Answer:
The graph is symmetric about the x-axis.
Step-by-step explanation:
1. Symmetry about the x-axis: If the point (r, θ ) lies on the graph, then the point (r, -θ ) or (-r, π - θ ) also lies on the graph.
2. Symmetry about the y-axis: If the point (r, θ ) lies on the graph, then the point (r, π - θ ) or (-r, -θ ) also lies on the graph.
3. Symmetry about the origin: If the point (r, θ ) lies on the graph, then the point (-r, θ ) or (r, π + θ ) also lies on the graph.
The given polar equation is
[tex]r=2\cos (5\theta)[/tex]
Check the equation by (r, -θ).
[tex]r=2\cos (-5\theta)=2\cos (5\theta)=r[/tex]
Therefore, the graph is symmetric about the x-axis.
Check the equation by (-r, -θ).
[tex]-r=2\cos (-5\theta)=2\cos (5\theta)=r\neq -r[/tex]
Therefore, the graph is not symmetric about the y-axis.
Check the equation by (-r, θ).
[tex]-r=2\cos (5\theta)=2\cos (5\theta)=r\neq -r[/tex]
Therefore, the graph is not symmetric about the origin.
Now that you have x² - 8x + 16 = 9 + 16, apply the square root property to the equation.
Answer: ( x - 4 )² = 25
The solutions to the quadratic equation
x2 – 8x – 9 = 0. are
-1 and 9
A minor league baseball team plays 117 games in a season. if the team won 13 more than 3 times as many as they lost. how many wins and losses
The net below is for a number cube. What are the three sums of the numbers on opposite surfaces of the cube?
If m<1 = 7x + 6 and m<2 = 8x - 6, find the value of x so that p is perpendicular to q
Answer:
x = 12
Step-by-step explanation:
Given: [tex]\angle 1=7x+6[/tex]
[tex]\angle 2=8x-6[/tex]
∠1 and ∠2 form by two intersection line p and q.
p is perpendicular to q.
Therefore, ∠1 = ∠2 = 90°
So, 7x + 6 = 90°
7x = 84
x = 12
8x - 6 = 90°
8x = 96
x = 12
7x + 6 = 8x - 6
x = 6 + 6
x = 12
So, we get x=12 from all three equations.
hence, The value of x is 12
Find the equation of the tangent line to the curve 4x3+2y2−11=4xy−x at the point (−1,2).
The following list shows the items and prices for a restaurant order. Calculate the total amount if there is a 7% tax and the customer leaves a 20% gratuity. 1 appetizer: $7.39 2 entrees: $16.99 each 1 dessert: $5.29 2 drinks: $2.30 each a. $65.82 b. $65.10 c. $54.85 d. $40.60
The length of a rectangle is five times its width. if the perimeter of the rectangle is 96 ft , find its area.
The width of the rectangle is 8 ft and the length is 40 ft. Therefore, the area of the rectangle is 320 square feet.
Explanation:To find the dimensions of the rectangle, let's use variables. Let the width of the rectangle be x. Since the length is five times the width, the length would be 5x. The perimeter of a rectangle is equal to twice the sum of its length and width. Therefore, we can set up the equation 2(5x + x) = 96 to find the width.
Simplifying the equation, we have 12x = 96. Dividing both sides by 12, we get x = 8. So the width of the rectangle is 8 ft.
Now, we can calculate the length by multiplying the width by 5. The length would be 5(8) = 40 ft. The area of a rectangle is equal to its length multiplied by its width. Therefore, the area of this rectangle is 8 ft * 40 ft = 320 square feet.
What is x in 7x+2x-5=0
How do I solve this
0. 135 written as a fraction
Explains how to write 0.135 as a fraction.
0.135 written as a fraction is 135/1000.
What Do You Call It When Police Interrogate a Cow's Husband? *the answer isn't " Question-a-bull** && the answer is 12 letters long
The key in this problem is to find the answer in each number and then cross out the box containing that solution. Here are the following answers with their corresponding letters that need to be crossed out.
1 . 12 LK
2. 9 AM
3. -8 ST
4. -15 SH
5. 33 IN
6. -36 OO
7. 44 OP
8. 14 CO
9. 27FT ME
10. 23 ED
11. $580 WS
12. 11 DEGREES CELSIUS TO
13. 29 IT
14. -35m JA
After crossing out those letters, the answer for what do you call a when a policeman interrogate a cow's husband is QUESTIONABLE.
number 4 I have absolutely no idea how to do. I generally understand finding distance on the coordinate plane but this has really confused me. Please help.
What are the solutions to the equations |x-10|-4=2x
Vivian solved an equation. she showed all her steps and got the correct answer. what kind of reasoning did vivian use to solve the equation? convenient inductive predictive deductive
The type of reasoning that Vivian used into solving the equation is the deductive. This type of reasoning is able to describe on how the equation is done and this could be seen in the given scenario above as she was able to show the steps in obtaining the correct answer.
Calculate the area of the figure below using the following information:
Area of triangle ABC = 23.85 square units
Area of triangle ACD = 29.4 square units
Area of triangle AED = 26.25 square units
The area of the Figure ABCDE is ______ square units.
Answer:
Area of pentagon ABCDE = 23.85 + 29.4 + 26.25 = 79.5 unit²
Step-by-step explanation:
Area of pentagon ABCDE is sum of area of triangles ABC, ACD and ADE
Area of pentagon ABCDE = Area of ΔABC +Area of ΔACD + Area of ΔADE
Area of ΔABC = 23.85 unit²
Area of ΔACD = 29.4 unit²
Area of ΔAED = 26.25 unit²
Area of pentagon ABCDE = Area of ΔABC +Area of ΔACD + Area of ΔADE
Area of pentagon ABCDE = 23.85 + 29.4 + 26.25 = 79.5 unit²
he editors found that 0.0016 of the words in the book were misspelled. if there were 250,000 words in the book how many words were spelled properly
Which transformation will be equivalent to rotating a figure 180° counterclockwise?
A) reflecting over the line y = x.
B) reflecting over the line y = -x.
C) reflecting over the x-axis and the y-axis.
D) translating left 3 units and down 5 units.
If we have given coordinates of the image are in form (h,k).
The resulting coordinates of image rotation of 180° around the origin would be (-h,-k).
We have rule (h,k) ---> (-h,-k).
We can see that x-coordinate is being multiplied by -1 and then y-coordinate is also being multiplied by -1.
Above rule could be break into two parts.
(h,k) ---> (-h,k) ----> (-h,-k).We can see in first step, (h,k) ---> (-h,k) is being reflecting over the x-axis and
in second step (-h,k) ----> (-h,-k) is being reflecting over the y-axis.
Therefore, correct option is C) reflecting over the x-axis and the y-axis.The transformation which is equivalent to rotating a figure [tex]180^{\circ}[/tex] counterclockwise is reflecting over the [tex]x[/tex]-axis and [tex]y[/tex]-axis. Therefore, the [tex]\fbox{\begin\\\ \bf option (C)\\\end{minispace}}[/tex] is correct.
Further explanation:
Consider a coordinate in the form [tex](a,b)[/tex] where [tex]a[/tex] and [tex]b[/tex] are real numbers.
If [tex]a[/tex] and [tex]b[/tex] are positive then the point [tex](a,b)[/tex] lies in the first quadrant.
If we rotate the coordinate [tex](a,b)[/tex] [tex]180^{\circ}[/tex] counterclockwise then the coordinates become [tex](-a,-b)[/tex].
The coordinate [tex](-a,-b)[/tex] lies in the third quadrant.
If we reflect the coordinate [tex](a,b)[/tex] about the [tex]x[/tex]-axis then the coordinates become [tex](a,-b)[/tex].
The coordinate [tex](a,-b)[/tex] lies in the fourth quadrant.
If we reflect the coordinate [tex](a,-b)[/tex] about the [tex]y[/tex]-axis then the coordinates become [tex](-a,-b)[/tex].
The coordinate [tex](-a,-b)[/tex] lies in the third quadrant.
This implies that rotating a figure [tex]180^{\circ}[/tex] counterclockwise is equivalent to transformation of reflecting over [tex]x[/tex]-axis and reflecting over [tex]y[/tex]-axis.
Option (A)
In option (A) it is given that reflection about the line [tex]y=x[/tex] is equivalent to rotating a figure [tex]180^{\circ}[/tex] counterclockwise.
If we reflect the coordinate [tex](a,b)[/tex] about the line [tex]y=x[/tex] then the coordinates become [tex](b,a)[/tex].
This is not same as rotating the figure [tex]180^{\circ}[/tex] counterclockwise.
Therefore, the option (A) is incorrect.
Option (B)
In option (B) it is given that reflection about [tex]y=-x[/tex] is equivalent to rotating a figure [tex]180^{\circ}[/tex] counterclockwise.
If we reflect the coordinate [tex](a,b)[/tex] about the line [tex]y=-x[/tex] then the coordinates become [tex](-b,-a)[/tex].
This is not same as rotating the figure [tex]180^{\circ}[/tex] counterclockwise.
Therefore, the option (B) is incorrect.
Option (C)
In option (C) it is given that reflection about [tex]x[/tex]-axis and [tex]y[/tex]-axis is equivalent to rotating a figure [tex]180^{\circ}[/tex] counterclockwise.
If we reflect the coordinate [tex](a,b)[/tex] about [tex]x[/tex]-axis and [tex]y[/tex]-axis then the coordinates become [tex](-a,-b)[/tex].
This is same as rotating the figure [tex]180^{\circ}[/tex] counterclockwise.
Therefore, the option (C) is correct.
Option (D)
In option (D) it is given that shifting a point [tex]3[/tex] units left and [tex]5[/tex] units down is equivalent to rotating a figure [tex]180^{\circ}[/tex] counterclockwise.
If we shift the point [tex](a,b)[/tex], [tex]3[/tex] units left and [tex]5[/tex] units down the coordinate is [tex](a+3,b-5)[/tex].
This is not same as rotating the figure [tex]180^{\circ}[/tex] counterclockwise.
Therefore, the option (D) is incorrect.
Therefore, the [tex]\fbox{\begin\\\ \bf option (C)\\\end{minispace}}[/tex] is correct.
Learn more
1. Learn more about the rotation of the triangle about the origin https://brainly.com/question/7437053.
2. Learn more about when a triangle is rotated about the origin https://brainly.com/question/2992432.
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Geometry
Keywords: Transformation, rotation, reflection, clockwise, geometry, counterclockwise, -axis, - axis, coordinates, graph, origin, line, degrees, translation, symmetry.
You lose 3 pounds per week on your new diet. What integer represents the change in your weight after 3 weeks
Which of the following shows the numbers ordered from least to greatest?
A)0.004, 0.07, 0.6, 0.32
B)0.004, 0.6 0.07, 0.32
C)0.004, 0.07, 0.32, 0.6
D)0.004, 0.32, 0.07, 0.6
Triangle MRN is created when an equilateral triangle is folded in half. What is the value of y?
A. 2√3 units
B. 4 units
C. 4√3 units
D. 8 units
we know that
If Triangle MRN is created when an equilateral triangle is folded in half
then
[tex]RM=\frac{1}{2}*MN[/tex]
[tex]MN=6+2=8\ units[/tex]
so
[tex]RM=\frac{1}{2}*8=4\ units[/tex]
Applying the Pythagorean Theorem in triangle MRN
[tex]MN^{2}=NR^{2}+RM^{2}[/tex]
we have
[tex]MN=8\ units[/tex]
[tex]RM=x=4\ units[/tex]
[tex]NR=y[/tex]
substitute
[tex]8^{2}=y^{2}+4^{2}[/tex]
solve for y
[tex]y^{2}=8^{2}-4^{2}[/tex]
[tex]y^{2}=48[/tex]
[tex]y=\sqrt{48}=4\sqrt{3}\ units[/tex]
therefore
the answer is the option C
[tex]4\sqrt{3}\ units[/tex]
Answer:
The correct option is C.
Step-by-step explanation:
It is given that triangle MRN is created when an equilateral triangle is folded in half.
It means original equilateral is triangle MNO and NR is a perpendicular bisector. The side length of the triangle is
[tex]MO=NO=MN=MS+SN=2+6=8[/tex]
Since NR is a perpendicular bisector, therefore
[tex]RM=\frac{MO}{2}=\frac{8}{2}=4[/tex]
Using Pythagoras property in triangle MNR,
[tex]MR^2+NR^2=MN^2[/tex]
[tex]4^2+y^2=8^2[/tex]
[tex]y^2=64-16[/tex]
[tex]y=\sqrt{48}[/tex]
[tex]y=4\sqrt{3}[/tex]
Therefore option C is correct.
Half of the product of two consecutive numbers is 105. Which equation can be used to solve for n, the smaller of the two numbers?
Answer with Step-by-step explanation:
We are given that:
Half of the product of two consecutive numbers is 105.
Let smaller number be n
Then, larger number will be n+1
[tex]\dfrac{1}{2}n(n+1)=105[/tex]
Multiplying by 2 on both sides, we get
n(n+1)=210
n²+n=210
n²+n-210=0
On splitting the middle term
n²+15n-14n-210=0
n(n+15)-14(n+15)=0
(n-14)(n+15)=0
either n-14=0 or n+15=0
either n=14 or n= -15
When n=14, n+1=15
when n= -15, n+1= -14
Hence, equation used to solve for n was:
[tex]\dfrac{1}{2}n(n+1)=105[/tex]
The area of a rectangle is 72 cm². The length of the rectangle is 6 cm longer than the width.
What is the width of the rectangle?
2 cm
6 cm
8 cm
10 cm
Answer:
6cm
step-by-step explanation
just dived each number bye 72 to find 12 witch we would get 6cm
help me ............
3 1/2 x 2 = 7
4 2/3 x 2 = 9 1/3
7 + 9 1/3 = 16 1/3 yards
Solve the quadratic equation by taking square roots. Allow for imaginary solutions. Enter your answer in simplest form. Equation: 5x (squared) - 5 = -17
t - 5w = 3j solve for t (literal equations)
The midpoint of a segment is (6,−4) and one endpoint is (13,−2). find the coordinates of the other endpoint.
Find the mode of this data set: 3, 3, 4, 8, 5, 8, 1, 6, 7.
Tonya is twice Kevin's age. In three years, Tonya will be 17. And in another three years, Uncle Rob will be three times Tonya’s age.
How old is Kevin and Uncle Bob
17-3 = 14 ( Tonya's age now)
14/2 = 7 ( Kevin's age)
14*3 = 42 ( Uncle Bob's age)
The distance formula is d=r/t. how long will it take (in hours) to travel 100 miles at a rate of 22mph? Show all work.
divide the distance ( 100 miles) by the speed ( 22 mph) to get the time
100/22 = 4.545454 hours (Round to 4.5 hours ?)
if you need hours and minutes multiply 0.545454 by 60 to get the minutes
4 hours 32.7 ( round to 33) 4 hours and 33 minutes
A limousine service determines that its per-mile cost is $.36 and that it incurs $48 in miscellaneous expenses for each reservation.The service charges $3.56 per mile. What number of miles represents the break-even point?