - 6y - 27}$

Factorizing the expression in the numerator:

y² - 12y + 27 = y² - 9y - 3y + 27

⇒ y(y - 9) - 3(y - 9)

⇒ (y - 3)(y - 9)

Factorizing the expression in the denominator:

y² - 6y - 27 = y² - 9y + 3y - 27

⇒ y(y - 9) + 3(y - 9)

⇒ (y + 3)(y - 9)

Since they have (y - 9) as the common factor, we can simplify,

$\frac{y^2 - 12y + 27 }{y^2 - 6y - 27}=\frac{(y-3)(y-9)}{(y+3)(y-9)}$

⇒ (y - 3)/(y + 3) where y ≠ -3(denomiantor)

Here there are no more common factors except 1; this is the simplest form of the given rational expression.

Learn more about simplifying rational expressions here:

brainly.com/question/1928496

#SPJ9

3 0

2 years ago

Find the maximum value or minimum value for the function f(x) = 0.15(x + 1)² - 3.

il63 [147K]

Answer:

The minimum value for $f(x) = 0.15(x + 1)^2 - 3$ is $-3$ .

Step-by-step explanation:

Given function is $f(x) = 0.15(x + 1)^2 - 3$

We need to find the maximum value or the minimum value for the function.

Now, differentiate $f(x) = 0.15(x + 1)^2 - 3$ w.r.t $x$ .

$f'(x) =\frac{d}{dx}(0.15(x + 1)^2 - 3)\\f'(x)=\frac{d}{dx}(0.15(x+1)^2-\frac{d}{dx}(3)\\$

$f'(x)=2\times 0.15(x+1)\frac{d}{dx}(x+1)-0\\f'(x)=0.3(x+1)(1)\\f'(x)=0.3(x+1)$

Now, we will equate $f'(x)=0$ to find critical point.

$0.3(x+1)=0\\x=-1$

Plug this critical point in to the function $f(x) = 0.15(x + 1)^2 - 3$ we get,

$f(-1) = 0.15(-1 + 1)^2 - 3\\f(-1)=-3$

Also, $f''(x)=0.3$ which is positive, We have minimum value.

So, the minimum value for $f(x) = 0.15(x + 1)^2 - 3$ is $-3$ .

7 0

4 years ago

Can someone help me?✨

GaryK [48]

Answer:

try right 3, up 4. if not, try right 4, up 3.

7 0

3 years ago

What is the equation of the line that is parallel to y-3x=2 and that passes through (6,1)?

Rudik [331]

Slope-intercept form: y = mx + b

(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)

For lines to be parallel, they need to have the same slope.

y - 3x = 2 Add 3x on both sides to change the equation to slope-intercept form

y - 3x + 3x = 2 + 3x

y = 3x + 2 The slope is 3, so the parallel line's slope is also 3.

Now that you know the slope, substitute/plug it into the equation

y = mx + b

y = 3x + b To find "b", plug in the point (6, 1) into the equation, then isolate/get the variable "b" by itself

1 = 3(6) + b

1 = 18 + b Subtract 18 on both sides to get "b" by itself

1 - 18 = 18 - 18 + b

-17 = b

y = 3x - 17 Your answer is the 1st option

8 0

3 years ago

Read 2 more answers

The volume of a cube is 343 cubic centimeters. how many centimeters long is each edge of the cube?

motikmotik

If the volume is 343 cubic cm the length of each side is 7cm.

3 0

3 years ago