Answer:
Evaluate from left to right
Evaluate using order of operations
Step-by-step explanation:
To evaluate any complex expression that contains addition, subtraction , multiply or divide, exponents , parenthesis etc we use order of operation.
Order of operation is PEMDAS
To evaluate , first we simplify the parenthesis part and then exponents
Then do the multiplication and division from left to right.
Finally we do addition and subtraction from left to right
So the rules for evaluating a complex expression is
Evaluate from left to right
Evaluate using order of operations
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
The product of (3 + 2i) and a complex number is (17 + 7i).
The complex number is ?
The product of (3 + 2i) and a complex number is (17 + 7i)
The product of (3 + 2i) and a complex number is (17 + 7i).
Let the complex number be a + ib
Product means we multiply
So (3+2i) * (a + ib) = (17+7i)
WE need to find a+ ib
Divie by 3 + 2i on both sides
a + ib = (17+7i) / (3+2i)
To divide multiply by the conjugate (3-2i)
[tex]a + ib = (\frac{ 17+7i)*(3-2i)}{(3+2i)(3-2i)}[/tex]
[tex]a + ib = (\frac{(17*3+7*2)+(7*3-17*2)i}{3^2-2^2}[/tex]
[tex]a + ib = (\frac{(65)+(-13)i}{13}[/tex]
[tex]a+ib = \frac{65}{13} - \frac{13}{13}[/tex]
a+ib = 5 - i
The required complex number is 5 - i
Answer:
37+55i
Step-by-step explanation:
The product of (3 + 2i) and a complex number is (17 + 7i) is expressed as shown below:
(3+2i)(17+7i)
Expanding the bracket,
= 51+21i+34i+14i²
= 51+55i+14i²
Note that in complex numbers i² = -1
Substituting this into the result, we have:
= 51+55i+14(-1)
= 51+55i-14
= 37+55i
The product of both complex number is 37+55i
Layla is saving up money for a trip. She already has $650 saved and plans to save an additional $150 each month for the trip. Complete the equation that represents the total amount of money Layla has saved, s, after m months.
The amount of money that Layla has saved, s, is going to be what the equation equals. She earns $150 each month, so that would be 150m (slope intercept form equation s=em+b). B is the y-intercept, or the amount that Layla already has saved, which is positive $650.
Your equation is:
s=150m+650
I hope this helps :)
What is the value of the expression? (5/2)2+33/4 Enter your answer in the box.
Answer:
Step-by-step explanation:
its 43
Simplify the expression. 12x^-6 y^10 times 3x^7 y
We need to simplify the expression:
[tex]12x^{-6}y^{10} \times (3x^{7}y)[/tex]
Now, we know that we can resolve the exponents of the variables with the like terms only and we can multiply the coefficients independently:
Now,
[tex]12x^{-6}y^{10} \times 3x^{7}y=(12 \times 3)\times (x^{-6}\times x^{7})\times (y^{10}\times y)[/tex]
On simplifying the above expression we get:
[tex]36\times x^{(-6+7)}\times y^{(10+1)}[/tex]
[tex]=36 \times x^{1}\times y^{11}[/tex]
[tex]=36 \times x \times y^{11}[/tex]
[tex]=36xy^{11}[/tex]
So the simplified form of the expression [tex]12x^{-6}y^{10} \times 3x^{7}y=36xy^{11}[/tex].
At a school concert the orchestra plays 8 songs that are 4.25 min long and 3 songs that are twice as long as each of the others. How long is the concert ?
Answer:
Total time of the concert = 59.5 min = 59 minute 30 seconds
Explanation:
At a school concert the orchestra plays 8 songs that are 4.25 min and 3 songs that are twice as long as each of the others.
Total length of 8 songs = 4.25*8 = 34 min
Length of 3 songs = 2*4.25 = 8.5 min
Total length of 3 songs = 3* 8.5 = 25.5 min
Total time of the concert = 34 + 25.5 = 59.5 min = 59 minute 30 seconds
The concert is 59.5 minutes long: 8 shorter songs at 4.25 min each and 3 longer songs at 8.5 min each.
To find the total duration of the concert, we first calculate the duration of the 8 shorter songs and then the longer ones.
1. Shorter songs:
Duration of each shorter song = 4.25 minutes
Total duration of 8 shorter songs = 8 × 4.25 = 34 minutes
2. Longer songs:
Each longer song is twice as long as the shorter ones, so its duration is 2 × 4.25 = 8.5 minutes
Total duration of 3 longer songs = 3 × 8.5 = 25.5 minutes
Now, add the durations of both types of songs to find the total duration of the concert:
Total duration = Duration of shorter songs + Duration of longer songs
Total duration = 34 minutes + 25.5 minutes = 59.5 minutes
So, the concert is 59.5 minutes long.
The table shows the steps for solving the given inequality for x.
−2(3−2x)
Select the reason for each step from the drop-down menus.
-6 + 4x < x +3 : Distributive property
-6 + 3x < 3 : Subtraction property of inequality
3x < 9 : Addition property of inequality
x <3 : Division property of inequality
Answer:
[tex]-2(3-2x)<x+3[/tex] Given,
[tex]-6+4x<x+3[/tex]: Distributive property,
[tex]-6+3x<3[/tex]: Subtraction property of order,
[tex]3x<9[/tex]: Addition property of order,
[tex]x<3[/tex]: Division property of order.
Step-by-step explanation:
We have been given an inequality. We are asked to match each step for solving the equation with reason.
[tex]-2(3-2x)<x+3[/tex]
Using distributive property, we will get:
[tex]-2\cdot3-(-2)\cdot2x<x+3[/tex]
[tex]-6+4x<x+3[/tex]
Subtract x from both sides:
[tex]-6+4x-x<x-x+3[/tex]
[tex]-6+3x<3[/tex]
Add 6 on both sides:
[tex]-6+6+3x<3+6[/tex]
[tex]3x<9[/tex]
Divide both sides by 3:
[tex]\frac{3x}{3}<\frac{9}{3}[/tex]
[tex]x<3[/tex]
Which complex number is represented by the point graphed on the complex plane below
See this explanation:
for the given point x=3 and y=-4.
It means, z=3-4i. Answer; C.
Answer:
Option (c)
Step-by-step explanation:
A complex number is a combination of a real number and an imaginary number.
Real number be represented on X axis and imaginary number be represented on Y axis.
Here real part of the complex number is 3 and the imaginary part is -4.
So, the complex number is 3 - 4i.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Andy and Samantha are performing an experiment in a science lab. The number of bacteria cells recorded by Andy in his experiment is represented by the equation below, where B represents the number of bacteria, x hours after beginning the experiment. The number of bacteria cells recorded by Samantha in her experiment is represented by the equation below, where B represents the number of bacteria, x hours after beginning the experiment. Using graphing technology, complete the statements. After hours, the total number of bacteria cells for both experiments will be the same. The total number of bacteria cells at that hour will be .
Answer:
after 5
time will be 35
Step-by-step explanation:
JK and JL in the xy-coordinate plane both have a common endpointJ(-4,11) and midpoints at M, (2,16) and M2(-3,5), respectively. What is the distance between M, and M2? Round to the nearest tenth.
okay so the coordinates are (2,16) & (-3,5) & what you have to do is use the distance formula. if you use it & solve your way through it, your answer should be 5 rounded to the nearest tenth
If 4x – 2y = 6, then y =
After solving the equation the value obtained for y will be equal to y = 2x - 3.
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given equation in the question,
4x – 2y = 6
Let's solve the equation to find the value in terms of y.
2y = 4x - 6
y = (4x - 6)/2
y = 2x - 3
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One US dollar is currently worth 0.79 euro (€). If you exchange $522 for euros, how many euros will you have?
I'm pretty sure you would have 412.38 (€) because the equation would be $522 × 0.79.
Answer:412.38
Step-by-step explanation:
Complete the numbers sentence using <,>, or. |-5 .25| ____ |-8|
The president of a certain university receives a salary that is three times the salary of one of the department heads. The total of the two salaries is $190,000.
What is the salary of the department head?
3(X)+X=190000 is how you'd find the answer the answer is 47,500
(-5,-7),(0,-5),(5,-3) Determine the intercepts of the line that passes through the following points.
x-intercept ( , )
y intercept ( , )
Answer:
x-intercept (12.5, 0)y-intercept (0, -5)Step-by-step explanation:
The slope of the line is ...
... (change in y)/(change in x) = (-3 -(-5))/(5 - 0) = 2/5
The y-intercept is given: (0, -5).
The slope-intercept form of the equation can be written from this information as ...
... y = (2/5)x - 5
Solving this for y=0 (to find the x-intercept), we have
... 0 = (2/5)x - 5
... 5 = (2/5)x
... 5·(5/2) = x = 12.5
So, the x-intercept is 12.5, and the y-intercept (given) is -5.
X(x+3)(x-5)=0 is a quadratic equation
True
False?
False. That is a cubic equation.
PLEASE HELP
Find the rectangular coordinates of the point with the polar coordinates (3, 3 divided by 2 pi).
Answer:
(0, -3)
Step-by-step explanation:
The terminal ray of the angle with measure 3π/2 radians is the negative y-axis. The point that is 3 units from the origin on that ray has x-coordinate 0 and y-coordinate -3. The point is (0, -3).
How many solutions are there to the equation below 6x+8-2x(7-2)=2(6+1)
The coefficient of x is not zero, so there is exactly one solution.
_____
6x +8 -2x(5) = 2(7) . . . . evaluate parentheses contents
6x +8 -10x = 14 . . . . . . . eliminate parentheses
-4x +8 = 14 . . . . . . . . . . collect x terms
-4x = 6 . . . . . . . . . . . . . . subtract 8
x = -6/4 = -3/2 . . . . . . . . divide by the coefficient of x
Jerry measured and timed the descent of a diving bell spider in a large fish tank. The spider reached a position 4 1/2 inches below the surface of the water after descending at a constant rate for 1 1/2 seconds. Jerry recorded this as −4 1/2 inches. What is the position of the spider relative to the surface after 1 second? Enter your answer in the box.
-3 is the answer when you do this equation. Or it could be 300 depending.
Answer:
-3
Step-by-step explanation:
30 POINTS
Which pair of complex numbers has a real-number product? (1 + 2i)(8i) (1 + 2i)(2 – 5i) (1 + 2i)(1 – 2i) (1 + 2i)(4i)
calculating each of the products
noting that i² = (√- 1 )² = - 1
(1 + 2i)(8i) ( distribute by 8i )
= 8i + 16i² = - 16 + 8i ← complex number
(1 + 2i)(2 - 5i) ( expand using FOIL )
= 2 - 5i + 4i - 10i²
= 2 - i + 10 = 12 - i ← complex number
(1 + 2i)(1 - 2i) ( expand using FOIL )
= 1 - 2i + 2i - 4i²
= 1 + 4 = 5 ← real number
(1 + 2i)(4i) ( distribute by 4i )
= 4i +8i² = - 8 + 4i ← complex number
(1 + 2i)(1 - 2i) is the only product which results in a real number
An adventure game has a number cube with 12 equal-size faces. Each face is labeled with a number from 1 to 12. What is the probability of rolling a 4 or a multiple of 5? Enter your answer as a fraction, in simplified form, in the box. $\text{Basic}$ $x$$y$$x^2$$\sqrt{ }$$\frac{x}{ }$$x\frac{ }{ }$$x^{ }$$x_{ }$$\degree$$\left(\right)$$\abs{ }$$\pi$$\infty$
the probability is a ratio of number of relevant outcomes and total number of possible cases.
In this scenario, the relevant outcomes are
4, 5, 10 (and their count is 3)
and the total number of possible outcomes:
12
so the probability is
3/12 = 1/4
the answer is 3/12 cause when you divied 12 by 4 you will get 3 and we know that there is 12 faces on the cube so that gives you the ratio 3/12.
Write an equation of the line passing through each of the following pairs of points. (−3, 1), (0, 3)
The 2-point form of the equation for a line is applicable. For points (x₁, y₁) and (x₂, y₂) that equation is ...
... y = (y₂ -y₁)/(x₂ -x₁)·(x -x₁) +y₁
Filling in your point values gives ...
... y = (3 -1)/(0 -(-3))·(x -(-3)) +1
This can be simplified to ...
... y = (2/3)(x +3) +1
... y = (2/3)x +3
Given the function f(x)=x^2 and k=3, which of the following represents the graph becoming more narrow?
A. f(x)+k
B. kf(x)
C. f(x+k)
D. f(k-x)
B
the spread of the graph of a parabola is determined by the multiplier k
the standard comparison is against k = 1
• If k > 1 then the graph narrows towards the y-axis
• If 0 < k < 1 then graph widens towards the x- axis
An analog clock loses 2 minutes every 3 hours. What is the shortest interval of time after which the clock will show the correct time?
In order to show the correct time again, the clock has to be exactly 12 hours, or 12*60=720 minutes, behind. With 2 minutes per 3 hours, the clock will have to run for 3 * 720/2 = 1080 hours. 1080 hours = 45 days. The shortest interval the clock need to show the correct time is 45 days.
Answer:
1152 hours - 42 days =)
Step-by-step explanation:
What is the answer to this? −4 1/2÷(−2 2/3) (it has to be a mixed number)
Here is you're answer:
In order to solve this equation you must first change the mixed numbers into improper fractions then use KCF. (Keep, Change, Flip)
[tex]-4\frac{1}{2} \div -2\frac{2}{3}[/tex]Change into improper fractions:[tex]-4\frac{1}{2} =\frac{-9}{2}[/tex][tex]-2\frac{2}{3} = \frac{-8}{3}[/tex][tex]\frac{-9}{2} \div \frac{-8}{3}[/tex]Apply KCF:[tex]\frac{-9}{2} \times \frac{-3}{8}[/tex]Now multiply: [tex]\frac{-9}{2} \times \frac{-3}{8} = \frac{27}{16}[/tex]Remember that a negative times a negative is a positive:[tex]= \frac{27}{16}[/tex]Change into a mixed number:[tex]\frac{27}{16} = 1\frac{11}{16}[/tex][tex]= 1\frac{11}{16}[/tex]Therefore you're answer is "1 11/16."
Hope this helps!
What is 659.003 as a mixed number??
*Thanks*
Six hundred fifty-nine and three thousandths is ...
... 659 3/1000
The school bookstore has 108 book covers. They will be equally distibuted among the students in the 2 sixth grade classes. Each class has 18 students. How many books covers does each student receive?
Each student will receive 3 book covers when 108 book covers are equally distributed among 36 students from two sixth-grade classes.
The question asks us to figure out how many book covers each student will receive if 108 book covers are distributed equally among students in two sixth-grade classes, with each class having 18 students.
First, calculate the total number of students by multiplying the number of classes by the number of students in each class: 2 classes * 18 students/class = 36 students.Then, divide the total number of book covers by the total number of students: 108 book covers / 36 students = 3 book covers per student.As a result, each student will receive 3 book covers.
Triangle ABC is similar to triangle QRS by the AA Similarity Postulate. Also, m∠A = 72° and m∠S = 56°. What is m∠B?
∠B = 52°
Since the triangles are similar then
∠C = ∠S = 56°
∠B = 180° - (72 + 56)° = 52°
Joel is getting a dog, a cat, and a hamster. He goes to the pet store and can choose from 8 dogs, 12 cats, and 5 hamsters. How many different combinations can he get? A) 3 B) 25 C) 75 D) 480
The answer is B) 25
Option: B is the correct answer.
B) 25
Step-by-step explanation:Joel is getting a dog, a cat, and a hamster.
He goes to the pet store and can choose from 8 dogs, 12 cats, and 5 hamsters.
i.e. the total number of combinations that are possible could be calculated with the help of Combination as:
[tex]8_C_1+12_C_1+5_C_1[/tex]
We know that:
[tex]n_C_r=\dfrac{n!}{(n-r)!r!}[/tex]
Hence, the value of [tex]8_C_1\times 12_C_1\times 5_C_1[/tex] is:
[tex]=\dfrac{8!}{(8-1)!1!}+\dfrac{12!}{(12-1)!1!}+\dfrac{5!}{(5-1)!1!}\\\\\\=\dfrac{8!}{7!}+\dfrac{12!}{11!}+\dfrac{5!}{4!}\\\\=8+12+5\\\\=25[/tex]
Hence, the number of combinations is:
25
an inch is 1/12 of a foot how much has a angelfish grown in a feet
To find out how much an angelfish has grown in feet, divide the number of inches by 12, since there are 12 inches in a foot. As an example, if an angelfish has grown 6 inches, it would be 6 inches / 12, equaling 0.5 feet.
Explanation:To convert a measurement from inches to feet, we use the fact that one foot is equal to 12 inches. For example, if an angelfish has grown 6 inches, we divide the number of inches by 12 to find the growth in feet:
Find the growth in inches (for example, 6 inches).Use the conversion factor, which is 1 foot = 12 inches.Divide the growth in inches by 12 to get the growth in feet. For 6 inches: 6 inches / 12 inches per foot = 0.5 feet.The angelfish has grown 0.5 feet.
Similarly, let’s convert 374 inches to feet as another example of going from a smaller unit to a larger unit:
Take the given number of inches and divide by 12 since there are 12 inches in a foot.374 inches divided by 12 equals 31(1/6) feet.Based on the graph, which of the following statements is true?
A.
The number of pumpkins depends on the total price.
B.
The total price depends on the number of crates.
C.
The number of crates depends on the total price.
D.
The total price depends on the number of pumpkins
Answer:
The total price depends on the number of crates.
Step-by-step explanation:
Without seeing the graph, we can't provide a definitive answer. Generally, in such situations, total price would likely depend on the quantity of goods (pumpkins or crates) purchased (Options D and B).
Explanation:To answer this question, we'd need to closely examine the given graph. However, generally, in a graph showcasing a transaction, the total price depends on the quantity of goods, such as pumpkins or crates, purchased. Hence without explicit information from the graph at hand, option D. 'The total price depends on the number of pumpkins', and option B. 'The total price depends on the number of crates' could potentially be accurate. But we cannot determine definitively without further information.
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