Answers
Answer:
Step-by-step explanation:
(6+8i)(3-2i)
use FOIL
18 - 12i + 24i - (16[tex]i^{2}[/tex])
18 + 12i - (-16)
18 + 12i + 16
34 + 12i
Related Questions
In a 2-digit number, the tens digit is 5 less than the units digit. If you reverse the number, the result is 7 greater than double the original number. Find the original number.
Answers
The original number is 38
A 2-digit number can be written as:
N = a*10 + b*1
Where a is the tens digit, and b is the units digit, these two are single-digit numbers.
We know that:
"the tens digit is 5 less than the units digit."
This means that:
a = b - 5
(notice that a must be larger than zero and smaller than 10, from this, we can conclude that b is a number in the range {6, 7, 8, 9})
"If you reverse the number, the result is 7 greater than double the original number"
The reverse number is:
b*10 + a
and this is 7 greater than 2 times the original number, then:
b*10 + a = 7 + 2*(a*10 + b)
Then we found two equations:
a = b - 5
b*10 + a = 7 + 2*(a*10 + b)
Replacing the first equation in the second, we get:
b*10 + (b - 5) = 7 + 2*((b - 5)*10 + b)
Now let's solve that:
b*10 + b - 5 = 7 + 2*(11*b - 50)
11*b - 5 = 7 + 22*b - 100
-5 - 7 + 100 = 22*b - 11*b
88 = 11*b
88/11 = b = 8
Now that we know that b = 8, we can use the equation:
a= b - 5
a = 8 -5 = 3
Then the original number is:
a*10 + b = 3*10 + 8 = 38
The original number is 38
If you want to read more about this, you can see:
https://brainly.com/question/19902993
Karen is having a party. She'll have 4 tables for every 12 guests. Complete the table below showing the number of tables and the number of guests.
Answers
Can someone please help me solve the equation?
Answers
Subtracting 10 from the original equation will shift the graph down 10 units
The answer is D.
Jua Kali Products Ltd has been in operation for the last 10 years. Its annual revenue and cost functions take form of quadratic functions. The following data was obtained from the records of the company. Year 2017 2018 2019 Units produced and sold (000) 5 10 15 Revenue (sh000) 1900 3600 5100 Cost (sh000) 7525 7100 6725 Required: The revenue and cost functions (10 marks) The breakeven number of units (5 marks)
Answers
Answer:
Step-by-step explanation:
vxcvxcvxcvxcvxcvcxvxcbcvbcvnxcgjfgjfgjghjghjghjghj
The revenue function is y₁ = –4x² + 400x, the cost function is y₁ = x² – 100x + 8000, and the break-even number of units is 20 or 80.
What is a quadratic equation?It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.
Jua Kali Products Ltd has been in operation for the last 10 years.
Its annual revenue and cost functions take the form of quadratic functions.
The following data was obtained from the records of the company.
Year Unit Sold Revenue Cost
2017 5 1900 7525
2018 10 3600 7100
2019 15 5100 6725
We know that the quadratic equation is given as
[tex]\rm y = ax^2 + bx + c[/tex]
Let y₁ be the revenue function, y₂ be the cost function and x be the unis sold.
Then the revenue function will be
1900 = 25a + 5b + c ...i
3600 = 100a + 10b + c ...ii
5100 = 225a + 15b + c ...iii
From equations (i), (ii), and (iii), we have
a = –4, b = 400, and c = 0
Then the revenue function will be
y₁ = –4x² + 400x
Similarly, the cost function will be
7525 = 25a + 5b + c ...1
7100 = 100a + 10b + c ...2
6725 = 225a + 15b + c ...3
From equations 1, 2, and 3, we have
a = 1, b = –100, and c = 8000
Then the cost function will be
y₁ = x² – 100x + 8000
For the break-even units, the cost function and the revenue function will be equal. Then we have
[tex]\begin{aligned} x^2 -100x + 8000 &= -4x^2 + 400x\\\\5x^2 -500x + 8000 &= 0\\\\x^2 - 100x + 1600 &= 0\\\\x^2 - 80 x - 20x + 1600 &= 0\\\\x(x-80) - 20 (x-80) &= 0\\\\(x-80)(x-20) &= 0\\\\x &= 20, 80 \end{aligned}[/tex]
More about the quadratic equation link is given below.
https://brainly.com/question/2263981
Please help out explanation need it
Answers
Answer:
[tex] \sin(θ) = \frac{19}{41} \\ θ = 27.6 \\ θ = 28[/tex]
The five number summary of a dataset is given as
0, 4, 12, 14, 20
An observation is considered an outlier if it is below _______
An observation is considered an outlier if it is above _______
The five number summary of a dataset is given as
2, 8, 14, 18, 20
An observation is considered an outlier if it is below _______
An observation is considered an outlier if it is above _______
.
.
Answers
Given:
The five number summary of two data sets are given as:
a) 0, 4, 12, 14, 20
b) 2, 8, 14, 18, 20
To find:
The range for the outliers.
Solution:
We know that,
An observation is considered an outlier if it is below [tex]Q_1-1.5(IQR)[/tex]
An observation is considered an outlier if it is above [tex]Q_3+1.5(IQR)[/tex]
Where, IQR is the interquartile range and [tex]IQR=Q_3-Q_1[/tex].
The five number summary of two data sets are given as:
0, 4, 12, 14, 20
Here, [tex]Q_1=4[/tex] and [tex]Q_3=14[/tex].
Now,
[tex]IQR=14-4[/tex]
[tex]IQR=10[/tex]
The range for the outliers is:
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[4-1.5(10),14+1.5(10)][/tex]
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[4-15,14+15][/tex]
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[-11,29][/tex]
An observation is considered an outlier if it is below -11.
An observation is considered an outlier if it is above 29.
The five number summary of two data sets are given as:
2, 8, 14, 18, 20
Here, [tex]Q_1=8[/tex] and [tex]Q_3=18[/tex].
Now,
[tex]IQR=18-8[/tex]
[tex]IQR=10[/tex]
The range for the outliers is:
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[8-1.5(10),18+1.5(10)][/tex]
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[8-15,18+15][/tex]
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[-7,33][/tex]
An observation is considered an outlier if it is below -7.
An observation is considered an outlier if it is above 33.
help fast I'm dum
and I'm sorry if I keep spamming this.
Curtis types 48 words in 1 minute how many words does Curtis type in 8 minutes? use the following equivalent rates to help solve the problem. how many words does Curtis type in 8 minutes?
Answers
Answer:
384
Step-by-step explanation:
Answer:
384 words
Step-by-step explanation:
Number of words typed in 1 minute = 48
So, number of words typed in 8 minutes
= Number of words typed in 1 minute × 8
= 48 × 8
= 384
So, Curtis types 384 words in 8 minutes.
Primo car rental agency charges $21 per day plus $0.20 por milo. Ultimo car rental agency charges $24 per day plus $1.00 per milo. Find the daily mileage for which the Ultimo charge is four times the Primo charge.
The mileage is
Answers
Answer:
300 miles
Step-by-step explanation:
Let us consider the miles they travelled is 'm'
Mileage for Primo= 21 + (m × 0.20) = 21+0.2m
Mileage for Ultimo= 24+ ( m× 1.00) = 24 + m
Question says The mileage is equal when Ultimo's charge is 4× Primo
Thus,
4 × (21+0.2m) = 24+ m
84 + 0.8m = 24 + m
60 = 0.2m
m = 300
look at the image below
Answers
Answer:
201.1 km²
Step-by-step explanation:
Surface area of the figure,
4πr²
= 4×π×4²
= 64π
= 201.1 km² (rounded to the nearest tenth)
For 32 = 5X + 2, what is the first step in solving for X?
Answers
Answer:
-2 from both sides
Step-by-step explanation:
32=5x+2
-2 -2
________
30=5x
__=__
5 5
6=x
The first step to solve for X is to use subtraction property of equality to subtract 2 from both sides.
How to solve algebraic equations?
We are given the algebraic equation;
32 = 5X + 2
The first step to solve for X is to use subtraction property of equality to subtract 2 from both sides to get;
32 - 2 = 5X + 2 - 2
30 = 5X
Divide both sides by 5 using division property of equality to get;
X = 6
Read more about Algebraic Equations at; https://brainly.com/question/16863577
#SPJ6
If the cube root parent function is horizontally stretched by a factor of 4, then translated 5 units right and 3 units up, write an equation to represent the new function?
Answers
Answer:
The cube root parent function:
f(x) = [tex]\sqrt[3]{x}[/tex]Horizontally stretched by a factor of 4:
g(x) → f(1/4x) = [tex]\sqrt[3]{1/4x}[/tex]Translated 5 units right:
h(x) → g(x - 5) = [tex]\sqrt[3]{1/4x - 5}[/tex]Translated 3 units up:
k(x) → h(x) + 3 = [tex]\sqrt[3]{1/4x - 5} + 3[/tex]You have $90 in your bank account. Each work you plan to deposit $3 from your allowance and $25 from your paycheck. The equation b: 90+ (25+5)w gives the amount b in your account after w woeks. How rary works from
now will you have $220 in your bank account?
There will be 5220 in the account after works
(Type a whole number
Answers
33w=220-90
33w=130 /33
W = 3.94
Find formulas for X, Y, and Z in terms of A, B, and C. It may be necessary to make assumptions about the size of a matrix in order to produce a formula.
[A B C 0] [1 0 X Y] = [0 1 Z 0]
Find the formulas for X, Y, and Z. Note that I represents the identity matrix and 0 represents the zero matrix.
Answers
Answer:
Here the answer is given as follows,
Factor this polynomial expression.
3x^2 - 12x+ 12
A. (3x - 2)(x-6)
B. 3(x-2)(x + 2)
C. 3(x-2)(x-2)
D. 3(x + 2)(x + 2)
Answers
In case you want to see the fully factored polynomial, I won’t explain the steps since you don’t need it here, but it’s 3(x-2)^2. This is equivalent to 3(x-2)(x-2). That’s the same as C.
if a circumference of a circle is 22cm.find it diameter take pie 22/7.
Answers
Answer:
➕
Step-by-step explanation:
i know the answer ok it is easy
A farmer wishes to construct a fence around his rectangular field. The farmer has 150 feet of fence and
wishes to have the length be three more than the width. What is the width of the field. Make sure and
include feet in your answer.
Help
Answers
Answer:
The width is 36 feet
Step-by-step explanation:
If the width of the fence is x then its length is x+3.
The perimeter is 150 feet, so we have the equation:
2(x + x + 3) = 150
4x + 6 = 150
x = 144/4 = 36 feet
what is 98×63-32×69=
Answers
Answer: plz marl brainilist
3966
Step-by-step explanation:
(98 × 63 - 32 × 69
98 * 63) - (32 * 69)
3966
Step-by-step explanation:
98 x 63 - 32 x 69 =
Multiply
6174 - 2208
Subtract
3966
What is the slope of a relation with ordered pairs of (-5, 3) and (4.1).
9/2
2/9
-9/2
-2/9
2
-2
Answers
2/-9
-2/9 is the answer
Mark earns $47,800 a year working for a delivery service. He is single and pays $2,152.60 in state income tax each year. He claims no dependents. What is the tax rate of Mark’s state he lives in?
Answers
Answer:
4.5%
Step-by-step explanation:
The tax rate=(2152.6/47800)*100=4.5%
A bicyclist is at point A on a paved road and must ride to point C on another paved road. The two roads meet at
an angle of 38° at point B. The distance from A to B is 18 mi, and the distance from B to C is 12 mi (see
the figure). If the bicyclist can ride 22 mph on the paved roads and 6.8 mph off-road, would it be faster for the bicyclist to ride from A to C on the paved roads or to ride a direct line from A to C off-road? Explain.
Answers
Answer:
Step-by-step explanation:
The diagrammatic expression to understand this question very well is attached in the image below.
By applying the law of cosine rule; we have:
a² = b² + c² - 2bc Cos A --- (1)b² = a² + c² - 2ac Cos B --- (2)c² = a² + b² - 2ab Cos C --- (3)From the diagram attached below, we need to determine the side "b" by using equation (2) from above:
b² = a² + c² - 2ac Cos B
From the information given:
a = 12 miles; c = 18 miles; ∠B = 38°
∴
replacing the values into the above equation:
b² = 12² + 18² - 2(12)(18) Cos (38°)
b² = 144 + 324 - 432 × (0.7880)
b² = 468 - 340.416
b² = 127.584
[tex]b = \sqrt{127.584}[/tex]
b = 11.30 miles
However, we are also being told that the speed from A → C = 6.8 mph
Thus, the time required to go from A → C can be determined by using the relation:
[tex]\mathbf{speed = \dfrac{distance}{time}}[/tex]
making time the subject of the formula, we have:
[tex]\mathbf{time= \dfrac{distance}{speed }}[/tex]
[tex]\mathbf{time= \dfrac{11.30}{6.8}}[/tex]
time = 1.66 hours
By using the paved roads, the speed is given as = 22 mph
thus, the total distance covered = |AB| + |BC|
= (18+12) miles
= 30 miles
∴
[tex]\mathbf{time= \dfrac{distance}{speed }}[/tex]
[tex]\mathbf{time= \dfrac{30}{22}}[/tex]
time = 1.36 hours
Therefore, the time used off-road = 1.661 hours while the time used on the paved road is 1.36 hours.
Since we are considering the shortest time possible;
We can conclude that it would be faster for the bicyclist to ride from A to C on the paved roads since it takes a shorter time to reach its destination compared to the time used off-road.
Learn more about Law of cosine here:
https://brainly.com/question/24077856?referrer=searchResults
It would be faster for the bicyclist to ride from A to C on the paved roads since the time to go from A to C on the paved roads is 1.4 h and the time to go from A to C off-road is 1.7 h.
To calculate which way would be faster we need to find the distance from point A to C with the law of cosines:
[tex] \overline{AC}^{2} = \overline{AB}^{2} + \overline{BC}^{2} - 2\overline{AB}\overline{BC}cos(38) [/tex]
Where:
[tex]\overline{AB}[/tex]: is the distance between the point A and B = 18 mi
[tex]\overline{BC}[/tex]: is the distance between the point B and C = 12 mi
[tex] \overline{AC} = \sqrt{(18 mi)^{2} + (12 mi)^{2} - 2*18 mi*12 mi*cos(38)} = 11.3 mi [/tex]
Now, let's find the time for the two following cases.
1. From point A to C on the paved roads (t₁)
[tex] t_{1} = t_{AB} + t_{BC} [/tex]
The time can be calculated with the following equation:
[tex] t = \frac{d}{v} [/tex] (1)
Where:
d: is the distance
v: is the velocity
Then, the total time that it takes the bicyclist to go from point A to C on the paved roads is:
[tex] t_{1} = t_{AB} + t_{BC} = \frac{18 mi}{22 mph} + \frac{12 mi}{22 mph} = 1.4 h = 84 min [/tex]
2. From point A to C off-road (t₂)
With equation (1) we can calculate the time to go from point A to C off-road:
[tex] t_{2} = \frac{\overline{AC}}{v_{2}} = \frac{11.3 mi}{6.8 mph} = 1.7 h = 102 min [/tex]
Therefore, it would be faster for the bicyclist to ride from A to C on the paved roads.
To find more about the law of cosines, go here: https://brainly.com/question/15740431?referrer=searchResults
I hope it helps you!
5.
A number is squared, then multiplied by 6. The result is 54. What was the number?
Answer:
Answers
Answer:
± 3
Step-by-step explanation:
let n be the number then the number squared is n² , so
6n² = 54 ( divide both sides by 6 )
n² = 9 ( take the square root of both sides )
n = ± [tex]\sqrt{9}[/tex] = ± 3
That is the number is 3 or - 3
2. Solve the following system of equations. y = 5 + x 2x + 2y = 30
Answers
since we know y= 5 + x , plug this into y in the second equation.
2x + 2 (5 + x) = 30
distribute 2 into the 5 and x
2x + 10 + 2x = 30
combine like terms
4x + 10 = 30
subtract 10 from both sides
4x = 20
divide four by both sides to isolate the variable
x = 5
Use a calculator to find
the mean of the data.
{217, 253, 214, 247,
217, 253, 232, 246,
223, 227, 229, 247,
206, 241, 239, 223,
222, 216, 252, 209,
236, 256}
A. 230.811
B. 231.045
C. 232.045
D. 232.811
Answers
Answer:
232.045
Step-by-step explanation:
217 + 253 + 214 + 247 + 217 + 253 + 232 + 246 + 223 + 227 + 229 + 247 + 206 + 241 + 239 + 223 + 222 + 216 + 252 + 209 + 236 + 256 = 5105
5105 / 22 = 232.045454545
Sydney has finished all his work on time, but many of his teammates are still struggling to complete their assignments. What should he do? a) Not distract them; they may get farther behind. O b) Listen to them complain about their workloads O c) Help them complete their work d) Share his thoughts on how they could get their work done faster
Answers
Answer:
I think the correct option is c
Answer:
I think the correct answer is (d)
Step-by-step explanation:
if he shares his thoughts on how they could get their work done faster like using an app like this, then it would be of great help to them
what is the aswer to 5 is 2 more than?
Answers
Answer:
Cuz 5 is greater than 2
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
Solve 5 (2x + 1 ) + 4 = 6 ( 3x + 2) - 7
Answers
5(2x+1)+4=6(3x+2)-7
10x+5+4=18x+12-7
10x-18x=12-7-5-4
-8x=-4 (-1)
8x=4
x=4/8 (/4)
x=1/2
Answer:
x = 1/2
Step-by-step explanation:
5(2x + 1) + 4 = 6 (3x + 2) - 7
~Simplify both sides
10x + 9 = 18x + 5
~Subtract 9 from both sides
10x = 18x - 4
~Subtract 18x to both sides
-8x = -4
~Divide -8 to both sides
x = 1/2
Best of Luck!
Each marble bag sold by Debra's Marble Company contains 8 yellow marbles for every 4 blue marbles. If a bag has 56 yellow marbles, how many blue marbles does it contain?
Answers
Answer:
28 blue marbles
Step-by-step explanation:
yellow: blue
8 4
To get to 56 yellow marbles multiply by 7
yellow: blue
8*7 4*7
56 28
There will be 28 blue marbles
Select the correct answer from each drop-down menu. Complete the statement. The solutions of sin2x= √3/2
are : 30 / 120 / 150 / 330
and
45 / 60 / 105 / 135
What are the correct solutions?
Answers
Answer:
henc X = 30°
Step-by-step explanation:
here is the proof
when X=30° then
sin2x = sin2×30
=sin 60°
= √3/2
or else,
putting value of X = 30° then
sin2x= 2sinxcosx
= 2×sin30°×cos30°
=2×1/2×√3/2
= 2√3/4
= √3/2
hence proved sin2x= √3/2.
Salaries of entry-level computer engineers have Normal distribution with unknown mean and variance. Three randomly selected computer engineers have following salaries (in $1000s): 70, 80, 90. The average and the standard deviation of the data in the sample are 80 and 10. Using hypothesis testing, determine if this sample provides a sufficient evidence, at a 10% level of significance, that the average salary of all entry-level computer engineers is different from $60,000.
a. Null hypothesis.
b. alternative hypothesis.
c. test statistic.
d. acceptance region.
Answers
Answer:
H0 : μ = 60000
H1 : μ ≠ 60000
Test statistic = 3.464
Step-by-step explanation:
Given :
Sample mean salary, xbar = 80000
Sample standard deviation, s = 10000
Population mean salary , μ = 60000
Sample size, n = 3
Hypothesis :
H0 : μ = 60000
H1 : μ ≠ 60000
The test statistic :
T = (xbar - μ) ÷ (s/√(n))
T = (80000 - 60000) ÷ (10000/√(3))
T = 20000 / 5773.5026
T = 3.464
The Decison region :
If Tstatistic >Tcritical
Tcritical at 10%, df = 2 ; two - tailed = 2.9199
Tstatistic > Tcritical ; He
HELPPPP PLZ
Witch statement is true about the value of |6|?
Answers
Answer:
The third choice is the correct one.
Step-by-step explanation:
The absolute value of six means that it's the distance from 0 to six, and that distance will be positive regardless of the number being negative or not.
Answer: The third answer is correct
Step-by-step explanation:
Since |6| is the absolute value of positive six, the value of an absolute value of any number is always positive.
