What is the product of the complex numbers below?(3 - 2i)(1 + 7i)A.-11 + 19iB.17 + 19iC.-11 - 23iD.17 - 23i
Answers
Solution:
Given:
[tex](3-2i)(1+7i)[/tex]To find the product, we multiply the terms in the second parentheses by each term in the first parentheses.
Thus, we have
[tex]\begin{gathered} 3(1+7i)-2i(1+7i) \\ open\text{ parentheses,} \\ 3+21i-2i-14i^2 \\ but\text{ i}^2=-1 \\ thus,\text{ we have} \\ 3+21i-2i-14(-1) \\ collect\text{ like terms,} \\ (3+14)+i(21-2) \\ \Rightarrow17+19i \end{gathered}[/tex]Hence, the product of the complex numbers is
[tex]17+19i[/tex]The correct option is B
Related Questions
The student Fun Club plans to go to the movies. At the matinee, tickets cost $6 and popcorn is $3. At evening shows, tickets cost $9 and popcorn is $4. The Fun Club attends a matinee and spends less than $60, and then attends an evening show and spends more than $36. If they purchased the same number of tickets and popcorns at each show, which of the following is a possible solution for the number of tickets and popcorns purchased?
Answers
Matinee
Cost of each ticket: $6
Cost of popcorn: $3
Evening:
Ticket: $9
Popcorn: $4
Number of tickets: x
Number of popcorns : y
The Fun Club attends a matinee and spends less than $60
6x + 3y < 60
Then attends an evening show and spends more than $36
9x+ 4y < 36
We have the system:
6x + 3y < 60 (a)
9x+ 4y >36 (b)
Graph each inequality:
The intersection of red and blue is the solution.
7 tickets and 5 popcorns (7,5) is inside the intersection, So, it is the solution.
Use the long division method to find the result when 8x3 + 30x2 + 3x – 1 is divided by 4x + 1. If there is a remainder, express the result in the form q(x) + r(3) b(x)
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Answer:
[tex]2x^2+7x-1[/tex]Explanation:
Given the polynomial division:
[tex]\frac{8x^3+30x^2+3x-1}{4x+1}[/tex]The long division table is attached below:
Therefore, we have that:
[tex]\frac{8x^3+30x^2+3x-1}{4x+1}=2x^2+7x-1[/tex]please help me I really need help in my math work
Answers
we need to know the formula of the area of a rectangle
[tex]A=l\cdot w\text{ }[/tex]we already know A and l we need to clear w
[tex]w=\frac{A}{l}=\frac{2x^2+5x-12}{2x-3}[/tex]we need to do the division
[tex]undefined[/tex]Use the substitution property of equality to complete the following statement.
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Given:-
[tex]8x+y=12[/tex]To find x when y is 3.
So now we substitute,
[tex]\begin{gathered} 8x+y=12 \\ 8x+3=12 \\ 8x=12-3 \\ 8x=9 \\ x=\frac{9}{8} \end{gathered}[/tex]So the value is,
[tex]\frac{9}{8}[/tex]Becca wants to make a giant apple pie to try and break the world record. If she succeeds in making a pie with 20 foot diameter, what will the size of the crust covering the pie be?
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ANSWER :
62.83 feet
EXPLANATION :
The pie has a diameter of 20 feet.
The size of the crust covering is the circumference of the pie.
The circumference formula is :
[tex]C=2\pi r[/tex]We know that the radius is half of diameter.
So the radius is 20/2 = 10 feet.
Using the formula above :
[tex]\begin{gathered} C=2\pi(10) \\ C=62.83 \end{gathered}[/tex]If f(x) = -2x + 8 and g(x) = v* + 9, which statement is true?
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We have the function;
[tex]f(x)=-2x+8[/tex]and
[tex]g(x)=\sqrt[]{x+9}[/tex]Let's obtain f(g(x) before we make conclusions on the statements.
[tex]f^og=-2(\sqrt[]{x+9})+8[/tex]The domain of f(g(x) starts from x= - 9, this is where the function starts on the real line.
But - 6 < -9 , and thus,
The answer is - 6 is in the domain of the function.
what is the scale factor from triangle PQR to triangle STU
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To find the scale factor from one triangle to another we need to divide the measurements of the second triangle by the corresponding measurements of the first triangle.
Since we need the scale factor from triangle PQR to triengle STU we need to divide the measurements of STU by the corresponding measurements of triangle PQR.
Sides PR and SU are corresponding sides, so we sivide 12 by 8:
[tex]\frac{12}{8}=\frac{3}{2}[/tex]To confirm, we also divide the measurements of sides UT and RQ:
[tex]\frac{9}{6}=\frac{3}{2}[/tex]Thus, the scale factor is: 3/2 = 1.5
how do I have to search x in a triangle??
Answers
1) the value of x is 7
Explanation:1) From the diagram, the angles with the red ink are equal.
SInce the two angles at the base are equal, we call the triangle an isosceles triangle.
This triangle have two sides and two angle equal.
As a result, the sides opposite the angles given in the triangle are equal to each other.
The sides opposite the angles are x and 7. So, x is equal to 7.
Hence, the value of x is 7
The same principle or procedure can be applied to question number 2.
The population P of a city is given by P = 115600e^0.024t, where t is the time in years. According to this model, after how many years will the population be 130,000?4.29 years4.89 years5.19 years4.49 years
Answers
Given:
The population P of a city is given by,
[tex]P=115600e^{0.024t,}[/tex]To find:
The time taken for the population to reach 130,000.
Explanation:
Substituting P = 130,000 in the given function, we get
[tex]\begin{gathered} 130000=115600 \\ e^{0.024t}=\frac{130000}{115600} \\ e^{0.024t}=1.1245 \\ 0.024t=\ln1.1245 \\ 0.024t=0.1174 \\ t=4.891 \\ t\approx4.89years \end{gathered}[/tex]Therefore, the number of years required for the population to reach 130,000 is 4.89years.
Final answer:
The number of years required is 4.89years.
-5 > 5 + x/3 I am so confused on these things
Answers
Let's solve the inequality:
[tex]\begin{gathered} -5>5+\frac{x}{3} \\ -5-5>\frac{x}{3} \\ -10>\frac{x}{3} \\ -10\cdot3>x \\ -30>x \\ x<-30 \end{gathered}[/tex]Therefore the solution for the inequality is:
[tex]x<-30[/tex]In interval form this solution is written as:
[tex](-\infty,-30)[/tex]This means that x has to be less than -30 for the inequality to be true.
Ramesh leaves 2/3 of his property for his wife and 1/4 for his son and remaining for his daughter what part does his daughter receive Help me fast
Answers
3×4 = 12
2x4 = 8
4x3= 12
1x4=4
So that would be 8/12 and 4/12
Then you would add the numerator so 8+4 = 12
so the mother and the son together get 12/12 of his property which is everything. So the daughter gets nothing.
Drag each expression to the correct location on the model. Not all expressions will be used.552 + 25r + 2071
Answers
Given
[tex]\frac{5x^2+25x+20}{7x}[/tex]To find: The equivalent rational expression.
Explanation:
It is given that,
[tex]\frac{5x^2+25x+20}{7x}[/tex]That implies,
[tex]\frac{5x^2+25x+20}{7x}[/tex]step by step guide I am stuck at the part where you have to divide, I have split them up into 2 and got GCF for p on first term and 6 on second term
Answers
We have the next expression:
[tex]pq\text{ - pr + 6q-6r}[/tex]Factorize using factor by grouping.
First, let's find the common terms. The one who is in all terms or majority terms.
In this case, let's use p:
[tex]p(q-r)+6q-6r[/tex]Factorize the common term 6.
[tex]p(q-r)+6(q-r)[/tex]Look at the expressions, both are multiply by (q-r), so we can rewrite the expression like this:
Factorize the common term (q-r)
[tex](q-r)(p+6)[/tex]Simplify the expression below. Share all work/thinking/calculations to earn full credit. You may want to do the work on paper and then upload an image of your written work rather than try and type your work. \sqrt[4]{ \frac{162x^6}{16x^4} }
Answers
1. If triangle ABC is congruent to triangle DEF, DE=17, EF =13, DF =9, and BC = 2x-5, then which of the following is the correctvalue of x?(1) 5(3) 9(2) 7(4) 11
Answers
If both trianlges are congruent, we get that:
[tex]BC=DE[/tex]This way,
[tex]2x-5=17[/tex]Solving for x :
[tex]\begin{gathered} 2x-5=17 \\ \rightarrow2x=17+5 \\ \rightarrow2x=22 \\ \Rightarrow x=11 \end{gathered}[/tex]This way, we get that x = 11
Answer: Option 4
Lucy sold some items at a garage sale. She spent 7/12 of her earnings on a new bike. She uses 3/5 of the remainder to purchase a gift for her mom. What fraction of her total earnings was spent on her mom's gift?
Answers
First we have to find what fraction remained after buying the bike.
Subtracting 7/12 from 12/12 ( which represents the total)
The result is 5/12
Then, we are going to multiply 3/5 by 5/12 ( the remainder) to find our final answer.
[tex]\begin{gathered} \frac{3}{5}\cdot\frac{5}{12}=\frac{15}{60} \\ \frac{15}{60}=\frac{5}{20}=\frac{1}{4}\text{ Simplifying our fraction} \end{gathered}[/tex]The fraction of her total earnings spent on her mom's gift was 1/4
7/8 = 7/16 =Reduce your answer to the lowest terms.
Answers
x[tex] {x}^{3} {y}^{8} term(x + y) ^{11} [/tex]find the coefficient of the given term in the binomial expansion
Answers
Using the binomial theorem, we have that the expansion of (x+y)^11 is:
[tex]\begin{gathered} (x+y)^{11}= \\ x^{11}+11x^{10}y+55x^9y^2+165x^8y^3+330x^7y^4+462x^6y^5+462x^5y^6+330x^4y^7+165x^3y^8+55x^2y^9+11xy^{10}+y^{11} \end{gathered}[/tex]notice that the coefficient of the term x^3 y^8 is 165
Given: D is the midpoint of segment AC, angle AED is congruent to angle CFD and angle EDA is congruent to angle FDCProve: triangle AED is congruent to triangle CFD
Answers
Since Angle AED is congruent to angle CFD and angle EDA is congruent to angle FDS, we can use the midpoint theorem to get the following:
[tex]\begin{gathered} D\text{ is midpoint of AC} \\ \Rightarrow AD\cong AC \end{gathered}[/tex]therefore, by the ASA postulate (angle,side,angle), we have that triangle AED is congruent to triangle CFD
You have a $250 gift card to use at a sporting goods store. a) Write an inequality that represents the possible numbers x of pairs of socks you can buy when you buy 2 pairs of sneakers. PRIO *12 SALE PRICE $80 b) Can you buy 8 pairs of socks? Explain.
Answers
Sale price 12
number of socks =X
Sneakers sprice 80
Amount disposable 250
Then
Part a)
250 - 2•80 = 12X
250 - 160 = 12X
90 ≥ 12 X
Part b)Can buy 8 pairs?
Answer NO , because 90 < 12•8
find all other zeros of p (x)= x^3-x^2+8x+10, given that 1+3i is a zero. ( if there is more than one zero, separate them with commas.)edit: if possible please double check answers would high appreciate it.
Answers
Since we have that 1 + 3i is one zero of p(x), then we have that its conjugate is also a root, then, we have the following complex roots for p(x):
[tex]\begin{gathered} x=1-3i \\ x=1+3i \end{gathered}[/tex]also, notice that if we evaluate -1 on p(x), we get:
[tex]\begin{gathered} p(-1)=(-1)^3-(-1)^2+8(-1)+10=-1-1-8+10 \\ =-10+10=0 \end{gathered}[/tex]therefore, the zeros of p(x) are:
x = 1-3i
x = 1+3i
x = -1
find the value of x,y,z
Answers
Answer: x =116 degrees
y = 88 degrees
Explanation:
[tex]\begin{gathered} \text{ Find the value of x, y, and z} \\ To\text{ find z} \\ \text{Opposite angles are supplementary in a cyclic quadrilateral} \\ 101\text{ + z = 180} \\ \text{Isolate z} \\ \text{z = 180 - 101} \\ \text{z = 79 degre}es \\ To\text{ find x} \\ 2(101)\text{ = x + 86} \\ 202\text{ = x + 86} \\ \text{Collect the like terms} \\ \text{x = 202 - 86} \\ \text{x = 116 degr}ees \\ \text{ find y} \\ 2z\text{ = y + 70} \\ z=\text{ 79} \\ 2(79)\text{ = y + 70} \\ 158\text{ = y + 70} \\ \text{y = 158 - 70} \\ \text{y = 88 degre}es \end{gathered}[/tex]Therefore, x = 116 degrees, y = 88 degrees, and z = 79 degrees
9+7d=16 how do i slove it
Answers
9 + 7d = 16
________________
Can you see the updates?
___________________
9 + 7 d = 16
1. we subtract 9 from the two sides
9 - 9 + 7 d = 16 -9
0 + 7 d = 7
2. We divide by 7 both sides
(7 d)/ 7 = 7/ /7
7/7= 1
d= 1
____________________
Answer
9 + 7d = 16
7d= 16 - 9
d= 7/ 7= 1
d= 1
how to write the indicated expression for[tex] \frac{1}{2} m \: inches \: in \: feet[/tex]
Answers
Answer:
Rewriting the given expression in feet gives:
[tex]\frac{1}{24}m\text{ feet}[/tex]Explanation:
We want to write the expression below in feet.
[tex]\frac{1}{2}m\text{ inches in f}eet[/tex]Recall that;
[tex]\begin{gathered} 1\text{ foot = 12 inches} \\ 1\text{ inch = }\frac{1}{12}foot \end{gathered}[/tex]so, converting the expression to feet we have;
[tex]\begin{gathered} \frac{1}{2}m\text{ inches =}\frac{1}{2}m\times\frac{1}{12}feet \\ =\frac{1}{2}\times\frac{1}{12}\times m\text{ f}eet \\ =\frac{1}{24}m\text{ f}eet \end{gathered}[/tex]Therefore, rewriting the given expression in feet we have;
[tex]\frac{1}{24}m\text{ feet}[/tex]10x + 50 + 6x = 58 if x is the solution to the given equation, what is the value of 32x
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The solution to the given equation is;
[tex]\begin{gathered} 10x+50+6x=58 \\ \text{Collect all like terms,} \\ 10x+6x=58-50 \\ 16x=8 \\ \text{Divide both sides by 16} \\ \frac{16x}{16}=\frac{8}{16} \\ x=\frac{1}{2} \end{gathered}[/tex]Therefore, the value of 32x shall be;
[tex]\begin{gathered} 32x \\ =32(\frac{1}{2}) \\ =\frac{32}{2} \\ =16 \end{gathered}[/tex]The answer is 16
How many terms are in 6b+b2+5+2b-3f
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In that polynomial there are 5 terms, they are separated by signs.
If we simplify the new number of terms is 4
6b + b^2 + 5 + 2b - 3f
8b + b^2 + 5 - 3f
In the function rule for simple interest A(t)=P(1+rt), is P a variable? Explain.
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P is a variable in the function rule for simple interest A(t)=P(1+rt).
What is a variable?Mathematically, a variable is any number, vector, matrix, function, argument of a function, set, or element of a set.
A variable assumes any possible values in a mathematical expression, problem, or experiment.
A simple interest function showing the amount after some periods is given as A(t)=P(1+rt). In this function, P represents a variable (the principal amount) because it can change depending on the amount invested or borrowed.
Thus, P is a variable in the simple interest function because it can assume any value.
Learn more about variables at https://brainly.com/question/27894163
#SPJ1
Answer:
when buying a house
Step-by-step explanation:
012Explanation34BCheck5Use the figure and the table to answer the parts below.67(a) Find the probability that a real number between 4 and 6 is picked.08(b) Find the probability that a real number between 4 and 7 is picked.0RegionABCXArea0.320.560.12 I need help with this math problem
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Given:
The graph is:
Find-:
(a)
Find the probability that a real number between 4 and 6 is picked.
(b)
Find the probability that a real number between 4 and 7 is picked.
Explanation-:
The area of the region
[tex]\begin{gathered} \text{ Region }\rightarrow\text{ Area} \\ \\ A\rightarrow0.32 \\ \\ B\rightarrow0.56 \\ \\ C\rightarrow0.12 \end{gathered}[/tex]The probability is:
[tex]P(A)=\frac{\text{ Favorable outcome}}{\text{ Total outcome}}[/tex]The total outcomes is:
[tex]\begin{gathered} =0.32+0.56+0.12 \\ \\ =1 \end{gathered}[/tex](a)
Probability to the 4 and 6
The 4 to 6v region is B
[tex]\begin{gathered} P(B)=\frac{\text{ favorable outcomes for B}}{\text{ Total outcomes}} \\ \\ P(B)=\frac{0.56}{1} \\ \\ P(B)=0.56 \end{gathered}[/tex](B)
Probability for 4 to 7
The region B and C
[tex]\begin{gathered} 1. \\ \\ P(B\text{ and }C)=\frac{0.56+0.12}{1} \\ \\ =0.68 \end{gathered}[/tex]Toy It Examine the worked problem and solve the equation. 4 4 1 (x) 1 = 9 3 3 1 1 + 3 3 4 3 :9+ 3 3 28 The solution is x=
Answers
Given:
[tex]\frac{4}{3}(x)-\frac{1}{3}=9[/tex]Let's evaluate and solve for x.
First step:
Add 1/3 to both sides of the equation
[tex]\begin{gathered} \frac{4}{3}(x)-\frac{1}{3}+\frac{1}{3}=9+\frac{1}{3} \\ \\ \frac{4}{3}(x)=\frac{28}{3} \end{gathered}[/tex]Cross multiply:
[tex]\begin{gathered} 4x(3)\text{ = 28(3)} \\ \\ 12x\text{ = }84 \end{gathered}[/tex]Divide both sides by 12:
[tex]\begin{gathered} \frac{12x}{12}=\frac{84}{12} \\ \\ x=7 \end{gathered}[/tex]ANSWER:
x = 7
Do anyone know the answer to these questions? Please explain as well
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given data:
[tex]\begin{gathered} \frac{7}{21}\text{ and }\frac{21}{24} \\ \end{gathered}[/tex]to find whether they form an proposition.
using cross product,
[tex]\begin{gathered} \frac{7}{21}\cdot\frac{21}{24} \\ 24\cdot7=21\cdot21 \\ 168\ne441 \end{gathered}[/tex]the cross product are not equal.
Thus, they donot form a proposition.