Answer:
[tex]y = x[/tex]
Step-by-step explanation:
Given
[tex]A =(6,3.7)[/tex]
[tex]B = (5.4,2)[/tex]
[tex]C = (1,3)[/tex]
[tex]A' = (3.7, 6)[/tex]
[tex]B' = (2, 5.4)[/tex]
[tex]C' = (3, 1)[/tex]
Required
The equation for the line of reflection
Taking points A and A' as a point of reference:
[tex]A =(6,3.7)[/tex] and [tex]A' = (3.7, 6)[/tex]
First, calculate the midpoint (M)
[tex]M = (\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})[/tex]
[tex]M = (\frac{3.7+6}{2},\frac{6+3.7}{2})[/tex]
[tex]M = (\frac{9.7}{2},\frac{9.7}{2})[/tex]
[tex]M = (4.85, 4.85)[/tex]
Calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{6 - 3.7}{3.7 - 6}[/tex]
[tex]m = \frac{2.3}{-2.3}[/tex]
[tex]m = -1[/tex]
The midpoint of a reflection is always perpendicular to the points being reflected.
So, the slope of [tex]M = (4.85, 4.85)[/tex] is:
[tex]m_2 = -\frac{1}{m}[/tex]
[tex]m_2 = -\frac{1}{-1}[/tex]
[tex]m_2 = 1[/tex]
The equation is then calculated as:
[tex]y = m_2(x - x_1) + y_1[/tex]
Where:
[tex](x_1,y_1) = (4.85,4.85)[/tex]
[tex]y = 1(x - 4.85) + 4.85[/tex]
[tex]y = x - 4.85 + 4.85[/tex]
[tex]y = x[/tex]
Hence, the equation of line of reflection is:
[tex]y = x[/tex]
Answer:
c
Step-by-step explanation:
Write an equation of the line that passes through (1,2) and is parallel to the line y = -5x+4
Answer:
y =-5x + 7
Step-by-step explanation:
y = -5x + 4
Slope = -5
Parallel lines have same slope
Slope of the parallel line to this line = -5
(1 , 2)
y -y1 =m(x - x1)
y - 2 = -5(x - 1)
y -2 = -5x + 5
y = -5x + 5 + 2
y = -5x + 7
y = 2x - 6
y = - 4x + 3
What is the missing reason for the 3rd step in the proof below?
A. If two lines are parallel, then alternate interior angles are congruent
B. Corresponding angles theorem
C. Vertical angles are congruent
D. If two lines are parallel, then alternate exterior angles are congruent
Answer:
The missing reason for the 3rd step in the proof below is;
C. Vertical angles are congruent
Step-by-step explanation:
In the two column proof, we have;
Statement [tex]{}[/tex] Reason
1. AB ║ CD [tex]{}[/tex] 1. Given
2. ∠3 ≅ ∠7 [tex]{}[/tex] 2. Corresponding angles theorem
3. ∠7 ≅ ∠6 [tex]{}[/tex] 3. Vertical angles are congruent
4. m∠3 = m∠7 [tex]{}[/tex] 4. Definition of congruence
m∠7 = m∠6
5. m∠3 = m∠6 [tex]{}[/tex] 5. Substitution
6. m∠3 ≅ m∠6 [tex]{}[/tex] 6. Definition of congruence
Vertical angles are the angles formed on the opposite sides of two straight lines when they cross each other
Other vertical angles in the diagram are;
1) ∠5 and ∠8
2) ∠1 and ∠4
3) ∠2 and ∠3
Write the equation for an exponential function that triples ever year, x, when the original amount is 4.
Answer:
y = 4(3)^x
Step-by-step explanation:
Here, we want to write the exponential equation
From the question, we have the equation tripling in x value every year and the original amount is 4
The exponential equation is of the form;
y = a(b)^n
In this case;
a = 4 , b = 3 and n = x
So we have the equation as;
y = 4(3)^x
Calculate the volume.
Plz hurry!! 40 points in it!!
Answer:
tell me the decimals number form
Step-by-step explanation:
In a small library, there are 55 nonfiction books for every 99 fiction books. There are 130130 nonfiction books.
a. How many fiction books are there? Use paper to draw a model to support your answer.
There are
fiction books.
b. How many more fiction books are there than nonfiction books?
There are
more fiction books than nonfiction books.
Show work, please
32 points!
Answer:
1.Equivalent
2.Equaivalent
3.Not Equivalent
4.Equivalent
a line is perpendicular to y=-2x+5 and intersects the point (-4,2). what is the equation of this perpendicular line?
Answer:
y = 1/2x + 4
Step-by-step explanation:
If the line is perpendicular to y = -2x + 5 then the new line has a slope of 1/2.
So solve for b: using y = mx + b
2 = 1/2(-4) + b
2 = -2 + b
4 = b
Put it all together
y = 1/2x + 4
Expand and simplify (x-3)(2x+1)(x+1)
Step-by-step explanation:
(x-3)(2x+1)(x+1)
(2x² - 6x + x - 3)(x+1)
(2x² - 5x - 3) (x+1)
2x³ -5x² -3x + 2x² -5x - 3
2x³ - 3x² - 8x -3
---------------------------FOLLOW MEA community centre organises a raffle to raise money for charity
There is one prize to be won
Daniel buys 17 raffle tickets.
A total of 280 tickets were sold
What’s the probability that Daniel does not win the prize
Answer:
263 / 280
Step-by-step explanation:
Given that :
Number of tickets bought = required outcome = 17
Total number of raffle = total possible outcomes = 280
Probability = required outcome / Total possible outcomes
P(winning) = 17 / 280
P(not winning) = 1 - 17/ 280
= 263 / 280
A triangle has side lengths 24,143 and 145 is it a right triangle?
Answer:
yes last one
Step-by-step explanation:
Is this correct?????
Answer:
yeah i think so
Step-by-step explanation:
Answer:
it is correct jbhsjsshsusuwwy
Find the midpoint between A (4, 2) and B (0, 6)
in order to get an A Mark needs to get at least 90% of the 650 points possible in the class. How many points must he earn of the 150-point final if he averaged 92 points on each of the five 100-point test
Answer:
at least 125 points on the final
Step-by-step explanation:
90% of 650 = 585
He needs at least 585 points to get at least 90%
Since he averaged 92 on the first 5 tests, he already has 5(92) = 460 pts
That means he needs to get at least 585 - 460 = 125 pts on the final exam
Combine the like terms for the following expressions -3+4b-6g+5-7b
Answer:
-3b-6g+2
Step-by-step explanation:
At the grand opening of a new store, every 9th customer will receive a balloon and every 12th customer will receive a $10 gift certificate. Which customer will be the first to get both a balloon and gift certificate?
Answer: 36th customer.
Step-by-step explanation: 36 is divisible by both 9 and 12, and is the least common multiple.
hello please help thank you!
Answer:
BC ≈ 5.44 m
Step-by-step explanation:
Using the cosine ratio in the right triangle
cosθ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] , that is
cos27° = [tex]\frac{BC}{6.1}[/tex] ( multiply both sides by 6.1 )
6.1 × cos27° = BC , then
BC ≈ 5.44 m ( to 3 significant figures )
need help i don't know of I got the the first problems rigth so just please tell me if I did and please answer second problem
Answer: Question 1 is correct and Question 2 is 12 degrees :)
Step-by-step explanation: hope this helped!
2y = 3/2 (16x+18) - 7
Answer:
y = 12x + 10
X = y/12 - 5/6
Answer:
y = 12x + 10
x = (y-10)÷12
Step-by-step explanation:
Find the value of x in the triangle.
A right triangle has one angle with a measure of 54 degrees and the other angle measure of x degrees.
A. 126°
B. 234°
C. 36°
D. 144°
Answer:
Agreed, the answer is 36
Step-by-step explanation:
Subtract 180-90=90-54=
36
There's your answer.
What is the surface area of this right square pyramid?
with a width of 5cm and a height of 9cm
A.90cm squared
B.115cm squared
C.205cm squared
D.250cm squared
Answer:
it isn't 205 but my guess is its 115
-7-(-4)= helpppppp pleaseeeee
Answer:
-3
Step-by-step explanation:
-7 + 4 = -3
-3
Have a beautiful day!
Hey.... can anybody help me with a question? If you can change one thing in your community with design, what would it be and how will it work towards racial justice?
my question is in the photo
Answer:
all the answers are there in safari can just check it
Step-by-step explanation
What is 4 & 1/2 ÷ 1/6?
Answer:
27
Step-by-step explanation:
4 1/2 = 9/5
9/2 : 1/6 =
9/2 x 6/1 =
(9x6) / (2x1) =
54/2 = 27
Can you please solve this
Answer: [tex]\frac{2(x-7)}{5(x-3)(x-2)}[/tex]
Step-by-step explanation:
I'll do the fraction on the left, then the one on the right. Follow the screenshots below to help you out.
1. Use distributive property. The first of the images is me distributing all the values on the fraction on the left. Now I will do the ones on the left.
2. I used the same method. Now I will multiply the two.
3. [tex]\frac{2(x-7)}{5(x-3)(x-2)}[/tex]
Rewrite the following using distributive property
1. 24+20
2. 12+16
3. 36+81
4. 49+84
5. 99+36
Thanks❤
Answer:
12+16
24+20
36+81
49+84
99+36
Dino finds the line-of-best fit for the data set shown. What is the equation of Dino's line-of-best fit?
Answer:
y = 2.0x + 0.6
Step-by-step explanation:
Dino's data:
X _____ Y
1 ______ 1
2 ______5
3 ______6
4 _____ 10
5 _____ 13
6 _____ 13
7 _____ 14
8 _____ 16
9 _____ 18
10 _____21
Using the linear regression calculator, the line of best fit for the data is :
y = 2.0X + 0.6
Where ;
Slope = 2 ; intercept = 0.6
The population of a small town, P, as a function of time, t, in years past 1940 is given below. P = 2,828 + 125t For which of the following years was the population of the town 8,453?
Answer:
Step-by-step explanation:
P = 2,828 + 125t
8,453 = 2,828 + 125t
5625 = 125t
t = 45
You didn't post the choices, hope that I can help you.
Answer:
Any year after 1985
Step-by-step explanation:
8453=2828+125t
5625=125t
45=t
1940+45=1985
there are 72 boys and 90 girls on a math team for the next competition mr. Johnson would like to arrange all the students in equal rows with only girls or only boys in each row. What is the greatest number of students that can be in each row
What is the length of the missing leg?