Which statement is true about figures ABCD and A'B'C'D'?
у
5
4
c
3/
D'
B
2
1 2 3 4 5
1
A
-5 -4 -3 -2 -1 0
AS - 1
-2
D
B
с
-41
-31
Answers
When figures are translated, rotated or reflected, the resulting figures are congruent to the original figure because the transformations are rigid. However, when a figure is dilated, the resulting figure is not congruent to the original figure.
ABCD and A'B'C'D are congruent because A'B'C'D is the result of rotating ABCD 180 degrees about the origin.
I've included the missing graph as an attachment.
Using points A and A' as our references.
We have:
[tex]A = (-1,1)[/tex]
[tex]A' = (1,-1)[/tex]
The rule of rotation 180 degrees about the origin is:
[tex](x,y) \to (-x,-y)[/tex]
So, we have:
[tex](-1,1) \to (-(-1),-1)[/tex]
[tex](-1,1) \to (1,-1)[/tex]
The above rule is applicable to other points in ABCD and A'B'C'D'
Since the rule of transformation is rotation (a rigid transformation), then ABCD and A'B'C'D are congruent.
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Related Questions
HELP ME !! find the value of x
Answers
Answer:
ERROR
Step-by-step explanation:
4(a)+8-a,if a=-2 evaluate each expression
Answers
Answer:
2
Step-by-step explanation:
4(a)+8-a
Combine like terms
4a-a +8
3a+8
Let a = -2
3(-2)+8
-6 +8
2
-(2x +y) - 2 ( -x - y)
....................
Answers
Answer:
First, we apply the Distributive property and then we combine like terms,
To combine like terms, we add or subtract.
[tex]-(2x +y) - 2 ( -x - y)[/tex]
[tex]=-2x-y+2x+2y[/tex]
[tex]=(-2x+2x)+(-y+2y)[/tex]
[tex]=0+y[/tex]
[tex]=y[/tex]
OAmalOHopeO
Answer:
y is the simplest result here.
Step-by-step explanation:
Perform the indicated multiplication as a first step towards simplifying this expression:
-2x - y + 2x + 2y
-2x and 2x cancel each other out, leaving 2y - y, or just y
when is it easy to show if a set is closed or not closed?
Answers
Answer:i think its if the dots are open they arent closed but if they are filled in its closed same with () and [] if its (x,y) then its not able to be used but if its [x,y] then it is able to be used
Step-by-step explanation:
Does anyone know the equation to this trigonometric function? Step by step?
Answers
A general cosine function (we could also use a sine function) is written as:
y = A*cos(k*x + p) + M
We will find that the function of the graph is:
f(x) = 2*cos(2*x + 2.09) - 2
Let's return to the general function:
y = A*cos(k*x + p) + M
A is the amplitude, it defines the distance between the value of a maximum and the value of the minimum, such that A is exactly half of that difference.
Here we can see that the maximum is 0, and the minimum is -4
The differene is: 0 - (-4) = 4
Then:
A = 4/2 = 2
f(x) = 2*cos(k*x + p) + M.
M is the midline, this is, the horizontal line that cuts the graph in two halves. Here we can see that the midline is x = -2, then:
M = -2
f(x) = 2*cos(k*x + p) - 2
p is the phase shift.
In the graph, we can see that f(0) = -3, so we have:
f(0) = 2*cos(0 + p) - 2 = -3
cos(p) = -1/2
p = Acos(-1/2) = 2.09
Then we have:
f(x) = 2*cos(k*x + 2.09) - 2
Finally, k is related to the frequency of the function.
We can see that the function does a complete cycle at x = pi
This means that:
f(x) = f(x + pi)
Knowing that the period of a cosine function is 2*pi, then:
k*(x + pi) = k*x + 2*pi
k = 2
Then the equation of the graph is:
f(x) = 2*cos(2*x + 2.09) - 2
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Answer(s):
[tex]\displaystyle y = 2sin\:(2x + 1\frac{1}{4}\pi) - 2 \\ y = 2cos\:(2x - 1\frac{1}{4}\pi) - 2[/tex]
Step-by-step explanation:
[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow -2 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{5}{8}\pi} \hookrightarrow \frac{-1\frac{1}{4}\pi}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 2[/tex]
OR
[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow -2 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{5}{8}\pi} \hookrightarrow \frac{1\frac{1}{4}\pi}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 2[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then by all means, go for it, but be careful and follow what is explained here. Now, as you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 2sin\:(2x - 1\frac{1}{4}\pi) - 2,[/tex] in which you need to replase “cosine” with “sine”, then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex] to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{\pi}{4}\:unit,[/tex] which means the C-term will be negative. Now, BEFORE we go any further, we must remember that this particular cosine graph [thank goodness it is a cosine graph we are working with] ALREADY has a horisontal shift and does not have a single crest oscıllαtıng about any endpoint on the y-axis. So, in this case we need to figure out how far the FIRST oscıllαtıng crest is from the origin, and that obviously would be [tex]\displaystyle \frac{5}{8}\pi\:units.[/tex] Though, sinse we want the sine equation of this graph, it must be “negative”; so, by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{5}{8}\pi} = \frac{-1\frac{1}{4}\pi}{2},[/tex] in which the value of C is [tex]\displaystyle -1\frac{1}{4}\pi.[/tex] So, the sine equation of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 2sin\:(2x + 1\frac{1}{4}\pi) - 2.[/tex] Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [\frac{7}{8}\pi, -2],[/tex] from there to [tex]\displaystyle [-\frac{\pi}{8}, -2],[/tex] they are obviously [tex]\displaystyle \pi\:units[/tex] apart, telling you that the period of the graph is [tex]\displaystyle \pi.[/tex] Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = -2,[/tex] in which each crest is extended two units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
**As you can see, this is one of those moments where you will really need to be careful because if you notised, both equations have OPPOCITE horisontal shifts and C-values. Now, the ONLY TIME this occurs is when all crests in a SINUSOIDAL graph cycle half-way in between endpoints. Your best bet is to jot this down for when you see graphs like these in the future.
I am delighted to assist you at any time.
Write the fraction or mixed number as a decimal.
Answers
1.725
Hope this helps *smiles*
HELP ME SOLVE THIS PLEASE
Answers
Find the center and radius of the circle and sketch its graph
X^2+y^2=9
Answers
Answer:
Centre (0,0)
Radius √9 = 3
I've attached a graph if the circle with it
Answered by GAUTHMATH
1) Jack and Jill have a Jill have a combined age of 25. Jack is 3 years older than Jill. How old are they?
2) A rectangle has an area of x^2+7x+12. Find the length and the width of the rectangle.
Answers
Answer:
1.) Jill = 11 yrs & Jack = 14 yrs. | 2.) (x + 4)(x + 3)
Step-by-step explanation:
1.)
Let j = Jill's age.
[tex]j+(j+3)=25\\2j+3=25\\2j=22\\j=11\\\\\\(11)+3=14[/tex]
Therefore, Jill is 11 and Jack is 14.
2.)
[tex]x^2+7x+12\\(x+4)(x+3)[/tex]
The graph of h(x) = (x - 3)2 is a translation of the
graph of f(x) ….. blank
by
…. Blank units.
Answers
Answer:
right by 3 I think
Step-by-step explanation:
Answer: Right by 3 Units
Step-by-step explanation:
Right on edge 2021
Solve for 2. Round to the nearest tenth, if necessary.
135°
X
78
BO
Submit
answer
Answer: 2 =
Submit Answer
PLS HELP I really need to get this done
Answers
Answer:
x = 63.9
Step-by-step explanation:
Since this is a right triangle, we can us trig functions
cos theta = adj/ hypotenuse
cos 35 = x/78
78 cos 35 =x
x=63.89385
Rounding to the nearest tenth
x = 63.9
what is the perimeter
A) 20.3
B)18.3
C)24.3
D)22.3
Answers
Answer:
b
Step-by-step explanation:
cuz u add them all
*WILL MARK BRAINLIEST* The triangle below is isosceles. Find the length of side xx in simplest radical form with a rational denominator.
Answers
Answer: 5sqrt2, 10sqrt2/2
Step-by-step explanation:
The isosceles triangle, or 45-45-90 rule states that the hypotenuse is x × square root of 2.
Divide the hypotenuse, 10, by sqrt 2 to get 5sqrt2
However , if you're looking to keep it in fraction form, you will need to rationalize the denominator. Multiply the numerator and denominator to get the fraction, 10sqrt2/2
HELP PLZ
Part A Translate the sentence into an expression.
2 less than 9 times h
Part B Create a scenario (word problem) using the expression above.
Part C Evaluate the expression if h is 1/3
Answers
Step-by-step explanation:
A
9×h - 2
B
the baseline of the triangle is 2 units less than 9 times the height long.
C
h = 1/3
9×1/3 - 2 = 3 - 2 = 1
Rewrite in simplest radical form the problem in the image below. Show and explain each step. Thank you for your time and help.
Answers
Answer:
Hello,
Step-by-step explanation:
[tex]\dfrac{x^{\frac{5}{6}} }{x^{\frac{1}{6}} } \\\\=x^{\frac{5}{6} -\frac{1}{6} }\\\\=x^{\frac{4}{6} }\\\\=x^{\frac{2}{3} }\\\\=\sqrt[3]{x^2}[/tex]
Hi there!
Look the picture for your answer.
Hope it helps!
If the mean of a normal distribution is 210, what is the median of the
distribution?
210
B. 315
C. 105
D. 420
Answers
Answer:
210
Step-by-step explanation:
In a normal distribtuion mean=mode=median
so 210=median
HELP NOW - Please help me
100 POINTS
Answers
Answer:
SAS
43ft
Step-by-step explanation:
We know that two sides are equal
PQ = ST and QR = TU and the angle between them is equal Q = T
We can use the SAS (side angle side)
Since the triangles are congruent
PR = SU
6y+5 = 8y
Subtract 6y from each side
6y+5-6y = 8y-6y
5 = 2y
Divide by 2
5/2 = y
2.5 = y
PR = ST = 8y = 8(2.5) =20
The perimeter is 9+14+20 = 43
Answer:
B. =35ft
Step-by-step explanation:
The perimeter of a right angled triangle is a+b+c
which is 9+4+6y+5 =90
collect like terms
9+4+5+6y=90
18 + 6y = 90
6y = 90 - 18
6y= 72
divide both sides by 6
6y/6 = 72/6
y = 12
so therefore, the perimeter of ∆PQR is
9 + 12 + 14
= 35ft
What is the length of AC?
Answers
Because all the angles are congruent (the same), this is an equilateral triangle. All equilateral triangles have congruent angles and congruent sides, so all sides has to be 14.
Somebody can help me please
Answers
Twice the difference between a number and 4 is twenty. Find the number.
А. 8
B. 9
C. 12
D. 14
Please help!!!
Answers
Answer:
D 14
Step-by-step explanation:
Let x be the number
2(x-4) = 20
Divide each side by 2
2/2(x-4) = 20/2
x-4 = 10
Add 4 to each side
x-4+4 = 10+4
x = 14
Answer:
The number is 14
Step-by-step explanation:
Let's call this unknown number of x:
2×(x – 4) = 20
2x – 8 = 20
2x = 20 + 8
2x = 28
x = 28/2
x = 14
Which expression is equivalent to −24x+72?
−24(x−72)negative 24 times open paren x minus 72 close paren
−24(x−3)negative 24 times open paren x minus 3 close paren
24(x+3)24 times open paren x plus 3 close paren
24(x+72)
Answers
Answer:-24(x-3) = -24x (-24)(-3)
Step-by-step explanation:
Answer:
eat my hand where the pic
Step-by-step explanation:
yeah
If sin A= 0.8, find the positive value of cos A
Answers
Answer:
cosA = 0.6
Step-by-step explanation:
Using the Pythagorean identity
sin²A + cos²A = 1 ( subtract sin²A from both sides )
cos²A = 1 - sin²A ( take the square root of both sides )
cosA = ± [tex]\sqrt{1-sin^2A[/tex]
Since only the positive value is required , then
cosA = [tex]\sqrt{1-(0.8)^2}[/tex]
= [tex]\sqrt{1-0.64}[/tex]
= [tex]\sqrt{0.36}[/tex]
= 0.6
Answer:
Answer:
Answer:x = 25°
Answer:x = 25°Step-by-step explanation:
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2}
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 2
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21 ( BD - FE ) = ∠ FGE, that is
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21 ( BD - FE ) = ∠ FGE, that is\frac{1}{2}
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21 ( BD - FE ) = ∠ FGE, that is\frac{1}{2} 2
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21 ( BD - FE ) = ∠ FGE, that is\frac{1}{2} 21
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21 ( BD - FE ) = ∠ FGE, that is\frac{1}{2} 21
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21 ( BD - FE ) = ∠ FGE, that is\frac{1}{2} 21 (135 - x) = 55 ( multiply both sides by 2 to clear the fraction )
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21 ( BD - FE ) = ∠ FGE, that is\frac{1}{2} 21 (135 - x) = 55 ( multiply both sides by 2 to clear the fraction )135 - x = 110 ( subtract 135 from both sides )
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21 ( BD - FE ) = ∠ FGE, that is\frac{1}{2} 21 (135 - x) = 55 ( multiply both sides by 2 to clear the fraction )135 - x = 110 ( subtract 135 from both sides )- x = - 25 ( multiply both sides by - 1 )
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21 ( BD - FE ) = ∠ FGE, that is\frac{1}{2} 21 (135 - x) = 55 ( multiply both sides by 2 to clear the fraction )135 - x = 110 ( subtract 135 from both sides )- x = - 25 ( multiply both sides by - 1 )x = 25°
8 cm 10 cm 15 cm surface area of a rectangle
Answers
Answer:
surface area of a square = 2 ( lb + bh + hl )
given that,
length = 8cm
breadth = 10cm
height = 15 cm
surface area = 2 ( 8* 10 + 10*15 + 15*8 )
= 2 ( 80 + 150 + 120 )
= 2 * 350
= 700 [tex]cm^{2}[/tex]
hope this answer helps you!!
Need help asapppppppppp
Answers
x²+x=0
x³-25x=0
x²=4x
4x²-4x=1
Answers
Answer:
x²+ x = 0
x ( x +1 ) = 0
x = -1
x³-25x=0
x ( x² - 25 ) = 0
x² = 25
x = 5
x²=4x
x² - 4x = 0
x ( x- 4 ) = 0
x = 4
4x²-4x=1
4x²-4x - 1 = 0
4 x² - 2x - 2x - 1 = 0
2x ( 2x - 1 ) - 1 ( 2x- 1 ) = 0
2x- 1 ) ² = 0
2x = 1
x = 1/ 2
mark me as brainliest
Answer it please ↓↓
Fubuki drives 18.4 miles in 16 minutes. He passes a sign which gives the speed limit as 60 mph. By how much, in mph, did Fubuki's average speed exceed the speed limit?
Answers
Step-by-step explanation:
hope this helps to u......
Evaluate the expression when a=-7 and x=6 .
X-2a
Answers
Answer:
=X-2a
= 6- 2× (-7)
= 6 + 14
= 20
✌✌✌✌
The buyer for a chain of stores purchased kitchen tables in bulk, paying $32 each. The stores will sell each kitchen table for $58. What percentage is the mark-up?
Answers
Answer:
The markup is 81.25%
Step-by-step explanation:
Take the new price and subtract the original price
58 - 32
26
Divide by the original price
26/32
.8125
Change to percent form
81.25%
The markup is 81.25%
A fencing company charges $22per foot to install a wood fence around a rectangular pool area that is 20 feet wide and 38 feet long? pls help me
Answers
I know that the fencing company charges $22 per foot. I can multiply 116 x 22 to give me $2552. The answer is $2552.
A car travels 52/5 kilometers in 23/4 minutes. What is the unit rate in kilometers per minute?
Answers
The unit rate of the car that travels 5 2/5 km in 2 3/4 mins is: 1.96 km/min.
What is Unit Rate?Unit rate can be defined as the ratio of one quantity in comparison to another.
Distance travelled by a car = 5 2/5 km = 5.4 km
Time travelled = 2 3/4 mins = 2.75 mins
Unit rate in km/min = 5.4/2.75
Unit rate in km/min = 1.96 km/min.
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