Answer:
3 (cos 93 + i sin 93)
Step-by-step explanation:
We are to find the cube roots of the following:
27 (cos 279° + i sin 279°)
[tex](cosx + i sin x) = cos (nx)) + i sin (nx)[/tex]
[tex]27 \times (cos 279+i sin 279)\frac{1}{3} =27\frac{1}{3} \times (cos 279+i sin 279)\frac{1}{3}[/tex]
Simplifying this to get:
[tex]3\times (cos279+i sin279)\frac{1}{3}[/tex]
[tex]3\times(cos 279+i sin 279)13=3(cos \frac{279}{3} +i sin \frac{279}{3})[/tex]
We know that [tex]\frac{279}{3}=3[/tex]
So, cube root = [tex]3(cos 93 + i sin 93)[/tex]
Match each function with the corresponding function formula when h(x) = 2 – 2x and g(x) = –2 x + 2.
Answer:
1 -> f
2 -> a
3 -> d
4 -> b
5 -> e
6 -> c
Step-by-step explanation:
We are given:
h(x) = 2 - 2x and g(x) = -2^x+2
a) k(x)= (g-h)(x) = g(x) - h(x)
= -2^x+2 - (2 - 2x)
= -2^x+2 - 2 + 2x
= -2^x+2x or 2x-2^x
k(x) = 2x-2^x = (g-h)(x)
So, 2 matches with a
b) k(x)= (g+h)(x) = g(x) + h(x)
= -2^x+2 + (2 - 2x)
= -2^x+2 + 2 - 2x
= -2^x+4-2x or 4 - 2^x -2x
So, k(x) = 4 - 2^x -2x = (g+h)(x)
So, 4 matches with b
c) k(x)= (2h - 2g)(x) = 2h(x) - 2g(x)
= 2(2 - 2x)-2(-2^x+2)
= 4 - 4x+2.2^x-4
= -4x+2^x+1 or 2^x+1-4x
So, k(x) = 2^x+1-4x = (2h - 2g)(x)
So, 6 matches with c
d) k(x) = (h-2g)(x) = h(x) - 2g(x)
= (2 - 2x)-2(-2^x+2)
= 2 - 2x+2.2^x-4
= -2-2x+2^x+1
= 2^x+1-2x-2
So, k(x) = 2^x+1-2x-2 = (h-2g)(x)
So, 3 matches with d
e) k(x) = (h-g)(x) = h(x) - g(x)
= (2 - 2x)-(-2^x+2)
= 2 - 2x+2^x-2
= -2x+2^x or 2^x-2x
So, k(x) = 2^x-2x = (h-g)(x)
So, 5 matches with e
f) k(x) = (2g+h)(x) = 2g(x)+h(x)
= 2(-2^x+2) + (2 - 2x)
= -2.2^x+4 + 2 - 2x
= -2^x+1+6-2x or 6 - 2^x+1-2x
So, k(x) = 6 - 2^x+1-2x = (2g+h)(x)
So, 1 matches with f
Final answer:
The function formulas are h(x) = 2 - 2x and g(x) = -2x + 2.
Explanation:
h(x) = 2 - 2x
g(x) = -2x + 2
Even function times an even function produces an even function, Odd function times an odd function produces an even function.
If the polynomials (2x^3+ax^2+3x-5)and (x^3+x^2-2x+a) leave the same remainder when divided by (x-2). Find the value of a. Also find the remainder in each case
The polynomial remainer theorem says that a polynomial [tex]p(x)[/tex] leaves a remainder of [tex]p(c)[/tex] when divided by [tex]x-c[/tex]. When [tex]x=2[/tex], we have
[tex]2x^3+ax^2+3x-5=4a+17[/tex]
[tex]x^3+x^2-2x+a=a+8[/tex]
Both operations leave the same remainder, which means
[tex]4a+17=a+8\implies3a=-9\implies\boxed{a=-3}[/tex]
Then the remainders are both 5.
A teacher asked her students how many pets they own. Here are the results:
Answer:
B.
Step-by-step explanation:
Basically, to draw a dot plot, what you do is place one circle above the corresponding value on the number line for each value in the data set, ie. if there is a 0 in the data set, then you would draw one 'dot' above 0 on the number line. If there was another 0, then you would draw another dot above the dot you drew for the first 0, and so on.
The data set given is:
0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 8
If we count the number of each value, then we can say that:
a) there are three 0's
b) there are four 1's
c) there are three 2's
d) there are two 3's
e) there are two 4's
f) there is one 8
Now you could draw this up on a dot plot and compare this with the answers, or you could technically also just look at the dot plots in the multiple choice answers and count each of the values to see which one matches up with the values we defined above. So:
A. There are three 0's (correct), four 1's (correct), three 2's (correct), but there are no 3's - therefor this is not the correct dot plot.
B. There are three 0's (correct), four 1's (correct), three 2's (correct), two 3's (correct), two 4's (correct) and one 8 (correct) - therefor this is the correct dot plot.
We could use the same method to check if C and D were correct; then we would see that C only has two 0's and one 3 and is thus incorrect, and D only has one 3 and one 4, and has an extra value of 5, thus it is also incorrect.
Therefor, the answer is B.
Whilst this method may be used, a quick sketch of the dot plot may be a little easier to work with to compare visually with the answers, however everyone has their own way so try both methods and see what works for you.
''Option B'' shows the correct dot plot.
We have to given that,
A teacher asked her students how many pets they own.
Here are the results:
0,0,0,1,1,1,1,2,2,2,3,3,4,4,4,8
Now, From the data set,
0 is repeat 3 times.
1 is repeat 4 times.
2 is repeat 3 times
3 is repeat 2 times.
4 is repeat 3 times
8 is repeat only 1 times.
Hence, Option B shows the correct dot plot.
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The segments shown below could form a triangle. 4,3,6 PLZ HELP ASAP
Answer:
Option A. True
Step-by-step explanation:
we know that
The Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side
we have
4,3 and 6
Applying the triangle inequality theorem
case 1) 4+3 > 6 -----> is true
case 2) 3+6 > 4 ----> is true
therefore
The given segments could form a triangle
Is true
Answer: true
Step-by-step explanation:
internal memoriam menino
The length of a rectangular garden is 30 yards more than the width. The perimeter is 300 yards. Find the length and width. L= yards, W=yards
Answer:
L = 90 yardsW = 60 yardsStep-by-step explanation:
The formula for the perimeter of a rectangle is ...
P = 2(L+W)
If the length is 30 yards more than the width, we can use L = W+30 and substitute known values into the above formula:
300 = 2((W+30) +W)
150 = 2W +30 . . . . . divide by 2 and collect terms
120 = 2W . . . . . . . . . subtract 30
60 = W . . . . . . . . . . . divide by 2
60+30 = L = 90
The length is 90 yards; the width is 60 yards.
Traffic on saturday, it took ms. torres 24 minutes to drive 20 miles from her home to her office. during friday's rush hour, it took 75 minutes to drive the same distance.
a. what was ms. torres's average speed in miles per hour on saturday?
b. what was her average speed in miles per hour on friday?
Answer:
a. 50 mph.
b. 16 mph.
Step-by-step explanation:
a.Convert minutes to hours using dimensional analysis:
[tex]\displaystyle \rm 24 \; minutes \times \frac{1\; hour}{60\; minutes} = \frac{2}{5}\; hours[/tex].
Average speed is distance traveled over time taken:
[tex]\displaystyle \text{Average Speed} = \frac{\text{Distance Traveled}}{\text{Time Taken}} = \rm \frac{20\; miles}{\dfrac{2}{5}\; hours} = (20 \times \frac{5}{2})\; mph= 50\; mph[/tex].
b.Similarly,
[tex]\displaystyle \text{Time Taken} = \rm 75 \; minutes \times \frac{1\; hour}{60\; minutes} = \frac{5}{4}\; hours[/tex].
[tex]\displaystyle \text{Average Speed} = \frac{\text{Distance Traveled}}{\text{Time Taken}} = \rm \frac{20\; miles}{\dfrac{5}{4}\; hours} = (20\times \frac{4}{5})\; mph= 16\; mph[/tex].
Identify the type of function represented by f(x)=2(1/2)^x
Answer:
B: Exponential decay
Step-by-step explanation:
Answer:
exponential decay
Step-by-step explanation:
[tex]f(x)= 2(\frac{1}{2})^x[/tex]
[tex]f(x)= ab^x[/tex] is an exponential function, where 'a' is the initial value and 'b' is the exponential factor
When the value of 'b' is between 0 and 1 then it is exponential decay
when the value of 'b' is greater than 1 then it is an exponential growth
In the given exponential function , the value of b is 1/2 that is 0.5
The value of 'b' is between 0 and 1 so it is an exponential decay
Identify the reflection of the figure with vertices P(−11,−13), Q(−17,19), and R(23,−27) across the x-axis.
P (−11, 13), Q (−17, −19), R (23, 27)
P (11, 13), Q (17, −19), R (−23, 27)
P (11, −13), Q (17, 19), R (−23, −27)
P (−13, −11), Q (19, −17), R (−27, 23)
Answer:
P (−11, 13), Q (−17, −19), R (23, 27)
Step-by-step explanation:
we know that
The reflection of a figure across the x-axis has the following rule
(x,y) -----> (x,-y)
so
P(-11,-13) -----> P(-11,13)
Q(-17,19) -----> Q(-17,-19)
R(23,-27) ----> R(23,27)
Answer:
P (−11, 13), Q (−17, −19), R (23, 27)
Step-by-step explanation:
Got it right on my test :)
a survey asked two age groups which summer sport they most preferred. the results are shown in the table below. which sport was most preferred by people by ages 20-29 and what is the relative frequency within this age group?
Answer: Hiking was most prefered between ages 20-29
Answer:
Step-by-step explanation:
Given that a survey asked two age groups which summer sport they most preferred. the results are shown in the table below.
We have to find which sport was most preferred by people by ages 20-29 and what is the relative frequency within this age group
From the table we find that age group 20-29 prefers s
ski 15 [tex]\frac{15}{268}[/tex]
Swim 88 [tex]\frac{88}{268}[/tex]
Kayak 42 [tex]\frac{42}{268}[/tex]
Hike 123 [tex]\frac{123}{268}[/tex]
Total 268 1
We find that hike liking are more in this age group
Relative frequency calculated as frequency/268 is shown above.
Solve the equation.
42x – 5 = 64
Answer:
23/14
Step-by-step explanation:
42x - 5 = 64
Add 5 to both sides in order to isolate 42x
42x = 64 + 5
42x = 69
Divide 42 from both sides in order to isolate x
x = 69/42
The answer gives an uneven decimal so it'd be best to leave it as a simplified fraction. The simplified fraction is 23/14.
Answer:
x = 1.64
Step-by-step explanation:
42x – 5 = 64
add 5 to both sides
42x - 5 + 5 = 64 + 5
42x = 69
divide via by 42
x = 69/42
x = 1.64
Hope this helps!
Which two types of people help generate revenue for an organization directly?\
A.
repeat customers
B.
online shoppers
C.
human resource staff
D.
sales executives
E.
security personnel
Answer:
Answer: The Answer Is B
Answer:
I think is D is the best answer
Line H is represented by the following equation:
2x + 2y = 8
What is most likely the equation for line K so the set of equations has infinitely many solutions? (4 points)
x + 2y = 2
x + y = 4
2x + y = 6
x – y = 8
Answer:
b. x + y = 4
Step-by-step explanation:
For to lines to have an infinite number of points that intersect, the lines have to have the exact same equation, so that every coordinate of H and K is the exact same.
Simplify the equation for H:
[tex]2x+2y=8\\2y=8-2x\\y=4-x[/tex]
Rearrange the equation:
[tex]x+y=4[/tex]
Part A: Sam rented a boat at $225 for 2 days. If he rents the same boat for 5 days, he has to pay a total rent of $480.
Write an equation in the standard form to represent the total rent (y) that Sam has to pay for renting the boat for x days. (4 points)
Part B: Write the equation obtained in Part A using function notation.(2 points)
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)
Answer:
Here's what I get.
Step-by-step explanation:
Part A. Equation in standard form
The question is asking you to find the equation of a straight line that passes through two points
Let x = the number of days
and y = the cost
Then the coordinates of the two points are (2,225) and (5,480).
(i) Calculate the slope of the line
[tex]\begin{array}{rcl}m & = & \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\& = & \dfrac{480 - 225}{5 - 2}\\\\& = & \dfrac{255}{3}\\\\& = & 85\\\end{array}[/tex]
In other words, the daily rental is $85/day.
(ii) Calculate the y-intercept
[tex]\begin{array}{rcl}y & = & mx + b\\480 & = & 85 \times 5 + b\\480 & = & 425 + b\\b & = & 55\\\end{array}[/tex]
(iii) Write the equation for the line
y = 85x + 55
That is, the cost is $55 plus $85/day
Part B. Equation in function notation
Replace y with ƒ(x)
ƒ(x) = 85x + 55
Part C. Graphing
Let's say you want to plot a graph of the rental cost for up to ten days.
(i) Calculate two points on the graph.
When x = 0, y = 85; when x = 10, y = 905.
(ii) Scale your axes
A good number of intervals is about ten.
Your x-axis should have tick marks at 1-day intervals.
Your largest y-value is 905. Ten intervals would make about $90/interval. However, you should round that up to $100/interval for easy interpolation.
Your y-axis will run from 0 to $1000 in $100 intervals.
Plot your two points and draw a straight line through them.
(iii) Axis labels
x represents the number of days, so the label on the x-axis could be "No. of days."
y represents the cost of renting the boat, so the label on the y-axis could be "Rental cost."
Your graph should resemble the one below.
The Great Pyramid is a square pyramid with a base area of 571,536 ft2 and a height of 48 stories. Each story is approximately 10 feet. Estimate the volume in cubic yards.
a. 274,337,280 yd3
b. 3,386,880 yd3
c. 91,445,760 yd3
d. 30,481,920 yd3
Answer: c. 91,445,760 yd3
Step-by-step explanation:
571,536 x 48 = 27,433,728
27,433,728 ÷ 3 = 9,144,576
9,144,576 x 10 = 91,445,760
PLEASE HELP ME WITH THIS MATH QUESTION
Answer:
The answer to your problem is 13%
There are 4 male freshmen and 30 students total.
Divide the amount of male freshmen by the amount of students and turn it into a percentage.
4/30= 0.1333 = 13%
7. Which of the following relations is a function?
A.{(2, 3), (-2, 3), (3, 2), (-3,-2)}
B.{(8,-4), (-4, 8), (-4, -8), (-8,4)}
C.{(9, -1), (-1, 9), (9, 2), (2, -1)}
D.{(5, -7), (4, 6), (-3, 8), (5,9)}
A function means that each x can only have one y-value
B, C, and D are NOT functions because they have x-values that have multiple y-values.
For example
B. has two values for -4:
(-4, 8) and (-4, -8)
C. has two values for 9:
(9, -1) and (9, 2)
D. has two values for 5:
(5, -7) and (5, 9)
This makes A. the only function
Hope this helped!
~Just a girl in love with Shawn Mendes
PLEASE HELP I WILL GIVE BRAINLIEST What is the last step in constructing this equilateral triangle?
Answer:
A. Draw line segment AB
Step-by-step explanation:
Please mark brainliest and have a great day!
Answer:
B
Step-by-step explanation:
The Guy Above Got It Wrong On The Exam.
Juan construyó una rampa que tiene 5 m de largo y 1 m de altura. ?Cuánto mide la distancia (d) que recorre al subir la rampa
Answer:
[tex]d=\sqrt{26}\ m[/tex] or [tex]d=5.1\ m[/tex]
Step-by-step explanation:
The question in English is
Juan built a ramp that is 5 m long and 1 m high. How much is the distance (d) he travels when he climbs the ramp?
let
x -----> the length of the ramp
y ----> the height of the ramp
d ----> the distance Juan travels when he climbs the ramp
we know that
Applying the Pythagoras Theorem
[tex]d^{2}=x^{2}+y^{2}[/tex]
we have
[tex]x=5\ m[/tex]
[tex]y=1\ m[/tex]
substitute the given values
[tex]d^{2}=5^{2}+1^{2}[/tex]
[tex]d^{2}=26[/tex]
[tex]d=\sqrt{26}\ m[/tex] -----> exact value
[tex]d=5.1\ m[/tex] ----> approximate value
What equation results from completing the square and then factoring?
Answer:
YOUR ANSWER IS C.(x-6)²=94
Step-by-step explanation:
(x-6)²=94x²+36-12x=94x²-12x=54HENCE PROVED
The probability of drawing an ace from a deck of cards is 1/13. If you drew one card at a time (and put the card back each time) for 400 tries, how many times total could you expect to draw an ace
Answer:
31 aces
Step-by-step explanation:
To find the number of aces you would expect, take the probability of an aces and multiply by the number of tries
1/13 * 400 =30.76923
Rounding up, approximately 31 aces
Answer:
30 times
Step-by-step explanation:
1/3 * 400
30.76923
31 times
Answer one of them!
1.Write a function that is shifted down 2 units and then reflected over the x-axis. Parent function is y = -5x - 8
2.Write a function that is reflected over the x-axis. Parent function is y = 5x - 8
3.Let g(x) be a vertical shift of f(x)= -x up 3 units followed by a vertical stretch by a factor of 4. Write the rule for g(x) .
4.Which transformation from the graph of a function f(x) describes the graph of 1/3 f(x)?
5.Write a function that is reflected over the x-axis. Parent function is y = -5x - 8
6. Let g(x) be a vertical shift of f(x)= -x up 4 units followed by a vertical stretch by a factor of 3. Write the rule for g(x).
Answer:
1. y=-5x+10
Step-by-step explanation:
if it reflect over the x it changes the y if it reflects over y it changes the x
The function y = f(x), when shifted down by 2 units and then reflected over the x-axis will become g(x) = 5x + 10.
What is reflection of line? What is the general equation of a straight line? What is triangle? What are parallel lines?A reflection over line is a transformation in which each point of the original figure (the pre-image) has an image that is the same distance from the reflection line as the original point, but is on the opposite side of the line The general equation of a straight line is : y = mx + cwhere : [m] → is slope of line and [c] → is the y - intercept
A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically : ∠x + ∠y + ∠z = 180°. There are different types of triangles such as : equilateral triangle , scalene triangle , isosceles triangle etc.Parallel lines are those lines that are equidistant from each other and never meet, no matter how much they may be extended in either directions. These lines have same slope.We have the some sub - questions given in question.
We will solve part [1].
We have -
y = - 5x - 8
Shifting down by 2 units, we get -
y = - 5x - 8 - 2
y = - 5x - 10
Reflection over the [x] axis, would be -
g(x) = - y
g(x) = - (- 5x - 10)
g(x) = 5x + 10
Therefore, the function y = f(x), when shifted down by 2 units and then reflected over the x-axis will become g(x) = 5x + 10.
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Hello to all, how is everything, I think every one is getting more from this website, and your views are fastidious in support of new viewers. Dfbdgdgdcbga
Answer: This website is the greatest thing ever wjsijrbejwisjfb
Need help with this math question
Answer:
83.0 degrees to the nearest tenth.
Step-by-step explanation:
17^2 = 8^2 + 16^2 - 2*8*16 cos X
cos X = (17^2 - 8^2 - 16^2) / - 2*8* 16
cos X = 0.12109
X = 83.04 degrees
Mercedes can download new songs for $1.39 each. Write an equation to show how many songs she can download for $15.00.
15x = 1.39
15 + x = 1.39
1.39x = 15
1.39 + x = 15
Answer:
1.39x=15
Step-by-step explanation:
each song is worth 1.39 dollers
If there are x songs, the total value would be 1.39x
1.39x=15
Answer:
Mercedes can download new songs for $1.39 each. Write an equation to show how many songs she can download for $15.00.
15x = 1.39
15 + x = 1.39
1.39x = 15
1.39 + x = 15
Step-by-step explanation:
The equation is the following:
1.39x = 15
15 $ is what you have to download the songs, and each unit is 1.39 $, by clearing the X of the equation, it is 15 / 1.39, and the result is the number of songs that Mercedes can download.
Solve the equation.
15x^2 – 28x + 5 = 0
Answer:
Step 1: Factor left side of equation.
(5x−1)(3x−5)=0
Step 2: Set factors equal to 0.
5x−1=0 or 3x−5=0
x=
1 /5
or x=
5 /3
Answer:::::::::
x=5/3 or x=1/5
If a seller prepaid the taxes of $4,400 and the closing is set for May 19, using the 12 month/30 day method what will the buyer owe the seller as prorated taxes?
Answer:
$2701.11
Step-by-step explanation:
The buyer owes for taxes for the remainder of the year, 11 days in May and 7 more months: 7 11/30 months out of 12.
(7 11/30)(1/12)(4400) = (221/360)(4400) = 2701 1/9 ≈ 2701.11
The buyer will owe prorated taxes of $2701.11.
Given the graph below state whether or not the relation is a function, and give the domain and
range.
Answer:
NOT a functiondomain: [-2, 2]range: [-4, 4]Step-by-step explanation:
A vertical line intersects the graph twice, so the relation is not a function. It is only allowed to intersect once if the relation is a function.
The domain is the horizontal extent, which is from -2 to +2.
The range is the vertical extent, which is -4 to +4.
The relation is indeed a function, and its domain is [-2, ∞), and its range is (-∞, ∞), as you assumed. The verification process aligns with your initial statements.
If the assumed domain is [-2, ∞) and the assumed range is (-∞, ∞), it suggests that you believe the relation is a function that is defined for all real numbers and can output any real number.
To determine whether the relation is indeed a function, we need to check whether each input (x-value) corresponds to a unique output (y-value) and ensure it satisfies the vertical line test. Let's proceed with the verification:
Function Test (Vertical Line Test):Trace a vertical line through the entire graph. If the vertical line intersects the graph at only one point for each x-value, then the relation is a function. If the vertical line intersects the graph at more than one point for any x-value, then the relation is not a function.
Based on the assumed domain and range, it appears that you are considering the relation to be a function defined for all real numbers. In such a case, the relation would be a function by definition, as it assigns a unique y-value to each x-value.
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NEED HELP WITH A MATH QUESTION
Answer:
5/75 in my opinion. 75 is total of hot drink
Step-by-step explanation:
Mr Solidarios charged Randolf Php 320.00 for parts and Php 150.00 per hour for labor to repair his bicycle.If he spent 3 hours repairing his bicycle,how much does Randolf owe him?
Answer:
Php 770.00
Step-by-step explanation:
The cost of labor is ...
(hours) × (hourly rate)
= (3 h) × (Php 150.00/h) = Php 450.00
The total cost is ...
total cost = cost of labor + cost of parts
= (Php 450.00) + (Php 320.00) = Php 770.00
Randolf owes Mr. Solidarios Php 770.00 for the repair.
Multiply the following using the vertical method
Answer:
Option C is correct.
Step-by-step explanation:
We need to multiply the following terms using vertical multiplication method
3x^2-5x+1
x x^2+2x+4
The vertical multiplication is shown in the figure attached.
The result is: 3x^4+x^3+3x^2-18x+4
So, Option C is correct.
The vertical method of multiplication involves multiplying each digit of one number by each digit of another, one at a time, recording partial results and adding them together for the final result.
Explanation:To perform multiplication using a vertical method, first write the numbers vertically aligning them properly. We will be multiplying like this:
123 (number 1) x456 (number 2)
Start from the rightmost digit of the second number (bottom number) and multiply it with each digit of the first number (top number), advancing from right to left. Record each result underneath, shifted appropriately (similar to 'carry digits' in addition). After fully multiplying by one digit, proceed to the next digit in the second number, remembering to shift your results accordingly. Finally, add all the results together to get the final answer. This is the vertical method of multiplication.
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