Answers
Answer:
9:30 A.M
Hope this helps! Have a nice day :)
Answer:
Total time they used = 2 hours 45min + 1 hour + 1 hour
= 4 hours 45min
To find the time they started watching
Subtract it from the time they came from playing soccer
that's 2:15pm
After subtracting we get
9:30 am
Hope this helps
Related Questions
how many millimeters are in a meter
Answers
Answer:
There are 1000 millimeters in a meter.
Step-by-step explanation:
I really hope this helps in any way.
Answer:
1,000
Step-by-step explanation:
The word millimeter has the prefix of 'milli-'.
'Milli-' means a thousand.
Applying the prefix meaning to the word, a millimeter would be a thousandth of a meter.
There are 1,000 millimeters in a meter.
Brainilest Appreciated.
Write equation Derek will get a bonus if he sells at least 50 sets of knives in a month use k to represent the number of knives he can sell to receive his bonus
Answers
Answer: k ≥ 50
Step-by-step explanation:
From the question, we are informed that Derek will get a bonus if he sells at least 50 sets of knives in a month. We are further told to us k to represent the number of knives he can sell to receive his bonus.
Since we are told that Derek will get a bonus if he sells at least 50 sets of knives in a month, this means that k will be greater than or equal to 50. Therefore,
k ≥ 50
which of the following angles is coterminal with 5pi/3? pi/3, 2pi/3, 4pi/3, 5pi/3
Answers
Answer:
5pi/3
Step-by-step explanation:
For two angles to be co-terminal, one must differ from the other by a multiple of 2pi.
The angle of consideration is 5pi/3
Let us consider the options one by one and see if they differ from the angle of consideration by a multiple of 2pi.
5pi/3 - pi/3 = 4pi/3
5pi/3 - 2pi/3 = 3pi/3 = pi
5pi/3 - 4pi/3 = pi/3
5pi/3 - 5pi/3 = 0 = 0(2pi)
5pi/3 is co-terminal with itself
How many distinct triangles can be formed for which mzA
= 75°, a = 2, and b = 3?
O No triangles can be formed.
One triangle can be formed where angle B is about 15°.
One triangle can be formed where angle B is about 40°.
Two triangles can be formed where angle B is 40° or
140°
Answers
We are given
m∠A = 75 deg
a = 2
b = 3
Apply the Law of Sines.
sin(B)/b = sin(A)/a
sin(B)/3 = sin(75)/2
sin(B) = (3*sin(75))/2 = 1.45
The value of the sin function cannot exceed 1.
This means that the triangle cannot exist.
Answer: No distinct triangles
Answer: A no triangles can be formed
Step-by-step explanation:
Find w please help me
Answers
Answer:
w = 77°
Step-by-step explanation:
From the picture attached,
WXYZ is a quadrilateral having 4 interior angles,
m∠y = 90°
Therefore, (2x - 10) = 90°
2x = 90 + 10
2x = 100
x = 50
Now, m∠z = (x + 15)° = 65°
m∠x = (3x - 22)° = 150 - 22
= 128°
Sum of interior angles of a polygon = (n - 2)×180°
where n = Number of sides of the polygon
If n = 4,
m∠u + m∠x + m∠y + m∠z = (4 - 2) × 180°
w + 128 + 90 + 65 = 360
w = 360 - 283
w = 77°
Therefore, measure of w = 77°
Need help quick plz I need this to be right thank u and plz
Answers
Answer:
1067 cm³Step-by-step explanation:
[tex]V=10^2\cdot7+\frac13\cdot10^2\cdot(18-7)=700+\frac13\cdot1100=700+366,(6)=1066,(6)\\\\V\approx1067\,cm^2[/tex]
Please answer it in two minutes
Answers
Answer:
2,700 degrees.
Step-by-step explanation:
17 gon is a heptadecagon.
The formula for the sum of interior angles is [tex](n-2)*180[/tex] degrees.
[tex](17-2)*180=\\15*180=\\2700[/tex]
Juan hiked to the top of a 3,000-foot mountain and back down without taking a break. Which graph best represents Juan's distance from the top of the mountain during the entire hike?
Answers
Answer:
Top left graph.
Step-by-step explanation:
If Juan didn't take a break, there is no plateau/flat line. And if he started hiking up and then down, then the graph should be an upside-down V shape.
Answer:
Graph A is the most acuurate
please solve it 90 POINTS please help- PLEASE HELP its Identify the following for the quadratic relations please slove it all please if you can save the picture and do it on the page -
i Will give brainliest
Answers
Answer:
[tex]\boxed{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
2)
a) elimination method
b) substitution method
c) substitution method
For the first part we can elimate the y variable by subtracting the equations. We can then find the value of x.
For the second part we can substitute y as 2x+5 in the second equation and solve for x.
For the third part we can substitute y as 4x+3 in the first equation and solve for x.
3)
[tex]\boxed{\mathrm{view \: attachment}}[/tex]
Consider the graph with four lines below. On a coordinate plane, line a has a positive slope and goes through points (negative 1, 0) and (1, 2), line b has a negative slope and goes through (negative 2, 2) and (negative 1, negative 1), line c has a negative slope and goes through (0, 3) and (1, 0), and line d is horizontal at y = 1. By inspection, which system would have no solution? line a and line b line a and line c line b and line c line b and line d
Answers
Answer:
C) line b and line c
Step-by-step explanation:
On edge
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The system of equations that do not have any solution is line b and line c. Hence, the correct option is C.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
The equation of line a passing through (-1,0) and (1,2) are,
m = (0-2)/(-1-1) = -2/-2 = 1
y= x + c
0 = -1 + c
c = 1
Equation of line 1, y=x+1
The equation of line b passing through (-2,2) and (-1,-1) are,
m = (2+1)/(-2+1) = 3/-1 = -3
y= -3x + c
-1 = -3(-1) + c
c = -4
Equation of line 1, y=-3x-4
The equation of line c passing through (0,3) and (1,0) are,
m = (3-0)/(0-1) = 3/-1 = -3
y= -3x + c
3 = -3(0) + c
c = 3
Equation of line 1, y=-3x+3
Also, the equation of line d is y=1
The solution of two-equation is the point at which the two equations are not intersecting. Therefore, the system of equations that do not have any solution is line b and line c.
Hence, the correct option is C.
Learn more about Equation of Line:
https://brainly.com/question/21511618
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What is the slope of a line perpendicular to the line whose equation is
x - 5y = -10. Fully reduce your answer
Answers
Answer:
The slope or incline is -5
Step-by-step explanation:
rewrite to get the form
y = ...
x - 5y = -10
- 5y = -10 -x
divide left and right if the = sign by -5 gives:
(-5/-5)y = (-1/-5)x + (-10/-5)
y = 1/5x +2
So the incline is 1/5
a perpendicular line has an incline of -1 *5/1 = -5
The slope or incline is -5
The table below shows the average attendance of school events by the day of the week on which they are held. Average Attendance at School Events Thursday Friday School Play 300 x Band Concert 184 250 Which values of x will indicate an association between the two variables in the two-way table? Check all that apply. 250 304 407 422 714
Answers
Answer:
A , B, E 1,2,5
Your the welcome my audience
Step-by-step explanation:
Answer:
a b e
Step-by-step explanation:
just believe me you $exy hunky man
convert the decimal to a simplified fraction 0.8=
Answers
Answer:
4/5
Step-by-step explanation:
You know 0.8 x 10 = 8, so 8/10 is the fraction.
Now, simplify 8/10.
8/10 = 4/5
Answer:
4/5
Step-by-step explanation:
Step 1: Convert decimal to fraction
0.8= 8/10
Step 2:Simplify
8/10=4/5
There is a bag filled with 5 blue, 6 red and 2 green marbles. A marble is taken at random from the bag, the colour is noted and then it is not replaced. Another marble is taken at random. What is the probability of getting 2 blues?
Answers
Answer:
Step-by-step explanation:
Total marbles = 5 + 6 + 2 = 13
P( getting blue ball from first draw) = 5/13
The marble is not replaced. So, Now total marbles will be 12 & number blue marbles will be 4
P( getting blue ball from second draw) = 4/12 = 1/3
P(getting two blues) = [tex]\frac{5}{13}*\frac{1}{3}\\[/tex]
= 5/39
EXCELLENT VOTE!! (only if u give the CORRECT answer)
Answers
Answer:
Option C
Step-by-step explanation:
Answer:
B.
You need to subtract 1 term because you don't include the starting 5
4^10 - 1 = 4^9
You multiply 5 by 4 each time for 9 times so it is 5 x 4^9
Hope this helps
Step-by-step explanation:
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match the circle equations in general form with their corresponding equations in standard form. x2 + y2 − 4x + 12y − 20 = 0
(x − 6)2 + (y − 4)2 = 56
x2 + y2 + 6x − 8y − 10 = 0
(x − 2)2 + (y + 6)2 = 60
3x2 + 3y2 + 12x + 18y − 15 = 0
(x + 2)2 + (y + 3)2 = 18
5x2 + 5y2 − 10x + 20y − 30 = 0
(x + 1)2 + (y − 6)2 = 46
2x2 + 2y2 − 24x − 16y − 8 = 0
x2 + y2 + 2x − 12y − 9 = 0
Answers
Answer:
1) For [tex]x^2 + y^2 - 4x + 12y - 20 = 0[/tex], the standard form is [tex](x-2)^2 + (y+6)^2 = 60\\[/tex]
2) For [tex]x^2 + y^2 + 6x - 8y - 10 = 0[/tex], the standard form is [tex](x + 3)^2 + (y - 4)^2 = 35\\[/tex]
3) For [tex]3x^2 + 3y^2 + 12x + 18y - 15 = 0[/tex], the standard form is [tex](x + 2)^2 + (y+ 3)^2 = 18\\[/tex]
4) For [tex]5x^2 + 5y^2 - 10x + 20y - 30 = 0[/tex], the standard form is [tex](x - 1)^2 + (y+ 2)^2 = 11\\[/tex]
5) For [tex]2x^2 + 2y^2 - 24x - 16y - 8 = 0[/tex], the standard form is [tex](x - 6)^2 + (y+ 4)^2 = 56\\[/tex]
6) For[tex]x^2 + y^2 + 2x - 12y - 9 = 0[/tex], the standard form is [tex](x+1)^2 + (y-6)^2 = 46\\\\[/tex]
Step-by-step explanation:
This can be done using the completing the square method.
The standard equation of a circle is given by [tex](x - a)^2 + (y-b)^2 = r^2[/tex]
1) For [tex]x^2 + y^2 - 4x + 12y - 20 = 0[/tex]
[tex]x^2 - 4x + y^2 + 12y = 20\\x^2 - 4x + 2^2 + y^2 + 12y + 6^2 = 20 + 4 + 36\\(x-2)^2 + (y+6)^2 = 60\\[/tex]
Therefore, for [tex]x^2 + y^2 - 4x + 12y - 20 = 0[/tex], the standard form is [tex](x-2)^2 + (y+6)^2 = 60\\[/tex]
2) For [tex]x^2 + y^2 + 6x - 8y - 10 = 0[/tex]
[tex]x^2 + 6x + y^2 - 8y = 10\\x^2 + 6x + 3^2 + y^2 - 8y + 4^2 = 10 + 9 + 16\\(x + 3)^2 + (y- 4)^2 = 35\\[/tex]
Therefore, for [tex]x^2 + y^2 + 6x - 8y - 10 = 0[/tex], the standard form is [tex](x + 3)^2 + (y - 4)^2 = 35\\[/tex]
3) For [tex]3x^2 + 3y^2 + 12x + 18y - 15 = 0[/tex]
Divide through by 3
[tex]x^2 + y^2 + 4x + 6y = 5[/tex]
[tex]x^2 + y^2 + 4x + 6y = 5\\x^2 + 4x + 2^2 + y^2 + 6y + 3^2 = 5 + 4 + 9\\(x + 2)^2 + (y+ 3)^2 = 18\\[/tex]
Therefore, for [tex]3x^2 + 3y^2 + 12x + 18y - 15 = 0[/tex], the standard form is [tex](x + 2)^2 + (y+ 3)^2 = 18\\[/tex]
4) For [tex]5x^2 + 5y^2 - 10x + 20y - 30 = 0[/tex]
Divide through by 5
[tex]x^2 + y^2 - 2x + 4y = 6[/tex]
[tex]x^2 + y^2 -2x + 4y = 6\\x^2 - 2x + 1^2 + y^2 + 4y + 2^2 = 6 + 1 + 4\\(x - 1)^2 + (y+ 2)^2 = 11\\[/tex]
Therefore, for [tex]5x^2 + 5y^2 - 10x + 20y - 30 = 0[/tex], the standard form is [tex](x - 1)^2 + (y+ 2)^2 = 11\\[/tex]
5) For [tex]2x^2 + 2y^2 - 24x - 16y - 8 = 0[/tex]
Divide through by 2
[tex]x^2 + y^2 - 12x - 8y = 4[/tex]
[tex]x^2 + y^2 - 12x - 8y = 4\\x^2 - 12x + 6^2 + y^2 - 8y + 4^2 = 4 + 36 + 16\\(x - 6)^2 + (y+ 4)^2 = 56\\[/tex]
Therefore, for [tex]2x^2 + 2y^2 - 24x - 16y - 8 = 0[/tex], the standard form is [tex](x - 6)^2 + (y+ 4)^2 = 56\\[/tex]
6) For [tex]x^2 + y^2 + 2x - 12y - 9 = 0[/tex]
[tex]x^2 + 2x + y^2 - 12y = 9\\x^2 + 2x + 1^2 + y^2 - 12y + 6^2 = 9 + 1 + 36\\(x+1)^2 + (y-6)^2 = 46\\[/tex]
Therefore, for[tex]x^2 + y^2 + 2x - 12y - 9 = 0[/tex], the standard form is [tex](x+1)^2 + (y-6)^2 = 46\\\\[/tex]
For Plato / Edmentum
Just to the test and got it right ✅
Find the total surface area of this cylinder. Give your answer to one decimal place PLEASE HELP THANK YOUUUU
Answers
Answer:
Step-by-step explanation:
surface area of cylinder=2 πr²+2πrh
=2πr(r+h)
=2π×12(12+18)
=24π×30
=720π
≈2261.9 cm²
Which of the following is the correct factored form of the given equation? 6x^2 -13x - 8 = 0
Answers
Answer:
the 2nd
Step-by-step explanation:
PLEASE HELP!!!
Helen has 48 cubic inches of clay to make a solid square right pyramid with a base edge measuring 6 inches. A solid right pyramid with a square base has a base edge measuring 6 inches. Which is the slant height of the pyramid if Helen uses all the clay? 3 inches 4 inches 5 inches 6 inches
Answers
Answer:
Answer is 5 inches on edg
Step-by-step explanation:
Answer:
The correct answer would be 5 inches.
Step-by-step explanation:
3. Solve 6k + 9 > k – 1.
use photo for options
Answers
Answer:
k > - 2
Step-by-step explanation:
Given
6k + 9 > k - 1 ( subtract k from both sides )
5k + 9 > - 1 ( subtract 9 from both sides )
5k > - 10 ( divide both sides by 5 )
k > - 2
Answer:
k> -2
Step-by-step explanation:
6k + 9 > k – 16k - k > - 1 - 95k > -10k > -10/5k> -2Line A has an x-intercept of -4 and a y-intercept of 8. What is its slope?
Answers
Answer:
Step-by-step explanation:
We can use the intercept form of the equation of a line, then solve for y.
Intercept form
x/(x-intercept) +y/(y-intercept) = 1
x/-4 +y/8 = 1
__
Solving for y, we have ...
-2x +y = 8 . . . . multiply by 8
y = 2x +8 . . . . add 2x
The coefficient of x is 2, so the slope is 2.
__
The graph shows you the rise is 8 for a run of 4, so ...
slope = rise/run = 8/4
slope = 2
I NEED HELP PLEASE, THANKS! :)
A gear of radius 6.1 cm turns at 11 revolutions per second. What is the linear velocity of the gear in meters per second?
v = linear velocity, d = distance traveled, and t = time.
Answers
Answer:
Velocity = 4.22 m/s
Step-by-step explanation:
Time = 1 second
Radius = 6.1 cm
Diameter = 12.2 cm = 0.122 m
Displacement = Revolution × π × Diameter
Displacement = 11 × 3.14 × 0.122
Displacement = 4.22 m
Now, Linear velocity:
Velocity = displacement / Time
Velocity = 4.22 / 1
Velocity = 4.22 m/s
Answer: 4.216 meters per second
Step-by-step explanation:
Notes: Use the following conversions:
1 revolution = 2π
100 cm = 1 meter
and the following formula: v = ωr/t where v is in meters per second
[tex]\dfrac{11\ revolutions\times 6.1\ cm}{1\ second}\times \dfrac{2\pi}{1\ revolution}\times \dfrac{1\ meter}{100\ cm}=\dfrac{1.342\pi\ meters}{second}\\\\\\=\large\boxed{\dfrac{4.216\ meters}{second}}}[/tex]
Determine if each statement is always, sometimes, or never true.
1. Parallel lines are
coplanar.
2. Perpendicular lines are
coplanar.
3. Distance around an unmarked circle can
be measured.
Answers
Answer:
Determine if each statement is always, sometimes, or never true.
1. Parallel lines are
coplanar: Always true
2. Perpendicular lines are
coplanar: Always true
3. Distance around an unmarked circle can be measured: Never true
Step-by-step explanation:
When we are say that lines are coplanar, this means that those lines happen to be or lie in the same plane , a flat surface or a 3- dimensional surface.
Co planar lines may or may not intersect with one another.
Parallel lines and Perpendicular lines are coplanar lines because they are found to be in the same plane. One of their differences is Parallel lines do not intersect with one another while Perpendicular lines intersect with one another.
Hence the statements:
Parallel lines and Perpendicular lines are coplanar is ALWAYS TRUE
Distance around an unmarked circle can be measured. This statement is never true
This is because a circle has to be marked in other to be able to measure it's distance properly. A marked circle will have its diameter and the diameter of a circle is also known as the distance around a circle.
Write a two-column proof. Given: <2 is congruent to <5; Segment AB is congruent to Segment DE Prove: Segment BC is congruent to Segment EC
Answers
Answer:
proof
Step-by-step explanation:
Statements
Reasons
<2 is congruent to <5; Segment AB is congruent to Segment DE
Given
<3≅<4
Vertical angle theorem
ΔCDB≅ΔCAE
AAS
Segment BC is congruent to Segment EC
CPCTC
The segment BC is congruent to segment EC and this can be proven by using the properties of a triangle and the given data.
Given :
Angle 2 is congruent to angle 5.Segment AB is congruent to Segment DE.The following steps can be used in order to prove that segment BC is congruent to segment EC:
Step 1 - Using the triangle properties it can be proven that segment BC is congruent to segment EC.
Step 2 - According to the vertical angle theorem, angle 3 is congruent to angle 4.
Step 3 - Now, according to the AAS (Angle Angle Side) postulate, triangle CDB is similar to triangle CAE.
Step 4 - So, according to the CPCTC, segment BC is congruent to segment EC.
For more information, refer to the link given below:
https://brainly.com/question/25813512
One number is 10 times as large as another, and their difference is 81. Find the numbers. If x represents the smaller number, then the larger number is x + 10 10x
Answers
Answer:
value of x=9
so value of large number is 90 and smaller number is 9
A large stand of fir trees occupies 24 hectares. The trees have an average density of 1 tree per 20m squared. A forester estimates that each tree will yield 300 board-feet. Estimate the yield of the stand if one-tenth of the trees are cut.
Answers
Answer:
The yield of the stand if one-tenth of the trees are cut is 360000 board-feet.
Step-by-step explanation:
First, let is find the total amount of fir trees that occupies the area of 24 hectares. (1 hectare = 10000 square meters)
[tex]n = \sigma \cdot A[/tex]
Where:
[tex]\sigma[/tex] - Surface density, measured in trees per square meter.
[tex]A[/tex] - Total area, measured in square meters.
Given that [tex]\sigma = \frac{1}{20}\,\frac{tree}{m^{2}}[/tex] and [tex]A = 24\,h[/tex], the total amount of fir trees is:
[tex]n = \left(\frac{1}{20}\,\frac{trees}{m^{2}} \right)\cdot (24\,h)\cdot \left(10000\,\frac{m^{2}}{h} \right)[/tex]
[tex]n = 12000\,trees[/tex]
It is known that one-tenth of the tress are cut, whose amount is:
[tex]n_{c} = 0.1 \cdot n[/tex]
[tex]n_{c} = 0.1 \cdot (12000\,trees)[/tex]
[tex]n_{c} = 1200\,trees[/tex]
If each tree will yield 300 board-feet, then the yield related to the trees that are cut is:
[tex]y = S\cdot n_{c}[/tex]
Where:
[tex]S[/tex] - Yield of the tress, measured in board-feet per tree.
[tex]n_{c}[/tex] - Amount of trees that will be cut, measured in trees.
If [tex]n_{c} = 1200\,trees[/tex] and [tex]S = 300\,\frac{b-ft}{tree}[/tex], then:
[tex]y = \left(300\,\frac{b-ft}{tree} \right)\cdot (1200\,trees)[/tex]
[tex]y = 360000\,b-ft[/tex]
The yield of the stand if one-tenth of the trees are cut is 360000 board-feet.
PLEASE HELP Which of the sets of ordered pairs represents a function? A = {(2, −2), (5, −5), (−2, 2), (−5, 5)} B = {(4, 2), (4, −2), (9, 3), (9, −3)} a. Only A b. Only B c. Both A and B Incorrect d. Neither A nor B
Answers
Answer: A. Only A
Step-by-step explanation:
A has exactly one output for every input but B has different outputs for an input.
Explication: If there is no repeated numbers in the x axis and the y axis it is a function you can also figure this out by doing the line test if you draw a horizontal line across your function and there is no repeated numbers on the x axis or y axis it is a function
3x = -2 (MOD. 4) pls
Answers
Answer:
x=-2/3
Step-by-step explanation:
1st you have to get rid of the number next to the x value
so you divide
Answer:
x = -2/3
Step-by-step explanation:
3x = -2
Divide both sides by 3.
3x/3 = -2/3
x = -2/3
A winter recreational rental company is fencing in a new storage area. They have two options. They can set it up at the back corner of the property and fence it in on four sides. Or, they can attach it to the back of their building and fence it in on three sides. The rental company has decided that the storage area needs to be 100 m2 if it is in the back corner or 98 m2 if it is attached to the back of the building. Determine the optimal design for each situation.
Answers
Answer:
Rectangular area attached to the back of the building
two sides of legth 7 m and one side of 14 m
Step-by-step explanation:
We need to compare quantity of fencing material to be used in both cases
1.Option
A = 100 m² dimensions of storage area "x" and "y"
x*y = 100 y = 100/x
The perimeter of the storage area is
p = 2*x + 2*y ⇒ p = 2*x + 2*100/x
p(x) = 2*x + 200/x
Taking drivatives on both sides of the equation
p´(x) = 2 - 200/x²
p´(x) = 0 ⇒ 2 - 200/x² = 0
2*x² - 200 = 0 x² = 100
x = 10 m
and y = 100/10
y = 10 m
Required fencing material in first option
2*10 + 2*10 = 40 m
2.-Option
Following the same procedure
A = 98 m² y = A/x y = 98/x
p = 2*x + y p(x) = 2*x + 98/x
p´(x) = 2 - 98/x² p ´(x) = 0
2 - 98/x² = 0
2*x² = 98 x² = 49
x = 7 m and y = 98/ 7 y = 14 m
Total quantity of fencing material
p = 2* 7 + 14 p = 28
Therefore option 2 is more convinient from economic point of view
Optimal design rectangular storage area with two sides of 7 m and one side of 14 m
Which triangle results from a reflection across the line x = 1?
Answers
Answer:
Correct answer is option D.
Step-by-step explanation:
Given that [tex]\triangle ABC[/tex] in the image 1 attached.
If we have a look at the image attached, the coordinates are:
[tex]A(1,1)\\B(2,5)\ and\\C(4,1)[/tex]
To find reflection of a point across any line, the distance of points from the line must be same.
Point A(1,1) lies on the line x = 1, so its reflection A' will be at the same point A'(1,1).
Point C(2,5) is at a distance 1 from x = 1 on right side, so C' will be 1 distance on the left side of x = 1 i.e. 1 will be subtracted from its x coordinate.
i.e. C'(1 - 1, 5)
C'(0, 5)
Point B(4, 1) is at a distance 3 from x = 1 on right side, so B' will be 3 distance on the left side of x = 1 i.e. 3 will be subtracted from its x coordinate.
i.e. B'(1 - 3, 1)
B'(-2, 1)
When we plot the above point A', B' and C', we get the option D as correct.
The vertices of the triangle after reflection across the line x = 1 are:
A'(1, 1),
B'(-2, 1),
and C'(0, 6).
The correct option is D.
Given information:
As per the diagram,
The vertices of the triangle are:
A(1, 1),
B(4, 1),
and C(2, 6).
To find the reflection of the triangle across the line x = 1, we can apply the reflection transformation.
The line x = 1 acts as the mirror or reflection axis. To reflect a point across this line, we can imagine folding the image over the line so that the distance between the point and the line is preserved, but the point is now on the other side of the line.
Let's reflect each vertex of the triangle across the line x = 1:
Reflecting point A(1, 1):
The distance between point A and the line x = 1 is 0 since A lies on the line itself. Therefore, the reflection of point A will also be (1, 1).
Reflecting point B(4, 1):
The distance between point B and the line x = 1 is 3 units. Reflecting across the line x = 1 will place B 3 units to the left of the line, resulting in the point (1 - 3, 1), which simplifies to (-2, 1).
Reflecting point C(2, 6):
The distance between point C and the line x = 1 is 1 unit. Reflecting across the line x = 1 will place C 1 unit to the right of the line, resulting in the point (1 - 1, 6), which simplifies to (0, 6).
Therefore, the vertices of the triangle after reflection across the line x = 1 are:
A'(1, 1),
B'(-2, 1),
and C'(0, 6).
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