Simplify the expression.
(5+i)(2-7i)
Answers
Answer:
17-33i
Step-by-step explanation:
Multiply using the foil method than combined the real and imaginary parts of the expression
Related Questions
3a^2 -3a - 36. solving quadratic by factoring. factor each expression. be sure to check for greatest common factor first.
Answers
we have the expression
\(3a^2-3a-36\)step 1
Factor 3
\(3(a^2-a-12)\)step 2
equate to zero
\(3(a^2-a-12)=0\)step 3
Solve
\((a^2-a-12)=0\)\(\begin{gathered} a^2-a=12 \\ (a^2-a+\frac{1}{4}-\frac{1}{4})=12 \\ (a^2-a+\frac{1}{4})=12+\frac{1}{4} \\ (a^2-a+\frac{1}{4})=\frac{49}{4} \end{gathered}\)Rewrite as perfect squares
\((a-\frac{1}{2})^2=\frac{49}{4}\)take the square root on both sides
\(\begin{gathered} a-\frac{1}{2}=\pm\frac{7}{2} \\ a=\frac{1}{2}\pm\frac{7}{2} \end{gathered}\)the values of a are
a=4 and a=-3
therefore
\(3(a^2-a-12)=3(a-4)(a+3)\)NO LINKS!! URGENT HELP PLEASE!!!
Express the statement as an inequality
d. d is between 2 and 1
1. d < 1 < 2
2. 1 < d < 2
3. 1 < 2 < d
4. 2 ≥ d ≥ 1
5. 1 ≤ d ≤ 2
e. t is not less than 5
1. t > 5
2. t < 5
3. t = 5
4. t ≥ 5
5. t ≤ 5
f. The negative of z is not greater than 4
1. -z < 4
2. z ≤ -4
3. z ≤ 4
4. z < 4
5. -z ≤ 4
Answers
Answer:
d. 1 < d < 2
e. t ≥ 5
f. -z ≤ 4
Step-by-step explanation:
Answer:
d. 5. 1 ≤ d ≤ 2
e. 4. t ≥ 5
f. 1. -z < 4
Step-by-step explanation:
d. d is between 2 and 1
The statement "d is between 2 and 1" means that d is greater than 1 and less than 2. We can represent this using the inequality 1 < d < 2. However, the answer choices do not match this exact form of inequality. To rephrase the inequality in a way that matches the answer choices, we can use the logical "and" operator to combine two inequalities: d is greater than or equal to 1, and d is less than or equal to 2. This gives us the inequality 1 ≤ d ≤ 2, which is answer choice 5.
e. t is not less than 5
The statement "t is not less than 5" means that t is greater than or equal to 5. This can be represented using the inequality t ≥ 5, which is answer choice 4.
f. The negative of z is not greater than 4
The statement "the negative of z is not greater than 4" means that -z is less than or equal to 4. We can represent this using the inequality -z ≤ 4, which is answer choice 2. However, the question does not include an answer choice for -z < 4, which is also true based on the statement.
the current in the electronic circuit in the mobile phone was 0.12a the potential difference across the battery was 3.9V. calculate the resistance of the electronic circuit in the mobile phone
Answers
Answer:
Step-by-step explanation:
V = 3.9V
I = 0.12A
Ohm's Law, V = IR
Rearranging Ohm's Law, R = V/I
R = 3.9/0.12 = 32.5Ω
Write an equation in slope-intercept form of the line that passes through the points (1, 2) and (-2, -1)
y=
Answers
Answer:
y=x+1
Step-by-step explanation:
Firstly, we need to know that the slope intercept form is known as:
y=mx+b, where y and x are coordinates, m is the slope and b is the y intercept.
We need to find m first, and then b. By doing that, we use the formula:
\(\frac{y1-y2}{x1-x2} \\\\\\y1=2\\y2=-1\\x1=1\\x2=-2\)
Plugging those values in, we get:
\(m= \frac{2-(-1)}{1-(-2)} \\\\= \frac{3}{3} \\=1\)
So with this information, we already know that y=1x+b. We just need to find b.
So we can pick one of the two coordinates given. Let's use (1,2) and plug those in.
2=1(1)+b
Now with that, we solve for b.
2=1+b
2-1=b
1=b
b=1
Therefore, we have the final equation of y=1x+1
or better,
y=x+1
Identify the domain and range for the table from problem #5 of your assignment. Also, determine if it represents a function.
Answers
Answer:
Domain: {4,5,7,10}
Range: {2,4,8}
Not a function
Step-by-step explanation:
The domain is all the x-values.
The range is all the y-values.
However, this isn't a function because two different inputs have the same output. If it were a function, there would be one unique output for every input.
Round to the nearest 10th if necessary
Answers
Answer:
Step-by-step explanation:
ah they are getting harder. :/ they didn't give any angles this time. so figure those out first, super hero math to the rescue :P oh and the question is just find angle C soo.
Angles C + B + A = 180
we can turn the law of cosines around and use it to find the angle, you are given the formula for that as well in the problem. it's nice of them to not expect you to memorize the formula I had to :/ your class is going easy on you. get out the ruler and smack some students , prof. Snape :D :D My prof. once threw an eraser at one person b/c they fell asleep in class :D when it hit him.. b/c it was all full of chalk.. the eraser.. it kinda "exploded" and he woke up coughing... :o anyway.. back to math :P
a= 28
b= 17
c = 15
C = arcCos [ (a^2 + b^2 - c^2) / (2 * a * b) ]
C = arcCos[ 28^2 + 17^2 - 15^2 / 2*28 *17 ]
C = arcCos[ 784 + 289 -225 / 952 ]
C = arcCos [ 848 / 952 ]
C = arcCos [0.8907563]
C = 27.03 °
rounded to nearest 10th then is
C = 27.0 °
:)
btw, does 27 seem right? to me it does b/c that angle is small
which expressions are equivalent to 3^4/9/3^2/9? select all that apply
Answers
Answer:
first and third expressions
Step-by-step explanation:
using the rule of exponents
\(\frac{a^{m} }{a^{n} }\) = \(a^{m-n}\)
then
\(\frac{3^{\frac{4}{9} } }{3^{\frac{2}{9} } }\)
= \(3^{\frac{4}{9}-\frac{2}{9} }\) ← first expression
= \(3^{\frac{2}{9} }\) ← third expression
Magic Realm, Inc., has developed a new fantasy board game. The company sold 15,000 games last year at a selling price of $20 per game. Fixed costs associated with the game total $182,000 per year, and variable costs are $6 per game. Production of the game is entrusted to a printing contractor. Variable costs consist mostly of payments to this contractor.
Required:
1) Prepare a contribution format income statement for the game last year and compute the degree of operating leverage.
2) Management is confident that the company can sell 18,000 games next year (an increase of 3,000 games, or 20%, over last year).
Compute:
a) The expected percentage increase in net operating income for next year.
b) The expected total dollar net operating income for next year.
Answers
The expected total dollar net operating Income for next year = $70,000
1) The contribution format income statement for the game last year, and the degree of operating leverage is computed below:
Contribution format income statement for the game last year Sales (15,000 × $20) = $300,000
Variable expenses (15,000 × $6) = $90,000
Contribution margin = $210,000
Fixed expenses = $182,000Net operating income = $28,000
Degree of operating leverage = Contribution margin / Net operating income= $210,000 / $28,000= 7.5 2)
The expected percentage increase in net operating income for next year:
The expected sales in next year = 18,000
games selling price per game = $20
Therefore, Total sales revenue = 18,000 × $20 = $360,000
Variable expenses = 18,000 × $6 = $108,000
Fixed expenses = $182,000
Expected net operating income = Total sales revenue – Variable expenses – Fixed expenses
= $360,000 – $108,000 – $182,000= $70,000
The expected percentage increase in net operating income = (Expected net operating income - Last year's net operating income) / Last year's net operating income*100= ($70,000 - $28,000) / $28,000*100= 150%
The expected total dollar net operating income for next year = $70,000
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(17- 4 1/6) + 10 3/8 help me
Answers
First lets transform the mixed fractions into improper fractions:
\(\begin{gathered} 4\frac{1}{6}=\frac{4(6)+1}{6}=\frac{25}{6} \\ 10\frac{3}{8}=\frac{10(8)+3}{8}=\frac{80+3}{8}=\frac{83}{8} \end{gathered}\)then, we can write the expression as follows:
\(undefined\)Ten cards numbered from 1 to 10 inclusive are placed in a hat Irene takes a card out of the hat without looking what is the probability that she takes out:
A] the number 10
B] an odd number
C] a number greater than 4
D] a prime number
E] a number between 5 and 9?
Answers
B] 5/10
C] 6/10
D] 4/10
E] 3/10
1. research institute reported that the average number of weeks an individual is unemployed is 17.5 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 17.5 weeks and that the population standard deviation is 4 weeks. Suppose you would like to select a random sample of 50 unemployed individuals for a follow-up study.
a. What is the probability that a simple random sample of 50 unemployed individuals will provide a sample mean of less than 1 week?
b. What is the probability that a simple random sample of 50 unemployed individuals will provide a sample mean within 1 week of the population mean?
Answers
The probability that a simple random sample of 50 unemployed individuals will provide a sample mean within 1 week of the population mean is 0.92
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Let X the random variable that represent the avergae number of weeks an individual is unemployed of a population, and for this case we know the distribution for X is given by:
X = N(17.5)
Where μ = 17.5 and σ = 4
Since the distribution for X is normal then, the distribution for the sample mean is given by:
X = N(17.5, σ/√n)
X =N(17.5.4/√50) = 0.566
We select a sample of n =50 people. And we want to find the following probability
P(16.5 < X < 18.5) = P((16.5 -17.5)/(4/√50) < Z < (16.5 -17.5)/(4/√50) )
And using the normal standard table or excel we find the probability:
P(-1.768 < Z 1.768) = P(Z < 1.768) - P(Z< -1.768) = 0.961 - 0.039 = 0.92
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Find the value of x.
Answers
Answer:
Its 9
Step-b(y-step explanation:
Can you make me brainlist??
Answer:
The answer is B just took the test!
2x-3y = -2
X + 24 = 15
Answers
Answer:
No
Step-by-step explanation:
2x-3y= 6xy
Using the following image, determine if the triangles are similar. If so, how?
Not Similar
SSS
AA~
SAS
Answers
Evaluate log4 exponent 0.5
Answers
We can claim that after answering the above question, the So, logarithm \(log4 (0.5^(1/2)) =-0.0752\)
what is logarithm?The logarithm is a power's reciprocal in mathematics. Accordingly, the exponent by which b must be raised to obtain a number x equals the logarithm of that number in base b. For instance, since 1000 = 103, its base-10 logarithm is 3, or log10 = 3. As an illustration, the base 10 logarithm of 10 is 2, while the square of 10 is 100. Log 100 = 2. To answer a question like, For example, how many times must a base of 10 be multiplied by itself to achieve 1,000, a logarithm (or log) is the mathematical term utilized. The solution is 3 (1,000 = 10 10 10).
Using the following property of logarithms:
\(log_a (b^c) = c * log_a (b)\\log4 (0.5^(1/2))\\(1/2) * log4 (0.5)\\log4 (0.5) = log (0.5) / log (4)\\log (0.5) ≈ -0.3010\\log (4) = 2\)
Therefore,
\(log4 (0.5) ≈ -0.3010 / 2 ≈ -0.1505\\(1/2) * log4 (0.5) ≈ (1/2) * (-0.1505) ≈ -0.0752\\\)
So, \(log4 (0.5^(1/2)) =-0.0752\)
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This month my metro water services bill was $36.34 and my Madison Suburban Utilty District bill was $26.03. My total water bill was $
Answers
Total water bill for the month is $62.37.
It seems that you may have accidentally left out the total amount of your water bill.
The total amount by simply adding the amounts of the individual bills together:
Total water bill =\($36.34 + $26.03\)
= \($62.37\)
You have not provided enough information to determine your total water bill.
You have only given the amounts of your individual bills from Metro Water Services and Madison Suburban Utility District.
To find your total water bill, you simply need to add the two bills together.
So, the total amount you owe for water this month would be:
Total water bill = \($36.34 + $26.03\)
= \($62.37\)
It appears that you may have forgotten to include the full amount of your water bill by accident.
Simple addition of the separate bill amounts yields the following sum:
Water bill total = \($36.34 + $26.03\)
= \($62.37\)
Your total water bill cannot be calculated because not enough information has been given.
Only the amounts of your individual Metro Water Services and Madison Suburban Utility District bills have been provided.
You just need to combine the two invoices together to get your total water bill.
As a result, this month's total water bill for you would be:
Water bill total = \($36.34 + $26.03\)
= \($62.37\)
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In the first 1/6 hour of a rainstorm, 1/10 inch of rain fell. If the rain continued to fall at the same rate, how much rain fell in 2 1/2 hours?
Answers
Answer:
you should multiply or add
Step-by-step explanation:
Find x in the diagram below
Answers
The value of the angle x is 30 degrees
How to determine the valueTo determine the value of the variable x, we need to know the triangle sum theorem.
The triangle sum theorem is a theorem in mathematics stating that the sum total of the interior angles in a triangle is equivalent to 180 degrees.
We should also note that angle at right angle is 90 degrees
Then, we have the angles written as;
90 degrees
2x degrees
x degrees
Equate the angles , we have;
2x + x + 90 = 180
collect the like terms, we have;
2x + x = 180 - 90
add or subtract the like terms, we have;
3x = 90
divide by the coefficient
x = 30
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answer plsplsplsplsplsplsplsplspls
Answers
Answer:
10 or 5
Step-by-step explanation:
I think 10
in an examination 30% of the candidates failed in English and 35% failed in general studies and 27% failed in both subjects.if310 candidates passed in both how many candidates appeared in the examination
Answers
Answer:
500
Step-by-step explanation:
Find two unit vectors orthogonal to both j-k and i+j.
Answers
The two unit vectors orthogonal to both j-k and i+j are \(\frac{i}{\sqrt{3} }- \frac{j}{\sqrt{3} } -\frac{k}{\sqrt{3} }\)
Let a bar = j- k = < 0,1,-1>
b bar = i+j = <1,1,0>
the cross product a x b bar is orthogonal to both a and b bar
= i ( 0-(-1) ) -j ( 0-(-1) ) + r (0-1)
= i-j-k
A unit vector is a vector whose length is 1 unit
There the unit vector is :
\(\frac{i-j-k}{\sqrt{1^2+(-1)^2+(-1)^2} } = \frac{i-j-k}{\sqrt{3} }\)
= \(\frac{i}{\sqrt{3} }-\frac{j}{\sqrt{3} }-\frac{k}{\sqrt{3} }\)
The second unit vector orthogonal to both a and b bar would be negative of the previous vector.
= \(-\frac{i}{\sqrt{3} }-\frac{j}{\sqrt{3} }-\frac{k}{\sqrt{3} }\)
Hence the two unit vectors orthogonal to both j-k and i+j are \(\frac{i}{\sqrt{3} }- \frac{j}{\sqrt{3} } -\frac{k}{\sqrt{3} }\)
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The point (5, -2) is rotated 90° about the origin. Its image is:
Answers
Please help me answer this question:
Answers
Answer:
Total area = 141,
the trapezoid = 117, the triangle=24
Darryl deposits $1,500 into a savings account that has a simple interest rate of 2.7%.
Lori deposits $1,400 into a savings account that has a simple interest rate of 3.8%.
If no other transactions are made, who will have more money in their account after 10 years? How much more?
Answers
Answer:
12
Step-by-step explanation:
solve for x simplify your radical answer completely 4 squared plus 4 squared is equal to what square root
Answers
Solution
For this case we can use the Pythagoras theorem and we got:
\(x=\sqrt[]{4^2+4^2}=\sqrt[]{32}=4\sqrt[]{2}\)
Carlos has 8 dollars and 48 cents. Alissa has 4 dollars and 14 cents. How much money does Carlos need
To give Alissa so that each of them has the same amount of money?
Answers
Answer:
.2 dollars and 17 cents
Step-by-step explanation:
Carlos has 8dollars and 48 cents --->8+0.48=8.48
Alissa has 4dollars and 14 cents--->4+0.14=4.14 let
x--->amount of money that Carlos needs to give Alissa
The linear equation that represents this situation is 8.48-x=4.14+x
solve for x2x=8.48-4.14
2x=4.34
x=2.17
therefore,the amount of money is 2 dollars and 17 cents.
thank you
by Angel osei
If a wagon is accelerating at a rate of 2 m/s and the
force acting on it is 20 N, what is the mass of the
wagon?
Answers
Answer:
40kg
Explanation:
a=2m/s^
f=20N
M=?
we know
f=m*a
or, 20=m*2
or, 2m=20
or, m= 20/2
:. m=10 kg
Is x/4-y/3=1 a linear question and what is it in standard form
Answers
Answer:
Step-by-step explanation:
so I believe the question is
\(\frac{1}{4}\)X - \(\frac{1}{3}\)Y=1
and we want to know if that is linear, and what the standard form for the equation would be
let's move a few things around using our algebra skillz
\(\frac{1}{4}\)X-1 = \(\frac{1}{3}\)Y
\(\frac{3}{4}\)X-3 = Y
y = \(\frac{3}{4}\)x-3 (in standard form y=mx+b)
y=\(\frac{3}{4}\)x + (-3)
we can see that this does make a line, so it's linear, and it's in standard form now.
1 point
6. Precipitation for the month of March was 4 inches less than average. In
April the precipitation was 14 inches less than average. How many inches
below average was the precipitation for both March and April?
Answers
Answer:
4 inches because March was 4 so april has to be 4 too
Step-by-step explanation:
Please help!!! Will give brainleist
Answers
Answer:
1. the difference in price is that Bigfoot is $60/$65 more expensive than lazer liner
lazer liner is $5 or 0 if its that misleading
2. no $5 difference
3. because electro is misleading and is only 11 dollars while The blade is 75$ The difference in price is $64
4. maker the bars that are misleading below and add the lower prices under with them. And add lines and small lines that says a dollar or 5 dollar per line.