Answers
1. You have the following expression:
(3+3i)-(13+15i)
2. If you want to substract both terms, you need to substract the real numbers and the complex numbers. Then, you obtain:
3+3i-13-15i
(3-13)+(3i-15i)
3. Then, you obtain the following result:
-10-12i
4. Therefore, as you can see, the correct answer is the last option (option D), which is:
D. -10-12i
Related Questions
if you flip a coin four times what is the probability of flipping tails four times
Answers
Out of all 16 outcomes, there is only one way to get the result T T T T.
Therefore, the probability is 1/16 or 0.0625
Which summation formula represents the series below?
13 + 9 + 5 + 1
Answers
The sum of the series is 28.
The series 13 + 9 + 5 + 1 is an arithmetic series with a common difference of -4. To express this in summation (sigma) notation and find its sum, we first identify the first term (a1) as 13 and the common difference (d) as -4.
Next, we determine the number of terms (n). The series decreases by 4 each time, so we find the number of steps it takes to go from 13 to 1, which are 4 terms in total (13, 9, 5, 1).
We can write the summation formula for an arithmetic series as Sn = n/2 * (2a1 + (n-1)d), where Sn is the sum of the first n terms. With n = 4, a1 = 13, and d = -4, we plug these into the formula:
S4 = 4/2 * (2(13) + (4-1)(-4))
S4 = 2 * (26 - 12)
S4 = 2 * 14
S4 = 28
The sum of the series is 28.
Find the midpoint of the segment with the given endpoints. P(–2, 1) and Q(–3, 2)
Answers
Answer:
(-5/2, 3/2)
Step-by-step explanation:
The midpoint is the average of the coordinates of the endpoints:
(P +Q)/2 = ((-2, 1) +(-3, 2))/2 = (-2-3, 1+2)/2 = (-5/2, 3/2)
hey can you please help me posted picture of question
Answers
The composition of the function and its inverse must be zero. So the composition of 7x with x/7 is:
[tex](F( F^{-1}x)) \\ \\ =F( \frac{x}{7}) \\ \\ = 7(\frac{x}{7}) \\ \\ = x [/tex]
Thus, 7x and x/7 are inverse of each other.
So the answer to this question is option B
the width of a rectangle is shown below:
Answers
B = A +(6, 0) = (-4, 4) +(6, 0) = (-2, 4)
D = C +(6, 0) = (-4, -3) +(6, 0) = (-2, -3)
The appropriate choice is the last one, ...
(-2, 4) and (-2, -3)
Marko is buying carpet for his bedroom floor. His room measures 13 feet by 12 feet. How many square feet of carpet will Marko need to cover the floor in his room?
Answers
Answer: 156 square feet of carpet would be needed to cover the floor in his room.
Step-by-step explanation:
Since we have given that
Dimensions of his room as follows :
Length of his room = 13 feet
Width of his room = 12 feet
We need to find the square feet of carpet which is used to cover the floor of his room.
so, we just need to find the area of his room.
Area of rectangle = Length × Breadth
So, Area of his room becomes
[tex]13\times 12\\\\=156\ sq.\ feet[/tex]
Hence, 156 square feet of carpet would be needed to cover the floor in his room.
each of 5 boys ate 2/3 of a pizza. what is the total amount of pizza the boys ate?
Answers
Turn 5 into a fraction. 5/1
Multiply the two fractions. 5/1 × 2/3 = 10/3
Simplify this to 3 1/3 pizzas.
Hope this helps!
We have that for the Question "each of 5 boys ate 2/3 of a pizza. what is the total amount of pizza the boys ate?" it can be said that each boy ate
Pt=3.333pizzaFrom the question we are told
each of 5 boys ate 2/3 of a pizza. what is the total amount of pizza the boys ate? total amount of pizza the boys ateGenerally the equation for the total amount of pizza the boys ate is mathematically given as
Pt=N*Ratio
Therefore
Pt=5*2/3
Pt=3.333pizza
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simplify leaving your answer with positive exponents.
Answers
[tex]\bf \left( \cfrac{n^{\frac{2}{3}\cdot \frac{2}{3}}}{5^{\frac{2}{3}}m^{\frac{4}{3}\cdot \frac{2}{3}}} \right)\left( \cfrac{8^{\frac{4}{3}}n^{5\cdot \frac{4}{3}}}{m^{4\cdot \frac{4}{3}}} \right)\implies \cfrac{n^{\frac{4}{9}}}{5^{\frac{2}{3}}m^{\frac{8}{9}}}\cdot \cfrac{8^{\frac{4}{3}}n^{\frac{20}{3}}}{m^{\frac{16}{3}}}\implies \cfrac{8^{\frac{4}{3}}n^{\frac{4}{9}+\frac{20}{3}}}{5^{\frac{2}{3}}m^{\frac{8}{9}+\frac{16}{3}}}[/tex]
[tex]\bf \cfrac{8^{\frac{4}{3}}n^{\frac{4+60}{9}}}{5^{\frac{2}{3}}m^{\frac{8+48}{9}}}\implies \cfrac{8^{\frac{4}{3}}n^{\frac{64}{9}}}{5^{\frac{2}{3}}m^{\frac{56}{9}}}[/tex]
Marcus baked a loaf of banana bread for a party. He cut the loaf into equal size pieces. At the end of the party, there 6 pieces left. Explain how you can find the number of pieces in the whole loaf if Marcus told you that 1/3 of the loaf was left.
Answers
Find the length and width of a rectangle that has the given area and a minimum perimeter. area: a square centimeters
Answers
Factor completely 56a2b3 − 35ab.
7ab(8ab2 − 5)
7a(8b2 − 5ab)
Prime
7a(8ab3 − 5b)
Answers
Both numbers have a factor of 7ab. Pull that out by dividing.
Answer:
7 ab ( 8 ab² - 5 ) .
Step-by-step explanation:
Given : 56 a²b³ − 35 ab.
To find : Factor completely.
Solution : We have given 56 a²b³ − 35 ab.
Taking 7ab common form both terms .
7 ab ( 8 ab² - 5 ) .
Therefore, 7 ab ( 8 ab² - 5 ) .
PLZ HELP ASAP CIRCLES
Answers
Therefore, the equation of the circle is:
(x + 1)^2 + (y - 1)^2 = 74
what is the domain and range of
y=-2(x-3)(x+4)
Answers
The vertex of this function is (-0.5, 24.5), so the range of y=-2(x-3)(x+4) is
-∞ < y ≤ 24.5
A triangle has interior angles measuring 40 and 52. Which triangle are similar to this triangle? select true or false for each triangle.
Answers
If you have a triangle with 40 and 52, then the third angle is 180 - 40 - 52 = 88 degrees.
Any triangle that has at least two of the three angles ( 40 , 52 and 88) will be similar
1. FALSE
2. FALSE
3. TRUE
4. TRUE
please help me with this if you can
Answers
(22.8 -22.3)/22.3 * 100% ≈ 2.2%
The equation of a circle is (x−2)^2+(y−16)^2=169 . What is the circle's radius?
Answers
The equation for a circle is
[tex] (x-h)^{2} +(y-k)^{2} = r^{2} [/tex]
r is the radius
To find the radius we take the square root of the number in the radius spot
sqrt169 = 13
The answer is 13
Hope this helps!
Today a clothing store took 30% off the price of a dress, and for the next 3 days, it will take 30% off the previous day's price. If the price of the dress yesterday was $300.00, what will be the price of the dress 3 days from now?
Answers
To find the new price, you can multiply by 0.7 (100%-30% = 70%/0.7).
300 x 0.7 = 210 (now)
1st day: 210 x 0.7 = $147
2nd day: $147 x 0.7 = $102.90
3rd day: 102.9 x 0.7 = $72.03
The price on the third day is $72.03.
Answer:72.03
Step-by-step explanation:
if 12 1/2% of a sum of money is $40 what is the total sum of money?
Answers
12.5% = $40
1% = 40 ÷ 12.5 = $3.20
100% = $3.20 x 100 = $320
Answer: $320
The total sum of money will be $320.
Let the total sum of money be represented by x.
Based on the information given, the equation to solve the question will be:
12 1/2% × x = 40
0.125x = 40
Divide by 0.125
x = 40/0.125.
x = 320
Therefore, the total sum of money will be $320.
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hey can you please help me posted picture of question
Answers
1. You have the following expression:
(11-7i)-(16-11i)
2. If you want to substract both terms, you need to substract the real numbers and the complex numbers. Then, you obtain:
11-7i-16+11i
(11-16)+(-7+11)
3. Then, you obtain the following result:
-5+4i
4. Therefore, as you can see, the correct answer is the second option (option B), which is:
B. -5+4i
Solution is shown below:
To add or subtract two complex numbers, the real part is added or subtracted from real part and the complex part is added to or subtracted from complex part as shown below:
(11 - 7i) - (16 - 11i)
= 11 - 7i - 16 + 11i
= -5 + 4i
So, the answer to this question is option B
One serving of Mike’s crackers has 150 calories and a mass of 30 grams. How many calories are in 6 grams of the crackers?
Answers
The amount of calories that are in 6 grams of crackers is 30 grams.
What is the amount of calories in the crackers?Division is the mathematical operation that is used to determine the quotient of a number. It is the process of grouping a number into equal parts using another number.
Calories in 6 grams = (150 / 30) x 6 = 30 grams
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Final answer:
To find the calories in 6 grams of Mike's crackers, divide the total calories by the total mass of one serving to get the unit rate (5 calories/gram) and then multiply by the mass in question (6 grams) to obtain 30 calories.
Explanation:
The question asks how many calories are in 6 grams of Mike's crackers, given that one serving of 30 grams has 150 calories. To find the calories in 6 grams of the crackers, we can use unit rate and proportions.
Step-by-Step Calculation
First, determine the calories per gram of the crackers by dividing the total calories by the total mass (in grams) of one serving. This gives us the unit rate: 150 calories / 30 grams = 5 calories per gram.
Next, since we're asked about the calories in 6 grams, we multiply the calories per gram (unit rate) by the mass: 5 calories/gram × 6 grams = 30 calories.
Therefore, there are 30 calories in 6 grams of Mike's crackers. This calculation illustrates the utility of understanding proportions and unit rates in everyday applications such as determining caloric intake from portions of food.
a player gets to throw 4 darts at the target shown. Assuming the player will always hit the target, the probability of hitting an odd number three times is *blank* times more than the probability of hitting an even number 3 times
Answers
Answer: The probability of hitting an odd number three times is [tex]3\dfrac{3}{8}[/tex] times more than the probability of hitting an even number 3 times.
Step-by-step explanation:
From the given picture , the total total number of sections in the spinner = 5
Sections having Odd numbers = 3
Sections having Even numbers =2
We know that , [tex]\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
So , probability of hitting an odd number = [tex]\dfrac{3}{5}[/tex]
Probability of hitting an even number = [tex]\dfrac{2}{5}[/tex]
Since all events are independent of each other ,
So , probability of hitting an odd number three times = [tex](\dfrac{3}{5})^3=\dfrac{27}{125}[/tex]
Probability of hitting an even number three times = [tex](\dfrac{2}{5})^3=\dfrac{8}{125}[/tex]
Divide [tex]\dfrac{27}{125}[/tex] by [tex]\dfrac{8}{125}[/tex] , we get
[tex]\dfrac{27}{125}\div\dfrac{8}{125}\\\\=\dfrac{27}{125}\times\dfrac{125}{8}=\dfrac{27}{8}=3\dfrac{3}{8}[/tex]
Hence, the probability of hitting an odd number three times is [tex]3\dfrac{3}{8}[/tex] times more than the probability of hitting an even number 3 times.
Answer:
3.375
Step-by-step explanation:
You are traveling to Chicago for a job interview. You leave Toledo, Ohio, at 5:45 A.M. and arrive in Elkhart, Indiana, at 8:15 A.M.. The distance from Toledo to Elkhart is 136 miles; the distance from Toledo to Chicago is 244 miles. The speed limit is 65 mph. What is the minimum speed you must maintain in order to arrive in Chicago before 10:30 A.M.
Answers
To get from Elkhart to Toledo is 108 miles. (244-136)
It will take 2.25 hours to get there. From 8:15 am to 10:30 am is 2 1/4 hours.
108 miles/2.25 hours = 48 miles per hour. You must travel at an average speed of 48 miles per hour.
hey can you please help me posted picture of question
Answers
We can conclude that the correct answer is B. Quadratic parent function.
As viewed from above, a swimming pool has the shape of the ellipse x24900+y22500=1, where x and y are measured in feet. the cross sections perpendicular to the x-axis are squares. find the total volume of the pool. v = cubic feet
Answers
a=sqrt(4900)=70
b=sqrt2500=50
The squares are parallel to the y-axis, thus their sides extend in the y-axis direction, hence the length of the sides are:
y=+/-50sqrt(1-x^2/4900))
The area of the square
=y^2=[2500-2500(x^2/4900)
Thus, the volume will be sum along the x-axis from one of the ends of the ellipse to the other. by definition, the limits are (-a to a)=(-70 to 70)
But since the ellipse is symmetrical we can go from (0 to 70) and double the integral.
thus
V=2*int(0 to 70)[2500-2500(x^2/4900)]dx
=int(0 to 70)[5000-(50/49)x^2]dx
=[5000x-50/147x^3] (0 to 70)
=233,333 1/3 ft^3
all I drink 3/4 of a 16 fluid ounce bottle of juice how many fluid ounces of juice are left in the bottle
Answers
multiply 16 oz. by 3/4 to find how many ounces are 3/4 of the bottle
=16 * 3/4
=(16*3)/4
=48/4
=12 ounces
STEP 2:
subtract step 1 answer from the whole 16 oz. to find number of ounces left
=16 - 12
=4 ounces left
CHECK:
multiply the whole 16 oz. by the fraction that would be left (4/4 - 3/4= 1/4). There are several ways to check this problem; this is just one way.
=16 * 1/4
=(16*1)/4
=16/4
=4
ANSWER: 4 ounces would be left
Hope this helps! :)
hello can you please help me posted picture of question
Answers
:)
Start from the inner most circle.
5 patrons like all 3 drinks.
8 patrons like Latte and Espresso. From these 8, 5 like all 3 drinks, so the patrons which only like Latte and Espresso will be 3.
Fill all the regions this way and you will get a diagram similar to the one given below.
Count all the numbers inside the circles. These add up to 47. This means 47 patrons like the drinks.
Total number of patrons was 50. So there are 7 such patrons which do not like any of these drinks.
So, the correct answer is option B
12+5v=2v-9 please show step by step!
Answers
Subtract 12 from both sides.
5v = 2v - 21
Subtract 2v from both sides.
3v = -21
Divide both sides by 3.
v = -7
To get it, combine like terms and restrain the variable. Segregating both sides by 3 gives the solution to the equation as v = -7.
How to solve the expressionTo solve the condition 12 + 5v = 2v - 9, take after these steps:
Step 1: Segregate the variable terms on one side of the condition and the steady terms on the other side.
Subtract 2v from both sides to move the variable term to the cleared outside:
12 + 5v - 2v = 2v - 9 - 2v
Alter both sides of the condition:
12 + 3v = -9
Step 2: Separate the variable term by moving the reliable term to the other side.
Subtract 12 from both sides to move the dependable term to the proper side:
12 + 3v - 12 = -9 - 12
Unwind both sides of the condition:
3v = -21
Step 3: Light up for v by confining both sides of the condition by the coefficient of v, which is 3.
Portion by 3 to clarify for v:
v = -21 / 3
Streamline the division:
v = -7
The solution to the equation is v = -7.
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Each square is one square meter
Answers
HURRY PLEASE ITS TIMED
In the year 2000, Franklintown had a population of 30,000 people. Its population had decreased by 3% each year since then. Part A: Can this situation be modeled by an exponential decay function, an exponential growth function, or neither? Explain. Part B: If the population continues to decrease at the same rate, what would you expect the approximate population to be in 2016? Show your work.
Answers
For this case we have a function of the form:
y = A * (b) ^ t
Where,
A: initial amount
b: decrease rate
t: time
Substituting values we have:
y = 30000 * (0.97) ^ t
Answer:
this situation can be modeled by an exponential decay function.
Part B:
We have the following function:
y = 30000 * (0.97) ^ t
For the year 2016 we have to:
t = 16
Substituting values:
y = 30000 * (0.97) ^ 16
y = 18427.6096
Rounding:
y = 18428
Answer:
The approximate population for 2016 is:
y = 18428
in the plane figure shown below. if the degree measures of the angle are as shown, then x+y=
Answers
the sum of the internal angles in the figure shown is 360 degrees
so
360°=100°+60+70°+y+80°+x
360°=(x+y)+310°
(x+y)=360°-310°-----> 50°
the answer is
x+y is 50°