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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Related Questions
What is (1.6x + 7.3) + (–0.6x + 2) – (7.8 – 3.4x), simplified?
Answers
Answer:
4.4x+1.5Step-by-step explanation:
[tex](1.6x + 7.3) + (-0.6x + 2) - (7.8 -3.4x)\\Ope- the- brackets\\1.6x+7.3-0.6x+2-7.8+3.4x\\Collect-like-terms\\1.6x-0.6x+3.4x+7.3+2-7.8\\4.4x+1.5[/tex]
Answer:
4.4
Step-by-step explanation:
Select the two values of x that are roots of this equation.
x - 5x+2=0
A. X=
5+33
B. X=
C. x=
5+ _17
2
D. x-5-3
Answers
Answer:
A and C
x = -(√17 - 5)/2, (√17 + 5)/2
Step-by-step explanation:
Quadratic Formula: [tex]x = \frac{-b +/-\sqrt{b^2-4ac} }{2a}[/tex]
Step 1: Use quadratic formula
a = 1, b = -5, c = 2
[tex]x = \frac{5 +/-\sqrt{(-5)^2-4(1)(2)} }{2(1)}[/tex]
[tex]x = \frac{5 +/-\sqrt{25-8} }{2}[/tex]
[tex]x = \frac{5 +/-\sqrt{17} }{2}[/tex]
Please answer this question now in two minutes
Answers
Answer:
A. 17.5
Step-by-step explanation:
4x+8 27
L-------------M-------------------------N
<------------------ 6x -------------------->
LM = 4x+8
MN = 27
LN = 6x
LM + MN = LN
4x+8 + 27 = 6x
35 = 2x
17.5 = x
Un campanario tarda 4s en tocar 5 campanadas , ¿Cuanto tardara en tocar 10 campanadas?
Answers
¿Cuanto tardara en tocar 10 campanadas?
Cameron Indoor Stadium at Duke University is one of the most revered sites in all of college basketball, as well as in all of sports period. Duke’s men’s and women’s basketball programs have attained quite a few wins in the building over the last seventy years. Cameron Indoor Stadium is capable of seating 9,460 people. For each game, the amount of money that the Duke Blue Devils’ athletic program brings in as revenue is a function of the number of people in attendance. If each ticket costs $45.50, find the domain and range of this function.
Answers
Answer:
Step-by-step explanation:
The domain of a function is the set of values that satisfies the independent variable while the range of the function is the set of values that satisfies the dependent variable.
Since for each game, the amount of money that the Duke Blue Devils’ athletic program brings in as revenue is a function of the number of people in attendance, then the dependent variable is the amount of money while the independent variable is the number of people. The domain is between 0 and 9460 people. Therefore, the domain of this function is
0 ≤ x ≤ 9460
Where x represents number of people.
For the range, the lowest total sales is 0 × 45.5 = $0
The highest total sales is
9460 × 45.5 = $430430
The range is
0 ≤ y ≤ 430430
Where y represents total sales
Find the value of x in the triangle
shown below.
Answers
Answer:
x=62
Step-by-step explanation:
In an isosceles triangle opposite sides are equal and sum of the sides is 180 degree
So, if we name them 'angle a', 'angle b' and 'angle c'
angle a= 56
a+b+c= 180
using the isosceles triangle formula b=c,
56+b+c=180
name b,c as x
56+2x=180
2x= 180-56
2x= 124
x=62
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The value of x in the triangle will be 62°
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
Two sides of triangle = 6
So, This is an isosceles triangle.
Third side of a triangle = 5.7
Now,
Since, The given triangle is an isosceles triangle.
So, It has measure of two angles = x°
And, The measure of third angle = 56°
Since, The sum of all angles of a triangle = 180°
Substitute all the value of angles, we get;
x° + x° + 56° = 180°
Solve for x as;
2x + 56 = 180
Subtract 56 both side,
2x + 56 - 56 = 180 - 56
2x = 124
Divide by 2, we get;
x = 62°
Thus, The value of x in the triangle will be 62°
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translate into an algebraic expression: 120 is increased by d % and increased by 25% . What is the result ?
Answers
The result is number [tex]r[/tex] where:
[tex]r=(120+120\cdot\frac{d}{100})+(120+120\cdot\frac{d}{100})\cdot\frac{25}{100}[/tex]
Hope this helps.
Solve for g. 3/16 = (-5/4) + g
Answers
Answer:
g = 23/16
Step-by-step explanation:
3/16 = (-5/4) + g
Add 5/4 on both sides.
3/16 + 5/4 = g
Make denominators equal and add.
3/16 + 20/16 = g
23/16 = g
FIND 2 RATIONAL NUMBER and two irrational numbers between 0.15 and 0.16
Answers
Answer:
Rational numbers:
Any terminating decimal is a rational number.
0.151
0.152
Irrational numbers:
Pi is irrational, so when pi is divided by a rational number, the result is irrational.
pi/20.8 = 0.151038108...
pi/20.7 = 0.151767761...
Factor this polynomial completely.
15x^2 - 11X - 12
Need help ASAP!!
Answers
Answer:
( 5 x + 3 ) ( 3 x − 4 )
A
Step-by-step explanation:
the answer is A. (5x+3) (3x-4)
4/5 of a number is 32
Answers
Answer:
x = 40
Step-by-step explanation:
Step 1: Write out an equation
4/5(x) = 32
Step 2: Solve by dividing both sides by 4/5
x = 32/(4/5)
Use KCF (Keep Change Flip) if you do not have a calc.
x = 40
Answer:
The answer is 40
Step-by-step explanation:
32 times 5 is 160
then: 160 divided by 4 is 40.
check the answer: 4/5 of 40 is 32
because 40 divided by 5 is 8 and then times 8 by 4, so the answer would be 40.
Hope this helps!!!Please help me with trig I’d really appreciate
Answers
Answer:
2 root 10/ 7, or the second option.
Step-by-step explanation:
If a is 3, then b is root 40. (Pythagorean)
root 40= root 4x10, or 2 root 10
Tangent= opposite/hypotenuse
Tangent= 2 root 10/ 7
After losing 3 baseball cards, Peter gave half of his remaining cards to Bobby. If Peter gave Bobby 9 baseball cards, how many cards did Peter start with?
Answers
Answer:
Peter started with 21 cards
Step-by-step explanation:
half of his card that gave to bobby =9
so the other half is 9
9+9=18
18+3 cards that he lost at the beginning=21
Answer:
Substitute 21 for X in the original equation YES
Substitute any number for X in the original equation NO
Bobby’s claims that x=21 is correct YES
The result of verifying Bobby's work is 9=9 YES
The result of verifying Bobby's work is 21=21 NO
Step-by-step explanation:
got right on edg
The second angle of a triangle is double the first angle. The third angle is 40 less than the first angle. Find the three angles.
Answers
Answer:
Angle 1: 55
Angle 2: 110
Angle 3: 15
Step-by-step explanation:
Angle 1: x
Angle 2: 2x
Angle 3: x-40
The total degrees for all the angles in a triangle add up to 180, so we now have the equation x+2x+x-40=180. From here we solve to get 55 degrees for x, so angle 1 is 40 degrees, angle 2 is 110 (2 times 40) and the third angle is 15 (55-40).
If you were to pull colored marbles out of the bag (one at a time, and putting the marble back each time) for 500 tries, approximately how many times would you select a red marble?
Answers
Answer:
We need to know the other marbles in the bag and how many there are of each.
I divided one hole number by another hole number and got 3.125 on my calculator. both my numbers are less than 50 but I'v forgotten what they are. Can you work out what they are?
Answers
Answer:
25 and 8
Step-by-step explanation:
a/b = 3.125
a/b = 3125/1000
make it simple (divide by 25)
a/b = 125/40
ah, can be more simple (divide by 5)
a/b = 25/8
see 25 + 8 is less than 50
Step-by-step explanation:
1.25/8=3.125
50/16=3.125
but it tells that both two numbers are less than 50 then,the numbers are 25 and 8
Meline has 4 different coloured crayons and 2 different boxes. How many different ways can Meline put all 4 different crayons into 2 boxes so that each box has at least 1 crayon?
Answers
Answer:
3 different waysStep-by-step explanation:
If Melinda has 4 different crayon and 2 different boxes and she is to put all 4 crayons into the two boxes so that each box has at least 1 crayon, this can be achieved as follows. Note that at least one crayon must be in each box, this means no box must be left empty. Each box can take any number of crayon from 1 and above.
First box Second box
1 crayon 3 crayons (first way)
2 crayons 2 crayons (2nd way)
3 crayons 1 crayon (3rd way)
This means that crayons can be divided into each box in 3 different ways provided that each box has at least 1 crayon.
TWO MINUTES HELP MY PLEASE
Answers
Answer: C
Step-by-step explanation:
Answer:
The third one. Y= -1/2x^2 -2x -1
Step-by-step explanation:
X=2 in standard form
Answers
Answer:
[tex]A2+By=C[/tex]
Step-by-step explanation:
Well standard form is [tex]Ax+By=C[/tex].
And we have x = 2 meaning that x is 2 so the standard is [tex]A2+By=C[/tex].
So basically if we know that x is 2 and x is in the standard for equation we can just plug it in.
So [tex]Ax+By=C[/tex]
x -> 2
So answer is [tex]A2+By=C[/tex]
2A+By=C is the standard form of X=2
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The standard form of a linear equation is Ax+By=C.
A times of x plus B times of y equal to C
A, B, and C are constants,
x and y are variables.
Standard form lets us quickly find the x- and y- intercepts.
By given x value is 2.
Now plug in the value of x in standard form of equation.
2 times of A plus B times of y equal to C
2A+By=C
Hence 2A+By=C is the standard form of X=2
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PLEASE HELP VERY URGENT ITS DUE TODAY PLEASE HELP Complete the table for the given rule. Rule: y=1/4x + 1
X Y
4
8
12
Answers
Answer: Y = 2 ; 3 ; 4
Step-by-step explanation:
Given the rule : y=1/4x + 1
X = 4, 8, 12
When x = 4
y = 1/4(4) + 1
y = 1 + 1
y = 2
When x = 8
y = 1/4(8) + 1
y = 8/4 + 1
y = 2 + 1
y = 3
When x = 12
y = 1/4(12) + 1
y = 12/4 + 1
y = 3 + 1
y = 4
Therefore ;
X - - - 4 - - - 8 - - - 12
Y - - - 2 - - - 3 - - - 4
Ifx=-3 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the
equation?
Answers
Answer:
D = 0
Step-by-step explanation:
Given
x-intercept = -3
Required
What does the discriminant represent?
The discriminant of a quadratic function can take any 3 values; these are as follows;
When D > 0 When D < 0When D = 0Which translates to
signifies that two different real roots existsignifies that only complex roots existsignifies that the two identical real roots existThe question says that x-intercept = -3 is the only value;
This means that: x = -3 or x = -3
Analyzing the roots
3 and -3 are identical-3 and -3 are realThis means they satisfy condition number 3;
Hence, D = 0
Work out the temperature after this change. The temperature starts at −2 °C and it falls by 8 °C.
Answers
Answer:
-10 degree celsius
Explaination:
(-2) - 8
= -2 + -8
= -10 degree celsius
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Which set of values could be the side lengths of a 30 60 90 triangle
Answers
Step-by-step explanation:
[tex]x \: and \: \frac{1}{2} x \: and \: \frac{ \sqrt{3} }{2} x[/tex]
because
[tex] \sin(30) = \frac{1}{2} \\ \sin(60) = \frac{ \sqrt{3} }{2} [/tex]
Answer: your answer is A
Step-by-step explanation: when you have a 30 6090 triangle your sides will always have a set pattern. Decide across from the 30 angle will be equal to n decide across from the 60 angle Will always be equal to n sqared
Question 5 PLEASE HELP What is the graph of 3x+6y=-18
Answers
Answer:
hope this helps uh...!!!
Answer:
Step-by-step explanation:
3x+6y=-18
y=-3x/6-18/6
y=-1/2 x-3
y is inversely proportional to x . When y = 25 , x = 4 Work out y when x = 20
Answers
Answer: 125
Step-by-step explanation:
4/25 = 20/Y
Cross multiply to get the equation
4Y = 500
Divide both sides by 4
Y=125
y=5 when x=20.
Given that, y is inversely proportional to x. When y = 25 , x = 4.
We need to find the y value when x=20.
What is inversely proportional?Inversely proportional variables or quantities are those in which if one variable increases the other will decrease, and if one variable decreases the other increases.
Now, y∝1/x
⇒y=k/x
⇒25=k/4
⇒k=100
Thus, the y value when x=20.
y=100/20=5
Therefore, y=5 when x=20.
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Calculate the area of this triangle.
16 cm
24 cm
20 cm
Answers
Answer:
Step-by-step explanation:
Area of triangle = 1/2 × b × h
= 1/2 × 24 × 16
= 192 cm^2
Hope this helps
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Answer:
192 cm²
Step-by-step explanation:
Area of a triangle is equal to base × height × 1/2.
24 × 16 × 1/2
384 × 1/2
= 192
Match each expression on the left to its simplified version on the right.
Answers
Answer:
In the photo
Step-by-step explanation:
Simply multiply the numbers out of the brackets to the numbers in them, adhering to algebraic rules.
Answer:
the one above me is right expet for 2 of them purple and orange
Step-by-step explanation:
it was right on edge
Francisco states the following: When two or more factors are multiplied and they have the same sign, the product is positive. List two examples that support Francisco's statement. Show their products.
Answers
Answer: Francisco is correct
Step-by-step explanation:
Positive 4 and positive 7
Negative 3 and negative 2
4 * 7 = 28
-3 * -2 = 6
simplify 3 x (x + 2) + 2 x ( 1 - x)
Answers
Answer:
x+8
Step-by-step explanation:
[tex]3\times(x+2)+2\times(1-x)=\\\\3(x)+3(2)+2(1)+2(-x)=\\\\3x+6+2-2x=\\\\x+8[/tex]
Hope this helps!
Answer:
x + 8
Step-by-step explanation:
3 × (x + 2) + 2 × (1 - x)
3(x + 2) + 2(1 - x)
Expand the brackets.
3(x) + 3(2) + 2(1) + 2(-x)
Multiply the terms.
3x + 6 + 2 + -2x
Rearrange.
3x + - 2x + 6 + 2
Add like terms.
1x + 8
If the computer costs $2150 and Melissa puts
$150 away each month, how long will it take her
to save enough money to buy the computer?
Answers
Answer:
14 months and 1/3 of a month
Step-by-step explanation:
We can find how many months it will take by dividing the cost by the amount she puts away each month:
2150/150 = 14.33
So, it will take her 14 and 1/3 of a month