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Slope= 9, (-5,2)

Answer:

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Answer:

√

−

49

=

7

i

Explanation:

A square root of a number  

n

is a number  

x

such that  

x

2

=

n

Note that if  

x

is a Real number then  

x

2

≥

0

.

So any square root of  

−

49

is not a Real number.

In order to be able to take square roots of negative numbers, we need Complex numbers.

That's where the mysterious number  

i

comes into play. This is called the imaginary unit and has the property:

i

2

=

−

1

So  

i

is a square root of  

−

1

. Note that  

−

i

is also a square root of  

−

1

, since:

(

−

i

)

2

=

(

−

1

⋅

i

)

2

=

(

−

1

)

2

⋅

i

2

=

1

⋅

(

−

1

)

=

−

1

Then we find:

(

7

i

)

2

=

7

2

⋅

i

2

=

49

⋅

(

−

1

)

=

−

49

So  

7

i

is a square root of  

−

49

. Note that  

−

7

i

is also a square root of  

−

49

.

What do we mean by the square root of  

−

49

For positive values of  

n

, the square root is usually taken to mean the principal square root  

√

n

, which is the positive one.

For negative values of  

n

, the square roots are both multiples of  

i

, so neither positive nor negative, but we can define:

√

n

=

i

√

−

n

With this definition, the principal square root of  

−

49

is:

√

−

49

=

i

√

49

=

7

i

Footnote

The question remains: Where does  

i

come from?

It is possible to define Complex numbers formally, as pairs of Real numbers with rules for arithmetic like this:

(

a

,

b

)

+

(

c

,

d

)

=

(

a

+

c

,

b

+

d

)

(

a

,

b

)

⋅

(

c

,

d

)

=

(

a

c

−

b

d

,

a

b

+

c

d

)

These rules for addition and multiplication work as expected with commutativity, distributivity, etc.

Then Real numbers are just Complex numbers of the form  

(

a

,

0

)

and we find:

(

0

,

1

)

⋅

(

0

,

1

)

=

(

−

1

,

0

)

That is  

(

0

,

1

)

is a square root of  

(

−

1

,

0

)

Then we can define  

i

=

(

0

,

1

)

and:

(

a

,

b

)

=

a

(

1

,

0

)

+

b

(

0

,

1

)

=

a

+

b

i

Step-by-step explanation:

23 of the chromosomes come from one parent , 23 from other parent.

4(+2)=8+4

1.Distribute

4(+2)=8+4

4+8=8+4

2.Rearrange terms

4+8=8+4

4+8=4+8

3.Subtract 8 from both sides of the equation

4+8=4+8

4+8−8=4+8−8

4.Simplify

4+8−8=4+8−8

4=4+8−8

2.Subtract the numbers

4=4+8−8

4=4

5.Subtract 4 from both sides of the equation

4=4

4−4=4−4

6.Simplify

1.Combine like terms

4−4=4−4

0=4−4

0=0

The Answer is 0=0.

[tex] \frac{1}{5}(25 - 5a) = 4 - a [/tex]

Rearrange terms

[tex] \frac{1}{5}(25 - 5a) = 4 - a \\ \frac{1}{5}( - 5a + 25) = 4 - a \\ [/tex]

2.Combine multiplied terms into a single fraction

[tex] \frac{1}{5}( - 5a + 25) = 4 - a \\ \frac{1( - 5a + 25)}{5} = 4 - a [/tex]

3.Multiply by 1

[tex] \frac{1( - 5a + 25)}{5} = 4 - a \\ \frac{ - 5a + 25}{5} = 4 - a [/tex]

4. Rearrange terms

[tex] \frac{ - 5a + 25}{5} = 4 - a \\ \frac{ - 5a + 25}{5} = - a + 4 [/tex]

5.Add  to both sides of the equation

[tex] \frac{−5+25}{5} = - a + 4 \\ \frac{−5+25}{5} + a= - a + 4 + a [/tex]

6. Simplify

Find common denominator

[tex] \frac{ - 5a + 25}{5} + a = - a + 4 + a \\ \frac{ - 5a + 25}{5} + \frac{5a}{5} = - a + 4 + a [/tex]

2.Combine fractions with common denominator.

[tex] \frac{ - 5a + 25}{5} + \frac{5a}{5} =−+4+ \\ \frac{−5+25 + 5a}{5} = - a + 4 + a [/tex]

3. Combine like terms

[tex] \frac{ - 5a + 25 + 5a}{5} = −+4+ \\ \frac{25}{5} = −+4+[/tex]

4. Cancel terms that are in both the numerator and denominator

[tex] \frac{25}{5} = −+4+ \\ 5 = −+4+[/tex]

5. Combine like terms

5 = - a + 4 + a

5=4

Answer: 5=4.

7

Answer:

53.94$

Step-by-step explanation:

Answer:

53.94$

Step-by-step explanation:

Answer:

[tex]\frac{1}{15}[/tex] cup of flour

Step-by-step explanation:

5 rolls = [tex]\frac{1}{3}[/tex] cup

? × 5 = [tex]\frac{1}{3}[/tex]

[tex]\frac{1}{3}[/tex] ÷ 5 = ?

[tex]\frac{1}{3}[/tex] ÷ [tex]\frac{5}{1}[/tex] = [tex]\frac{1}{3}[/tex] × [tex]\frac{1}{5}[/tex] = [tex]\frac{1}{15}[/tex]

Answer:

0.35 and 35%

Step-by-step explanation:

7/20=35/100

35/100=0.35=35%

Answer:

Step-by-step explanation:

[tex]15*10^{4}=15*10000 = 150,000[/tex]

Answer:

Tom need to rent the court in order for it to be cheaper more than 15 times.

Step-by-step explanation:

Answer:

Tom needs to rent it atleast 17 times.

Step-by-step explanation:

1) First, write your equations. x in this case equals the # of times you rent the court.

For members: y = 135 + 3x (members)

Non-members: y = 11x (non-members)

From here, there can me many methods that can work. Right now I can only think of one though :/.

So what you can do is plug in numbers and see what happens. I suggest you work with easy numbers when you plug stuff in. Once you find that non-members is greater than the amnt for members have, that's your answer!

a) x = 10

For members: 135 + 3(10) = 165

Non-members: 11(10) = 110

Didn't work. :(

b) x = 20

For members: 135 + 3(20) = 195

Non-members: 11(20) = 220

Aha! We have a valid answer. However, we need to find the minimum number of times Tom needs to rent it.

c) x = 15

For members: 135 + 3(15) = 180

Non-members: 11(15) = 165.

So our answer is between 15 and 20.

If you keep doing this, you'll find that 18 is the minimum number of times tom will have to rent the court. So your answer is anything greater than equal to 17.

x = 17

For members: 135 + 3(17) = 186

Non-members: 11(17) = 187

Sorry I made this tedious, but this is one method. Though I helped you find the answer, I hope someone else can help you find the best method!

Answer:

ifk

Step-by-step explanation:

what is a nice party in the car going right be in a call to get place to go out and to some of these things for you to take care and party and to parties place party on the phone case pink or something like else is one nice good to of rid if not you a bit of longer health way your family or

Answer:

Step-by-step explanation:

The coordinates of point J are (10,-2) and L os a point on the y axis.

Answer:

12, 14, 16, and 18 are all even numbers between 10 and 19

Step-by-step explanation:

They are all even numbers because they end in 2, 4, 6, or 8. 0 is considered neither even nor odd.

Answer:

12 is an even number because it is divisible by 2

Area of the rectangle is 60

Area of the semi circle 14.13 ir 14.1

60 plus 14.1 is 74.1

I hope its right

Answer:

x=42

Step-by-step explanation:

3x+1+x+11=180

Combine like terms

4x+12=180

subtract 12 from each side

4x=168

divide by 4

x=42

Hope this helps! Have a great day!!

Step-by-step explanation:

1. [tex](fg)' = f'g + fg' [/tex] (chain rule)

2 [tex]f(x) = x^5\sin{x}[/tex]

[tex]\Rightarrow f'(x) = 5x^4\sin{x} + x^5\cos{x}[/tex]

The gcf of 250, 45, and 30 is 5

9514 1404 393

Answer:

  $35.00

Step-by-step explanation:

The number of pints sold is ...

  (12.5 gal)×(8 pt/gal) = 100 pt

Then the total amount received for the milk is ...

  (100 pt)($0.35/pt) = $35.00

Answer:

..............................

Answer:

I think 164

Step-by-step explanation:

1312/8

Answer:

95

Step-by-step explanation:

1. First, the binary to decimal formula is:  

2. Now, let's apply it:

Therefore, the answer is 95.

Answer:

These are rational numbers.

Answer:

$45.33

Step-by-step explanation:

First we find 4.25% of $3200 to find the interest in 1 year.

For simple interest, use this formula:

I = Prt

where

I = amount of interest

P = principal amount (the amount deposited or borrowed)

r = annual interest rate

t = number of years

We have

I = ?

P = $3200

r = 4.45% = 0.425

t = 1 year

I = ($3200)(0.0425)(1)

I = $136

The interest in 1 year is $136.

Now we convert 4 months to years

1 year = 12 months

4/12 = 1/3

4 months are only 1/3 of a year, so he pays only 1/3 of the interest of an entire year.

1/3 * $136 = $136/3 = $45.3333...

Answer: $45.33

Answer:

no

Step-by-step explanation:

if a=0 it's y=0, it's not one to one

if ais not 0, it's a even function and it's not 1 to 1, for example a=1, x=8 and x=2 have same f(x)

Answer:

ii cud givee uu an explanation for understandment for help if still don't understand im sowwyy thenn.

Step-by-step explanation:

It is given that the number of bacteria doubles every hour.

Therefore, the number of bacteria after every hour will form a G.P.

with first term (a=30) and common ratio (r=2)

∴a

3

​

=ar

2

=(30)(2)

2

=120

Therefore, the number of bacteria at the end of 2nd hour will be 480.

a

5

​

=ar

4

=(30)(2)

4

=480

and a

n+1

​

=ar

n

=(30)(2)

n

Thus the number of bacteria at the end of nth hour will be (30)(2)

n

Geometric sequence can model the considered situation. The number of bacteria in 18 hours for the considered situation will be 264

There are three parameters which differentiate between which geometric sequence we're talking about.

Suppose the initial term of a geometric sequence is [tex]a[/tex] and the term by which we multiply the previous term to get the next term is [tex]d[/tex]  

Then the sequence would look like

[tex]a, ad, ad^2, ad^3, ad^4,...[/tex] (till the terms to which it is defined)

Thus, the nth term of such sequence would be

[tex]T_n = ad^{n-1}[/tex]

We can model the given situation with the geometric sequence since each previous count is being doubled(multiplied by 2) per 4 hours.

We're given initial number of bacteria = a = 22

Each new element will be denoting number of bacteria after 4 hours from previous count.

So, from 0 to 16 hours, there are four set of 4 hours. Thus, n = 4

Since number of bacteria are doubling, thus, d= 2

We get fourth term  = number of bacteria after 16 hours

[tex]T_n = a(d)^{n-1} = 22 \times (2)^3 = 176[/tex]

Now, in the last 2 hours, assuming that if x -> 2x in 4 hours(which is increment of x), then in 2 hours, only x/2 must be incremented.(assuming linear growth in each 4 hour group).

Thus, after 18 hours, 176 + 176/2 will be the number of bacteria.

Thus, Number of bacteria after 18 hour for the given case = 176 + 88 = 264

Learn more about geometric sequence here:

https://brainly.com/question/2735005