A principal of $1,000 is invested in an account paying an annual interest rate of 6%.

If x=3+bi, then

[tex]|x|=\sqrt{3^2+b^2}.[/tex]

You know that [tex]|x|^2=13,[/tex] then

[tex]\left(\sqrt{3^2+b^2}\right)^2=13,\\ \\ 9+b^2=13,\\ \\b^2=4,\\ \\b=\pm 2.[/tex]

Two possible complex numbers satisfy these conditions:

[tex]x_1=3+2i, \ x_2=3-2i.[/tex]

As you can see the possible value of b is 2.

Answer: correct choice is A.

The possible value of b in the given complex number is 2 (Option A). This is found by using the definition of modulus of a complex number and solving the resulting equation.

This question requires understanding of complex numbers and their modulus. A complex number is a number of the form a + bi, where a and b are real numbers and i is the imaginary unit with the property i^2 = -1.

|x|^2 represents the square of the modulus (or absolute value) of the complex number x which is defined as |x|^2 = a^2 + b^2. Given in the question, x = 3 + bi and |x|^2 = 13. Thus, by substitution, we get 13 = 3^2 + b^2.

Performing arithmetic operations, it's equivalent to b^2 = 13 - 3^2 = 4. To solve for b, we take the square root of both sides. Because b can be positive or negative, we get b = ±2. Therefore, from the options given, the possible value of b is 2 (Option A).

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Answer: It is best solve using elimination method

Step-by-step explanation:

4x + y = 1 --------(1)

2x + y = 8---------(2)

subtract (2) from (1)

2x = -7

divide bothside by 2

2x/2 = -7/2

x= -7/2

we can substitute x = -7/2 in any of the equations.

Lets take equation (1)

4x + y = 1

4(-7/2) + y =1

2(-7) + y = 1

-14 + y = 1

y = 1+14

y =15

Its not clearly given that whether EBF = 2x + 9 or 2x - 9.

I have written the solution for both.

If EBF = 2x + 9,

then ABF = 6x + 26 and ABE = 11x - 31.

Now, ABE = ABF + EBF

11x - 31 = (6x + 26) + (2x + 9)

           = (6x + 2x) + (26 + 9)

           = 8x + 35

11x - 8x = 35 + 31

3x = 66

x = 22

Therefore, ABF = 6x + 26 = 6(22) + 26 = 132 + 26 = 158°

If EBF = 2x - 9,

then ABF = 6x + 26 and ABE = 11x - 31.

Now, ABE = ABF + EBF

11x - 31 = (6x + 26) + (2x - 9)

           = (6x + 2x) + (26 - 9)

           = 8x + 17

11x - 8x = 17 + 31

3x = 48

x = 16

Therefore, ABF = 6x + 26 = 6(16) + 26 = 96 + 26 = 122°

The expression for angle ABF:  ABF = 6x + 26 = 6(16) + 26 = 96 + 26 = 122°

From the question: If EBF = 2x + 9, then ABF = 6x + 26 and ABE = 11x - 31.

When, ABE = ABF + EBF

11x - 31 = (6x + 26) + (2x + 9)

          = (6x + 2x) + (26 + 9)

          = 8x + 35

11x - 8x = 35 + 31

3x = 66

x = 22

Hence, ABF = 6x + 26 = 6(22) + 26 = 132 + 26 = 158°

When EBF = 2x - 9,

So, ABF = 6x + 26 and ABE = 11x - 31.

When, ABE = ABF + EBF

11x - 31 = (6x + 26) + (2x - 9)

          = (6x + 2x) + (26 - 9)

          = 8x + 17

11x - 8x = 17 + 31

3x = 48

x = 16

So,  ABF = 6x + 26 = 6(16) + 26 = 96 + 26 = 122°

Learn more about angle  from

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f(x) = (x - 4 )(x - 6) = 0

because you can see when each factor is equal to zero

x - 4 = 0 ⇒ x = 4

x - 6 = 0 ⇒ x = 6

Hi,

all of them multiplied together is 480.

1x8=8

8x5=40

40x2=80

Answer: 480

Step-by-step explanation:

Since commutative property can be used for multiplication, rewrite it as:

(1 x 8) x (5 x 12)

= 8  x  60

= 480

[tex]4y+8=2\qquad|\text{subtract 8 from both sides}\\\\4y=-6\qquad|\text{divide both sides by 4}\\\\y=-\dfrac{6}{4}\\\\\boxed{y=-\dfrac{3}{2}\to y=-1.5}[/tex]

Hello there!

[tex]4y+8=2[/tex]

Explanation:

↓↓↓↓↓↓

First you had to subtract by 8 from both sides of the equations.

[tex]4y+8-8=2-8[/tex]

Simplify

[tex]4y=-6[/tex]

Then you divide by 4 from both sides of the equations.

[tex]\frac{4y}{4}=\frac{-6}{4}[/tex]

Simplify it should be the correct answer.

[tex]y=-\frac{3}{2}[/tex]

Answer⇒⇒⇒⇒⇒y=-3/2

Hope this helps!

Thank you for posting your question at here on Brainly.

Have a great day!

-Charlie

Hello!

[tex]x + 6 = x\\[/tex]

Explanation:

↓↓↓↓↓↓↓↓↓

First you had to subtract by the x from both sides of the equation.

[tex]x+6-x=x-x[/tex]

Then refine.

[tex]6=0[/tex]

Answer⇒⇒⇒⇒⇒The sides are not equal.

Answer⇒⇒⇒⇒⇒⇒There are no solution.

Hope this helps!

Thank you for posting your question at here on Brainly.

Have a great day!

-Charlie

Write an expression that shows how to use the halving and doubling strategy to find 28x50

Halving strategy means we divide by 2

Doubling strategy means we multiply by 2

We apply halving strategy for 28 and doubling strategy for 50

Half of 28 is 14

Double of 50 is 100

So 14 * 100 = 1400

Now we check with 28 * 50

28 x 50 = 1400

So required expression is

[tex]\frac{28}{2} * (50*2)[/tex]

Hey there!!

Remember :-

=> Anything to the power 0, is always one.

In the question, is states at the last that the final answer is powered with zero.

Hence, the required answer is "1".

Hope my answer helps!!

Answer:

|2a|

Step-by-step explanation:

Note that distance is positive.  a less -a comes out to +2a, which is the distance between and -a.

Answer:

325 hamburgers were sold on Thursday.

Step-by-step explanation:

Let h be the number of hamburgers and c be the number of cheeseburgers.

Using this information we can set up two equation as:

[tex]h+c=593\\c=h-57[/tex]

Now we need to solve these two equations to get the value of number of hamburgers. For that we use substitution method as shown below:

[tex]h+h-57=593\\2h-57=593\\2h=650\\h=325[/tex]

Therefore, the number of hamburgers sold on Thursday were 325.

By definition an irrational number is one that is not rational. Therefore, it is not possible for a number to both rational and irrational.

Answer:

Part 1) The units rates are

A) [tex]0.1165\frac{\$}{oz}[/tex]

B) [tex]0.1656\frac{\$}{oz}[/tex]

C) [tex]0.0516\frac{\$}{oz}[/tex]

D) [tex]0.0579\frac{\$}{oz}[/tex]

Part 2) The best buy is the size 48 1/4 oz

Step-by-step explanation:

we know that

To find out the unit rate divide the total cost by the total volume

Part 1) Calculate the unit rate for each size

case A) we have

8 1/2 ounce bottle costs $0.99

Convert mixed number to an improper fraction

[tex]8\frac{1}{2} =\frac{8*2+1}{2}=\frac{17}{2}\ oz[/tex]

Find the unit rate

[tex]\frac{0.99}{(17/2)}= 0.1165\frac{\$}{oz}[/tex]

case B) we have

18 2/2 oz. bottle costs $1.49

Convert mixed number

[tex]18\frac{2}{2} =18+1=19\ oz[/tex]

Find the unit rate

[tex]\frac{1.49}{19}= 0.1656\frac{\$}{oz}[/tex]

case C) we have

48 1/4 oz. carton costs $2.49

Convert mixed number to an improper fraction

[tex]48\frac{1}{4} =\frac{48*4+1}{4}=\frac{193}{4}\ oz[/tex]

Find the unit rate

[tex]\frac{2.49}{(193/4)}= 0.0516\frac{\$}{oz}[/tex]

case D) we have

64 3/4 oz. carton costs $3.75

Convert mixed number to an improper fraction

[tex]64\frac{3}{4} =\frac{64*4+3}{4}=\frac{259}{4}\ oz[/tex]

Find the unit rate

[tex]\frac{3.75}{(259/4)}= 0.0579\frac{\$}{oz}[/tex]

Part 2) which size is the best buy

we know that

The best buy is the one with the smallest unit rate

so

[tex]0.0516\frac{\$}{oz}[/tex]

The best buy is the size 48 1/4 oz

Answer:Expert's right here WHY U LOOK AT ME

Step-by-step explanation:

Hello!

So, to answer this question we need to note that quadruple = x4

25 (our initial count) x 4 = 100

100 (after one hour) x 4 = 400

400 (after two hours) x 4 = 1600

1600 (after three hours) x 4 = 6400

6400 (after four hours) x 4 = 25600

25600 (after five hours) x 4 = 102400

So to answer your question, after six hours, there will be 102,400 of that bacteria in the jar.

Hope this helps!

the original price was $1800 because if you multiple 1800 by 75 percent you get 1350 and 1800 - 1350 is equal to 450 your sale price

Without knowing the ages of all the different members of the club, I believe that the mean would go down due to 24 being an outlier. You generally take the mean by adding up all the numbers and dividing by all the # of given values. Outliers such as 24 would skew the results leaning none way or the other, in this case making it lower than the previous mean.

Answer:it decreased

Step-by-step explanation:

need the image to see the answer

3.2c+1.7=24.1

First subtract 1.7 from both sides

3.2c=22.4

Now divide both sides by 3.2

c=7

Now put it in the equation.

3.2(7)+1.7=24.1

3.2c + 1.7 = 24.1'

c = (24.1 - 1.7) : 3.2

c = 22.4 : 3.2

c = 7

The word form of 53,200.4 would be fifty-three thousand, two hundred and four tenths.

Now remember, to say a number in a decimal in word form, you must remember the names for each placement.

.1 the one would be in the tenths

.01 the one would be in the hundredths; and

.001 the one would be in the thousandths.

MPG= 30 4/5 or 30.8 is I think is the answer.

Answer:

[tex]unit\ rate=114 \frac{miles}{gallon}[/tex]

Step-by-step explanation:

Hello, I think I can help you with this

remember some properties of mixed numbers

[tex]a\frac{b}{c}=\frac{(a*c)+b}{c}\\ example\\3\frac{1}{5}= \frac{(3*5)+1}{5}=\frac{16}{5}\\[/tex]

Step 1

covert 28 1/2

a=28

b=1

c=2

[tex]a\frac{b}{c}=\frac{(a*c)+b}{c}\\28\frac{1}{2}= \frac{(28*2)+1}{2}=\frac{57}{2}=28.5\\[/tex]

Hence, the distance she drove is 28.5 miles

Step 2

find the  number of gallons

[tex]\frac{1}{4}=0.25[/tex]

then, she used 0.25 gallons to travel 28.5 miles

Step 3

find the unit rate for miles per gallon

[tex]unit\ rate=\frac{number\ of\ miles}{number\ of\ gallons}\\ unit\ rate=\frac{28.5\ miles}{0.25\ gallons}\\unit\ rate=114 \frac{miles}{gallon}[/tex]

Have a great day.

9/200

Find the GCD (or HCF) of numerator and denominator

GCD of 45 and 1000 is 5

Divide both the numerator and denominator by the GCD

45 ÷ 5

1000 ÷ 5

Naya has $60. Each box of cupcakes costs $12.

60÷12=5

Naya can buy 5 boxes of cupcakes.

Answer:

{x | x = 0.5 or x = 4.5}

Explanation:

Before we begin, remember that:

The modulus gives the positive value of what's inside it.

This means that:

|a| = |-a| = a

Now, for the given, we have:

|2x-5| = 4

From the above rule, we can deduce that:

either:

2x - 5 = 4

2x = 4 + 5 = 9

x = 4.5 ............> first solution

Or:

2x - 5 = -4

2x = 5-4 = 1

x = 0.5 ..........> second solution

Now, we check:

at x = 4.5: |2(4.5)-5| = |9-5| = |4| = 4 ..........> first solution verified

at x = 0.5: |2(0.5)-5| = |1-5| = |-4| = 4 .........> second solution verified

Hope this helps :)

Answer:

{x | x = 0.5 or x = 4.5}

Step-by-step explanation:

Answer: $9000

A gym employee has earned in 3 months =$4500

Then his monthly salary =$4500/3 =$1500

After six months he will earn = 6 × his monthly salary

= 6×$1500=$9000

His salary table will be as follows

C.

Any number that is over the denominator 9, will be repeating it self.

the answer will be  is V=8/t

i think the answer is 37/20