Answer:
[tex]\displaystyle \left(\frac{-(m^{2}-1)\, x + 2\, m\, y - 2\, m \, c}{m^{2} + 1},\, \frac{(m^{2} - 1)\, y + 2\, m \, x + 2\, c}{m^{2} + 1}\right)[/tex].
Step-by-step explanation:
Consider the line that is perpendicular to [tex]y = m\, x + c[/tex] and goes through [tex](x,\, y)[/tex].
Both [tex](x,\, y)[/tex] and the reflection would be on this new line. Besides, the two points would be equidistant from the intersection of this new line and line [tex]y = m\, x + c[/tex].
Hence, if the vector between [tex](x,\, y)[/tex] and that intersection could be found, adding twice that vector to [tex](x,\, y)\![/tex] would yield the coordinates of the reflection.
Since this new line is perpendicular to line [tex]y = m\, x + c[/tex], the slope of this new line would be [tex](-1/m)[/tex].
Hence, [tex]\langle 1,\, -1/m\rangle[/tex] would be a direction vector of this new line.
[tex]\langle m,\, -1\rangle[/tex] (a constant multiple of [tex]\langle 1,\, -1/m\rangle[/tex] would also be a direction vector of this new line.)
Both [tex](x,\, y)[/tex] and the aforementioned intersection are on this new line. Hence, their position vectors would differ only by a constant multiple of a direction vector of this new line.
In other words, for some constant [tex]\lambda[/tex], [tex]\langle x,\, y \rangle + \lambda\, \langle m,\, -1 \rangle = \langle x + \lambda \, m,\, y - \lambda \rangle[/tex] would be the position vector of the reflection of [tex](x,\, y)[/tex] (the position vector of [tex](x,\, y)\![/tex] is [tex]\langle x,\, y \rangle[/tex].)
[tex]( x + \lambda \, m,\, y - \lambda )[/tex] would be the coordinates of the intersection between the new line and [tex]y = m\, x + c[/tex]. [tex]\lambda\, \langle m,\, -1 \rangle[/tex] would be the vector between [tex](x,\, y)[/tex] and that intersection.
Since that intersection is on the line [tex]y = m\, x + c[/tex], its coordinates should satisfy:
[tex]y - \lambda = m\, (x + \lambda \, m) + c[/tex].
Solve for [tex]\lambda[/tex]:
[tex]y - \lambda = m\, x + m^{2}\, \lambda + c[/tex].
[tex]\displaystyle \lambda = \frac{y - m\, x - c}{m^{2} + 1}[/tex].
Hence, the vector between the position of [tex](x,\, y)[/tex] and that of the intersection would be:
[tex]\begin{aligned} & \lambda\, \langle m,\, -1 \rangle \\= \; & \left\langle \frac{m\, (y - m\, x - c)}{m^{2} + 1},\, \frac{(-1)\, (y - m\, x - c)}{m^{2} + 1}\right\rangle \\ =\; &\left\langle \frac{-m^{2}\, x + m\, y - m\, c }{m^{2} + 1},\, \frac{-y + m\, x + c}{m^{2} + 1}\right\rangle \end{aligned}[/tex].
Add twice the amount of this vector to position of [tex](x,\, y)[/tex] to find the position of the reflection, [tex]\langle x,\, y \rangle + 2\, \lambda \,\langle m,\, -1 \rangle[/tex].
[tex]x[/tex]-coordinate of the reflection:
[tex]\begin{aligned} & x + 2\, \lambda\, m \\ = \; & x + \frac{-2\, m^{2}\, x + 2\, m \, y - 2\, m \, c}{m^{2} + 1} \\ =\; & \frac{-(m^{2} - 1) \, x + 2\, m \, y - 2\, m \, c}{m^{2} + 1}\end{aligned}[/tex].
[tex]y[/tex]-coordinate of the reflection:
[tex]\begin{aligned} & y + (-2\, \lambda)\\ = \; & y + \frac{- 2\, y + 2\, m\, x + 2\, c}{m^{2} + 1} \\ =\; & \frac{(m^{2} - 1) \, y + 2\, m \, x + 2\, m \, c}{m^{2} + 1}\end{aligned}[/tex].
Kim just turned 10 years old her mother is four times older than Kim how old is Kims mother
Answer:
40 years old
Step-by-step explanation:
Help!! Please photo art attached below
Answer:
C
Step-by-step explanation:
180 degrees + 30 =210 degrees
210 degrees equals 7π/6
A 3-gallon jug of water costs $15.00. What is the price per quart?
Answer:
1.25 dollars per quart
Step-by-step explanation:
There are 4 quarts per gallon
3 gallons * 4 quarts/ gallon = 12 quarts
15 dollars/ 12 quarts
1.25 dollars per quart
What is the range of the function?
{(1.2, 11.6), (3.6, 11.5), (1.9, 11.4), (2.7, 11.5)}
Answer:
Range: 10.4
Step-by-step explanation:
Range = maximum(xi) - minimum(xi), where xi represents the set of values
= 11.6 - 1.2
= 10.4
Answer:
Range-
{
11.6
,
11.5
,
11.4
}
Step-by-step explanation:
in a fruit punch drink,the 3 ingredients are apple juice,orange juice and cramberry juice.if 3/4 of the drink is apple juice and 1/10 is orange juice then write the ratio of cranberry juice to apple juice to orange juice in its simplest form
Answer:
3 : 15 : 2
Step-by-step explanation:
Let cranberry juice = x,
3/4 + 1/10 + x = 1
x = 3/20
Ratio = cranberry : apple : orange
= 3/20 : 3/4 : 1/10
= 3 : 15 : 2 (Times everything with 20)
Solve by completing the square. 2x^2 – 2x – 4 = 0
Step-by-step explanation:
Factor out 2,
x² - x - 2 = 0
x² - x = 2
x² - x + (-1/2)² = 2 + (-1/2)²
(x - 1/2)² = 9/4
x = ±3/2 + 1/2
x = 2 or x = -1
What are all the factors of 618?
Answer:
1, 2, 3, 6, 103, 206, 309, 618
If M ABD = 65 and DBC=60 then m ABC=
Answer:
∠ ABC = 125°
Step-by-step explanation:
∠ ABC = ∠ ABD + ∠DBC that is
∠ ABC = 65° + 60° = 125°
Which phrase describes the linear relationship between the values of x and y shown in the table?
x l y
-3 l 9
0 l 0
3 l -9
A. y is 3 times x
B. x is 6 more than y
C. y is 12 more than x
D. y is -3 times x
Answer:
The answer is D. Y is -3 times x
The phrase which describes the linear relationship between the values of x and y is y is -3 times x.
What is linear relationship between two variables?
A linear relationship is any relationship between two variables that creates a line when graphed in the x y -plane.
According to the given question.
We have a linear relationship between x and y.
From the first we can see that
When,
x = -3 and y = 9
⇒ y = -3x = -3 × (-3) = 9
when,
x = 0, and y = 0
⇒ y = -3x = -3 × 0 = 0
when,
x = 3, and y = -9
⇒ y = -3x = -3 × 3 = -9
Hence, this shows that y is -3 times x.
Thus, option D is correct.
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Vertical plane R intersects horizontal plane P. Points D, and B are on the line of the intersecting planes. Point F is on the top half of plane R. Point G is on the bottom half of plane G. Point C is on the left half of plane P. Point E is on the right side of plane P. There is a line formed between points C and E. Point H to above and to the right of the planes. Point L is below and to the left of the planes.
The intersection of plane R and plane P is
.
Point
is not on plane P.
Line C E and Line D B intersect at point
.
Answer:
The intersection of plane R and plane P is line DB
Point H is not on plane P.
CE and DB intersect at point D
Explanation:
got it right on edge 2021 :)
Answer:
there right^
Step-by-step explanation:
edge 22
the area of a rectangular park is 7/8 sqaure mile. the length of the park is 3/4 mile. what is the width of the park?
Answer:
7/6
Step-by-step explanation:
since the formula of area is length times width,you have to divide the area by the length to find the width
area=length×width
the width will be
width=area÷length
=7/8÷3/4
7/8×4/3
7/2×1/3
7/6
that's the width you can prove it by multiplying the length times the width to see if you will get 7/8..
I hope this helps
The area of a triangle is 24 square inches. What is the height of the triangle if the base length is 4 inches?
6 inches
8 inches
12 inches
20 inches
Answer:
[tex]\boxed {\boxed { \sf 12 \ inches}}[/tex]
Step-by-step explanation:
The area of a triangle can be calculated using the following formula.
[tex]a=\frac{1}{2} bh[/tex]
The area of the triangle is 24 square inches and the base is 4 inches long.
a= 24 in² b= 4 inSubstitute the values into the formula.
[tex]24 \ in^2 = \frac {1}{2} * 4 \ in * h[/tex]
Multiply on the right side of the equation.
[tex]24 \ in ^2 = ( \frac{1}{2} * 4 \ in ) * h[/tex]
[tex]24 \ in ^2 =2 \ in *h[/tex]
We are solving for the height of the triangle, so we must isolate the variable h. It is being multiplied by 2 inches. The inverse of multiplication is division, so we divide both sides by 2 inches.
[tex]\frac { 24 \ in ^2 }{2 \ in }= \frac{ 2 \ in *h}{ 2 \ in}[/tex]
[tex]\frac { 24 \ in ^2 }{2 \ in }= h[/tex]
[tex]12 \ in = h[/tex]
The height of the triangle is 12 inches.
help fast pleasee
find the unit rate for Dion and Emily who read faster?
Dion: 36 pages in 3 days
emily: 45 pages in 5 days
36 pages
__________= ? pages per day.
3 days
45 pages
_________=? pages per day.
5 days
deon read _____ pages per day than emily.
Step-by-step explanation:
36 pages in 3 days, 36/3=12 pages per day.
45 pages in 5 days, 45/5=9 pages per day.
Difference is 3 pages per day
Answer:
Deon read 3 more pages per day than Emily.
What I got to do please
Answer:
4
Step-by-step explanation:
[tex]3 \div \frac{3}{4} \\ = \frac{3}{1} \div \frac{3}{4} \\ = \frac{3}{1} \times \frac{4}{3} \\ = \frac{12}{3} \\ = \frac{4}{1} \\ = 4[/tex]
Answer:
4
Step-by-step explanation:
3÷3/4
3*4/3
12/3
4
What is the y value when x is -5? What about 5?
I’ve done all three functions and the answers are -9, 24 and -4 but I don’t know which one to answer as the y value with. Please help.
Consider the line 9x + 8y = -8.
What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?
Answer:
Step-by-step explanation:
The slope of the line is -9/8. The slope of any parallel to the line is also -9/8.
Find the inequality represented by the graph.
9514 1404 393
Answer:
y < 3x -4
Step-by-step explanation:
The boundary line has a slope (rise/run) of 3/1 = 3. It has a y-intercept of -4. The shaded area is below the line and the solution does not include the line. The relevant inequality can be written ...
y < 3x -4
.........................................................
Answer:
..............................what this
..............................
Answer:
[tex]x=17[/tex]
Step-by-step explanation:
[tex](6x+10)(x+17)(4x-34)[/tex]
[tex]6x+10+x+17+4x-34=180[/tex]
Add:- [tex]6x+x+4x=11x[/tex]
and [tex]10+17-34=-7[/tex]
So, [tex]11x-7=180[/tex]
Add 7 to both sides:-
[tex]11x=187[/tex]
Divide both sides by 11:-
[tex]\frac{11x}{11}=\frac{187}{11}[/tex]
[tex]x=17[/tex]
OAmalOHopeO
Company A charges a $125 annual fee plus $7 per hour car share fee.
Company B charges $110 plus $10 per hour. What is the minimum number of
hours that a car share needs to be used per year to make company A a better
deal?
A. 6
O Ο Ο
B. 5
C. 9
D. 11
SUBMIT
PREVIOUS
Answer:
6 hours
Step-by-step explanation:
A: y=125+7x
B: y=110+10x
for A to be a better deal than B, 125+7x<110+10x has to be true
subtract 7x from both sides and subtract 110 from both sides of the inequality: 15<3xdivide by 3: 5<xso x has to be greater than 5, im pretty sure it's 6 hours but it might also be 5 depending on how it's taught for youAnswer:
B 5
Step-by-step explanation:
Company A
total cost = 125+7h where h is the number of hours
Company B
total cost = 110 + 10h where h is the number of hours
125 + 7h < 110 + 10h
Subtract 7 h from each side
125 + 7h-7h<110+10h-7h
125 < 110+3h
Subtract 110 from each side
125-110< 110+3h
15 <3h
Divide by 3
15/3 <3h/3
5 <h
More than 5 hours
What is the reciprocal of 0.025 (not -0.025)
Answer:
1000/25 or 40
Step-by-step explanation:
~ A reciprocal is the fraction's reverse
For example 2/3=3/2
.025 is also 25/1000
The reverse of 25/1000 is 1000/25
Simplified into 40 wholes
1000/25 is the reciprocal of 0.025
What is Fraction?A fraction represents a part of a whole.
Given,
Decimal value is 0.025
Zero point zero two five.
Firstly let us convert this to the fraction form.
When twenty five is divided by thousand we get 0.025
25/1000=0.025
So the fraction is 25/1000.
Now we need to find the reciprocal of fraction 25/1000.
Reciprocal means the numerator changes to denominator and denominator changes to numerator.
So 25/1000 reciprocal is 1000/25
Hence, 1000/25 is the reciprocal of 0.025
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Which of the following graphs is the inverse of f(x) = x2 + 4?
Answer:
Step-by-step explanation:
Instructions: Determine whether the following polygons are
similar. If yes, type in the similarity statement and scale factor. If
no, type 'None' in the blanks.
Answer:
No they aren't similar different measurements but same angle so they can't be said to be similar
Line A passes through the points (-2, 27) and (1, -9). Line B passes through the points (-1, 15)
and (3,-33).
Which statement is true?
Line A overlaps line B.
Line A does not intersect line B.
Line A intersects line B at exactly one point.
Answer:
Line A overlaps line B
Step-by-step explanation:
find gradient of both A and B and use it to find the equation of both lines
final answer will reveal that both lines are the same implying that one overlaps the other
Finding Perimeter Practice Pages continued Name: 3 A rectangular garden has a width of 90 feet. The perimeter is 500 feet. What is the length of the garden? 500 = (2x) + .......... .........) 500 = 2€ + = 20 = 2 = = € The length of the garden is ................. feet. inchor lona Tell w
Step-by-step explanation:
After putting the values:-
What are the ratio of 1:6 and 3:8, 2:14and 3:42
The ratio of 1:6 is 1/6
The ratio of 3:8 is 3/8
The ratio of 2:14 is 1/7
The ratio of 3:42 is 1/14
Please mark brainliest if that helped!
Find the value of x. Round to the nearest tenth.
Answer:
1.6 ft
Step-by-step explanation:
If you use the Pythagorean Theorem to solve for x, you get:
[tex]x=\sqrt{2.1^2-1.4^2}[/tex]
[tex]x=\sqrt{2.45} = 1.56524758425[/tex]
Rounded to the nearest tenth, the answer is 1.6
For the function y=f(x), find f’(a)
Answer:
-1/4
Step-by-step explanation:
f(x) = 1/(x+1)
f(a) = 1/(a+1)
f'(a) = {(a+1)×d/da (1) - d/da (a+1) × 1}/(a+1)²
f'(a) = {(a+1)×0 - 1×1}/(a+1)²
f'(a) = (0-1)/(a²+2a+1)
f'(a) = -1/(1+2a+a²)
putting a = 1
f'(a) = -1/(1+2+1)
f'(a) = -1/4
help, please!
find x
This shape consists of two primary special triangles, 30-60-90 and 45-45-90.
the side with the 60° will be half of the hypotenuse because 30° is across from it.
the side with the 30° will be 5.5√3 because 60° is across from it, and any sides that has 60° across from it is associated with a √3.
x is 5.5√6 because any sides that is "below" the 45° angles are associated with a √2 times the side that's above the 45°
4) (20 pts) A box contains 5 apples and 6 oranges. Four children each receive a fruit from the box, one after the other, randomly chosen, without replacement. What is the probability that all four children receive the same fruit
Answer:
Probability of an event = Number of outcomes favourable to that event/ Number of all possible outcomes.
The set of all possible outcomes is called the sample space and is denoted by S.
Any 3 fruits out of 11 in the box can be randomly selected in 11C3= (11x10 x 9)/(1 x 2x3) = 165 ways. Hence n(S) = 165.
We want the desired event E that the 1 fruit of each type is chosen. Now 1 apple out of 5 can be chosen in 5C1 = 5 ways, 1 out of 4 oranges in 4C1 = 4 and 1 banana out of 2 in 2C1 = 2 ways. Therefore, by fundamental counting principle, one of each type of fruit can be chosen in 5x4x2 = 40 ways So n(E) = 40.
Hence the probability of getting three fruits one of each type is = n(E)/ n(S) = 40/165 = 8/33.
The probability that all four children receive the same fruit is 2/33.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
We have 5 apples and 6 oranges.
So, if we choose 4 apples then the probability can be
= 5 /11 x 4/10 x 3/9 x 2/8
= 120/ 7920
and, if we choose 4 oranges then the probability can be
= 6/11 x 5/10 x 4/9 x 3/8
= 360/ 7920
Thus, the combined probability
= 120/7920 + 360/7920
= 480/ 7920
= 2/33
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