Point Q was rotated about the origin (0,0) by -45 degrees
Answers
Answer:
0,0
Step-by-step explanation:
The point Q was rotated about the origin (0,0) by -45 degrees, so the new coordinate point is (√2, 4√2).
From the given graph, the coordinates of point Q are (-3, 5).
Rotating the co-ordinate axes through an angle of 45° in anti-clockwise direction is equivalent to rotating the point through an angle of -45° about origin.We will use rotation from complex numbers to solve this.
Let x + iy the new complex number
(-3+5i)[tex]e^{\frac{-\pi i}{4} }[/tex]
= (-3+5i)((1-i)/√2)
= (-3+5i)(1-i) ×1/√2
= (-3+5i+3i-5i²) ×1/√2
= (-3+8i+5) ×1/√2
= (2+8i) ×1/√2
= (2/√2 + 8i/√2)
= (√2 + 4√2i)
So, the coordinates are (√2, 4√2)
Therefore, the point Q was rotated about the origin (0,0) by -45 degrees, so the new coordinate point is (√2, 4√2).
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Related Questions
Fernando is trying to incorporate more exercise into his busy schedule. He has several short exercise routines he can complete at home. Last week, he worked out for a total of 88 minutes by doing 2 arm routines and 3 abdominal routines. This week, he has completed 4 arm routines and 1 abdominal routine and spent a total of 66 minutes exercising. How long does each routine last?
Answers
Answer: Arm routine = 11 minutes
Abdominal routine = 22 minutes
Step-by-step explanation:
Let the minutes used for an arm routine be represented by x.
Let the minutes used for an abdominal routine be represented by y.
Last week, he worked out for a total of 88 minutes by doing 2 arm routines and 3 abdominal routines. This can be expressed as:
2x + 3y = 88
This week, he has completed 4 arm routines and 1 abdominal routine and spent a total of 66 minutes exercising. This can be expressed as:
4x + y = 66
2x + 3y = 88 ...... i
4x + y = 66 ...... ii
Multiply equation I by 4
Multiply equation ii by 2
8x + 12y = 352 ...... iii
8x + 2y = 132 ...... iv
Subtract iv from iii
10y = 220
y = 220 / 10
y = 22
An abdominal routine last for 22 minutes
From equation I
2x + 3y = 88
2x + 3(22) = 88
2x + 66 = 88
2x = 88 - 66
2x = 22
x = 22/2
x = 11 minutes
An arm routine last for 11 minutes
I need help !! this is geometry hw
Answers
Answer:
angle a=64, longest side AV : shortest side: TV
angle c=55 longest side: BW shortest side: CB
angle z =24 longest side: XZ shortest side: XP
Step-by-step explanation:
Y’all I need help!!! {picture}
Answers
Answer:
first and second choice
need help finding out something, refer to picture
Answers
Answer:
He made a mistake in the second line.
Step-by-step explanation:
He factored out x out of 6-2x and 5+4x, which is not possible because there is not an x in both 6 and 5.
Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. (-5, -8): y = - 3x + 2
Answers
Given:
The equation of line is
[tex]y=-3x+2[/tex]
To find:
The equation of line parallel to given line and passes through (-5,-8).
Solution:
Slope intercept form of a line is
[tex]y=mx+b[/tex]
where, m is slope and b is y-intercept.
On comparing the equation [tex]y=-3x+2[/tex] with the slope intercept form, we get
[tex]m=-3[/tex]
Slope of given line is -3.
Slope of two parallel lines are same. So, the slope of parallel line is -3.
Equation of line passes thorough the point (-5,-8) with slope -3 is
[tex]y-y_1=m(x-x_1)[/tex]
where, m is slope of the line.
[tex]y-(-8)=-3(x-(-5))[/tex]
[tex]y+8=-3(x+5)[/tex]
[tex]y+8=-3x-15[/tex]
Subtract 8 from both sides.
[tex]y=-3x-15-8[/tex]
[tex]y=-3x-23[/tex]
Therefore, the equation of required line is [tex]y=-3x-23[/tex].
It took Sharon 85 minutes to wash three cars. She spent x minutes on
each car and 10 minutes putting everything away. Solve 3x + 10 = 85 to
find how long it took to wash each car.
A)5.5
B)28.3
C)25
D)31,67
Answers
Answer:
25
Step-by-step explanation:
2(2.8s + 2.5) =
Please use the distributive property and answer the expression.
Answers
Answer: 5.6s+5
Step-by-step explanation: hope this helps
btw can i have brainliest?
What is the length of segment JK
A. 6
B. 8
C. 9
D. 10
Answers
You have to set up a proportion, i’m going to use LM and DC
i’m going from the biggest quad to smallest quad, while setting up a proportion. 20/15=12/x
cross multiply, getting 20x=180
then divide both sides by 20, getting 9!
Which word below means ¨to make as small as possible
Answers
Answer:
Minimize
Step-by-step explanation:
Hope this helps!
A fundraiser is being held to support a local nonprofit organization. Admission costs $10, and each raffle ticket costs $3. There are no other possible costs. If an event-goer pays the admission fee and buys x number of tickets, what type of function should be used to model the total amount spent by the event-goer at the event?
Answers
Answer:
y= 10+ 3x
10 is the admission fee
3x is the cost for each ticket
y is the total
The function for the total cost (y) spent by the event-goer at the event is
y = 3x+10
What is a function?A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output.
Given that, Admission costs $10, and each raffle ticket costs $3. There are no other possible costs.
Let the total cost be y,
Therefore, establishing the function, for x number of tickets.
y = 3x+10
Hence, the required function is y = 3x+10
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24=−3(2a−14)−3a
what is A?
Answers
Answer:
a = 2
Step-by-step explanation:
Hope this helps and have a nice day :)
Answer:
a=3
Step-by-step explanation:
24=3(2a-14)-3a
distribute
24=6a-42-3a
subtract 3a from 6a
24=3a-42
add 42 to both sides
66=3a
divide 3
3=a
a=3
hope this helps :)
Item 4
Write an equation in point-slope form of the line that passes through the point (2,−8) and has a slope of 4.
Answers
Answer:
y = 4x - 16
Step-by-step explanation:
Plug in the slope and point into y = mx + b, and solve for b:
y = mx + b
-8 = 4(2) + b
-8 = 8 + b
-16 = b
Then, plug in b and the slope into y = mx + b
y = 4x - 16 is the equation in point slope form
9514 1404 393
Answer:
y +8 = 4(x -2)
Step-by-step explanation:
Point-slope form of the equation of a line is ...
y -k = m(x -h) . . . . . line of slope m through point (h, k)
Filling in the given point and slope, you have ...
y -(-8) = 4(x -2)
y +8 = 4(x -2)
Which sequence of transformations proves that shape I is similar to shape II?
A.
a reflection across the x-axis, and then a translation 6 units right
B.
translation 6 units right, and then a 90° clockwise rotation about the origin
C.
a 180° counterclockwise rotation about the origin
D.
a reflection across the y-axis, and then a translation 4 units up
E.
a reflection across the x-axis, followed by a 180° counterclockwise
rotation about the origin, and then a translation 4 units down
Answers
Answer:
E
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
simplify polynomial expressions with multiplication:
(8p-7)(5p^2+7p-3)
Answers
Answer:
-2p3 • (62p2 + 72p - 143)
Step-by-step explanation:
Solve the system.
x+2y=0
2x-y=4
The solution is ___
Explain your choice of method.
Answers
Answer:
x = 8/5 and y = -4/5
The method used was SUSTITUION METHOD
Step-by-step explanation:
x = -2y
2(-2y)-y = 4
-4y-y = 4
-5y = 4
y = -4/5
then
x= -2(-4/5)
x = 8/5
HELPP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
a warm front is happening
Answer:
hot
Step-by-step explanation:
The salesman gave me 20% off of my new laptop regularly priced $500. How
much did I save? *
Answers
Answer:
100
Step-by-step explanation:
20% of 500 is 100
Answer:
$100
Step-by-step explanation:
20% is the same as 1/5. 1/5 of 500 is 100. Then add dollar signs, and you have your answer.
Lupe spent $6.48 on a notebook and a pack of pencils, including tax. If the notebook cost $2.00 and the pencils cost $3.99, how much was the tax?
Answers
What is the area of rectangle ABCD?
Answers
Answer:
8 squares
Step-by-step explanation:
i think 8 squres iscorrect answer
Answer:
8 square units
Step-by-step explanation:
count the number of squares the rectangle is taking
or length times width
2x4
Find the value of the trigonometric ratio.
9) sin z
Answers
Answer:
SinZ=24/40 = 12/20 = 3/5
C)
The value of the trigonometric ratio Sin Z for the given triangle XYZ will be [tex]\frac{3}{5}[/tex], i.e. option C.
What are trigonometric ratios?The trigonometric ratios are the ratios of sides of two sides of right angled triangle used in trigonometry. Trigonometric ratios are used to find the value of the acute angles in a right triangle when the sides of the triangle are given.
We have,
A right-angled triangle XYZ with the given values,
Angle Y = 90°
And,
YZ = 32, XY = 24 and XZ = 40,
Now,
Using the trigonometric ratios,
i.e.
[tex]Sin Z=\frac{Perpendicular}{Hypotenuse}[/tex]
i.e.
[tex]Sin Z=\frac{XY}{XZ}[/tex]
So,
[tex]Sin Z=\frac{24}{40}[/tex]
On simplifying,
We get,
[tex]Sin Z=\frac{3}{5}[/tex]
So,
The option C is the correct answer for the given triangle find out using trigonometric ratio,
Hence, we can say that the value of the trigonometric ratio Sin Z for the given triangle XYZ will be [tex]\frac{3}{5}[/tex], i.e. option C.
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Pls help I will give brainlist!
Match each inequality with the number line that represents it.
Answers
Answer:
-3 [tex]\leq[/tex] x matches with 6,
3 < x matches with 5,
x [tex]\geq[/tex] 3 could not simplify any further
x < 3 could not simplify any further
x [tex]\leq[/tex] -3 could not simplify any further
-3 > x matches with 3
Step-by-step explanation:
i used a inequality calculator
What is the rental rate, in dollars per person, if 6 people plan to rent the houseboat?
1
Number of People (X)
Rental Rate (P dollars per person)
2
3
240
120
80
Answers
Answer: 120 i think
Step-by-step explanation:
In a recipe, for every 3/4 cup of flour, 1/3 cup of sugar is needed. How many cups of sugar are needed for 1 cup of flour? (Leave your answer in fraction form).
Answers
Answer:
1/9 cup of sugar for every 1/4 cup of flour
Step-by-step explanation: Turn the 1/3 into 3/9 and I'm sure you can figure it out from there.
Help Plz 10pts will be given
Answers
Answer:
Is the first one 3 over 7
Step-by-step explanation:
In softball, Marissa hits the ball 40% of the time when she is up to bat. Based on this information, how many times will Marissa hit the ball if she goes to bat 30 times?
Answers
Answer:
Marissa hit the ball 12 times if she goes to bat 30 times.
Step-by-step explanation:
Given that:
Marissa hits the ball 40% of the time when she is up to bat.
Marissa gets to bat for 30 times.
Balls hit by Marissa = 40% of the times Marissa goes to bat
Balls hit by Marissa = [tex]\frac{40}{100}*30[/tex]
Balls hit by Marissa = 0.4 * 30
Balls hit by Marissa = 12
Hence,
Marissa hit the ball 12 times if she goes to bat 30 times.
What is the value of f -1 (12)
Answers
-1 us a answer for your questions or support
I WILL MARK BRAINIEST
PLEASE HELP ASAP
Answers
Answer:
2101
Step-by-step explanation:
Apply -12 to the x
-(-12)^3+3(-12)^2+5(-12)+1
Then Simplify
2101
I hope it's right
Which type of data would be best displayed in a box plot?
Answers
Answer:c
Step-by-step explanation:i took the test
option C, The number of votes received by each of four candidate can be best displayed in a box plot.
Explanation:
We need to find which type of data can be displayed in a box plot from the given options.
The box plot can used to show the shape of a distribution, the lower value , higher value , the central value, and its variability.
The graph shows how the values of the data are spread out .It is the distribution of numerical data. Box plot can be used to compare multiple groups .
So, the answer can be option C
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When writing an equation in slope-intercept form, you need the values of the
Answers
Answer:
slope, m
y-intercept
Step-by-step explanation:
When writing an equation in slope-intercept form, there will be need for slope and y- intercept.
What is the slope intercept form of an equation ?When any equation is represented in the y = mx +c form, it is called the slope intercept form of the equation.
Here m is slope and c is constant.
To writing the slope intercept form of the equation,
There will be requirement of slope,
and y intercept, it will be in form of (0, a), here a will be value of y coordinate.
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Find the product.
(4x2 + x - 5)(2x + 1)
Answers
Hope this helps