Which expression is equivalent to x^4-y^4?

Answers

Answer 1

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

Answer 2

Answer: $x^4-y^4=(x^2)^2-(y^2)^2=(x^2-y^2)(x^2+y^2)=(x-y)(x+y)(x^2+y^2)$

Related Questions

Eight less than ten times a number is 82
What is the end behavior of the polynomial function?
You are given a standard deck of 52 cards. Three cards are chosen at random with replacement. What is the probability of choosing an ace, a spade, and a four?
Find nth term of 14,23,32,41
FUNCTIONS h(x)= 3^xa) Solve the equation h^-1(x)= 2

derive the equation of the parabola with a focus at (4,-7) and a directrix of y=-15. put the equatiom in standard form

Answers

Answer:

The equation of the parabola with a focus at (4,-7) and a directrix of y=-15 is $y=(x^(2))/(16)-(x)/(2)-10$

Step-by-step explanation:

we need to drive the equation of the parabola with a focus at ( 4, -7) and a directrix of y= -15

From the given focus ( 4, -7) and equation of directrix y = - 15 calculate p

$p=(1)/(2)(y_0-y)$

where $y_0$ is is ordinate of focus and y is equation of directrix.

$p=(1)/(2)(-7-(-15))$

$p=(1)/(2)(-7+15)$

$p=(1)/(2)(8)$

$p=4$

Calculate the vertex (h,k)

$h=4\; \text{and}\; k=(-7+(-15))/(2)=-11$

vertex (h,k) =(4,-11)

Since, vertex form is :

$(x-h)^(2)=4p(y-k)$ (positive 4p shows it open upward)

$(x-4)^(2)=4(4)(y-(-11))$

$(x-4)^(2)=16(y+11)$

$x^(2)+16-8x=16y+176$

subtract both the sides by 176,

$x^(2)-8x-160=16y$

Divide both the sides in above by 16,

$(x^(2))/(16)-(8x)/(16)-(160)/(16)=y$

$(x^(2))/(16)-(x)/(2)-10=y$

Hence, the equation of the parabola with a focus at (4,-7) and a directrix of y=-15 is $y=(x^(2))/(16)-(x)/(2)-10$

$\sqrt{(x_(0) - 4)^(2) + (y_(0) - (-7))^(2)} = |y_(0) - (-15)|$
$(\sqrt{(x_(0) - 4)^(2) + (y_(0) + 7)^(2))^(2)} = (y_(0) + 15)^(2)$
$(x_(0) - 4)^(2) + (y_(0) + 7)^(2) = (y_(0) + 15)^(2)$
$(x_(0)^(2) - 8x_(0) + 16) + (y_(0)^(2) + 14y_(0) + 49) = y_(0)^(2) + 30y_(0) + 225$
$x_(0)^(2) + y_(0)^(2) - 8x_(0) + 14y_(0) + 16 + 49 = y_(0)^(2) + 30y_(0) + 225$
$x_(0)^(2) + y_(0)^(2) - 8x_(0) + 14y_(0) + 65 = y_(0)^(2) + 30y_(0) + 225$
$x_(0)^(2) - 8x_(0) - 16y_(0) - 160 = 0$
$16y_(0) = x_(0)^(2) - 8x_(0) - 160$
$(16y_(0))/(16) = (x_(0)^(2) - 8x_(0) - 160)/(16)$
$y_(0) = (1)/(16)x_(0)^(2) - (1)/(2)x_(0) - 10$
$y = (1)/(16)x^(2) - (1)/(2)x - 10$

URGENTWhat is the area of trapezoid ABCD ?

Enter your answer as a decimal or whole number in the box. Do not round at any steps.

units²

Answers

Answer:

The answer to your question is Area = 62.5 u²

Step-by-step explanation:

Area = $c (a + b)/(2)$

a and b are bases

c = heigth

dAD = $\sqrt{(x2 - x1)^(2) - (y2 - y1)^(2) }$

dAD = $\sqrt{(-1 + 13)^(2) - (5 + 11)^(2) }$

dAD = $\sqrt{(12)^(2) - (16)^(2) }$

dAD = $√(144 + 256)$

dAD = $√(400)$

dAD = 20 u

dBC = $\sqrt{(3 - 0)^(2) - (2 + 2)^(2) }$

dBC = $√(9 + 16)$

dBC = $√(25)$

dBC = 5 u

dAB = $\sqrt{(3 + 1)^(2) - (2 - 5)^(2) }$

dAB = $\sqrt{(4)^(2) - (-3)^(2) }$

dAB = $√(16 + 9)$

dAB = $√(25)$

dAB = 5u

Area = $5 (20 + 5)/(2)$

Area = $5 (25)/(2)$

Area = 5(12.5)

Area = 62.5 u²

Answer:

62.5 units^2

Step-by-step explanation:

The rectangular vegetable garden in 6 feet longer than 2 times its width. If the perimeter is 48 feet, what is the garden's width? Remember, the perimeter of a rectangle is the sum of all its sides.

Answers

Since there are 4 sides in a rectangle, we'll divide 48 by 4

$(48)/(4)$ = 12

We know that the length is 6 feet longer than 2 times it width.

12 + 6 = 18

The length of one side of a rectangle is 18.

The total length of both sides is 36 because 18 + 18 = 36

48 - 36 = 12

The width of both sides of a rectangles is 12. Now if we divide 12 by 2 we'll get the width of one side of a rectangle..

$(12)/(2)$ = 6

The width of one side of the rectangle is 6.
The length of one side of the rectangle is 18.

Let's check and see if our answer is correct. We need to get a 48 as an answer since that's the perimeter of the rectangle.

2 × ( length + width )
2 × ( 18 + 6 ) = 48

Yay! We got it right!! Hope you understood this :)

Final answer:

The width of the garden is 6 feet. We found this by expressing the length in terms of width, substituting into the perimeter equation, simplifying to find the value of width.

Explanation:

In solving this problem, we will follow a few simple steps. First, we know that the perimeter of a rectangle is given by the formula: Perimeter = 2*length + 2*width. We know from the problem that the perimeter is 48 feet and the length of the garden is 6 feet longer than 2 times its width.

Let's denote the width as 'w'. Then, the length would be 2w + 6. Substituting these into the perimeter equation, we have: 48 = 2*(2w+6) + 2*w. Simplifying this equation gives 48 = 4w + 12 + 2w, which further simplifies to 48 = 6w + 12. If we now deduct 12 from both sides, we have: 36 = 6w. Finally, dividing by 6 gives us the width: w = 6 feet.

Learn more about Perimeter here:

brainly.com/question/31695951

#SPJ2

What does 7x - 9y equal when x = 4 and y = 130?

Answers

7(4)-9(130)
28-1170
answer: -942

A circular skating rink has a radius of 40 feet. Which expression can be used to find the circumference of the skating rink, in feet?

Answers

The expression used is the circumference of a circle which is 80π

What are the circumference and diameter of a circle?

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

Given, A circular skating rink has a radius of 40 feet.

∴ The expression can be used to find the circumference of the

skating rink is 2π(40) = 80π feet.

learn more about circles here :

brainly.com/question/11833983

#SPJ2

Circumference of a circle = $2 \pi r$

They are all multiplied by each other
r = radius
we know our radius is 40
and... $\pi$ = 3.14

so we would use this expression
3.14 x 40 x 2

As a added bonus ill solve it for you :P
3.14 x 40 x 2 = 251.2
The circumference of this ice skating rink is 251.2 feet

Express scientific notation for 0.00032

Answers

$0.00032 < 1\n\n0.\underbrace{0003}_(4\to)2=3.2\cdot10^(-4)$

3.2•10^-4.

^=exponent

Other Questions

What is the sum of 5

The graph represents f(x) = x + 3On a coordinate plane, a step graph has horizontal segments that are each 1 unit long. The left end of each segment is an open circle. The right end of each segment is a closed circle. The left-most segment goes from (negative 5, negative 1) to (negative 4, negative 1). Each segment is 1 unit higher and 1 unit farther to the right than the previous segment. The right-most segment goes from (1, 5) to (2, 5).What is f(−2.2)?-2012

$6.50 is what percent of $130

Nina has 84 stickers. She wants to divide the stickers equally among 5 friends. How many stickers does each friend get? how many stickers are left over?