Which statement best describes the function f (x)=2x^2-3x+1

Which of the following is a polynomial with roots: − square root of 5 , square root of 5 , and 3? (6 points)

Karo-lina-s [1.5K]

Let's check the first polynomial , that is

$P(x)= x^3 -3x^2 -5x+15$

We need to factor it first and for that we have to do grouping and factoring .

$P(x) = x^2(x-3)-5(x-3) \\ P(x) = (x^2 -5)(x-3)$

TO find the roots, we need to set P(x) to 0, that is

$(x^2 -5)(x-3)=0 \\ x^2 - 5= 0 , x-3 =0 \\ x^2 = 5 , x=3 \\ x = \pm \sqrt{5} , x=3$

SO the correct option is A .

5 0

4 years ago

Four thousands and 7 hundreds equals what?

Ainat [17]

4.700 decimal form or maybe 4700 without decimal

8 0

4 years ago

These ordered pairs, {(2,4) (3,6) (4,8) (5,10)}, are a function. True False

ki77a [65]

Answer:

True

Step-by-step explanation:

In order for a relation (a set of ordered pairs) to be considered a function, every value in the domain (the set of all the first numbers in the pair) is associated with one value in the range (the set of all second numbers in the pair). This is easiest to see visually. Our domain is the set {2, 3, 4, 5} and our range is the set {4, 6, 8, 10}, and we can visualize the ordered pair (2, 4) as an "arrow" starting a 2 in the domain and ending at 4 in the range. When seen this way, a relation is a function if every value in the domain only has one arrow coming out of it. We can see from the attached picture that the ordered pairs in the problem are a function, so this statement is true.

8 0

4 years ago

Write the equation of the ellipse 4x^2+9y^2+72x+108y+612=0 in standard form.

natka813 [3]

Answer:

(x+9)^2 + (y+6)^2

9 4 =1

Step-by-step explanation:

I believe this is correct, if not feel free to let me know and I will fix it. I'm sorry in advance if it is incorrect.

5 0

3 years ago

Read 2 more answers

A large fish tank at an aquarium needs to be emptied so that it can be cleaned. When its

VikaD [51]

Answer:

The draining time when only the big drain is opened is 2.303 hours.

The draining time when only the small drain is opened is 5.303 hours.

Step-by-step explanation:

From Physics, we know that volume flow rate ( $\dot V$ ), measured in liters per hour, is directly proportional to draining time ( $t$ ), measured in hours. That is:

$\dot V \propto \frac{1}{t}$

$\dot V = \frac{k}{t}$ (Eq. 1)

Where $k$ is the proportionality constant, measured in liters.

From statement, we have the following three expressions:

(i) Large and small drains are opened

$\dot V_{s}+\dot V_{l} = \frac{k}{2}$ (Eq. 2)

$\frac{\dot V_{s}+\dot V_{l}}{k} = \frac{1}{2}$

(ii) Only the small drain is opened

$\dot V_{s} = \frac{k}{t_{l}+3}$ (Eq. 3)

$\frac{\dot V_{s}}{k} = \frac{1}{t_{l}+3}$

(iii) Only the big drain is opened

$\dot V_{l} = \frac{k}{t_{l}}$ (Eq. 4)

$\frac{\dot V_{l}}{k} = \frac{1}{t_{l}}$

By applying (Eqs. 3, 4) in (Eq. 2) and making some algebraic handling, we find that:

$\frac{1}{t_{l}+3}+\frac{1}{t_{l}} = \frac{1}{2}$

$\frac{t_{l}+t_{l}+3}{t_{l}\cdot (t_{l}+3)} = \frac{1}{2}$

$2\cdot t_{l}+3 = t_{l}^{2}+3\cdot t_{l}$

$t_{l}^{2}-t_{l}-3 = 0$ (Eq. 5)

Whose roots are determined by the Quadratic Formula:

$t_{l,1}\approx 2.303\,h$ and $t_{l,2} \approx -1.302\,h$

Only the first roots offers a solution that is physically reasonable. Hence, the draining time when only the big drain is opened is 2.303 hours. And the time needed for the small drain is calculated by the following formula:

$t_{s} = 2.303\,h+3\,h$

$t_{s} = 5.303\,h$

The draining time when only the small drain is opened is 5.303 hours.

7 0

3 years ago