Answers
Answer:
1) 8 + 2i
2) -13
3) 15 + 3i
4) 1
5) 24 - 10i
Step-by-step explanation:
Working with imaginary numbers is similar to working with a variable when it comes to addition and subtraction, so for problems 1 and 3, it is a matter of combining like terms.
1) The like terms are 7i and -5i; 5 and 3. We can combine them.
8 + 2i
2) We can start to compute the problem by noticing it is a special product of difference of squares. The expression can also be written as:
(3i)^2 - (2)^2
9i^2 - 4
i is defined as the square root of negative 1, so i^2 is -1. We can substitute that in:
9(-1) - 4
-9 - 4
-13
3) We can combine the like terms, 12i and -9i; 5 and 10:
15 + 3i
4)The powers of i repeat every four numbers. For example:
i^1 = i
i^2 = -1
i^3 = -i
i^4 = 1
i raised to a power divisible by four is always 1, so i^24 is 1.
5) We can start by normally distributing in this problem:
12 - 18i + 8i - 12i^2
As said before, i^2 is -1:
12 - 10i + 12
24 - 10i
Related Questions
For the straight line defined by the points (2,57) and (4,83), determine the slope (m) and y-intercept (b).
Answers
Step-by-step explanation:
the answer is in the image above
2³ x 6 ÷ 12 =
4 + (5² - 2³) =
Answers
Answer:
The first one is 4
The second on is 21
Answer:
12 ÷12 = 1
Step-by-step explanation:
hsjshxudbdodbdgekddvdke
Suppose that IQ scores have a bell-shaped distribution with a mean of 97 and a standard deviation of 17. Using the empirical rule, what percentage of IQ scores are between 46 and 148
Answers
Answer:
99.7% of IQ scores are between 46 and 148.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 97, standard deviation of 17.
What percentage of IQ scores are between 46 and 148?
97 - 3*17 = 46
97 + 3*17 = 148
Within 3 standard deviations of the mean, so:
99.7% of IQ scores are between 46 and 148.
You deposit $10,000 in an account that pays 4.5% interest compounded quarterly. Find the future value after one year.
Answers
Answer:
11800
Step-by-step explanation:
4.5%=0.045
0.045x10,000=450
450x4(quarterly)=1800
10,000+1800= 11800
Answer:
After 1 year, $10,457.65
Step-by-step explanation:
P = $ 10, 000
r = 4.5% = 0.045
T = 1 year
n = 4 ( compounded quarterly )
[tex]A = P( 1 + \frac{r}{n})^{nt}[/tex]
[tex]= 10000( 1 + \frac{0.045}{4})^{4 \times 1}\\\\=10000 \times 1.01125^{4}\\\\= 10000 \times 1.04576508633\\\\= 10457.6508633\\\\= \$ 10, 457.65[/tex]
what is the inverse of A(r)=15+3r ?
Answers
Answer:
[tex] \frac{r}{3} - 15[/tex]
Step-by-step explanation:
Swap places with A(r) and r so we have
[tex]r = 15 + 3a(r)[/tex]
Solve for a(r).
[tex] \frac{r}{3} = 15 + a(r)[/tex]
[tex] \frac{r}{3} - 15 = a(r)[/tex]
An item costs $370 before tax and the sales tax is $11.10. Find the sales tax rate::Write your answer as a percentage.
Answers
Answer:
3%
Step-by-step explanation:
Cost x sales tax rate =tax
370 x sales tax rate = 11.10
sales tax rate =11.10/370
sales tax rate=.03 or 3%
The sales tax rate is 3% if an item costs $370 before tax and the sales tax is $11.10.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
To determine the sales tax rate, we need to divide the amount of sales tax paid by the cost of the item before tax and then multiply the result by 100% to express it as a percentage.
As per the question, the amount of sales tax paid is $11.10, and the cost of the item before tax is $370. Therefore, the sales tax rate is:
sales tax rate = tax paid / (cost of the item before tax) x 100%
sales tax rate = $11.10 / $370 x 100%
Apply the division operation,
sales tax rate = $0.03 x 100%
Apply the multiplication operation,
sales tax rate = 3%
Therefore, the sales tax rate is 3%.
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In an experiment, equal amounts of heated water and soil were left to cool down. The initial and final temperatures of each were recorded. A partial record of the temperature is shown. Experimental Record Substance Initial Temperature Final Temperature Water 27 °C 24 °C Soil 27 °C ? Which statement about the final temperature of soil is correct? (3 points) It will be less than 24 °C as soil loses heat relatively faster than water. It will be less than 24 °C as water loses heat relatively faster than soil. It will be more than 24 °C as it takes relatively longer to change soil temperature than water temperature. It will be more than 24 °C as it takes relatively longer to change water temperature than soil temperature.
Answers
Answer:less than 24 °C as soil loses heat relatively faster than water. It will be less than 24 °C as water loses heat relatively faster than soil. It will be more than 24 °C as it takes relatively longer to change soil temperature than water temperature. It will be more than 24 °C as it takes relatively longer to change water temperature than soil temperature.
Step-by-step explanation:
less than 24 °C as soil loses heat relatively faster than water. It will be less than 24 °C as water loses heat relatively faster than soil. It will be more than 24 °C as it takes relatively longer to change soil temperature than water temperature. It will be more than 24 °C as it takes relatively longer to change water temperature than soil temperature.
Tìm cực trị của hàm số
z=x^{4} - 8x^{3} + 16x^{2} + y^{2} - 2y +1
Answers
Answer:
do it yo fawkin self pluck pluck
Determine if segment AB is tangent to the circle.
Answers
Answer: Segment AB is tangent to the circle
Step-by-step explanation:
3 sides are 16, 20, and 12
If angle a is 90 then ab is tangent
now check using Pythagorean theorem
since 12^2 + 16^2 =20^2, this means angle a is a right angle meaning segment AB is tangent to the circle
Simplify this algebraic expression.
Z-4/4+8
O A. Z+7
O B. z+ 9
O c. z-3
O D. Z-7
Answers
Answer:
Z +7
Step-by-step explanation:
Z-4/4+8
Divide first
Z -1 +8
Add and subtract
Z +7
HELP PLEASE 20points!!!
At a high school, 9th and 10th graders were asked whether they would prefer
robotics or art as an elective. The results are shown in the relative frequency
table.
Answers
Answer:
61%
Step-by-step explanation:
We can see that out of all the people that were surveyed, 54% were 10th graders. Since 33% out of all the ones surveyed were 10th graders that chose robotics, the fraction would be 33/54 which is 0.611.
This is 61% approx.
Answer:
61%
Step-by-step explanation:
A P E X
Low concentrations of EDTA near the detection limit gave the following dimensionless instrument readings: 175, 104, 164, 193, 131, 189, 155, 133, 151, and 176. Ten blanks had a mean reading of 50.0. The slope of the calibration curve is 1.75 x 10^-9 M^-1.
a. Estimate the signal detection limit for EDTA.
b. What is the concentration detection limit?
c. What is the lower limit of quantification?
Answers
Answer:
Step-by-step explanation:
From the given information:
The mean of the readings is:[tex]=\dfrac{175+104+164+193+131+189+155+133+151+ 176}{10}[/tex]
[tex]= \dfrac{1571}{10}[/tex]
= 157.1
The standard deviation (SD) can be computed by using the expression:
[tex]SD =\sqrt{ \dfrac{\sum_f(x_i - \bar x)^2}{n-1}}[/tex]
[tex]SD =\sqrt{ \dfrac{(175-157.1)^2+(104-157.1)^2+(164-157.1)^2+...+(176-157.1)^2}{10-1}}[/tex]
Standard deviation = 28.195
∴
FOr the EDTA complexes;
The signal detection limit = (3*SD) + [tex]y_{blanks}[/tex]
= (3*28.195) + 50
= 84.585 + 50
= 134.585
We need to point out that the value of the calibration curve given is too vague and it should be (1.75 x 10^9 M^-1) as oppose to (1.75 x 10^-9 M^-1)
The concentration of detection limit is:
[tex]=\dfrac{3 \times SD}{slope }[/tex]
[tex]=\dfrac{3 \times 28.195}{1.75 \times 10^{9} \ M^{-1} }[/tex]
[tex]\mathbf{= 4.833\times 10^{-8} \ M}[/tex]
The lower limit of quantification is:
[tex]=\dfrac{10 \times SD}{slope }[/tex]
[tex]=\dfrac{10 \times 28.195}{1.75 \times 10^{9} \ M^{-1} }[/tex]
[tex]\mathbf{= 1.611 \times 10^{-7} \ M}[/tex]
Use the order of operations to simplify the expression
9²-72+6²•8-3
Answers
Answer:
294
Step-by-step explanation:
Use the order of operations or PEMDAS
Parentheses
Exponents
Multiply
Divide
Add
Subtract
Explanation: PEMDAS
the hull speed of a boat is approximated by the function
where l is the hull length in feet an v is the hull speed knots.
Answers
Answer:
sk,m
Step-by-step explanation:
Answer:
a=1.34
b=-10
>10
Step-by-step explanation:
I need help I’ll mark u as brainlest
Answers
Answer:
V = 6 in ^3
Step-by-step explanation:
The formula for volume is
V = Bh where B is the area of the base
The base is a triangle and the height is 2 inches
B = 1/2 bh where b is 3 and h is 2
B =1/2 (3)*2 = 3 in^2
V = 3 *2
V = 6 in ^3
Answer:
[tex]V=6[/tex] cubic inches
Step-by-step explanation:
The Volume formula for a triangular prism is [tex]V=\frac{1}{2} bhl[/tex]
[tex]V=\frac{1}{2} (3)(2)(2)[/tex]
[tex]V=\frac{1}{2} (12)[/tex]
[tex]V=6[/tex]
Hope this helps
Please help is for now :(
Answers
Answer:
d
Step-by-step explanation:
d part it is. this is the answer
A rocket is launched from the ground and travels in a straight path. The angle of inclination of the rocket's path is 1.2 radians. (That is, the rocket's path and the ground form an angle with a measure of 1.2 radians.)]
Required:
a. What is the slope of the rocket's path?
b. If the rocket has traveled 85 yards horizontally since it was launched, how high is the rocket above the ground? _____yards.
c. At some point in time, the rocket is 313 yards above the ground. How far has the rocket horizontally (since it was launched) at this point in time? _____yards
Answers
Answer:
a)[tex]S=2.57[/tex]
b)[tex]H=203.2yard[/tex]
c)[tex]X=121.79yards[/tex]
Step-by-step explanation:
From the question we are told that:
Angle [tex]\theta=1.2=68.755^o[/tex]
a)
Generally the equation for Slope is mathematically given by
[tex]S=tan \theta[/tex]
[tex]S=tan 68.755[/tex]
[tex]S=2.57[/tex]
b)
Given the right Angle triangle with horizontal distance [tex]x=85yard[/tex]
Generally the equation for Height traveled is mathematically given by
[tex]H=tan\theta*x[/tex]
[tex]H=2.57*85[/tex]
[tex]H=218.45[/tex]
[tex]H=203.2yard[/tex]
c)
Generally the equation for Horizontal Distance traveled at 313 height traveled is mathematically given by
[tex]X=\frac{313}{tan65.75}[/tex]
[tex]X=\frac{313}{2.57}[/tex]
[tex]X=121.79yards[/tex]
Using the projectile principle, the slope of the rockets path, height above the ground and the distance traveled at a height of 313 yards would be 2.57, 218.63, 121.69 respectively.
Given the Parameters :
Angle of inclination = 1.2 radianConverting to degree :
θ = 1.2 rads × 180/π = 68.755°A.)
The slope of the rocket's path :
Slope = tanθSlope = tan(68.755) = 2.57
B.)
Horizontal distance, = distance along the x-axis = 85 yards
Vertical distance = height = distance along y-axis, y
y = tanθ × xy = slope × x
y = tan(68.755) × 85
y = 218.63 yards
C.)
Vertical distance, y = 313 yards
From :
[tex] y = x tan\theta [/tex]
[tex] x = \frac{y}{tan\theta} [/tex]
[tex] x = \frac{313}{tan(68.755°)} [/tex]
x = 121.69 yards
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Four veterinarians at an animal clinic were surveyed about the type of animals they had seen as patients in a particular week. The results of the survey are shown in the table.
Veterinarian
Dr. Greene
Dr. Fluke
Dr. Johansen
Dr. Ponce
Type of animal)
dog)
cat)
bird)
Dr. Greene)
Dog) 77
Cat) 56
Bird) 0
Total) 133
Dr. Fluke
Dog) 64
Cat) 54
Bird) 7
Total) 125
Dr. Johansen
Dog) 59
Cat) 30
Bird) 21
Total) 110
Dr. Ponce
Dog) 39
Cat) 52
Bird) 16
Total) 107
TOTAL animals
Dog) 239
Cat) 192
Bird) 44
Total) 475
Of the patients that are cats, what percent were seen by Dr. Fluke? Express your answer to the nearest whole percent.
Answers
Answer:
28.125%
Nearest whole percent: 28%
Step-by-step explanation:
54/192 = .28125
move decimal to the right (two times)
28.125%
Using the percentage concept, it is found that 28% of the patients that are cats were seen by Dr. Fluke.
What is a percentage?The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
[tex]P = \frac{a}{b} \times 100\%[/tex]
In this problem, 54 out of 192 cats were seen by Dr. Fluke, hence the percentage is given by:
[tex]P = \frac{54}{192} \times 100\% = 28.1\%[/tex]
Rounding to the nearest percent, 28%.
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Trong một lớp học có 50 sinh viên. Hỏi có bao nhiêu cách bầu ra một ban cán sự lớp gồm 3 người: 1 lớp trưởng, 1 lớp phó, 1 bí thư và không kiêm nhiệm chức vụ.
Answers
Answe
SI Si olla amigo lel just spammin here
Step-by-step explanation:
The mid point of the line segment joining the points A(4,7) and B(2,5)
Answers
Answer:
hope it helps you.......
It May Help You
Thank You:)
Write 6.7 multiple 10 in expanded form
Answers
Answer:
(6×10) + (0.7×10)
60+7=67
how to do 10 divded by 50
Answers
Answer:
0.2Step-by-step explanation:
10 divided by 50
[tex] = \frac{10}{50} [/tex]
[tex] = \frac{1}{5} [/tex]
= 0.2 (Ans)
0.2 is the correct answer
Giải phương trình : y' - xy = x^{3} + x. Điều kiện y(1) = 1
Answers
Все детали на приложенном фото.
Sally works 40 hours a week and makes $30 an hour, but her kids are in child care each day and the day care center charges her $70 per day. If you deduct her child care expenses, how many dollars per hour does she actually make? (Assume Sally works five days per week.)
Answers
Answer:
Sally will earn $21.25 per hour after she removes daycare charges from her total earnings.
What does Sally earn each week?
Let's start by solving how much money Sally earns per week.
To find this value, we will find the product of 40 hours per week and 30 dollars per hour.
[tex]40\times30=1200[/tex]
We now know that Sally makes $1,200 a week without deducting the daycare charges per day.
However, we know we need to deduct 70 dollars for each day that Sally works. Since she works for five days a week, we will find the product of 70 dollars per week and five days a week.
[tex]70\times5=350[/tex]
Therefore, the daycare charges $350 per week.
What does Sally take home each week?Finally, we need to subtract the daycare charges from the amount of money that Sally earns to find how much she actually makes in a week.
[tex]1200-350=850[/tex]
Therefore, for forty hours of work that Sally works each week, she earns $850.
However, we are not done. The question asks us to find how many dollars per hour does she actually make? Therefore, we need to find the quotient of 850 dollars and 40 hours per week.
[tex]\displaystyle \frac{850}{40}=21.25[/tex]
Therefore, Sally earns $21.25 each hour after deducting daycare costs.
19. Which of the following would best be solved using factoring the difference of squares?
O x^3 + 5x^2 - 9x - 45 = 0
O 3x² + 12x = 8
O x^2 - 25 = 0
O x^2 + 3x – 10 = 0
Please hurry!
Answers
Answer:
x² + 3x - 10 = 0
x² - 25 = 0
Maria's Pizza Palace offers 4 types of crust, 7 toppings, and 6 kinds of cheese for the mega calzone. How many different mega calzones can be made if a mega calzone contains 5 different toppings and 3 different cheeses
Answers
Answer:
210 different mega calzones can be made.
Step-by-step explanation:
Fundamental counting principle:
States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.
Additionally:
The order in which the toppings and the cheeses are chosen is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Toppings:
5 from a set of 7. So
[tex]C_{7,5} = \frac{7!}{5!2!} = 21[/tex]
Cheeses
3 from a set of 6. So
[tex]C_{6,3} = \frac{6!}{3!3!} = 20[/tex]
How many different mega calzones can be made if a mega calzone contains 5 different toppings and 3 different cheeses?
Toppings and cheeses are independent, and thus, by the fundamental counting principle:
21*20 = 210
210 different mega calzones can be made.
-7x - 3 equals 5x + 3
solve for x
Answers
-7x-3=5x+3
-3=12x+3
-6=12x
-6/12=12x/12
x=-6/12
Simplify to x= -1/2
Answer:
x = -0.5
Step-by-step explanation:
-7x-3=5x+3
+7x +7x
-3=12x+3
-3 -3
-6=12x
x=-0.5
A line passes through (1, - 1) and (3, 5). What is the equation of the line in slope-intercept form?
Answers
Answer: a+b+c=0 and 3a+5b+c=0
Step-by-step explanation:
If you find a solution to these equations, you will find an equation of your line. Please notice that (a,b,c) defines the same line as (ka,kb,kc) and for any non-zero k, and a=b=c=0 defines no line equation at all. Now you can take a=1 and solve for b and c, or take b=1 and solve for a and c, or take c=1 and solve for a and b, at least one of these will work.
3x-4=8 what is the value of X
Answers
Answer:
x = 4
Step-by-step explanation:
Given
3x - 4 = 8 ( add 4 to both sides )
3x = 12 ( divide both sides by 3 )
x = 4
Which of the following equations is NOT an example of inverse variation?
I. f(x)=kx
II. f(x)=2kx
f
(
x
)
=
2
k
x
III. f(x)=−kxz
Answers
Based on the equation,the equation which is not an inverse variation is f(x) = kx
Inverse variationf(x) = kx
= k × x
f(x) = 2k/x
= k(2/x)
f(x) = -kx/z
= k(-x/z)
Inverse variation is given by:
y = k(1/x)
where,
k = constant of proportionalityTherefore, f(x) = kx is not an inverse variation.
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