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alexandr1967 [171]
3 years ago
10

Find an equation for a quartic function containing the following points: (2, 60), (-3, 0), (-1, 0), (4, 0), (1, 0).

Mathematics
2 answers:
olga nikolaevna [1]3 years ago
5 0

Answer:

a

Step-by-step explanation:

tia_tia [17]3 years ago
3 0

Answer:

f(x) = -2(x + 3)(x + 1)(x - 4)(x - 1)  or

f(x) = -2x^4 + 2x^3 + 26x^2 - 2x  -24.

Step-by-step explanation:

The zeros of the function are  at (-3, 0), (-1, 0), (4, 0), (1, 0) so in factor form the function is:

a(x + 3)(x + 1)(x - 4)(x - 1)      where a is some constant.

We find a by substituting the point (2, 60)

60 = a(2+3)(2+1)(2-4)(2-1)

-30a = 60

a = -2.

So the function is -2(x + 3)(x + 1)(x - 4)(x - 1) .

You might be interested in
Identify the graph of 9X^2+4xy+5y^2-40=0 and find theta to the nearest degree.
lubasha [3.4K]

Answer:

The answer is ellipse; 23° to the nearest degree ⇒ answer (d)

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy²  + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

- 9x² + 4xy + 5y² - 40 = 0

∵ A = 9 , B = 4 , 5 = 5

∴ B² - 4 AC = (4)² - 4(9)(5) = -164 < 0

∴ B² - 4AC < 0

∴ If a conic exists, it will be either a circle or an ellipse.

* To find the type of the graph lets check;

- If A and C are nonzero, have the same sign, and are not

 equal to each other, then the graph is an ellipse.

- If A and C are equal and nonzero and have the same

 sign, then the graph is a circle.

∵ A and C have same signs and are not equal

∴ The graph is an ellipse

* If we have term xy ⇒ B ≠ 0

∴ The graph is rotate by angle Ф

* To find the angle of rotation use the rule:

- cot(2Ф) = (A - C)/B

∵ A = 9 , B = 4 , C = 5

∴ cot(2Ф) = (9 - 5)/4 = 4/4 = 1

∴ tan(2Ф) = 1

∴ 2Ф = 45°

∴ Ф = 22.5° ≅ 23° to the nearest degree

* The answer is ellipse; with angle of rotation = 23°

4 0
3 years ago
What is the value of x? Show your work in arriving at your answer.
Trava [24]

Answer: x = 18

Step-by-step explanation:

First, since both angles shown are equal to each other, you can immediately set your equation.

5x + 5 = 95

Next, move 5 to the opposite side of the equation to isolate your x value (5x). This step is simply subtracting the hanging 5.

5x + 5 (-5) = 95 (-5)

5x = 90

Finally, you need to divide both sides of the equation by 5 (the 5 next to the x) to *fully* isolate the x value.

5x / 5 = 90 / 5

x = 18

final answer: x = 18

Hopefully this helps with the remainder of your lesson! :)

5 0
2 years ago
Which of the following expressions is equal to 5^6/5^2
Natali5045456 [20]

Answer:

\dfrac{5^6}{5^2} = 5{\cdot}5{\cdot}5{\cdot}5

Step-by-step explanation:

The given expression is :

\dfrac{5^6}{5^2}

We need to find this expression is equal to what.

\dfrac{5^6}{5^2}=\dfrac{5^4\times 5^2}{5^2}\\\\=5^4\\\\=5\times 5\times 5\times 5\\\\\text{or}\\\\=5{\cdot}5{\cdot}5{\cdot}5

Hence, \dfrac{5^6}{5^2} is equal to 5{\cdot}5{\cdot}5{\cdot}5. Hence, the correct option is (c).

5 0
2 years ago
Liam has 3 boxes of baseball cards with 50 cards in each box. He also has 5 boxes with 40 basketball cards in each box. If Liam
horsena [70]

Answer:

400 (Sorry if its wrong.)

Step-by-step explanation:

50×3=150

5×40= 200

150+200= 350

350+50=400

3 0
2 years ago
Read 2 more answers
22. The area of a triangle can be represented by the expression 14x^5 + 63x^2. If the base is 7x^2, write
kkurt [141]

Answer:

h = 4x ^ 3 + 18

Step-by-step explanation:

The first thing you should know for this case is that the area of a triangle is given by:

A = (1/2) * (b) * (h)

Where,

b: base.

h: height.

Clearing the height we have:

h = ((2) * (A)) / (b)

Substituting the values

h = ((2) * (14x ^ 5 + 63x ^ 2)) / (7x ^ 2)

Simplifying the expression:

h = ((2) * (2x ^ 3 + 9))

h = 4x ^ 3 + 18

answer

an expression to represent its height is

h = 4x ^ 3 + 18

4 0
3 years ago
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