What is the purpose of multiplying by the conjugate of a complex denominator when finding the quotient of complex numbers?

a.Radicals in the denominators of fractions are considered unsimplified. Multiplying by the conjugate of a complex denominator will simplify the fraction by cancelling the denominator.

b.Complex numbers in a fraction are considered unsimplified. Multiplying by the conjugate of a complex denominator will simplify the fraction by cancelling the denominator.

c.Radicals in the denominators of fractions are considered unsimplified. You need to multiply a fraction by a value that removes radicals or imaginary numbers in the denominator, which is the complex conjugate of the denominator.

d.Complex numbers in a fraction are considered unsimplified. You need to multiply a fraction by a value that removes radicals or imaginary numbers in the fraction, which is the conjugate of the denominator.

Answer:

[tex]7\frac{11}{35}[/tex]

Step-by-step explanation:

[tex]2\frac{5}{7}+4\frac{3}{5}[/tex]

add the whole numbers

[tex]2+4=6[/tex]

combine the fractions

[tex]\frac{5}{7}+\frac{3}{5}[/tex]

LCM is 35 because 7 * 5 =35

[tex]\frac{5}{7}=\frac{5\cdot \:5}{7\cdot \:5}=\frac{25}{35}[/tex]

[tex]\frac{3}{5}=\frac{3\cdot \:7}{5\cdot \:7}=\frac{21}{35}[/tex]

[tex]\frac{25}{35}+\frac{21}{35}=\frac{25+21}{35}[/tex]

[tex]=\frac{46}{35}[/tex]

change the improper fraction into mixed number

[tex]6+1\frac{11}{35}[/tex]

[tex]=7\frac{11}{35}[/tex]

Answer:

The following characteristics of experiments are not also characteristics of surveys:

- The first one is B. The study compares two or more treatments (possibly including "no treatment").

- The other one is D. The study involves one or more treatment groups and a control group.

Step-by-step explanation:

surveys are tested with one group

The two options are B) and C) because they are characteristics of science.

The main characteristics of surveys are as follows:

1.measurable survey objectives.

2.sound research design.

3.effective survey question design.

4.sound sampling strategy, when needed.

5.effective survey response strategy.

6.meaningful data summary.

7.effective data display and reporting.

Given: In the option A and B talk about surveys but the other two options are characteristics of science.

Hence, The two options are B) and C) because they are characteristics of science.

Learn more about surveys here:

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Answer:

a and c are vertical angles

b and d are vertical angles

Step-by-step explanation:

Vertical angles are angles formed from the same lines, sharing the same vertex and opposite each other

a and c are vertical angles

b and d are vertical angles

Answer:

a and c are vertical angles

b and d are vertical angle

Step-by-step explanation:

Answer:

y=8.4

Step-by-step explanation:

inverse proportion means y=k/x

k is the constant

y=12, x=7

k=xy ⇒7*12=84

y=84/x

y=84/10

y=8.4

As y varies inversely with x the value of y is 42/5 when x is 10.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, y varies inversely with x.

∴ y = k/x.

12 = k/7.

k = 84.

Now, x = 10.

∴ y = 84/10.

y = 42/5.

learn more about proportion here :

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Answer:

Step-by-step explanation:

f(x) = - x + 6

g(x) = 4x - 6

In order to find g(f(x)) substitute f(x) into g(x) that's for every x in g(x) replace it with f(x)

That's

We have the final answer as

Hope this helps you

Answer:The answer is 79

Step-by-step explanation:

Answer:

2.75, and - 2.75

Step-by-step explanation:

Both have an absolute value of 2.75 which is how far away they are from 0.

Hope this helped!

Answer:

17. xy + z = 51

18 yz - x = 18

21. 5z + ( y - x ) = 20

22. 5x - ( y2 - 4x ) = -10

23 . x2 + y2 - 10z = 70

24. z3 + ( y2 - 4x ) = 1

25. y + xz / 2

26 .3y + x2 / z = 30

Step-by-step explanation:

17.(6 x 8)+3=

    48+3=51

18.(8 x 3)- 6 =

     24 - 6 = 18

21. 15 + ( 8 - 3 )

      15 + 5=

        20

22 .30 - (64 - 24)=

      30 - 40=

       -10

23. 36 + 64 - 30

      100 - 30

        70

24.  9 + (16 - 24 )=

       9 + -8 =

        1

25. 8 + 48 / 2

      56 / 2

       28

26. 24+ 36/3

      60/3=

       30

Answer:

-4w = 24 then

w = -6

Step-by-step explanation:

Answer:

w = -6

Step-by-step explanation:

Solve for w:

-4 w = 24

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of -4 w = 24 by -4:

(-4 w)/(-4) = 24/(-4)

Hint: | Any nonzero number divided by itself is one.

(-4)/(-4) = 1:

w = 24/(-4)

Hint: | Reduce 24/(-4) to lowest terms. Start by finding the GCD of 24 and -4.

The gcd of 24 and -4 is 4, so 24/(-4) = (4×6)/(4 (-1)) = 4/4×6/(-1) = 6/(-1):

w = 6/(-1)

Hint: | Simplify the sign of 6/(-1).

Multiply numerator and denominator of 6/(-1) by -1:

Answer: w = -6

Answer:

58

Step-by-step explanation:

If k = 6 and j = 2 all you have to do is plug in the numbers

So

5 x 6 x 2 - 2

and then you think of PEMDAS

so multiplication comes first  so

5 x 6 x2 = 60 and then

60 - 2 = 58

Answer:   [tex]\dfrac{1}{3}[/tex].

Step-by-step explanation:

Experimental probability = [tex]\dfrac{favorable\ outcomes}{Total\ outcomes}[/tex]

Given: Total pieces of fruit = 18  (Total outcomes)

Number of oranges = 6 (Favorable )

Then, the experimental probability that the nest piece of fruit Albert sells will be an orange = [tex]\dfrac{6}{18}[/tex]   [By formula of experimental probability]

[tex]=\dfrac{1}{3}[/tex]

Hence, the required probability is [tex]\dfrac{1}{3}[/tex].

Answer:  

part 1 : 41f[tex]t^{2}[/tex]

part 2: 87f[tex]t^{2}[/tex]

Step-by-step explanation:

part 1 : 8*2=16      1*10=10         10*3*1/2 = 15

16+10+15= 41f[tex]t^{2}[/tex]

part 2:      16*2= 32         2*8= 16            1*6=6         3*6=18    10*3*1/2 =15

32+16+6+18+15= 87f[tex]t^{2}[/tex]

Answer:

√64 = rational

Step-by-step explanation:

√64 = 8

8 = 8/1 = rational

Answer: The number 64 is an irrational number.

Step-by-step explanation:

Answer:

fg = 7x in the question only it is given

Answer:

6.5

Step-by-step explanation:

5.5x5.5= 30.25.        30.25 divide 30 and 25 by 5 then you get 6.5

Answer:

Step-by-step explanation:

Answer:

3.5

Step-by-step explanation:

The constant of proportionality is the slope of the line

slope = [tex]\frac{rise}{run}[/tex] = [tex]\frac{3.5}{1}[/tex] = 3.5

Answer:

3.5

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

128

Step-by-step explanation:

6 / 3 + 32 * 4 - 2.

We first calculate 6/3 and 32 * 4:

6 / 3 = 2

32 * 4  = 128

Our expression then becomes 2 + 128 - 2.

We can evaluate, getting 128.

Answer:

36

Step-by-step explanation:

6 ÷ 3 + 3^2 · 4 − 2

= 2 + 9 · 4 - 2

= 2 + 36 - 2

= 38 - 2

= 36

Answer:

(3, 10, 17, 24....)

Step-by-step explanation:

f(x) =  7x - 4

x = 1:

f(1) = 7*1 - 4 = 7 - 4 = 3

x = 2:

f(2) = 7*2 - 4 = 14 - 4 = 10

x = 3

f(3) = 7*3 - 4 = 21 - 4 = 17

then the sequence is:

(3, 10, 17, 24.....)

Answer:

1. [tex]x = \pm 5[/tex]

2. [tex]x = \pm i[/tex]

3. [tex]x = 5, -4[/tex]

Step-by-step explanation:

1.

[tex]x^2-25=0[/tex]

[tex]x^2 = 25[/tex]

[tex]x = \pm \sqrt{25}[/tex]

[tex]x = \pm 5[/tex]

2.

[tex]x^2 + 1 = 0[/tex]

[tex]x^2 = -1[/tex]

[tex]x = \pm \sqrt{x-1}[/tex]

[tex]x = \pm i[/tex]

3.

[tex]x^2=x+20[/tex]

[tex]x^2 - x - 20 = 0[/tex]

[tex](x-5)(x+4)=0[/tex]

[tex]x = 5, -4[/tex]

Answer:

{x,y}={−5,−7}

Explain:

// Solve equation [2] for the variable  y [2]    3y = 7x + 14 [2]    y = 7x/3 + 14/3 // Plug this in for variable  y  in equation [1] [1]    8x - 3•(7x/3+14/3) = -19 [1]    x = -5 // Solve equation [1] for the variable  x [1]    x = - 5 // By now we know this much : x = -5 y = 7x/3+14/3 // Use the  x  value to solve for  y y = (7/3)(-5)+14/3 = -7 Solution : {x,y} = {-5,-7}

Hoped I helped

Answer:

Input:

f(x, y) = x^2 - y^2

Geometric figure:

hyperbolic paraboloid

3D plot:

3D plot

Contour plot:

Contour plot

Alternate form:

f(x, y) = (x - y) (x + y)

Alternate form assuming x and y are positive:

x^2 = f(x, y) + y^2

Properties as a function:

Domain

R^2

Range

R (all real numbers)

Parity

even

Partial derivatives:

d/dx(x^2 - y^2) = 2 x

d/dy(x^2 - y^2) = -2 y

Indefinite integral assuming all variables are real:

integral(x^2 - y^2) dx = x^3/3 - x y^2 + constant

Answer:

D

Step-by-step explanation:

So we have the equation:

[tex]A=\frac{1}{2}(12)(3+7)[/tex]

And we want to find out which of the answer choices is not equivalent.

Thus, let's go through each of the choices.

A)

We have:

[tex]\frac{12(3+7)}{2}[/tex]

This is correct.

Our original equation can be written as:

[tex]A=\frac{1}{2}(\frac{12(3+7)}{1})[/tex]

And if we multiply straight across:

[tex]A=\frac{12(3+7)}{2}[/tex]

We'll get choice A. So choice A is correct.

B)

We have:

[tex]6(3+7)[/tex]

This is also correct.

From our original equation:

[tex]A=\frac{1}{2}(12)\cdot(3+7)[/tex]

If we multiply the first term together:

[tex]A=6(3+7)[/tex]

We'll get choice B. So, choice B is correct.

C)

We have:

[tex]0.5(12)(10)[/tex]

This is correct as well.

If we reduce 1/2 to decimal form and add the operations within the parentheses in the original equation, we will get:

[tex]A=\frac{1}{2}(12)(3+7)\\A=0.5(12)(10)[/tex]

So, C is also correct.

D)

We have:

[tex]\frac{12}{2}\times\frac{10}{2}[/tex]

Note that this is not correct.

This attempted to use the distributive property. However, the distribute property does not work for multiplication. For instance:

[tex]3(2+1)\text{ indeed equals } 3(2)+3(1)[/tex]

However:

[tex]3(2\times1)\text{ does not equal} 3(2)\times3(1)[/tex]

So, choice D is not equivalent.

So choice D is our answer :)

If we evaluate it, we will get 30, in contrast to the 60 of the others.

Answer:

$1615

Step-by-step explanation:

500(1+.05/1)^24

500(1+.05)^24

500*1.05^24

500*3.23

1615

Answer:

3

Step-by-step explanation:

[tex] \frac{j}{4} = \frac{12}{4} = 3[/tex]

4*3=12

3*4=12

12/4=3

12/3=4

Hope this helps ;) ❤❤❤

Answer:

We need to evaluate [tex]\frac{j}{4}[/tex] for j = 12.

First, we need to replace j by 12 on [tex]\frac{j}{4}[/tex], so we get [tex]\frac{12}{4}[/tex] and now, we only need to divide:

[tex]\frac{12}{4}=3[/tex]

So the result is 3

Answer:

11 hours

Step-by-step explanation:

To find how many hours it took, divide -33 by -3

-33/-3

= 11

So, it took 11 hours for the change to be -33°F

Answer:

h(8)=-67

Step-by-step explanation:

We know that x=8 so we solve the solution on the right by replacing x with 8

5-9*8

5-72

-67

So h(8)=-67

Answer:

See below

Step-by-step explanation:

Q1. when 3b-4a is evaluated for a=0.5 and b=-0.333333333. what is the answer?

[tex]3b-4a, a=0.5 \text{ and } b=-0.333333...[/tex]

Once

[tex]$-0.3333333... = -\frac{1}{3} \text{ and } 0.5=\frac{1}{2} $[/tex]

[tex]$3\cdot \left(-\frac{1}{3}\right) - 4 \cdot \frac{1}{2} = -1 - 2 =\boxed{-3}$[/tex]

Q2. solution for equation  

[tex]5(x+1)-3(3x-1)=15(x-2)[/tex]

[tex]5x+5-9x+3 = 15x-30[/tex]

[tex]-4x+8 = 15x-30[/tex]

[tex]38 = 19x[/tex]

[tex]$x=\frac{38}{19} = \boxed{2}$[/tex]

Q3. which is not equivalent to [tex]4(2x-1)=3(x+1)-2[/tex]

Just try all the values.

None of them makes the equation equivalent.

[tex]8x-4=3x+1-2[/tex]

[tex]5x=5[/tex]

[tex]\boxed{x=1}[/tex]

Q4. if a<0 and b<0 which of the following is not positive

B. a+b

[tex]a<0 \implies \text{a is negative}[/tex]

[tex]b<0 \implies \text{b is negative}[/tex]

[tex]a \cdot b \implies \text{positive value}[/tex]

[tex]$\frac{a}{b} \implies \text{positive number}$[/tex]

[tex]a:b \text{ is just another notation for division}[/tex]

[tex]a+b \implies \text{negative number}[/tex]

Answer:

1000 times greater.

Step-by-step explanation:

10^9 / 10*6

= 10^(9-6)

= 10^3

= 1000.

Answer:

just took the test answer is C

Step-by-step explanation: