Find the product z1z2 in standard form. (Simplify your answer completely.)
z1 = 9 + 3i, z2 = −9 + 3i
Answers
Answer:
See image
Step-by-step explanation:
These are "complex numbers" because they have the imaginary number, i, in the expression.
The 9 (and the -9) is the real part and the 3i is the imaginary part. But when you add or subtract, multiply or divide them you can manipulate them just as if the i was a variable (like x or n or y) If you learned to multiply
(x+2)(x+5)
= x^2 + 7x + 10
This problem will work the same way. You may have learned "FOIL" or using a box to multiply two binomials (two-piece things like x+2)
**SUPER IMPORTANT NOTE: i^2 is equal to -1
These particular complex numbers are called conjugates which means they have the same 'pieces' the 9 and the 3i, with only one sign different. So there is a short cut for this problem and the imaginary number falls out and we get a real number answer. This doesn't happen for every question, only when you multiply conjugates, but the method shown here works for multiplying complex numbers all the time.
Related Questions
Write the slope-intercept form of the equation of the line.
Answers
Which of the functions below could have created this graph? O A. F(x) = - x ^ 0 + x ^ 3 - x ^ 2 O B. F(x) = - x ^ 2 + 4x ^ 3 - 2x ^ 2 C. F(x) = x ^ 9 + 12x ^ 8 + x ^ 7 D. F(x) = x ^ 2 + 4x ^ 4 + 20x ^ 2
Answers
Answer:
B
Step-by-step explanation:
even roots bounce at (0,0)
negative leading coefficient: initial graph descending to right, curve up
4 local extremes means remaining 5 degree of the function
The function F(x) = - x⁷ + 4x³ - 2x² could have created the given graph. which is the correct answer would be an option (B).
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
To create a graph of the function F(x) = - x⁷ + 4x³ - 2x², you can follow these steps:
Choose a range of x-values to use for the graph. For example, you might choose x = -2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2.
Substitute each x-value into the function to find the corresponding y-value. For example, if x = -1, then y = F(-1) = - (-1)⁷ + 4(-1)³ - 2(-1)² = -1 + 4 + 2 = 5.
Plot the points (x, y) on a coordinate plane. For example, you would plot the point (-1, 5) on the coordinate plane.
Connect the points with a smooth curve to create the graph of the function.
Therefore, we can conclude that function F(x) = - x⁷ + 4x³ - 2x² could have created the given graph.
Learn more about the graphs here:
brainly.com/question/16608196
#SPJ2
Which expression can be used to find the surface area of the following triangular prism?
5
5
2.
11
8.
Answers
Answer:
214.
Step-by-step explanation:
To get Surface area take
(cross section area) × 2 +(perimeter of crossection area × length)
the cross section area is a triangle
so area of a triangle =1/2 base times height
1/2×8×2=8
let's get perimeter of cross section
the cross section is still at triangle so let's find its perimeter.
5+5+8=18
18×length of which is 11
18×11=198
and 188 + 16=214. that's the answer
maybe you can get a expression from the work that I've just done cuz I can't see the answers clearly in the picture you have taken.if you don't mind just send the picture back then I'll get the answer.
Which values from the set negative 6, negative 4, negative 3, negative 1, zero, 2, satisfy this inequality?
Negative one half x, plus 3, is greater than or equal to 5.
Answers
Answer:
- 6
Step-by-step explanation:
- [tex]\frac{1}{2}[/tex] x + 3 ≥ 5 ( subtract 3 from both sides )
- [tex]\frac{1}{2}[/tex] x ≥ 2 ( multiply both sides by 2 to clear the fraction )
- x ≥ 4
Multiply both sides by - 1, reversing the symbol as a result of multiplying by a negative quantity.
x ≤ - 4
The only value from the set which satisfies the inequality is
x = - 6
What is the solution to this quadratic equation
Answers
(0,12)
(2,0)
(6,0)
if p(q) = q^2 4q- 12 then what is p(-1)
Answers
(1): "q2" was replaced by "q^2".
Step by step solution :
STEP
1
:
Trying to factor by splitting the middle term
1.1 Factoring q2-4q-12
The first term is, q2 its coefficient is 1 .
The middle term is, -4q its coefficient is -4 .
The last term, "the constant", is -12
Step-1 : Multiply the coefficient of the first term by the constant 1 • -12 = -12
Step-2 : Find two factors of -12 whose sum equals the coefficient of the middle term, which is -4 .
-12 + 1 = -11
-6 + 2 = -4 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 2
q2 - 6q + 2q - 12
Step-4 : Add up the first 2 terms, pulling out like factors :
q • (q-6)
Add up the last 2 terms, pulling out common factors :
2 • (q-6)
Step-5 : Add up the four terms of step 4 :
(q+2) • (q-6)
Which is the desired factorization
Equation at the end of step
1
:
(q + 2) • (q - 6) = 0
STEP
2
:
Theory - Roots of a product
2.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
2.2 Solve : q+2 = 0
Subtract 2 from both sides of the equation :
q = -2
Solving a Single Variable Equation:
2.3 Solve : q-6 = 0
Add 6 to both sides of the equation :
q = 6
Supplement : Solving Quadratic Equation Directly
Solving q2-4q-12 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
Parabola, Finding the Vertex:
3.1 Find the Vertex of y = q2-4q-12
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Aq2+Bq+C,the q -coordinate of the vertex is given by -B/(2A) . In our case the q coordinate is 2.0000
Plugging into the parabola formula 2.0000 for q we can calculate the y -coordinate :
y = 1.0 * 2.00 * 2.00 - 4.0 * 2.00 - 12.0
or y = -16.000
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = q2-4q-12
Axis of Symmetry (dashed) {q}={ 2.00}
Vertex at {q,y} = { 2.00,-16.00}
q -Intercepts (Roots) :
Root 1 at {q,y} = {-2.00, 0.00}
Root 2 at {q,y} = { 6.00, 0.00}
It takes 5 minutes to fill an empty aquarium to a depth of
5/8
meters. What is the unit rate in minutes per meter?
Answers
Answer:
1/8 meters per minute
Step-by-step explanation:
5/8 ÷ 5
I hope this helps!!
Manolo and Annalisa make handbags. Manolo made 16 handbags the first day and 12 each day after
that. Annalisa made 8 the first day and 12 each day after that.
Answers
Based on the amount being made by Manolo and Annalisa every day, the amount both made on the various days were:
Annalisa made 8 bags on Day 1Manolo had made 40 bags by Day 3Annalisa is said to have made 8 bags on the first day so this is the number of bags that should be put in the table for having been made in the first day.
Manolo made 16 bags on the first day and then 12 bags each day after that. The total number of bags made by the third day by Manolo would be:
= 16 + 12 + 12
= 40 bags
In conclusion, Annalisa made 8 bags on Day 1 and Manolo had made 40 bags on the 3rd day.
Find out more about this at https://brainly.com/question/11864663.
If f(x) = 2x - 1 and g(x) = x^2 - 3x - 2, find (f + g)(x).
Answers
Answer:
SEE attched pic
Step-by-step explanation:
Download symbolab
plz help with my math hw
Answers
Answer:
cant see
Step-by-step explanation:
HELP ME WITH THIS PLEASEEE !
Answers
Answer:
34 i think i got it really wrong but...
Step-by-step explanation:
Find ℎ(x) = f(x) − g(x)
Answers
Answer:
h(x) = 7x - 3
Step-by-step explanation:
f(x) = 4x − 1 and g(x) = −3x + 2
h(x) = f(x) - g(x)
h(x) = 4x - 1 - (-3x + 2)
h(x) = 4x - 1 + 3x - 2
h(x) = 7x - 3
Please help :)
M is the midpoint of segment AT.
Solve for X and AM
Answers
So AM = TM
<=> 5x = 3x + 4 <=> 5x - 3x = 4
<=> 2x = 4 <=> x = 2
The answer: x = 2
Ok done. Thank to me :>
Plz HELP...(MATH)........
Answers
Answer:
36 times
Step-by-step explanation:
Because half the marbles are blue, you can predict that about half of the 72 times you will choose the blue marble, or 36 times.
2+2=4 but you plus me = forever
i got smooth with it
Answers
dam bro
thats pretty smooth
Will mark brainliest
Answers
Answer:
Point H is in the first Quadrant (5,4)
Step-by-step explanation:
Answer:
quadrant 1
Step-by-step explanation:
yw:)
Un terreno Forma rectangular mide X +4 de alto y de base X +10 indica la expresión algebraica que expresa el área del terreno
Answers
Answer:
X^2+14x +40
Step-by-step explanation:
La base es x+4 y la altura es x+10 multiplicas la base por la altura
Help me find three different ratios that are equivalent to 3:11!! I need a explanation too!
Answers
3 * 2 and 11 * 2 which would be 6:22 and is still equal to the ratio 3:11. Your explanation can be the when divided by 2 or the number you multiplied by, you would get the original ratio
Examples:
6:22
9:33
12:44
No files or links please!
graph y= -4/3 x+2 using the slope and y-intercept
slope: 3
y-intercept: (0,-2)
Answers
Will give brainliest
Answers
The distance of the points is 4 units down and 2 units right
-4/2 = -2
Slope = -2
Please helpppppppppppp
Answers
Answer:
5/4
Step-by-step explanation:
35/4 ÷ 14 = 5/4
That means 14 was multiplied by 5/4 to get 35/2
HELP!!!
42 is the product of 6 and y
Answers
Answer:
7
Step-by-step explanation:
Divide the 42 by 6 to get your answer. 42/6=7
This also works in reverse. 6*7=42
The answer: 42 is the product of 6 and y=7
Ok done. Thank to me :>
An equation of a line is y = 3x -7. What would the SLOPE of a line parallel to this equation be?
Answers
Answer:
3
Step-by-step explanation:
If two lines are parallel then their slope is the same
y=mx+b
m= slope
b= y-intercept
please help me quick
Answers
Answer:
D) The answer is AB and HG
Step-by-step explanation:
sides that are equal:
AD=EH
DC=EF
BC=FG
AB=HG
How many solutions does the system of equations below have?
4x + 10y = –7
–3x + 9y = –14
No solution
One solution
Infinitely solutions
Answers
Answer:
There is one solution to this system of equations
Step-by-step explanation:
When solving, there is a specific point of intersection which is (7/6,-7/6), making the answer one solution.
lesson 5 practice problems
Answers
Answer:
Step-by-step explanation:
ok ill help but can soke one help me too
Find the distance travelled by Rubina if she takes 4 rounds of rectangular park whose length and breadth is 45m and 30m
please give me a valid answer with a step by step explanation and i will mark you as brainliest
Answers
Answer:
The distance travelled by Rubina is 600 m.
Hope you could get an idea from here.
Doubt clarification - use comment section.
George has $3 in his savings account. He then adds $4 per day to the account. Let y represent the total amount in the account after x days.
Which equation represents this situation in the form of y=mx+b ?
Question 9 options:
y = 4x + 3
y = 3x + 4
y = 3/4x - 3
y = 4/3x - 4
Answers
Answer:
The answer is the 1st option, y = 4x + 3
Step-by-step explanation:
x is the amount of days that the 4 dollars will be multiplied by
( 4 * x )
The + 3 is the money that George already had in his savings account, so that money will be added to the total amount in his savings account.
( 4x + 3 )
Lastly, the y stands for the total amount of money in his savings account so the answer is the 1st option.
y = 4x + 3
Hope this helps! :)
solve the following methods
Answers
don't know when you find out tell me
URGENT!!! THANK YOU!!!!!
Answers
Answer:
101,100
280
Here's your answer