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.
Explanation: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).
Learn more about Complex Numbers here:https://brainly.com/question/20566728
#SPJ3
orange juice is sold in four different sizes the 8 1/2 ounce bottle costs $0.99 the 18 2/2 oz. bottle costs $1.49 the 48 1/4 oz. carton costs $2.49 and the 64 3/4 oz. carton costs $3.75
1.calculate a unit rate for each size
2. which size is the best buy
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:
Please help ! Mark brainly !
it would be positive because the positive number is bigger than the negative number.
Combine the two terms. Note that one negative sign and one positive sign will result in a negative sign.
8704 + (-7725) = 8704 - 7725 = 979
979 is the resulting number, which is a positive number
Positive is your answer
hope this helps
Jenny writes a story for 60 mind if she starts writing her story at 11:50 Am when will she Finnish writing
Answer:
12:50 AM
Step-by-step explanation:
60 minutes is 1 hour. add one hour to the start time to get 12:50 AM
Answer:
12:50 AM
Step-by-step explanation:
Add one hour to the start time
What is -35,840-(-14,764)
Which one is greatest to least ?
0.23, 1/5, 19%
i believe that is correct
yesterday grace drove 28 1/2 miles she used 1/4 gallons of gasoline.what is the unit rate for miles per gallon
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.
Somebody help!!!! Please
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
Complete the table for the given rule.
Rule: y=x−4
x y
4
6
8
Answer:
x y
4 0
6 2
8 4
Step-by-step explanation:
y=x-4
Replace x each x variable
4-4=0
6-4=2
8-4=4
To complete the table for the given rule y = x - 4, the values of y are found by substituting the x-values into the equation, resulting in y-values of 0, 2, and 4 for x-values of 4, 6, and 8, respectively.
The student has asked to complete a table for the given rule: y = x - 4. To find the value of y for each given x, we simply substitute the x values into the equation and solve for y.
For x = 4, y = 4 - 4 = 0.
For x = 6, y = 6 - 4 = 2.
For x = 8, y = 8 - 4 = 4.
Therefore, the completed table is:
x = 4, y = 0
x = 6, y = 2
x = 8, y = 4
local Readers Club has a set 36 hardback books and a set of 30 paperback books each set can be divided equally among the club members what is the greatest possible number of club members
john is saving money at a constant rate. Suppose he initially has $110 saved and after 2 months he has $160 saved. at what rate is john saving
The rate John is saving is 25. How? You can do 160-110 (to find difference). After this, you will get 50. You can now divide this by 2 (because the problem says two months), which is 25. You can see if this is correct by adding 25 to 110 two times.
110 + 25
= 135
135+25
=160
John is saving money at a constant rate is $25.
Given that, suppose he initially has $110 saved and after 2 months he has $160 saved.
What is the rate?The definition of a rate is a quantity measured and compared to another quantity measured (such as a number of miles per hour) or is the cost of something.
Now, money saved=160-110=$50, time 2 months
Rate of money per month=50/2=$25
Therefore, John is saving money at a constant rate is $25.
To learn more about the rate of money saved visit:
https://brainly.com/question/11616721.
#SPJ2
If Fernando paid $450 for a netbook that was 75% off the original price what was the original price?
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
3x-2+5x=-4x+5-2x solve
Hey there!!
Given equation :
... 3x - 2 + 5x = 4x + 5 - 2x
Combining like terms :
... 8x - 2 = 2x - 5
Subtracting 2x on both sides :
... 6x - 2 = - 5
Adding 2 on both sides :
... 6x = - 3
Dividing by 6 on both sides :
... x = -1/2 = -0.5
Hence, the answer is -0.5
Hope my answer helps!
[tex]4y + 8 = 2[/tex]
[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
If the measure of angle ABF=6x+26 and the measure of angle EBF=2x9 and measure of angle ABE= 11x-31 find the measure of angle ABF
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°
What is the angleFrom 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
https://brainly.com/question/25716982
#SPJ4
Consider the system of equations. Which is the Best method to use for solving the system? 4x+y=1 2x+y=8
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
Solve for b , then find the value of b when a= 3
4a=2b-7
I AM NOT GOOD @ WORD PROBLEMS
Here are you're answers:
Number sentence: 25 - 14 = 11
Word sentence: twenty-five minus fourteen equals eleven
The three boxes:
11
25 14
Hope this helps!
word form of 53,200.4
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.
order these numbers from least to greatest -3/5 , 7/9, 1.7,-7/2,0.3
A certain bacteria is placed in a jar. Initially, there are 25 bacteria. Every hour, the number of bacteria quadruples. How much bacteria will there be in 6 hours?
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!
3.5 inches divided by 24.5 inches
could a number ever be both rational and irrational
By definition an irrational number is one that is not rational. Therefore, it is not possible for a number to both rational and irrational.
find the range of the following peicewise functiom
f(x) = x + 4 ; -4 ≤ x < 3
f(-4) = (-4) + 4
= 0
f(3) = (3) + 4
= 7
R: 0 ≤ y < 7 ⇒ [0, 7)
***************************
f(x) = 2x - 1 ; 3 ≤ x < 6
f(3) = 2(3) - 1
= 6 - 1
= 5
f(6) = 2(6) - 1
= 12 - 1
= 11
R: 5 ≤ y < 11 ⇒ [5, 11)
******************************
Now, put them together: [0, 7) U [5, 11) = [0, 11)
Answer: B
answer is [0,11)
f(x) = x+4 is the first function
We plug in -4 for x in f(x) = x+4
f(-4) = -4 + 4 = 0
So the graph starts at (-4,0)
Now plug in 3 for x in f(x) = x+4
f(3) = 3 + 4 = 7
So the first function ends at (3,7)
Second function is f(x) = 2x - 1
We plug in 3 for x in f(x) = 2x-1
f(3) =2(3)-1 = 5
So the second graph starts at (3,5)
We plug in 6 for x in f(x) = 2x-1
f(6) =2(6)-1 = 11
So the second graph ends at (6,11)
3<=x<6 so 6 is excluded from x
The range of the following piece wise function is 0 to 11
answer is [0,11)
I need help
~~~~~
Hggffv
Complete the ratio table to show ratios equivalent to 16:10. The blank parts are what's missing. Thank you
2 8
36 9 72
The ratio table is completed by finding values that are equivalent to the ratio 16:10, which simplifies to 8:5. The corresponding values are calculated by setting up proportions based on the original ratio.
Explanation:To complete the ratio table that shows ratios equivalent to 16:10, we first understand that the ratio can be simplified to 8:5 by dividing both terms by 2.
We can use this simplified ratio to find missing values in the table.
For the row with 2 in the first column, the second column should be 2 times 5/8 (since 8:5 is equivalent to 16:10) to maintain the ratio equivalency.
This gives us the value 2*(5/8)=1.25.
In the row where the second column is 36, we need to determine the equivalent in the first column.
We set up the proportion 8/5=x/36, and solving for x gives us 8*(36/5)=57.6.
The last row given is 72 in the second column.
To find the corresponding first column value, we use the ratio 8/5=x/72 and solve for x to find 8*(72/5)=115.2.
The filled in ratio table should look like this:
2 : 1.2557.6 : 36115.2 : 72Write an expression that shows how to use the halving and doubling strategy to find 28x50
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]
A local garden club had 14 members with a mean age of 34. Then two new members joined. One was 24 years old, and the other was 36 years old. How did the mean age change after they joined?
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:
If a and −a are numbers on the number line, which expression MUST give the distance between them?
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.
In science class Abigail's frog weighed 0.88 kilograms what is the value of the digit in the tenths place
In decimals, the tenths place is right after the decimal point. Therefore, the value of the digit in the tenths place of 0.88 is 8.
3.2c + 1.7 = 24.1'
c=
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