The simplified representation of the complex number expression is
23 + 37i
a + bi, where a and b are real numbers, can be used to represent any complex number.
A complex number is a component of a number system that includes an element with the symbol I, sometimes known as the imaginary unit, and that extends the real numbers by satisfying the equation i² = -1. i was described as an imaginary number by René Descartes since no real number can fulfil the aforementioned equation. The complex number a + bi is known as having real and imaginary parts, respectively, A and b. The group of complex numbers is denoted by the letter C.The complex number expression is (6-4i)(1+5i)-(3-i)
now let us simplify,
or, (6-4i)(1+5i)-(3-i)
or, 6 + 30i - 4i -20i² -3 + i
or, 6 + 36i + 20 - 3 + i (we know that i² = -1)
or, 23 + 37i
Therefore the simplified complex expression is 23 + 37i
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A 22-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is one inch more than four times the length of the first piece. Find the lengths of the pieces.
A 22-inch piece of steel is divided into three parts, the length of 1st 2nd and 3rd piece are 3 inch,6 inch and 13 inch.
Given that,
A 22-inch piece of steel is divided into three parts, the second of which is twice as long as the first and the third of which is one inch longer than the first.
We have to find the parts' lengths.
Let us take, the length of the first piece is x inch.
Then the length of the second piece is 2x.
Then the length of the third piece is 4x + 1 inch.
We know total length of the steel is 22 inch.
We can write as,
x + 2x + 4x + 1 = 22
7x = 21
x = 3.
Then, the length of the first piece is 3 inch.
Then the length of the second piece is 2×3=6 inch.
Then the length of the third piece is 4×3 + 1=12+1=13 inch.
Therefore, the length of 1st 2nd and 3rd piece are 3 inch,6inch and 13 inch.
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MATH WIZARDS HELP PLEASE!!!!
Equation: h(t) = 96t - 16t²
This equation will form a parabolaThe zeros of the parabola will indicate the start time and height (0,0) and the end time and height (x, 0)The maximum point will be the maximum height the ball will reachThe maximum point will be the halfway point between the two zerosStep-by-Steph(t) = 96t - 16[tex]t^{2}[/tex]
Find the zeros of the given equation:
Factor out the greatest common factor (GCF)
h(t) = 8t (12 - 2t)
The two factors are:
0 = 8t
0 = 12 - 2t
For both factors, solve for t
8t = 0
8t/8 = 0/8
t = 0
12 - 2t = 0
-2t = -12
t = 6
Now we have the x-values (t) of our zeros:
t = 0
(0, 0)
t = 6
(6, 0)
The ball will land on the ground at 6 seconds
Recall that the maximum point of the graph is halfway between the two zeros:
6 + 0 = 6
6 ÷ 2 = 3
The ball will reach its maximum height in 3 seconds
To find this height, substitute t for 3 in the given equation, and solve for h:
t = 3
h(3) = 96(3) - 16(3)²
= 288 - 16(9)
= 288 - 144
= 144
The maximum height the ball will reach is 144 feet
***Refer to the graph below to check your answer:
=======================================================
Explanation:
I'll use x in place of t
And use y in place of h(t)
The equation we have is y = 96x - 16x^2
This rearranges to y = -16x^2 + 96x
Compare this to y = ax^2+bx+c to find that
a = -16b = 96c = 0The x coordinate of the vertex is
h = -b/(2a)
h = -96/(2*(-16))
h = 3
Then plug this into the equation to find the value of y
y = -16x^2 + 96x
y = -16(3)^2 + 96(3)
y = 144
The y coordinate of the vertex is k = 144
The vertex is located at (h,k) = (3, 144) to represent the highest point of the parabola.
The max height of 144 feet occurs when the ball is in the air for 3 seconds.
Xbxbxbdndbdndbdnsndnsnsnnssn
SOLUTION:
Case: Simple Interest
Method:
Simple Interest, I
[tex]\begin{gathered} I=PRT \\ Hence \\ T=\frac{I}{PR} \end{gathered}[/tex]Where
P= $500
R= 7.5% or 0.075
I= $225
Therefore, Time T
[tex]\begin{gathered} T=\frac{225}{500\times0.075} \\ T=6 \end{gathered}[/tex]Final answer:
6 years
Write the vector shown by the image below:
the vectors are : (i+5j) , (5i+j)
Here a vector is an object that has both a magnitude and a direction. Geometrically, able to picture a vector as a coordinated line fragment, whose length is the magnitude of the vector, and with an arrow demonstrating the direction. The direction of a vector is from its tail towards its head. Two vectors are the same on the off chance that they have the same magnitude and direction. We signify vectors utilizing boldface as in a or b. In the given graph we can see, for the vector T, it is 1 unit on the x-axis and 5 units on the y-axis, whereas for the vector S its 5 units on the x-axis and 1 unit on the y-axis. Since the unit vectors for the x-axis and y-axis are i and j,
So, the vectors will i+5j and 5i+j
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In a classroom of 28 students 75% of the students have met their reading goal. Label the double number line.How many students met their reading goal?What fraction of 28 students met their reading goal? Explain.
Explanation:
Total number of students = 28
75% of 28 = 75% × 28
= 0.75 × 28 = 21
This means 21 students have met their reading goal
Fraction of 28 students that met their reading goal = 21/28
Divide numerator and denominator by 7
3/4
Attaching the label:
I omitted the first label on both lines: it should be 0 and 0% respectively
28/4 = 7
100%/4 = 25%
Each demacation represent 7 units on the first line
Each dividing line represent 25% on the second line
How do I convert 65 mi/hr to centimeters per minute
In the metric system, centimeters per minute (cpm) represents speed or velocity. It counts the centimeters that are covered in a minute.
65 mi/hr to 174346 centimeters per minute.
How to convert Miles Per Hour to Centimeters Per Minute (mi/h to cm/min ?$1 mi/h = 2682.2346355307 cm/ min.
65 × 2682.2346355307 cm/min = 174345.2513095 Centimeters Per Minute.
Always check the results; rounding errors may occur.
The base unit of [speed] (meters per second), 1 Miles Per Hour (mi/h) exists equivalent to
0.44704 meters-per-second,
while 1 Centimeters Per Minute (cm/min) = 0.000166667 meters-per-second.
65 Miles Per Hour to common speed units
65 mi/ h = 65 miles per hour (mi/h)
65 mi/h = 1.0833333333333 miles per minute (mi/m)
65 mi/h = 174346 centimeters per minute
Therefore, the correct answer is 174346 centimeters per minute.
The base unit for speed is meters per second (Non-SI Unit)
[Miles Per Hour] symbol/abbreviation: (mi/h)
[Centimeters Per Minute] symbol/abbreviation: (cm/min)
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Assume that 40% of a country's population has had Covid and that 55% of the country's population has been vaccinated. There is some overlap between the two groups, and 25% of the country's population has both had Covid and has also been vaccinated. Either having Covid or being vaccinated gives some protection against getting Covid. Based on these assumptions, if you choose a resident of this country at random what is the probability that the person has either had Covid or has been vaccinated and therefore has some protection against Covid?
The probability that the person has either had Covid or has been vaccinated and therefore has some protection against Covid is 45%
Data obtained from the questionFrom the question given, the following data were obtained:
40% of a country's population has had Covid55% of the country's population has been vaccinated25% of the country's population has both had Covid and has also been vaccinatedHow to determine the required probabilityThe probability that the person has either had Covid or has been vaccinated and therefore has some protection against Covid can be obtained as follows:
The percentage of person that had Covid and not vaccinated
= 40% - 25%
= 15%
The percentage of person that has been vaccinated and never had Covid
= 55% - 25%
= 30%
The probability that the person has either had Covid or has been vaccinated
= 15% + 30%
= 45%
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a cycle wheel does 2096 full turns in 8 minutes work out the number of full turns per minute
So basically you do 2096 divided by 8
Answer : 262 Minutes is alr i got u bro
Help me solve this please it’s the last question
Answer:
32?
Step-by-step explanation:
????????tell me if it is correct??
What is the area of this shape
Given a figure of a right trapezoid
The bases are the sides, 4 and 6
And the height = 4
The area of the trapezoid = 1/2(sum of the bases) times the height
So, the area =
[tex]\frac{1}{2}(4+6)\cdot4=\frac{1}{2}\cdot10\cdot4=20[/tex]So, the answer will be: Area = 20 unit²
Let x, y, z, and w represent the population in millions of four cities A, B, C, and D, respectively. Express the given statement as an equation in x, y, z, and w. If the equation is linear, express it in the standard form
ax + by + cz + dw = k.
(If the equation is not linear, enter NONLINEAR.)
City A has three times as many people as cities B and C combined
Answer:
x -3y -3z = 0
Step-by-step explanation:
You want to write "City A has three times as many people as cities B and C combined" as an equation in standard form, letting x, y, z, w represent the populations of cities A, B, C, D, respectively.
TranslationThe populations of cites B and C combined can be expressed by ...
y +z
Three times the combined population is then ...
3(y +z)
This is equal to the population of city A, so we can write ...
x = 3(y +z)
Standard formThis equation is in standard form when all of the variable terms are on one side of the equal sign, and the expression is simplified.
x -3(y +z) = 0 . . . . . . . subtract the right side expression
x -3y -3z = 0 . . . . . . . eliminate parentheses; standard form
Solve the following inequalities,express the solution in interval notation and graph it 4.a)
The inequality is given to be:
[tex]\mleft|x-6\mright|\ge2[/tex]Recall the Absolute Rule:
[tex]\mathrm{If}\: |u|\: \ge\: a,\: a\: >\: 0\: \mathrm{then}\: u\: \le\: -a\: \quad \mathrm{or}\quad \: u\: \ge\: a[/tex]Applying this to the inequality, we have:
[tex]\begin{gathered} x-6\ge2 \\ x\ge2+6 \\ x\ge8 \end{gathered}[/tex]or
[tex]\begin{gathered} x-6\le-2 \\ x\le-2+6 \\ x\le4 \end{gathered}[/tex]Therefore, the solution to the inequality is:
[tex]x\le\: 4\quad \mathrm{or}\quad \: x\ge\: 8[/tex]Is 10.6 x 10^14 scientific notation
Is 2.019 x 10^12 scientific notation
is 9.5 x 10^-7 scientific notation
0.526 x 10^-2 scientific notation
Answer:
The top and the bottom numbers are not in scientific notation; the other two are in scientific notation.
A quality assurance engineer randomly checks manufactured parts to ensure that they are within 0.002 mm of the desired specifications. If the desired length of the part is 3 mm, then the compound inequality
-0.002
Choose the absolute value inequality that represents the situation.
The value of absolute inequality will be given by 0.002 ≥ |x-3|.
Inequality may be defined as the expression which shows unequal behavior between two entities while absolute inequality expression includes inequality along with an absolute value. For example, |x| > 3, |x| <3, |x| ≤3 or |x| ≥3. Now, let us assume the length of the part in the question as x. Since, the desired length is given as 3mm and also the parts are within 0.002 mm of the desired specifications.
Therefore, the maximum length of the part can be = 3 + 0.002
and the minimum length of the part can be = 3 - 0.002
Therefore, we can write the inequality as
3 - 0.002 ≤ x ≤ 3 + 0.002
⇒ 3 - 0.002 ≤ x and x ≤ 3 + 0.002
⇒ -0.002 ≤ x-3 and x-3 ≤ 0.002
⇒ 0.002 ≥ -(x-3) and x-3 ≤ 0.002 (Because a > b ⇒ -a<-b)
⇒ 0.002 ≥ | x - 3 |
Thus, the required absolute inequality is 0.002 ≥ |x-3|.
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Answer:
A: |x - 3| ≤ 0.002
Step-by-step explanation:
Probability of dependent
Events
Dependent events: The likelihood of one event happening influences the likelihood of the other event happening.
What are dependent events?
When the result of one event affects the result of another, two events are said to be dependent events.
The likelihood of two connected events is the sum of the probabilities of the occurrences X and Y that happen after X.
The likelihood of one event does influence the likelihood of the other happening.
For instance, the likelihood of drawing another King decreases if you remove a King from a deck of cards without replacing it.
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The sum of two numbers is 50 the smaller number is 16 less than the larger number
The larger number is 33 and the smaller number is 17.
Let the larger number be x
Then, the smaller number will be x-16
According to the question,
Larger number + smaller number = 50
So,
x+(x-16) = 50
2x = 50+16
2x = 66
x = 66÷2
x = 33
Hence,
Larger number = x = 33
Smaller number = x-16 = 33-16 = 17
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Riders for the Kiddie Koaster at the State Fair must be no more than 48 inches tall. Which inequality best expresses the height of the riders?
[tex]x \leqslant 48[/tex]
On a roll. Suppose that you roll a fair, 6-sided die 10 times. What's the probability that
you get at least one 6?
Tyne a responro
?
Solve the inequality.
a-6<8
no real solutions
O all real numbers
O 2
O a < 14
O a< -2 or a> 14
[tex]a < 8 -+ 6 \\ =a < 14[/tex]
The second option is the answer.
Anders discovered an old pay statement from 12 years ago. His monthly salary at the time was $2800 versus his current salary of $4970 per month. At what (equivalent) compound annual rate has his salary grown during the period
The (equivalent) compound annual rate at which Anders' salary has grown during the 12 years is 4.9%.
What does the compound annual rate signify?The compound annual rate is the equivalent rate of interest at which the present value of money grows to attain a future value.
At a 4.9% compound annual rate, Anders' salary has been growing by adding the growth amount to the initial salary and compounding both the principal and subsequent interest amounts until 12 years.
N (# of periods) = 12 years
PV (Present Value) = $2,800
PMT (Periodic Payment) = $0
FV = $-4,971.23
Results:
I/Y (Interest per year) = 4.9%
Total Interest = $2,171.23
Thus, using the online finance calculator, we can determine that Anders' salary has been compounded at 4.9% annually.
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write an expression with a value that is twice as much as 236+912
The table represents a quadratic function. Write an equation of the function in
standard form.
X- -3,-2,-1,0
f(x)-6,0,-2,0
An equation of the quadratic function in standard form is equal to -2x² - 7x - 6 = 0.
What is a quadratic function?A quadratic function can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph.
In Mathematics, the standard form of a quadratic equation is given by;
ax² + bx + c = 0
y = f(x) = ax² + bx + c
Next, we would formulate a system of equations from the data contained in the table above:
-6 = a(-3)² + b(-3) + c ⇒ -6 = 9a - 3b + c .......equation 1.
0 = a(-2)² + b(-2) + c ⇒ 0 = 4a - 2b + c .......equation 2.
-2 = a(-1)² + b(-1) + c ⇒ -2 = a - b + c .......equation 3.
From eqn. 2, we have:
c = -4a + 2b .....equation 4.
Substituting eqn. 4 into eqn. 1 and 3, we have:
-2 = a - b - 4a + 2b ⇒ -2 = -3a + b
-6 = 9a - 3b - 4a + 2b ⇒ -6 = 5a - b
By using the elimination method, we have:
-8 = 2a
a = -4
For the value of b, we have:
-2 = -3a + b
b = -2 + 3a
b = -2 + 3(-4)
b = -2 - 12
b = -14
For the value of c, we have:
c = -4a + 2b
c = -4(-4) + 2(-14)
c = 16 - 28
c = -12.
Substituting the values of a, b and c into the standard form of a quadratic equation:
ax² + bx + c = 0
-4x² - 14x - 12 = 0
-2x² - 7x - 6 = 0
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seth bouth pencils 1/2 are red and 1/6 are blue how many are blue or red
Answer:
3 red and 1 blue 3 of another color
Step-by-step explanation:
well you can converte the fraction 1/2 to 3/6 so ye i believe this is correct :) atleast i hope :)
If ΔEFG ~ ΔLMN with a ratio of 2:1, which of the following is true?
Step 1
Given;
Step 2
Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles and squares of any side length are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
[tex]\begin{gathered} Triangle\text{ EFG}\approx\text{ Triangle LMN in the ratio 2:1} \\ Thus, \\ \frac{EF}{L\text{ M}}=\frac{FG}{MN}=\frac{EG}{LN}=\frac{2}{1} \end{gathered}[/tex]Thus, the answer is;
What is A-1? A=[-2 -3 3 12] Enter your answer by filling in the boxes. Enter any fractions as simplified fractions.
In this Matrix A= [-2 -3
3 12]
the matrix of A - 1 is
[-4/5 -1/5
1/5 2/15]
According to the question, given that
[-2 -3
3 12 ] ^ -1
First, we find the determinant
-2 * 12 - (-3 *3) = -24 - (-9) = -24 +9 = -15
Multiply 1 over the determinant by The matrix with the -2 and 12 switched and negate the -3 and the 3
1/-15 [12 3
-3 -2 ]
after multiply by 1/ - 15, we get
[-4/5 -1/5
1/5 2/15]
Therefore, In given Matrix A, after solving we get the value A- 1 is
[-4/5 -1/5
1/5 2/15]
Matrix
If there are m rows and n columns, the matrix is said to be an “m by n” matrix, written “m × n.” For example,
Matrix. [ 5 6 3
-2 3 2 ]
is a 2 × 3 matrix. A square matrix of order n have n rows and n columns. Ordinary numbers can be thought of as 1 1 matrices, making the number 3 the matrix [3]A row vector is a matrix with one row and n columns, and a column vector is a matrix with one column and n rows.
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Answers:A.(a,-2b)B.(-a,2b)C.(-a,-2b)D.(a,2b)
Midpoint formula
[tex](x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]where (x1, y1) and (x2, y2) are two points and (xm, ym) are the coordinates of the midpoint between (x1, y1) and (x2, y2).
In this case, we want to find the coordinates of the midpoint between Y(0, -4b) and Z(-2a, 0). Substituting into the above formula:
[tex]\begin{gathered} (x_m,y_m)=(\frac{0+(-2a)}{2},\frac{-4b+0}{2}) \\ (x_m,y_m)=(\frac{-2a}{2},\frac{-4b}{2}) \\ (x_m,y_m)=(-a,-2b) \end{gathered}[/tex]slove system of equations x+y=4 -x + y = 2
The solution for the equations x = 1 and y = 3
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
x + y=4
-x + y = 2
Add the equations
So, we have
2y = 6
Divide both sides by 2
y = 3
Substitute y = 3 in x + y = 4
x + 3 = 4
Evaluate
x = 1
Hence, the solution for the system of linear equations x + y=4 and -x + y = 2 are x = 1 and y = 3
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I can send the other options? I just need this explained?
The standard equation of a circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle.
For:
[tex]\begin{gathered} (x+3)^2+(y+1)^2=16 \\ \end{gathered}[/tex]Rewrite the equation as:
[tex]\begin{gathered} (x-(-3))^2+(y-(-1))^2=4^2 \\ so\colon \\ h=-3 \\ k=-1 \\ r=4 \end{gathered}[/tex]We can conclude it is a circle with center at (-3,-1) and radius of 4
The table shows the worldwide box office (in billions of
dollars) for the movie industry during the years shown.
Year
2001
2003
2005
2007
2009
Box office
(in billions of dollars)
17.1
18.2
19.3
21.5
23.7
a. Write this paired data as a set of ordered pairs of
the form (year, box office).
What is the ordered pair that corresponds to the first
row of data given in the table?
Answer:
193 is it I'm not lying
Step-by-step explanation:
what's the difference AAA,ASA and SSS
There are three main distinctions between AAA, ASA, and SSS:
AAA: A triangle is said to be comparable to another if any two of its three angles are equal to any two of its three angles.
ASA: According to the ASA rule, two triangles are said to be congruent if any two angles and the side located between the angles of one triangle are equal to the corresponding two angles and the side located between the angles of the second triangle.
SSS: According to the SSS rule, two triangles are considered to be congruent if all three sides of one triangle are comparable to the corresponding three sides of the other triangle.
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