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3 years ago

Consider the function f (x) = x2.

Mathematics

2 answers:

klio [65]3 years ago

5 0

Answer: The graph is shifted 2 units to the right.

Step-by-step explanation:

Given a function f(x), we know that one transformation rule is:

If $f(x-k)$ then the function is shifted "k" units to the right.

Therefore, for the function $f(x)=x^{2}$ , when we subtract 2 from the input, then we get the function g(x) in the form:

$g(x)=(x-2)^{2}$

We can conclude that subtracting 2 from the input of the function $f(x)=x^{2}$ , then the graph is shifted 2 units to the right.

Gre4nikov [31]3 years ago

3 0

The answer is right graph shifted 2 units to the right

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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

A.Find the total and area of the compound figures

goldfiish [28.3K]

Answer:

(a) The total area of compound figure is $284.52ft^2$ .

(b) The total perimeter of compound figure is 68.84 ft.

Step-by-step explanation:

Perimeter: The total distance covered by the figure.

Area: It is defined as the space occupied by the figure.

Given:

Length of rectangular figure = 19 ft

Breadth of rectangular figure = 12 ft

Radius of circle, r = $\frac{12ft}{2} = 6 ft$

Part (a):

Now calculating the total area of the compound figure.

$\text{Total area}=\text{Area of rectangular figure}+\frac{1}{2}\times \text{Area of circle}\\\\\text{Total area}=\text{Length}\times \text{Breadth}+\frac{1}{2}\times \pi r^2$

Now putting all the given values in this formula, we get:

$\text{Total area}=(19ft\times 12ft)+\frac{1}{2}\times 3.14\times (6ft)^2\\\\\text{Total area}=284.52ft^2$

Part (b):

Now calculating the total perimeter of the compound figure.

$\text{Total perimeter}=2\times \text{Length}+Breadth+(\frac{1}{2}\times \text{Circumference})\\\\\text{Total perimeter}=2\times \text{Length}+Breadth+(\frac{1}{2}\times 2\times \pi \times r)$

Now putting all the given values in this formula, we get:

$\text{Total perimeter}=2\times \text{Length}+Breadth+(\frac{1}{2}\times 2\times \pi \times r)\\\\\text{Total perimeter}=2\times 19ft+12ft+(\frac{1}{2}\times 2\times 3.14 \times 6ft)\\\\\text{Total perimeter}=68.84ft$

8 0

3 years ago

Use the elimination method to solve this system.

leva [86]

Answer:

The solution for this system is: $x = -1, y = 1$

Step-by-step explanation:

The problem states that we have to solve this system by the elimination method

In the elimination method, we transform the system in such a way that one variable can cancel each other. With this, we find the result of the other variable. Then, we can replace the variable we found in any of the equations, and we have the value of the variable that we had initially canceled.

In this problem, we have the following system:

$1) -6x + 5y = 1$

$2) 6x + 4y = -10$

If we add equations 1) and 2), the variable x is going to be eliminated

$1) + 2)$

$-6x + 6x + 5y + 4y = 1 - 10$

$9y = -9$

$y = \frac{-9}{9}$

$y = -1$

Now, we can replace the value of y in any of the equations, to find x:

I will replace in equation 2)

$6x + 4y = -10$

$6x + 4(-1) = -10$

$6x = -6$

$x = \frac{-6}{6}$

$x = -1$

The solution for this system is: $x = -1, y = 1$

5 0

2 years ago

Is 63 even or odd

frutty [35]

c'mon bro you can't be this helpless

odd, even, even, even, even

3 0

2 years ago

Read 2 more answers

Twin brothers, Billy and Bobby, kid mother grandparents lawn together for 60 minutes. Billy could mow the lawn by himself in 20

Dovator [93]

Answer:

Bobby around 131 minutes and Billy around 111 minutes

Step-by-step explanation:

To solve the problem it is important to raise equations regarding what happens.

They tell us that Billy (Bi) and Bobby (Bo) can mow the lawn in 60 minutes. That is to say that what they prune in a minute is giving as follows:

1 / Bo + 1 / Bi = 1/60 (1)

They say Billy could mow the lawn only in 20 minutes less than it would take Bobby, therefore

1 / Bi = 1 / (Bo-20) (2)

Replacing (2) in (1) we have:

1 / Bo + 1 / (Bo-20) = 1/60

Resolving

(Bo - 20 + B0) / (Bo * (Bo-20) = 1/60

120 * Bo - 1200 = Bo ^ 2 - 20Bo

Rearranging:

Bo ^ 2 - 140Bo -1200 = 0

Now applying the general equation

Bo = 130.82 or Bo = 9.17, <em>this last value cannot be because Billy took 20 minutes less and neither can he prune faster than the two together</em>, therefore Bobby only takes around 131 minutes and Billy around 111 minutes

Checking with equation 1:

1/131 +1/111 = ~ 1/60

3 0

3 years ago