Multiply: (–4 + i)(2 – 3i)
a. –5 – 10i
b. –8 + 11i
c. –5 + 14i
d. –11 + 14i
The result of the product of the given complex numbers as required to be determined is; Choice C; -5 + 14i.
What is the product of the given complex numbers?It follows from the task content that the result of the product of the given complex numbers is to be determined.
On this note, since the required product to be evaluated is; (–4 + i) (2 – 3i).
We can therefore multiply as follows;
-8 + 12i + 2i - 3i².
However, it is noteworthy to know that; i² = -1.
Hence, we have that;
-8 + 14i + 3
= -5 + 14i
On this note, it follows that the result of the product of complex numbers as required is; -5 + 14i.
Read more on product of complex numbers;
https://brainly.com/question/29278325
#SPJ1
Ms.Metz had her students estimate the length and width of a math book. Dana's estimate was 40cm by 20cm. The book measured 24cm by 16cm. How far off was her estimate?
Dana's estimated length was 66.67% far off the actual length and her estimated width was 25% far off the actual width.
What is percent error?Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words, the percent error is the relative error multiplied by 100.
Percent Error Formula
The formula for percent error is:
PE = (|Estimated value-Actual value|/ Actual value) × 100
Given,
Actual length of the book = 24 cm
Actual width of the book = 16 cm
Dana's estimated length of the book = 40 cm
Dana's estimated width of the book = 20 cm
Error in measurement of length of the book =
(Measured Length - Actual Length/Actual length) × 100
= (40 - 24/24) ×100 = 66.67%
Error in measurement of width of the book =
(Measured width - Actual width/Actual width) × 100
= (20 - 16 / 16) × 100 = 25%
Hence, Dana's estimated length and breadth was 66.67% and 25% far off the actual length and width of the book respectively.
Learn more about percent error here:
https://brainly.com/question/10501147
#SPJ1
Round 0.295833333 to the nearest hundredth
Answer:
The answer is 0.30.
I wish you luck in your assignments.
Answer:
0.3
Step-by-step explanation:
Since 5 rounds up, that would cause the 0.09 to become a 0.1, so it would be 0.3
Describe the error in each problem below. 36÷3+(3²•2)36÷3+9•2 36÷12•2 3•2 6
Answer:
Step-by-step explanation:
In the last part of the problem, you have to follow PEMDAS.
Instead of you added before dividing. After the step of 36÷3+9x2 you have to divide.
Work out
2/3 - 2/5
Give your answer in its simplest form.
Answer:
4/15
Step-by-step explanation:
find common denominators, which is 15
multiply 2/3 by 5 and and 2/5 by 3
2 x 5 = 10 and
3 x 5 = 15
10/15
2 x 3 = 6 and
5 x 3 = 15
6/15
subtract numerators
10 - 6
15
= 4/15
A blueprint of a house has a scale in which 1 inch equals 4 1/2 feet. If the living room wall measures 7 1/4 inches on the drawing, what is the actual length of the wall?
The actual length of the wall is ___ feet
Answer:
Step-by-step explanation:
1 : 4 1/2 :: 8 1/5 : x proportion
x = (4 1/2)(8 1/5) product of means/extremes
x = (9/2)(41/5) change improper fraction
x = 369/10 multiply
x = 36.9 change to decimal
The actual length is 36.9 feet.
The table represents a quadratic function C(t).
t C(t)
−2 1
−1 4
0 5
1 4
2 1
What is the equation of C(t)?
C(t) = −(x − 5)2
C(t) = (x − 5)2
C(t) = −x2 + 5
C(t) = x2 + 5
The equation that presents the table will be C(t) = - t² + 5. Then the correct option is C.
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The table represents a quadratic function C(t).
t C(t)
−2 1
−1 4
0 5
1 4
2 1
From the table, the coordinate of the vertex will be at (0, 5). Then the equation is given as,
C(t) = a(t - 0)² + 5
C(t) = at² + 5
The equation is passing through the point (1, 4), then we have
4 = a (1²) + 5
4 = a + 5
a = - 1
The equation that presents the table will be C(t) = - t² + 5. Then the correct option is C.
More about the equation of the parabola link is given below.
https://brainly.com/question/20333425
#SPJ1
Gemma has 3 rose bushes, each with the same number or roses. She picks 4 of the roses. There are 20 roses left on the rose bushes. How many roses were on each rose bush?
There were 8 roses on each bushes
How to calculate the number of roses on each bush?
Gemma has 3 rose bushes
Each bush has the same number of roses
She picks 4 of the roses
After picking the roses, there are 20 left in the bushes
Therefore the number of rose on each bush can be calculated as follows
20 + 4
= 24
24/3
= 8
Hence there are 8 roses in each bush
Read more on roses here
https://brainly.com/question/20699993
#SPJ1
Each other 11 letters of the word mathematics with written on a separate piece of paper and placed in a bowl what is the probability of drawing
Therefore, the probability of drawing "OBJ" from the bowl is (1/11) * (1/11) * (1/11) = 1/1331
Define Probability.The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Define Statistics.The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. It is customary to start with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem.
The word "mathematics" has 11 letters, so there are 11 letters in the bowl. The probability of drawing the letter "O" is 1/11, since there is only 1 "O" in the 11 letters. Similarly, the probability of drawing the letter "B" is 1/11, and the probability of drawing the letter "J" is 1/11 as well.
Since the events of drawing the letter "O", "B", and "J" are independent of each other, the probability of drawing all three letters in order is the product of their individual probabilities.
Therefore, the probability of drawing "OBJ" from the bowl is (1/11) * (1/11) * (1/11) = 1/1331
It is a very low probability, the chances of drawing that sequence are very low.
To learn more about statistics visit:
https://brainly.com/question/29093686
#SPJ1
Calculate The Double Integral. ∫∫ 4x 1 + Xy DA, R = [0, 4] × [0, 1]
Answer:
[tex]20\ln(5)-16\approx16.18876[/tex]
Step-by-step explanation:
[tex]\displaystyle\int\int\limits^{}_R {\frac{4x}{1+xy} } \, dA\\\\\\=\int\limits^4_0\int\limits^1_0 {\frac{4x}{1+xy} } \, dy \, dx\\\\\\=\int\limits^4_0 {\ln(1+xy)\biggr|_0^1} \, dx\\\\\\=\int\limits^4_0 {\ln(1+x)} \, dx\,\,\,\,\,\,\,\,\,\,\,\,\bigr(u=\ln(1+x),\,dv=dx\bigr)\\\\\\=4\biggr(x\ln(1+x)\biggr|_0^4-\int\limits^4_0 \frac{x}{1+x} \,dx\biggr)\\\\=4\biggr(4\ln(5)-\bigr[x-\ln(1+x)\bigr]\biggr|_0^4\biggr)\\\\=4\biggr(4\ln(5)-\bigr[4-\ln(5)\bigr]\biggr)\\\\=4\biggr(5\ln(5)-4]\biggr)\\\\=20\ln(5)-16[/tex]
Select the correct answer from each drop-down menu. Let d(t) be the total number of miles Joanna has cycled, and let t represent the number of hours after stopping for a break during her ride. So, d(4) = 68 . This means that after a 4 hour break , Joanna cycled 68 miles total .
The numeric value of the function d(t) = 12t + 20 at t = 4 is given as follows:
d(4) = 48.
The interpretation of this numeric value is that after a time of 4 hours, Joanna has cycled 68 miles.
How to interpret the function?The function for this problem is defined as follows:
d(t) = 12t + 20.
The meaning of each variable is given as follows:
t: time in hours after the break.d(t): distance cycled after t hours.The numeric value at t = 4 is obtained replacing the lone instance of t in the function by 4, as follows:
d(4) = 12(4) + 20
d(4) = 48 + 20
d(4) = 68 miles.
Meaning that after a time of 4 hours, the distance cycled by Joanna was of 68 miles.
Missing InformationThe function for this problem is defined as follows:
d(t) = 12t + 20.
More can be learned about functions at https://brainly.com/question/24808124
#SPJ1
Solve for 0. Round to the nearest tenth of a degree. Sin 0=0.85
The value of the angle theta is 58 degrees
How to determine the value of the angle thetaFrom the question, we have the following parameters that can be used in our computation:
Sin 0=0.85
Express the angle in the equation properly
So, we have the following representation
sin(Ф) = 0.85
Take the arc sin of both sides of the equation
So, we have the following representation
sin⁻¹(sin(Ф)) = sin⁻¹(0.85)
Evaluate the arc sin of one side of the equation
So, we have the following representation
Ф = sin⁻¹(0.85)
Evaluate the arc sin of the other side of the equation
So, we have the following representation
Ф = 58.2116693829
Approximate the equation
Ф = 58 degrees
Hence, the solution is 58 degrees
Read more about trigonometry at
https://brainly.com/question/24349828
#SPJ1
Richard has 11 markers in a backpack. One of them is red and one is purple. What is the probability Richare
will reach into the backpack without looking and grab the red marker and then reach in a second time and
grab the purple marker if:
(a) the first marker is not replaced?
(b) the first marker is replaced?
Express your answers as fractions in simplest form.
The probability Richard marker is 11.The probability of anything occurring is known as probability.
How are probabilities calculated?The probability of anything occurring is known as probability. To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur.
The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.
The probability of anything occurring is known as probability. To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur.
According to question:-
11/1 = 11
11/1 = 11
The probability Richard marker is 11.The probability of anything occurring is known as probability.
To know more about probability visit:
brainly.com/question/24756209
#SPJ1
d= c/n solve for n, I've been trying to solve this by multiplying by n but i want to solve for n so that's wrong thank you guys :D
Answer:
You started correctly....
Step-by-step explanation:
d = c/n Multiply both sides by 'n'
dn = c now divide both sides of the equation by 'd'
n = c/d Done.
if 11 is to 22, and 22 to 242, then from 242 to what
Answer:
it's equal to = 242 =484. I think so that's the right answer please
make x the subject of the formula in R = ax-p/q+bx
R = (ax - p)/(q + bx)
(ax - p) = R(q + bx)
ax - p = Rq + Rbx
ax - Rbx = Rq + p
x(a - Rb) = Rq + p
x = (Rq + p)/(a - Rb)
The morning temperature is -29.8 degrees. The temperature rose 33.2 degrees during the day.
What is the new temperature in degrees?
Answer:
Step-by-step explanation:use a calculator
Answer:
Step-by-step explanation:
-29.8+33.2=3.4
Which graph represents a function?
Answer:
The fourth graph since it passes the vertical line test.
Each input has one output.
Hope this helps :)
Let |r| = 6 at an angle of 30° and |s| = 11 at an angle of 225°. Which expression represents |r – s|?
The resultant of subtraction of both vectors is
|r - s| = √(r² + s² - 2rscos{15})
What are vectors?A vector is an object that has both a magnitude and a direction.
Given is that |r| = 6 at an angle of 30° and |s| = 11 at an angle of 225°.
For the subtraction of vectors, we can write its magnitude as -
|r - s| = √(r² + s² - 2rscos{15})
Therefore, the resultant of subtraction of both vectors is
|r - s| = √(r² + s² - 2rscos{15})
To solve more questions on vectors, visit the link below -
https://brainly.com/question/29740341
#SPJ1
Select each equation that the number 10^3 makes true.
6.01 x
= 601
O 0.305 x
= 305
0.54 x
= 540
O 0.097 x
970
0.97 x
= 97
All of the equations which the number 10³ makes true include the following:
B. 0.305 × __ = 305
C. 0.54 × __ = 540
How to determine the true equations?In this exercise, you are required to determine the equations which the number 10³ makes true. This ultimately implies that, we would substitute the number 10³ into each of the given equations as follows;
6.01 × 10³ = 601
By expanding the exponent, we have the following equation:
6.01 × 1,000 = 601
6010 = 601 (False).
0.305 × 10³ = 305
By expanding the exponent, we have the following equation:
0.305 × 1,000 = 305
305 = 305 (True).
0.54 × 10³ = 540
By expanding the exponent, we have the following equation:
0.54 × 1,000 = 540
540 = 540 (True).
0.097 × 10³ = 970
By expanding the exponent, we have the following equation:
0.097 × 1,000 = 970
97 = 970 (False).
Read more on equation here: brainly.com/question/28949611
#SPJ1
Help me I do t know how to do this
x divided by 6 is what
Answer:x/6
Step-by-step explanation:
Here the value of x is not given and hence the answer to the question is
x/6
To know more about x/6,
https://brainly.com/question/22945575
simplify the expression 14+5(x+3) - 7x
Answer:
- 2x +29
Step-by-step explanation:
Open up the parenthesis, then simplify
14 + 5x + 15 - 7x
5x - 7x + 14 + 15
-2x + 29
[tex]14+5(x+3) - 7x[/tex]
Distribute:
[tex]14+(5)(x)+(5)(3)-7x[/tex]
[tex]14+5x+15-7x[/tex]
Combine Like Terms:
[tex](5x-7x)+(14+15)[/tex]
[tex]\fbox{-2x + 29}[/tex]
Can someone solve 18?
The piecewise function f(x) = 1/2 |x| is equivalent to -
1/2 |x| = {- x/2} {x < 0}
1/2 |x| = {x/2} {x ≥ 0}
What is a piecewise function?A piecewise function is a function that is defined on a sequence of intervals. A common example is the absolute value function. Piecewise functions are implemented in the Wolfram Language as PiecewiseAdditional piecewise functions include the Heaviside step function, rectangle function, and triangle function.Given is the absolute value function -
f(x) = 1/2 |x|
We can write it as a piecewise function as follows. The given function is as follows :
f(x) = 1/2 |x|
The absolute value function is given as -
|x| = - x {x < 0}
|x| = x {x ≥ 0}
So, we can write the piecewise function as -
1/2 |x| = {- x/2} {x < 0}
1/2 |x| = {x/2} {x ≥ 0}
Therefore, the piecewise function f(x) = 1/2 |x| is equivalent to -
1/2 |x| = {- x/2} {x < 0}
1/2 |x| = {x/2} {x ≥ 0}
To solve more questions on piecewise function, visit the link below -
https://brainly.com/question/12700952
#SPJ1
Find the midpoint and distance between (-3,10) and (15,-2)
11-(-2)x4 step by step pls my hm is due tmr
Answer:
Step-by-step explanation:
11 -(-2) x 4
11 + 2 x 4
11 +8
= 19
The angle bisectors of triangle ABC are , , and . They meet at a single point . (In other words, is the incenter of .) Suppose , , , and .
To solve this we must be knowing each and every concept related to triangle. Therefore, the angle bisector is indeed the ray, line, or fragment that splits a particular angle in two equal pieces.
What is triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The denotes a triangle having vertex A, B, and C. In Euclidean geometry, every three non-collinear points define a unique triangle and, by extension, a unique plane.
In geometry, the angle bisector is indeed the ray, line, or fragment that splits a particular angle in two equal pieces.
Therefore, the angle bisector is indeed the ray, line, or fragment that splits a particular angle in two equal pieces.
To know more about triangle, here:
https://brainly.com/question/14712269
#SPJ1
Canvas Reproductions, Inc has RM4,500 researching a new project. The project requires RM20,000 worth of new machinery which would cost RM3,000 to install. The company would realize RM4,500 in after tax proceeds from the sale of the old machinery. If Canvas’s working capital is unaffected by this project, what is the initial investment amount for this project?
Hi. This is an informal letter .
The body of letter goes like this
Hi friend hope u are enjoying ur life and luck find u in best state of mind. My exam have been over and wanted to share my experience with my near and dear one so I was planning to come to ur place to enjoy my vacationHi. This is an informal letter .
The body of letter goes like this
Hi friend hope u are enjoying ur life and luck find u in best state of mind. My exam have been over and wanted to share my experience with my near and dear one so I was planning to come to ur place to enjoy my vacationHi. This is an informal letter .
The body of letter goes like this
Hi friend hope u are enjoying ur life and luck find u in best state of mind. My exam have been over and wanted to share my experience with my near and dear one so I was planning to come to ur place to enjoy my vacationHi. This is an informal letter .
The body of letter goes like this
Hi friend hope u are enjoying ur life and luck find u in best state of mind. My exam have been over and wanted to share my experience with my near and dear one so I was planning to come to ur place to enjoy my vacation
Which expression is equivalent to 5-3(x+2)?
A. -3x - 1
B. -3x+10
C. 2x + 4
D. 2x-6
What is x + y when x = 4 and y = -5
Answer:
x + y = -1
Step-by-step explanation:
4 plus -5 is equivalent (equal to) the equation 4 - 5 which equals -1