Factor the following expression completely
X4-y4
Factor the following expression completely X4-y4 - 1

Answers

Answer 1
Answer: x^4-y^4=\left(x^2\right)^2-\left(y^2\right)^2=(x^2-y^2)(x^2+y^2)=(x-y)(x+y)(x^2+y^2)\n\n\na^2-b^2=(a-b)(a+b)
Answer 2
Answer: 1)(x-y)(x+y)(x^2+y^2)
=(x^2-y^2)(x^2+y^2)
=x^4-y^4

2)(x-y)^2(x+y)^2
=(x^2-2xy+y^2)(x^2+2xy+y^2)
=x^4+y^4

3)(x-y)^4
=x^4-4x^3y+6x^2y^2-4xy^3+y^2

4)(x^2-y^2)(x^2+y^2)
=x^4-y^4

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Ray Cupple bought a basic car costing $26,500.00, with options costing $725.00. There is a 6% sales tax in his state and a combined $50.00 license and registration fee. What was Ray's total cost?A. $28,865.00
B. $28,911.50
C. $27,275.00
D. $28,908.50

Answers

Answer: D. $28,908.50


Step-by-step explanation:

Given: Cost price of car= $26,500

Cost of options= $725

Therefore, the total cost=$26,500+ $725=$27225

As there is a 6% sales tax in his state .

⇒ Tax amount = 6% of Total cost

=0.06*\$27225=\$1,633.5

⇒Tax amount=$1,633.5

Combine $50 licence, registration fee and tax amount to the total cost , we get

Total cost=$27225+$1,633.5+$50

∴Total cost=$28,908.5

Adding the basic car costing and the additional options costing, we have (26500 + 725) = $ 27 225. Since sales tax is to be included for the payment, Ray must pay for 1.06 of the basic cost. Which is equal to 1.06(27 225) = $ 28 858.50 Adding the license and registration fee into the price, we have $28 908.50. Hence, the total cost is D: $28, 908.50.

The area, A, of a square is equivalent to the square of its side lengths. choose more than one!1::: A = (6)(6) square units
2::: A = s2 square units
3::: A = (x)(x) square units
4::: A = (x+x) square units
5::: A = 2(6) square units

Answers

Answer:

I think is 1 and 4

Step-by-step explanation:

complete the following steps to find an equation of the tangent plane to the surface at the point : step 1: determine the function that describes the surface in the form : step 2: find step 3: find step 4: find step 5: find step 6: find step 7: find the equation of the tangent plane at the given point is

Answers

The point-normal form of a plane equation: (Fx(x0, y0, z0))(x - x0) + (Fy(x0, y0, z0))(y - y0) + (Fz(x0, y0, z0))(z - z0) = 0.

To find the equation of the tangent plane to a surface at a given point, follow these steps:

Step 1: Determine the function that describes the surface in the form F(x, y, z) = 0.

Step 2: Find the partial derivative of F with respect to x, denoted as Fx.

Step 3: Find the partial derivative of F with respect to y, denoted as Fy.

Step 4: Find the partial derivative of F with respect to z, denoted as Fz.

Step 5: Evaluate Fx, Fy, and Fz at the given point (x0, y0, z0).

Step 6: Use the gradient vector, which consists of the evaluated partial derivatives (Fx(x0, y0, z0), Fy(x0, y0, z0), Fz(x0, y0, z0)), as the normal vector to the tangent plane.

Step 7: Use the point-normal form of a plane equation: (Fx(x0, y0, z0))(x - x0) + (Fy(x0, y0, z0))(y - y0) + (Fz(x0, y0, z0))(z - z0) = 0. This is the equation of the tangent plane at the given point.

By following these steps, you will find the equation of the tangent plane to the surface at the specified point.

For more about plane equation:

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Please help me with question 10 (i). Thanks!

Answers

V=πr²h+(2/3)πr³
πr²h+(2/3)πr³=V
πr²h=V-(2/3)πr³
h=(V-(2/3)πr³) / (πr²)
h=V/
πr² - 2/3r

Answer i:  
h=V/πr² - (2/3)r

Data:
V=245
r=7

h=(245 / 49
π) - (14/3)
h=(5/π) - (14/3)
h=(15-14π)/3π
h=-3.075

Answer ii: h=-3.075

Suface areas- cones
wdh

Answers

Answer:

65

Step-by-step explanation:

The slant height of a cone is the length of a segment from the base to the vertext along the surface of the cone.

You can use the given dimenstions as the legs of a right triangle, and the slant heifght is rthe hyopotenuse.

L^2 = r^2 + h^2

L^2 = 5^2 + 12^2

L^2 = 169

L = 13

The slant heiht is 13 cm.

LA = (pi)rL

LA = (pi)(5 cm)(13 cm)

LA = 65(pi) cm^2

Which of the following statement best describes the effect of replacing the graph of f(x) with the graph of f(x) - 3?A) the graph shifts 3 units up.
B) The graph shifts 3 units down. i think is correct?
C) the graph shifts 3 units left.
D)the graph shifts 3 units right.

Answers

The statement that best describes the effect of replacing the graph of f(x) with the graph of f(x) - 3 is; B) The graph shifts 3 units down.

what is graph?

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it. If we know that the function crosses x axis at some, then for some polynomial functions, we have those as roots of the polynomial.

The parent function is function of x and we the translated function is in the form f(x)-3.

Transformation Rule state that if the parent function is f(x) and if we subtract some constant 'a' in f(x) then the function will move down by 'a' units.

Thus, from the transformation rule, we can conclude that f(x) graph will shift down by 3 units.

Therefore, the correct option is; B) The graph shifts 3 units down.

Learn more about finding the graphed function here:

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to move a graph up c units, add c to the whole function

so basicaly what you did is you subtraced 3 from the whole function

the whole graph shifts 3 units down

B is answer