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3 years ago

What is the factored form of the expression over the complex numbers? 4x2+25y2?

Mathematics

2 answers:

Helen [10]3 years ago

4 0

The factored form is 25y^2 + 8 if the 2 was supposed to be an exponent.

Rzqust [24]3 years ago

3 0

Answer:

$(2x+5iy)(2x-5iy)$

Step-by-step explanation:

If a and b are two positive numbers, then

$a^2+b^2=(a+ib)(a-ib)$ .... (1)

The given expression is

$4x^2+25y^2$

It can be rewritten as

$2^2x^2+5^2y^2$

Using distributive property of exponent we get

$(2x)^2+(5y)^2$ $[\because a^mb^m=(ab)^m]$

Using formula (1) we get

$(2x+5iy)(2x-5iy)$ $[\because a^mb^m=(ab)^m]$

Therefore, the factored form of the given expression is $(2x+5iy)(2x-5iy)$ .

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DerKrebs [107]

The slope of a horizontal line is always 0 because all its points have the same y-coordinate

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3 years ago

Use the drop-down menu to complete the statement.

natita [175]

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A model rocket is launched straight upward. The solid fuel propellant pushes the rocket off the ground at an initial velocity of

anastassius [24]

Answer:

a) 72.25sec

b) 6.25secs

c) after 10.5secs and 2 secs

Step-by-step explanation:

Given the height reached by the rocket expressed as;

s(t)= -4t^2 + 50t - 84

At maximum height, the velocity of the rocket is zero i.e ds/dt = 0

ds/dt = -8t + 50

0 = -8t + 50

8t = 50

t = 50/8

t = 6.25secs

Hence it will reach the maximum height after 6.25secs

To get the maximum height, you will substitute t - 6.25s into the given expression

s(t)= -4t^2 + 50t - 84

s(6.25) = -4(6.25)^2 + 50(6.25) - 84

s(6.25) = -156.25 + 312.5 - 84

s(6.25) = 72.25feet

Hence the maximum height reached by the rocket is 72.25feet

The rocket will reach the ground when s(t) = 0

Substitute into the expression

s(t)= -4t^2 + 50t - 84

0 = -4t^2 + 50t - 84

4t^2 - 50t + 84 = 0

2t^2 - 25t + 42 = 0

2t^2 - 4t - 21t + 42 = 0

2t(t-2)-21(t-2) = 0

(2t - 21) (t - 2) = 0

2t - 21 = 0 and t - 2 = 0

2t = 21 and t = 2

t = 10.5 and 2

Hence the time the rocket will reach the ground are after 10.5secs and 2 secs

3 0

3 years ago

Can you help with this please and also explain?

stira [4]

Answer:

avocado=4

Step-by-step explanation:

Hi there!

We are given the following equations:

snail + snail - cellphone=avocado

maple leaf * cellphone=10

0+maple leaf=5

snail = cellphone + 1

avocado=?

This may seem confusing at first, but let's try to find the value of one of the items to help us to solve for the others

For example, we have the equation 0 + maple leaf= 5

Which means if we subtract 0 from both sides, we should get the value of the maple leaf

Which means that the maple leaf= 5

Now we know that maple leaf * cellphone = 10

So that means 5*cellphone=10

Divide by 5 on both sides

cellphone= 2

We know that snail = cellphone + 1

As we learned from above, cellphone= 2

Which means that snail = 2+1=3

We know that snail + snail - cellphone = avocado

And as calculated from above, snail = 3 and cellphone = 2

Which means:

3 + 3 - 2= avocado

Add

6-2=avocado

Subtract

4=avocado

Hope this helps!

5 0

3 years ago

How many times does 2 go into 400

bogdanovich [222]

2 goes into 400, that is $\frac{400:2}{2:2} = \frac{200}{1}$ ,

However, 2 goes into 400, 200 times.

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3 years ago

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