[tex] \Large{\boxed{\sf (10 + 6i)(-2 - 4i) = 4 - 52i}} [/tex]
[tex] \\ [/tex]
Explanation:To find the algebraic form, also called 'a + bi form', of the given complex number, we will have to expand its expression using FOIL method.
[tex] \\ [/tex]
[tex] \Large{ \sf \: \underline{FOIL \: method \text{:}}} \\ \\ \Large{\boxed{\sf (A + B)(C + D) = AC + AD + BC + BD}} [/tex]
[tex] \\ [/tex]
Let's identify our coefficients and expand the given expression:
[tex] \sf (\underbrace{\sf 10}_{A} + \overbrace{\sf 6i}^{B})(\underbrace{\sf -2}_{C} \overbrace{\sf -4i}^{D}) = 10 \times (-2) + 10 \times (-4i) + 6i \times (-2) + 6i \times (-4i) \\ \\ \\ \sf = -20 - 40i - 12i - 24i^2 = -20 - 52i - 24i^2 [/tex]
[tex] \\ [/tex]
In the complex number system, i² = -1. Therefore, our final answer is:
[tex] \sf (10 + 6i)(- 2 - 4i) = -20 - 52i - 24(-1)= \boxed{\boxed{\sf 4 - 52i}} [/tex]
[tex] \\ \\ [/tex]
▪️Learn more about the algebraic form of a complex number here:
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increase £40 by 35% =
Answer:
£54
Step-by-step explanation:
An increase of 35% on the original 100% is 100% + 35% = 135% = 1.35 , so
1.35 × £40 = £54
James wants to buy a new cell phone package. There are three packages available, each offering a different deal.Package 1$160 for 4 monthsPackage 2$128 for 4 monthsPackage 3$60 for 2 monthsWhich package offers the best deal?A.Package 3B.Package 1C.Package 2D.Both Package 1 and Package 2
Answer:
to get which one is the best we have to bring them packages to the same terms
so to do that we have to find what each package offers per month by divided the amount by the number of months
so
160/4= 40
128/4=32
60/2=30
so the best package is
B. package 1
The distributive property simplify each expression. Question 3. 3(4+3r)
Answer:
12 + 9r
Step-by-step explanation:
3(4 + 3r)
= 12 + 9r
Answer:
12 + 9r
Step-by-step explanation:
just multiply 3 by 4 and then 3r.
HELP ME PLEASE I AM DESPERATE THIS IS ALMOST DUE!!!!!
What is the slope for this graph?
Answer: The answer is 2
Step-by-step explanation:
Please mark me as Brainiest
Answer: The answer is 2
Step-by-step explanation:
To find out how fast a tree grows, you can measure its trunk. A giant red oak's diameter was 248 inches in 1965. The tree's diameter had grown to 251 inches in 2005. Find the average rate of change in the diameter of the tree per year.
CLEAR CHECK
1313 inches per year
-0.075 inch per year
0.075 inch per year
3 inches per year
I think it's 0.075 inch per year
Answer:
Your answer is C. or 0.075 inches per year.
Step-by-step explanation:
251-248 = 3 ( To figure out how much it grew )
2005 -1965 = 40 ( To figure out how long it took )
3/40 = 0.075
SOMEONE PLEASE HELP AND SHOW WORK i will give you brainliest!
Katy invests a total of $26,500 in two accounts. The first account earned a rate of return of 15% (after a year). However, the second account suffered a 8% loss in the same time period. At the end of one year, the total amount of money gained was $985.00. How much was invested into each account?
Answer:
Step-by-step explanation:
0.15x-0.08(26,500-x)=98.00
15x-212000+8x=98,500
23x+212000=98,500+212000
23x/23= 310500/23
x = 13500 (was invested in the account that gained 15% )
26500-13500=13000 (was invested in the account that lost 8%.)
WILL GIVE BRAINLIEST
solve for x : -4 = (2/3)x
show steps please
To solve for x, we have to find a way to make x the subject of the equation (get x on one side and everything else on the other side)
since -4 = (2/3)x [mutiply both sides by 3]
⇒ -4 × 3 = 2x [divide both sides by 2]
⇒ (-12/2) = x [simplify by dividing -12 by 2]
∴ x = -6
Answer:
X = 6
Step-by-step explanation:
2/3 x 6/1 = 4
2 x 6 = 12
3 x 1 = 3
12/3 = 4
12 divided by 3 is 4
The answer is 6 , x = 6
[tex]\sf x-12=14[/tex]
What do all similar circles have in common?
Answer:
Explanations (4) Similarity is a quality of scaling: two shapes are similar if you can scale one to be like the other, like these triangles ABC and DEF. Since all circles are of the same shape (they only vary by size), any circle can be scaled to form any other circle. Thus, all circles are similar!
Step-by-step explanation:
Welcome
please help I dont understand
Answer:
3rd option
Step-by-step explanation:
A direct variation is expressed in this form:
y = kx
1. y - 4x = 8
y = 4x + 8 is not a direct variation
2. y + 2 = 7x
y = 7x - 2 is not a direct variation
3. y - 3x = 0
y = 3x is a direct variation
4. y = 5x - 2
y = 5x - 2 is not direct variation
Find the area and perimeter of
the parallelogram:
17ft
12ft
15ft
Step-by-step explanation:
The area = base × height
= 12 × 17 = 204
the perimeter = 2(17 + 15) = 2 × 32 = 64
please give me a brainliest answer
Simplify the expression to a + bi form:
(11 + 9i)2
Answer:
22+18i
Step-by-step explanation:
distribute the 2
22+18i
Which of the following is not true?
p+q = q+p
p x q = q x p
p x (q x r)=(p x q ) x r
p - q = q - p
Plz answer my exam is going on right now
Step-by-step explanation:
the number 4 is false
p-q =-(q-p)
Subtract 2y - 3 from 8y-2.
Answer:
2(3y-2)
Step-by-step explanation:
Collect like terms
6y-4
Simple terms
2(3y-2)
3|-d + 2| + 1 if d = 4
Answer:
7
Step-by-step explanation:
reminder that the absolute value function always gives a positive result.
3 | - d + 2 | + 1 ( substitute d = 4 )
3 | - 4 + 2 | + 1
= 3 | - 2 | + 1
= 3 × 2 + 1
= 6 + 1
= 7
i need some frikin help on equations like this 4x>2 i used to do questions like this 4x=2 (basically one step equations) im just really confused
Answer:
x>1/2
Step-by-step explanation:
4x>2
4x/4
2/4
x>2/4
2/4 divided by 2= 1/2
x>1/2
6. Cafe A offers 2 free bottled waters or juices for every 20 purchased. What is the ratio of free drinks to purchased drinks? *
Answer:
1: 10
Step-by-step explanation:
2/2 =2
20/2 = 10
I need help with a and b!
Answer: first a it’s left side is shorter while on the other polygoes there left sides longer for the first two
in the third one it goes size wise
Step-by-step explanation:
NEED ASAP IT WAS DUE LAST WEEK
1.Explain why the equation (x-4)^2-28=8 has two solutions. Then solve the equation to find the solutions. Show your work.
pls help!!!!!!! i will give brainliest!!!!!
Answer:
There is a strong positive correlation
Step-by-step explanation:
The graph shows as more students study the higher the test score is.
Simplify the expression. -17+[(8-3)-(-14-19)]=
Answer:
21
Step-by-step explanation:
trust (used a calculator)
PLEASE HELP ME I REALLY NEED ITTT
Answer:
bru you have a head
Step-by-step explanation:
use ittt
Find the cube of the number 50
Answer:
125000
Step-by-step explanation:
HELP PLEASE I DON´T UNDERSTAND RATIOS!
Answer:
Jake made 7 bead strings
Step-by-step explanation:
The ratio is 2:6 next would be 4:12 then 6:18 and so on. You just add what you started with to the corresponding side. 8:24, 10:30, 12:36, 14:42. The right side is 3x the left side.
Answer:
Step-by-step explanation:
You don't really need to use ratios for this question. You need to understand that for each necklace he uses 2 red and 6 whites.
Let the number of necklaces he can make = x
The total number of beads = 56
2x + 6x = 56
8x = 56 Divide by 8
8x/8 = 56/8
x = 7
So the number of necklaces possible is 7.
If you insist on doing this with ratios then you could do it as
2/8 = x/56 What this means is that 2 reds to the total = x / 56. The 56 is the total number of beads used. The x represents the number of reds.
2/8 = x/56 Cross multiply
2 * 56 = 8x Divide both sides by 8
2 * 56/8 = x
x = 14.
That means of the 56 beads used, 14 of them are red.
6/8 = y / 56 Cross multiply
6*56 = 8y
336 = 8y Divide by 8
336/8 = 8y/8
y = 42
This means that 42 beads were white
The total is 56. But here's the catch. The highest prime common to both is 7 and that's how many necklaces can be made.
please help me or I'm gonna fail math
Answer:
length = x+6
width = x-6
Step-by-step explanation:
The area of rectangle is:
[tex] \displaystyle \large{ A= l \times w}[/tex]
where A is area, l is length and w is width.
We know the area of this rectangle or table since we are given A = x^2-36.
First, substitute A = x^2-36 in.
[tex] \displaystyle \large{ {x}^{2} - 36 = lw}[/tex]
Then we factor x^2-36, use the difference of two squares:
[tex] \displaystyle \large{ (x + 6)(x - 6) = lw}[/tex]
Compare the terms.
First, we have to understand that length is always longer or greater or have more values than width.
Hence length cannot be x-6 and width cannot be x+6 either.
Thus:
[tex] \displaystyle \large{length = x + 6} \\ \displaystyle \large{width = x - 6}[/tex]
if 3^x = 1, find the value of x.
3x-1=?
maybe 3x-1=5
3x=5+1
3x=6
X=6/3
X=2
$300, 5%, 2 years
explain
300+5%+2YEARS=16,000
HOPE IT HELPS YOU
CAN YOU BRAINLEST ME
Answer:
16,000
Step-by-step explanation:
trust me it's right
So, if the average family earned $4,000 per month, how much would they send back
out to pay debreach month
What kinds of things could you do with that money?
solve please :3 will mark brainliest !!
__________
[tex] \: [/tex]
6f = $15
8f = $20
10f = ?
Soo :
2f = 5
f = 2,5
10f = 10(2,5) = $25✔
The cost of the wire of the third length in the table is, 25 dollars
We have to give that,
The cost of a certain type of wire varies directly with its length.
Now, From the table the equation between cost and length is,
y - 15 = (20 - 15)/(8 - 6) (x - 6)
y - 15 = (5/2) (x - 6)
y - 15 = 2.5x - 15
y = 2.5x
Where y represents the cost and x represent the length.
Hence, At x = 10 feet
y = 2.5 (10)
y = 25 dollars
So, The cost of the wire is, 25 dollars
To learn more about the equation visit:
brainly.com/question/28871326
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Donna bought 4 bags of dog treats for $10.72. What is the cost per bag of dog treats?
Answer:
2.68
Step-by-step explanation:
Answer: The bags cost about $2.68 each
Step-by-step explanation: All I did was simple Division: ($10.72 ÷ 4 = $2.68) If you need to double check to see if this is accurate, you can do ($2.68 x 4= 10.72) Therefore, this equation has an accurate answer.~
Hope this helps, have a great day/night!
~IFoundJiminsLostJams~