Which polynomial represents the sum below? (3x2 + 3) + (3x2 + x + 4)

Solve the given inequality :

tigry1 [53]

Answer:

x < -5 or x = 1 or 2 < x < 3 or x > 3

Step-by-step explanation:

Given rational inequality:

$\dfrac{(x-1)^2(x-2)^3}{(x^2-5x+6)^2(x+5)}\geq 0$

$\textsf{Factor }(x^2-5x+6):$

$\implies x^2-2x-3x+6$

$\implies x(x-2)-3(x-2)$

$\implies (x-3)(x-2)$

Therefore:

$\dfrac{(x-1)^2(x-2)^3}{(x-3)^2(x-2)^2(x+5)}\geq 0$

Find the roots by solving f(x) = 0 (set the numerator to zero):

$\implies (x-1)^2(x-2)^3=0$

$\implies (x-1)^2=0\implies x=1$

$\implies (x-2)^3=0 \implies x=2$

Find the restrictions by solving f(x) = undefined (set the denominator to zero):

$\implies (x-3)^2(x-2)^2(x+5)=0$

$\implies (x-3)^2=0 \implies x=3$

$\implies (x-2)^2=0 \implies x=2$

$\implies (x+5)=0 \implies x=-5$

Create a sign chart, using closed dots for the roots and open dots for the restrictions (see attached).

Choose a test value for each region, including one to the left of all the critical values and one to the right of all the critical values.

Test values: -6, 0, 1.5, 2.5, 4

For each test value, determine if the function is positive or negative:

$f(-6)=\dfrac{(-6-1)^2(-6-2)^3}{(-6-3)^2(-6-2)^2(-6+5)}=\dfrac{(+)(-)}{(+)(+)(-)}=+$

$f(0)=\dfrac{(0-1)^2(0-2)^3}{(0-3)^2(0-2)^2(0+5)}=\dfrac{(+)(-)}{(+)(+)(+)}=-$

$f(1.5)=\dfrac{(1.5-1)^2(1.5-2)^3}{(1.5-3)^2(1.5-2)^2(1.5+5)}=\dfrac{(+)(-)}{(+)(+)(+)}=-$

$f(2.5)=\dfrac{(2.5-1)^2(2.5-2)^3}{(2.5-3)^2(2.5-2)^2(2.5+5)}=\dfrac{(+)(+)}{(+)(+)(+)}=+$

$f(4)=\dfrac{(4-1)^2(4-2)^3}{(4-3)^2(4-2)^2(4+5)}=\dfrac{(+)(+)}{(+)(+)(+)}=+$

Record the results on the sign chart for each region (see attached).

As we need to find the values for which f(x) ≥ 0, shade the appropriate regions (zero or positive) on the sign chart (see attached).

Therefore, the solution set is:

x < -5 or x = 1 or 2 < x < 3 or x > 3

As interval notation:

$(- \infty,-5) \cup x=1 \cup (2,3) \cup(3,\infty)$

4 0

2 years ago

-13 is 4 less than. A number n

Kobotan [32]

Answer:

no

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

A young female lion was brought into the wildlife zoo weighing 53.5 pounds. After two years, she weighed 5.5 times

Lera25 [3.4K]

Answer:

324

Step-by-step explanation:

This is because when rounding you multiply 55 by 6 that is equal to 330 which is near 324. However if you want the answer spot on it would be 294

3 0

3 years ago

Read 2 more answers

Given the directrix of y = -1 and focus of (0, 3), which is the equation of the parabola?

guajiro [1.7K]

Answer:

$y=\dfrac{1}{8}x^2+1$

Step-by-step explanation:

Since the vertex is right between the vertex and the directrix, the y value of the vertex must be (3+(-1))/2=1. The x coordinate will just be the same as that of the focus, or in this case 0. This means that the vertex will be at (0,1). Since the graph opens toward the focus, it will be opening up, and since its vertex is at (0,1), it will have an equation of:

$y=\dfrac{1}{8}x^2+1$

Hope this helps!

3 0

3 years ago

If the ratio football players two basketball players at your school is 7:5 then how many basketball players are there if they ar

Levart [38]

Answer:

I think that there are 15 basketball players.

Step-by-step explanation:

If there is a ratio of football to basketball players of 7:5, and there are 21 football players. i just divide 21 by 7 and get 3. so if we multiply the 5 in the ratio by 3 we get 15. so I think the answer is 15. if not then ignore my answer. if so the brainliest please?

8 0

3 years ago