Use the polynomial remainder theorem. The remainder upon dividing a polynomial [tex]p(x)[/tex] by a linear factor [tex]x-c[/tex] is exactly [tex]p(c)[/tex].
In this case,
[tex]p(x) = 2x^{10} - 3ix^8 + (1+i)x^2 - (3+2i)x + 1[/tex]
and [tex]c=i[/tex]. Then the remainder is
[tex]p(i) = 2i^{10} - 3i^9 + (1+i)i^2 - (3+2i)i + 1[/tex]
Since [tex]i^2=-1[/tex] and [tex]i^4=1[/tex],
[tex]p(i) = -2 - 3i - 1 - i - 3i + 2 + 1 = \boxed{-7i}[/tex]
5 divided by the sum of 5 and a number
Answer: 5/(5+n)
Step-by-step explanation:
Let "a number" be represented by "n"
[tex]5/(5+n)[/tex]
Which step is included in the graph of the function f(x)=[x-1] ?
O y=-5 for-4≤x <-3
O y=-2 for -2
Oy=-2 for 2
O y=-5 for -4
The step which is included in the graph of the function is Option(a)
y=-5 for -4≤ x <-3.
What is the greatest integer function?A function that yields an integer that is closest to the input real number is said to be the greatest integer function. The step function is another name for it. When rounding a number, the greatest integer function chooses the integer less than or equal to a given number. It is symbolized by the letter [x] where x can represent any number.The greatest integer function has R as its domain and Z as its range.From the properties of the greatest integer function y = [x], we know that
y = 0 for, 0 ≤ x < 1
y = -1 for, - 1 ≤ x < 0
y = -2 for, - 2 ≤ x < -1
Here,we are given a greatest integer function f(x) or y =[x-1]
Hence, the step which is included in the graph of the function is
y=-5 for -4 ≤ x <-3.
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Pablo randomly picks three marbles from a bag of seven marbles (four red ones, two green ones, and one yellow one).
How many outcomes are there in the sample space?
How many outcomes are there in the event that all of the marbles he picks are red?
Answer:
354Step-by-step explanation:
You want to know the number of outcomes in the sample space when 3 marbles are chosen from 7. If four are red marbles, you want to know the number of outcomes when all chosen are red.
OutcomesThere are C(7,3) = 7!/(4!·3!) = 35 ways to choose 3 marbles from 7. Given that there are different colored marbles involved, not all of these outcomes are unique.
There are 35 possible outcomes.
3 RedThere are C(4, 3) = 4 ways to choose 3 red marbles from 4 red marbles.
There are 4 possible outcomes with all red marbles.
__
Additional comment
The 35 possible outcomes are ...
(RRR) - 4, (RRG) - 12, (RRY) - 6, (RGG) - 4, (RGY) - 8, (GGY) - 1
<95141404393>
Please help me it’s due tonight!
Help me find the y intership form (y=mx+B)
13.parallel to 2x - 3y = through point (-1, 2)
14. perpendicular to 1/3X+4
through point (0, 5)
15. perpendicular to 3x - y =-4 through point (0, -2)
16. perpendicular to 4x + 5y = 20
through point (1, 1)
17. perpendicular to 4x +7y = 13
through point (-2, 6)
The linear functions for this problem are given as follows:
13. y = 2x/3 + 8/3.
14. y = -3x + 5.
15. y = -1/3x - 2.
16. y = 5/4x - 1/4.
17. y = 7/4x + 19/2.
What is a linear function?A linear function is modeled by the following rule:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, the change in y divided by the change in x.b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.The slope is also related with parallel and perpendicular lines, as follows:
If the lines are parallel, they have the same slope.If the lines are perpendicular, the multiplication of their slopes is of -1.In item 13, the line in slope-intercept form is:
y = 2x/3.
The line we want to find is parallel, hence it has the same slope, that is:
y = 2x/3 + b.
When x = -1, y = 2, hence:
2 = -2/3 + b
b = 8/3.
Hence the line is:
y = 2x/3 + 8/3.
For item 14, the line is perpendicular to:
y = 1/3x + 4.
Hence the slope is found as follows:
1/3m = -1
m = -3.
Then:
y = -3x + b.
When x = 0, y = 5, hence b = 5 and the line is:
y = -3x + 5.
For item 15, the line is perpendicular to:
y = 3x + 4.
Then the slope is found as follows:
3m = -1
m = -1/3.
Then:
y = -1/3x + b.
When x = 0, y = -2, hence b = -2 and the line is:
y = -1/3x - 2.
For item 16, the line is perpendicular to:
y = 4 - 4/5x.
Then the slope is found as follows:
-4m/5 = -1
m = 5/4.
Hence:
y = 5/4x + b.
When x = 1, y = 1, hence:
1 = 5/4 + b
b = -1/4.
Then the line is:
y = 5/4x - 1/4.
For item 17, the line is perpendicular to:
y = 13/7 - 4/7x
Then the slope is found as follows:
-4m/7 = -1
m = 7/4.
Hence:
y = 7/4x + b.
When x = -2, y = 6, hence:
6 = -14/4 + b
b = 19/2.
Hence the line is given by:
y = 7/4x + 19/2.
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Solve for y.
d = 5x + 5y
d=5x
5
O y = 5(d - 5x)
Oy =
0y = d-Sx
X
Oy=
5x-d
5
Neon (Ne), hydrogen (H), helium (He), and Carbon (C) are examples of...
a. Compounds- you can tell because they all have chemical formulas
b. Mixtures- because they don't have definite compositions
c. Elements- you can tell because they can be found on the periodic table
Neon (Ne), hydrogen (H), helium (He), and Carbon (C) are examples of; C: elements you can tell because they can be found on the periodic table
What are the chemical elements?
Elements are pure substances which are composed of only one type of atom. Compound are substances which are formed by two or more different types of elements that are united chemically in fixed proportions.
Now, Neon (Ne), hydrogen (H), helium (He), and Carbon (C) are examples of elements. This is because they are all composed of only one type of atom and they can as well be found in the periodic table that contains only elements.
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Simon says that 7 x 2 is equal to 8 x 1 because both sets of factors add to 9. Do you agree with Simon's reasoning? Explain why or why not.
Answer:
No, I do not agree with Simon's reasoning.
Step-by-step explanation:
7*2=14
8*1=8
BUT
7+2=9
8+1=9
YET
Simon isn't properly solving the equation with the right basic operation of arithmetic. He must multiply, not use addition.
Hope this helps.
Jen and her friends have a half-day at school, so they plan to spend the afternoon
paddleboarding at Lake Evergreen. They want to spend the rest of the day on the water, but
it starts to rain after paddleboarding for only of an hour! Jen is disappointed when she
realizes the sun doesn't go down for another 4
hours.
Use an equation to find the amount of time Jen planned to spend paddleboarding.
To write a fraction, use a slash (/) to separate the numerator and denominator.
Using proportions, it is found that Jen planned to spend 19/4 hours paddleboarding.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
In this problem, we have that:
She spent 3/4 of an hour paddleboarding.The sun doesn't go down for another 4 hours.4 + 3/4 = 4.75 hours = 19/4.
Jen planned to spent 19/4 hours paddleboarding.
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pls help. ;0 This is for iready.
Answer:
10.6 ounces
Step-by-step explanation:
1. Divide the total spent by the cost per ounce to get number of ounces bought.
2.65 ÷ 0.25 = 10.6 ounces
please help will give Brainly look at the picture’
Answer:
Step-by-step explanation:
The minimum is the smallest value in a data set.
Ordering the data from least to greatest, we get:
1 2 3 5 6 7 9 11 12 13 14 16 17 19 20
So the minimum is 1
The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.
Quartile 1 is 5,
1 2 3 5 6 7 9 11 12 13 14 16 17 19 20
The first half is
1 2 3 5 6 7 9, the median of these numbers is 5 so Quartile 1 = 5
The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.
The median is 7, 1 2 3 5 6 7 9 11 12 13 14 16 17 19 20
The third quartile (or upper quartile or 75th percentile) is the median of the second half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.
Quartile 3 is 16,
1 2 3 5 6 7 9 11 12 13 14 16 17 19 20
The upper half is
12 13 14 16 17 19 20, the median of these numbers is 16 so Quartile 3 = 16
The maximum is the greatest value in a data set.
Ordering the data from least to greatest, we get:
1 2 3 5 6 7 9 11 12 13 14 16 17 19 20
So, the maximum is 20.
Please help me fast. Trying to figure this out. Answer a-C. You don’t need to explain
Hands-On Activity 2
Maria is also collecting books. She wants to make packages that have 3 fiction
books and 4 nonfiction books. She already has 9 fiction books. How many
nonfiction books will she need?
q
Use a multiplication table to compare the numbers.
Step 1 Complete the rows for 3 and 4 on a multiplication table. non a cas
9 12 15 18 21 24 27 30.
8 12 16 20 24 28
24 28 32 36 40
fiction
nonfiction
Sten 2
136
4
Road across the top until you reach 9. Find the corresponding number.
what is the pattern being used in the table?
Maria need 12 fiction books.
Multiplication table: A multiplication chart is a table that shows the products of two numbers. Usually, one set of numbers is written on the left column and another set is written as the top row. The products are listed as a rectangular array of numbers.
Given that She wants to make packages that have 3 fiction books and 4 nonfiction books. She already has 9 fiction books
Step 1
Complete the rows for 3 and 4 on multiplication table
Fraction : 3,6,9,12, 15, 18, 21, 24,27,30.
Notification : 4,8,12,16,20,24,28,32,36,40.
Step 2
Read across the top until you reach 9. The corresponding number bottom row.
The top untill you reach 9 the corresponding number bottom row is 12
Maria need 12 fiction books.
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A health food store was charging $4.10 for a small salad but raised the price 8%. The new price after the increase is $4.43.Enter an expression to show how the new price was calculated.
Answer: $4.10*0.08%=0.33
Step-by-step explanation:
Which expression is equivalent to the given expression? 3 x 2 + 5 x − 7 ( x 2 + 4 ) A. - 4 x 2 + 5 x − 4 B. x 2 + 4 C. x 2 + 28 D. - 4 x 2 + 5 x − 28
According to the solving the non of the quadratic equations equivalent.
4X² + 5x - 3.
What is a quadratic equation and how does it work?A quadratic equation seems to be a second-order polynomial equation in a variable, x ax2+bx+c=0, with a 0 as the coefficient. The fundamental theorem of algebra ensures that it has at least one solution as it is a second-order polynomial problem. The solution could be straightforward or difficult.
What exactly is the equivalent formula?Equivalent equations are those that have the same solutions or roots. An equivalent equation is produced by adding or subtracting the identical number or expression from both sides of an equation. Equivalent equations are produced by multiplying and dividing both sides of such an equation by the same non-zero value.
According to the given equation:3 X² + 5 x − 7 + ( X² + 4 ).
Simplifying this equation:
3 X² + 5 x − 7 + X² + 4
= 4X² + 5x - 3
According to the solving the non of the quadratic equations equivalent.
4X² + 5x - 3.
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I understand that the question you are looking for is:
Which expression is equivalent to the given expression?
3 X² + 5 x − 7 + ( X² + 4 ).
A. - 4X² + 5X − 4
B. X² + 4
C. X² + 28
D. - 4 X² + 5x − 28
Imani spent a third of her savings on airfare for a vacation. She then spent another $300 on hotels. If she has $250 left for meals and souvenirs, with how much did she have in savings before the trip?
The amount the she had in her savings before the trip was $825
Calculating amountFrom the question, we are to calculate how much Imani has in her savings before the trip
Let the amount she has in her savings before the trip be x
From the given information,
"Imani spent a third of her savings on airfare for a vacation"
That is,
She spent (1/3)x
The amount remaining after this time will be x - (1/3)x = (2/3)x
"She then spent another $300 on hotels"
The amount remaining after this time will be (2/3)x - $300
"If she has $250 left for meals and souvenirs"
That is,
(2/3)x - $300 = $250
Now, solve for x
(2/3)x - $300 = $250
(2/3)x = $250 + $300
(2/3)x = $550
x = $550 × 3/2
x = $825
Hence, the amount the she had in her savings before the trip was $825
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Please Help Me, I’d Really Appreciate It.
Write the following fraction as a decimal: 2/5
0.25
2.5
0.4
4.0
Answer:
It's 0.4
Step-by-step explanation:
2/5 = 40/100 = 4/10 = 0.4
Hope that helps :)
10. Alice bought 2.3
pounds of apples for $2.99
per pound. How much did
she spend on apples?
Answer:
2.3(2.99)=$6.877
Step-by-step explanation:
Multiply the pounds (2.3) by the price of apples per pound.
Hope this helps! :)
Answer:
2.3(2.99)=$6.877
Step-by-step explanation:
Hope this helps!
From the top of abuilding, Cecilia finds that the angle of depression of a table on the ground is 30 degrees. If the table is 40 m from the base of the building, find the height of the building
The height of the building is 23.09m.
Let the height of the building be "h".The distance between the table and the base of the building is 40 m.From the top of the building, the angle of depression of the table on the ground is 30°.The angle of depression is the angle formed by the horizontal line and the item as seen from the horizontal line. It is mostly used to calculate the distance between two objects where the angles and distance from the ground are known.We can also say that, from the table, the angle of elevation of the top of the building is 30°.For a better visualization of the problem, see the image attached below.Apply trigonometry.Tan(30°) = h/401/√3 = h/40h = 40/√3h = 23.09mTo learn more about angles, visit :
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To charter a bus to carry students to New York City, the cost is $100 to make the booking , plus $25 for each student who is a passenger on the bus. Then, the cost function C(x) giving the cost if x students are ( what is m and b) mxtb
The value of m is $25 and value of b is $100, the cost is $300 and the number of students is 12.
As per the given relation in the question, we see that b is calculated once and m is calculated based on the variable value x, which is the number of students. Hence, for correct calculation, value of m is $25 and value of b is $100.
The cost if 8 students are passengers will be calculated by keeping the value of x and other constants as per the above answer.
Cost = 25×8 + 100
Cost = 200 + 100
Cost = $300
Number of students will again be found as the value of x, by keeping the values as specified above.
400 = 25x + 100
25x = 400 - 100
25x = 300
x = 300 ÷ 25
x = 12
Hence, value of m is $25 and value of b is $100, the cost is $300 and the number of students is 12.
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The complete question is attached in figure.
At a bakery, one customer pays $5.67 for 3 bagels and 4 muffins. Another customer pays $6.70 for 5 bagels and 3 muffins. Which system of equations can be used to determine the cost x (in dollars) of one bagel and the cost y (in dollars) of one muffin at the bakery?
The bagel costs $0.89 and a muffin costs $0.75
How to create a system of equations?Let B = Bagel cost
Let M = Muffin cost
Thus, from the given question parameters, the system of equations that can be used to determine the cost x is;
3B + 4M = 5.67 ------(1)
5B + 3M = 6.70 ------(2)
Multiply the 1st equation by 3 and the 2nd equation by (-4) to get;
9B +12M = 17.01 ------(3)
-20B - 12M = -26.80 ------(3)
Add equations 3 and 4 together to get;
-11B = -9.79
B = 0.89
Plug this value for B in to the 1st equation and solve for M to get;
3(0.89) + 4M = 5.67
2.67 + 4M = 5.67
4M = 3.00
M = 0.75
Thus, a bagel costs $0.89 and a muffin costs $0.75
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Find the (perpendicular) distance from the line given by the parametric equations
x(t)= -2-6t
y(t)= 1-3t
z(t)= -5+7t
to the point (-8,9,8)
Answer:
[tex]\sqrt{(-\frac{806}{94}+8)^2+(-\frac{215}{94}-9)^2+ (-\frac{251}{94}-8)^2}[/tex] Whatever this number may be
Step-by-step explanation:
The distance will be on the plane containing the point, and perpendicular to the line - which exists as long as the point doesn't sit on the line, but in that case our distance will simply be zero. Good news, since the line is given in parametric equation, the equation of the plane is easy to write by simply computing the dot product between the vector generating the line - or any multiple of it! - and the vector joining a random point x y z of the space with our given point, and setting it equal to zero. The equation of our plane is thus
[tex]6(x-(-8)) + 3(y-9) -7(z-8) = 0\\6(x+8)+3(y-9)-7(z-8)=0[/tex]
We could multiply now or later, doesn't matter, so let's wait. Now, we need to know when the line passes through the plane, so let's plug the (parametric) coordinate of the line and let's see for which value of t that happens:
[tex]6(-2-6t+8) +3(1-3t -9) -7(-5+7t-8) =0\\6(6-6t) -3(8+3t)+7(13-7t)=0\\36-36t-24-9t+91-49t = 0\\t=103/94[/tex]
Found this value of t, we can use it to find the coordinate of the point in common between the line and the plane:
[tex](-2-6\frac {103}{94};1-3\frac {103}{94}; -5+7\frac {103}{94}) = (-\frac{806}{94};-\frac{215}{94};-\frac{251}{94})[/tex]
At this point it's simply a matter of calculating the distance between two points in 3D space, given by the usual [tex]\sqrt{\Delta x^2+\Delta y^2+\Delta z^2}[/tex], whatever abomination of a number it might become:
[tex]\sqrt{(-\frac{806}{94}+8)^2+(-\frac{215}{94}-9)^2+ (-\frac{251}{94}-8)^2}[/tex]
At this point is a simple exercise in number crunching which I refuse to entertain more - but please double check all calculation above in case I didn't notice something.
solve the expression when k=6 and c=2
5 x k - 10c + 8
Answer:
18
Step-by-step explanation:
5*(6)-10(2)+8 = 18
Substitute k = 6 and c = 2 into the equation and solve it.
PLS HELP!!! algebra 2.
Z(z + 2) = (z + 6)(z - 6)
z=
4 more than 3 times a number is equal to 6 more than 2 times the number
Answer:
x=2
Step-by-step explanation:
3x+4=2x+6
3x=2x+2
x=2
Find 3 consecutive odd integers such that the sum of 2 times the first and the last term is equal to 5 times the middle integer.
The 3 consecutive odd integers are -3, -5 and -7
Linear functionLet the 3 consecutive odd integers be 2x-1, 2x+1 and 2x+3
If the sum of 2 times the first and the last term is equal to 5 times the middle integer, then;
2(2x-1)+2x+3 = 5(2x+1)
Expand
4x-2 + 2x +3 = 10x+5
6x +1 = 10x + 5
6x - 10x = 5 - 1
-4x = 4
x = -1
Determine the numbers
First number = 2(-1) - 1 = -3
Second number = -5
Third number = -7
Hence the 3 consecutive odd integers are -3, -5 and -7
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What is the answer to 1/3 + -5/6?
1. Find the value of Y
2. Find angle 1
3. Find angle 2
4. Find the value of X
Could someone please lend me a hand with this?
Describe the meaning of |−36|.(1 point) the absolute value of negative 36 the absolute value of negative 36 one divided by negative 36 one divided by negative 36 the absolute value of 36 the absolute value of 36 negative 36 minus zero
The meaning of |-36| is the absolute value of negative 36.
We know that, the absolute value of any real number m is the positive value of m.
For any ±m ∈ R,
| ±m | = m
The absolute value of a number is also know as modulus of number.
In this question we have been given an absolute value |-36|
|-36| = 36
So, the meaning of |-36| would be,
- the absolute value of negative 36
Therefore, the meaning of |-36| is the absolute value of negative 36.
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A school is organizing a weekend trip to a nature preserve. For each student, there is a $60 charge, which covers food and lodging. There is also a $40 charge per student for the bus. The school must also pay a $30 cleaning fee for the bus. If the total cost of the weekend is $4,030, how many students will be going on the trip?
31 students
40 students
41 students
66 students
The number of students who will be going on the trip is B. 40 students.
What is a mathematical expression?A mathematical expression is a rule-based set of numbers, variables, and mathematical operations performed to compute the output value.
The mathematical operations used to solve mathematical expressions include additions, subtractions, divisions, and multiplications.
Data and Calculations:The total of the weekend trip = $4,030
The cost of cleaning for the bus = $30
The cost of food and lodging per student = $60
The bus charge per student = $40
Total cost per student = $100 ($60 + $40)
The total cost, y = 4,030 - 30 - 100x
The number of students = x
x= (4,030 - 30)/100
= (4,000/100)
= 40.
Thus, the number of students who will be going on the trip is B. 40 students.
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