*. If (2,3) and (-6,5) are the end points of diagonal of a square. Find the equation of another diagonal.
Please help with this question..
Answers
Answer: y = 4x + 12 (edited to reflect a SQUARE)
Step-by-step explanation:
Opposite Diagonal of a square means the line goes through the midpoint and has the opposite reciprocal slope.
Use the Midpoint formula: \(M=\bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)\)
\(M=\bigg(\dfrac{2-6}{2},\dfrac{3+5}{2}\bigg)\\\\\\.\ =\bigg(\dfrac{-4}{2},\dfrac{8}{2}\bigg)\\\\\\.\ =(-2,4)\)
Use the Slope formula: \(m=\dfrac{y_2-y_1}{x_2-x_1}\)
\(m=\dfrac{3-5}{2+6}\quad =\quad \dfrac{-2}{8}\quad =\quad -\dfrac{1}{4}\)
Opposite Diagonal slope is opposite (change the sign) and reciprocal (flip the fraction) → m⊥ = + 4
Now use the Point-Slope formula: y - y₁ = m⊥(x - x₁) where
(x₁, y₁) is the midpoint (-2, 4)m = 4y - 4 = 4(x + 2)
y - 4 = 4x + 8
y = 4x + 12
Simple question
slope of on le diagonal,whose coordinates are given=
\( \frac{y2 - y1}{x2 - x1} = \frac{5 - 3}{ - 6 - 2} = \frac{2}{ - 8} or \: \frac{ - 1}{4} \)
now we know that diagonals of square are perpendicular to each other
and we also know that if there are two perpendicular lines have slope m1 and m2 respectively,then
\(m1 = \frac{ - 1}{m2} \)
so if one diagonal's slope is -1/4 then other diagonal's slope will be 4
now we know that all the equation of a line is in the form
y=mx+c
where m is slope
so simply put the value of m=4
y=4x+c...i)
we also know that the line of equationi) will pass through the midpoint coordinates of first diagonal
mid point of first diagonal ={(2-6)/2 ,(5+3)/2}=(-2,4)
put this value of x and y in i) equation
4=-8+c
c=12
hence putting the value of c in equation I) we get the equation of line as
y=4x+12
y-4x-12=0
Related Questions
12. If a newly-discovered exo-planet Le Grosse Homme orbits around a solar-mass star in 2.8284 years, what would be its distance to the star, using Kepler's Third Law?
P2 = a3 (years) 2 = (distance in AU) 3
a) 7.03 AU
b) ~2.0 AU
c) 6.69 AU
d) 0.669 AU
e) 3.0 AU
Answers
Using Kepler's Third Law, we can find the distance of the exo-planet from its star. The formula is P^2 = a^3, where P is the orbital period in years and a is the average distance from the planet to the star in astronomical units (AU).
the average distance of Le Grosse Homme from its star is approximately 2 AU, which is answer choice b).
To determine the distance of the exo-planet Le Grosse Homme to the star, we will use Kepler's Third Law, which states that the square of the orbital period (P) of a planet is proportional to the cube of the semi-major axis (a) of its orbit. The formula is given as:
P² = a³
In this case, the orbital period P is 2.8284 years. We can now solve for the semi-major axis (a), which represents the distance from the planet to the star in astronomical units (AU).
Step 1: Square the orbital period
(2.8284)² = 7.99968336
Step 2: Find the cube root of the squared orbital period to get the distance (a)
a = ∛(7.99968336) ≈ 2.0 AU
So, the distance of the exo-planet Le Grosse Homme to the star is approximately 2.0 AU. The correct answer is option (b) ~2.0 AU.
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if you spin the spinner 11 times, what is the best prediction possible for the number of times it will land on blue?
Answers
If the spinner is fair and has an equal chance of landing on each color, then the best prediction possible for the number of times it will land on blue when spun 11 times is 2.
If the spinner is fair, then the probability of it landing on each color is equal. Since the spinner has four colors, the probability of it landing on blue is 1/4 or 0.25.
To determine the best prediction possible for the number of times it will land on blue, we can multiply the probability of it landing on blue (0.25) by the total number of spins (11):
0.25 x 11 = 2.75
However, since we cannot have a fractional number of spins, we must round to the nearest whole number. Since 2.75 is closer to 3 than to 2, we might initially think that the best prediction for the number of times it will land on blue is 3. However, since we are looking for the best prediction possible, we need to consider the probabilities of landing on other colors as well. If we predict that the spinner will land on blue 3 times, then we are predicting that it will land on each of the other colors 2 times. This means that our total prediction is:
Blue: 3
Red: 2
Green: 2
Yellow: 2
However, this prediction is not the best possible prediction because it is not possible to have the spinner land on each of the other colors exactly 2 times. This means that we need to adjust our prediction to get as close as possible to landing on each color 2 times. The best prediction possible is:Blue: 2
Red: 3
Green: 3
Yellow: 3
This prediction is the best possible because it gets as close as possible to landing on each color 2 times while still being a whole number. Therefore, the best prediction possible for the number of times the spinner will land on blue when spun 11 times is 2.
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A North American river otter wants to cross the North Saskatchewan river. It can swim at a speed of 2. 75 m/s. In that location, the distance directly across the river is 45. 0 m and the current velocity is 2. 5 m/s.
a) How much time does the otter take to get to the other side, if it points directly across the river?
b) How many metres downstream will the current have carried the otter when it gets to the other side?
c) Calculate the otter's velocity, relative to the bank from where it started
Answers
The otter takes approximately 12.10 seconds to get to the other side if it swims directly across the river. The current will have carried the otter approximately 30.25 meters downstream when it reaches the other side. The otter's velocity, relative to the bank from where it started, is 0.25 m/s.
a) To find the time it takes for the otter to get to the other side, we can use the concept of relative velocity. The otter's swimming speed is 2.75 m/s, and the current velocity is 2.5 m/s. Since the otter is swimming directly across the river, its swimming speed and the current speed are perpendicular. Using the Pythagorean theorem, we can find the resultant velocity of the otter:
Resultant velocity = √(swimming velocity² + current velocity²)
= √(2.75² + 2.5²)
≈ √(7.5625 + 6.25)
≈ √13.8125
≈ 3.72 m/s (rounded to two decimal places)
The time it takes to cross the river is given by the distance divided by the resultant velocity:
Time = Distance / Resultant velocity
= 45.0 m / 3.72 m/s
≈ 12.10 seconds (rounded to two decimal places)
b) To find how many meters downstream the current carries the otter when it gets to the other side, we can calculate the distance using the time it takes to cross and the current velocity.
Distance downstream = Time × Current velocity
= 12.10 s × 2.5 m/s
= 30.25 m
c) The otter's velocity, relative to the bank from where it started, can be calculated by subtracting the current velocity from the otter's swimming velocity.
Relative velocity = Swimming velocity - Current velocity
= 2.75 m/s - 2.5 m/s
= 0.25 m/s
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The quantities x and y are proportional. Find the constant of proportionality (r) in the equation y=rx
Answers
Answer:
y=rx 1/4/5/5/5
Step-by-step explanation:
Answer:
r = \(\frac{1}{2}\)
Step-by-step explanation:
The proportional equation is
y = rx ( divide both sides by x )
\(\frac{y}{x}\) = r
Substitute any ordered pair from the table
Using (14, 7 ) , then
r = \(\frac{7}{14}\) = \(\frac{1}{2}\)
Mrs. Sing invests $12,876 for her business at an annual interest rate of 7 percent for 3 years. Which number will Mrs. Sing substitute for r in the simple interest formula? I = p r t
Answers
Answer:
she wills substitute r with 7%.
Step-by-step explanation:
Just did it.
Answer:
R = 7%
Principal (P)
Rate (R)
Time (t)
Step-by-step explanation:
The full intrest rate formula is i=prt
You are looking for r
R is the interest rate 7%
So i = 12,876*7%*3years will be the full equation.
Assume that a real estate investor that rents for $2,000 per month. Which payment plan would the nvestor prefer for the current 12-month lease? payment of $2,000 at the first of each month upfront payment of $24,000 payment of $2,000 at the end of each month payment upfront of $12,000 and $12,000 half-way through the lease
Answers
To determine which payment plan the real estate investor would prefer, we need to compare the present value of each payment option. Assuming a discount rate of 0%, meaning no time value of money is considered, we can directly compare the payment amounts.
1. Payment of $2,000 at the first of each month: This results in a total payment of $24,000 over the 12-month lease.
2. Upfront payment of $24,000: This option requires paying the full amount at the beginning of the lease.
3. Payment of $2,000 at the end of each month: Similar to option 1, this results in a total payment of $24,000 over the 12-month lease.
4. Upfront payment of $12,000 and $12,000 half-way through the lease: This option requires paying $12,000 at the beginning of the lease and another $12,000 halfway through the lease.
Since all the payment options have a total cost of $24,000, the real estate investor would likely prefer the payment plan that offers more flexibility or matches their cash flow preferences. Options 1 and 3 provide the investor with the option to pay monthly, while options 2 and 4 require a larger upfront payment. The choice would depend on the investor's financial situation and preferences.
PLSS HELP ASAP What slope- intercept form equation represents the line
Answers
y = -5
Hope this helps have a great day!!
Answer:
y = -5
Step-by-step explanation:
the line shown does not have a slope, it does not go up nor down
so the slope is zero, leaving us only with needing to write the y-intercept in the equation
we can see that the line intercept the y axis at -5
so the equation for this line is y = -5
divide -3 1/3 by 1 1/5
Answers
Decimal form: -0.6
Vince is married with 5 withholding, he earns $4,200. Find weekly withholding.
Answers
There are 108 girls and 124 boys in the fifth grade at Ridgeview Intermediate School. The school has eight fifth grade classes. If each fifth grade class has the same number of students, how many students are in each class?
Answers
There are 29 students in each fifth-Grade class at Ridgeview Intermediate School.
The students are in each class, we need to divide the total number of students by the number of classes.
Total number of students = Number of girls + Number of boys
Total number of students = 108 girls + 124 boys
Total number of students = 232
Number of classes = 8
To find the number of students in each class, we divide the total number of students by the number of classes:
Number of students in each class = Total number of students / Number of classes
Number of students in each class = 232 / 8
Number of students in each class = 29
Therefore, there are 29 students in each fifth-grade class at Ridgeview Intermediate School.
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A 2-column table with 10 rows. the first column is labeled x with entries 0.5, 1, 1, 1.5, 2, 2, 2.5, 3.5, 3.5, 4. the second column is labeled y with entries 1, 1, 2, 3, 2, 5, 4, 5, 6, 7. a graph shows the horizontal axis numbered 1 to 4 and the vertical axis numbered 1 to 7. a line increases from 0 to 4. the regression calculator shows the relationship between the hours devin spent playing a video game, x, and the levels he achieved, y. which number of hours can be used to make an extrapolation of the level he could achieve? 2 3 4 5
Answers
Based on the graph of this regression calculator, the number of hours that can be used to make an extrapolation of the level he could achieve is: A. 2.
What is a regression line?A regression line can be defined as a statistical line that best describes the behavior of a data set and such, it is a line that best fits a set of data.
How to determine number of hours?From the graph of this regression calculator, we can deduce that the linear regression is given by this function y ≈ 1.62x + 0.117; r ≈ 0.92.
Thus, the extrapolation would be given by:
0.14999 ≤ x ≤ 4.35.
0.39999 ≤ y ≤ 7.6.
Therefore, two (2) number of hours can be used to make an extrapolation of the level he could achieve.
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Answer:
answer is 5
Step-by-step explanation:
Pls Answer A and B. You don’t need to explain. Thank you!!
Answers
a). Amount of money in Kareem’s acc:
650 - 40x
Amount of money in Karen’s acc:
850 - 65x
b). 650 - 40(8) = 850 - 65(8)
Pythagorean Theorem question
Answers
a^2 + b^2 = c^2
18^2 + 24^2 = c^2
18 and 24 are both divisible by 6, so you can divide them both by 6 to make the equation easier to solve.
3^2 + 4^2 = c^2
25 = c^2, so c = 5
Multiply 5 by the 6 we divided by earlier to get a hypotenuse of 30.
The area equals base times height divided by two, so we can divide 84 by 2 and then multiply by 30 to get the area.
84/2= 42
42 x 30 = 1260 inches squared is the area
Your answer is going to be 1260
Explanation:
Your Welcome
Indicate below weather the equation in the box is true or false
Answers
Answer:
False
Step-by-step explanation:
4/8 equals to 1/2 but 6/10 equals to 3/5. Correct would be if it was 5/10
Find the value of a that makes each system a dependent system.
3y = 2x , 6y - a - 4x = 0
Answers
The value of 'a' that makes the given system a dependent system is 4.
To make the given system a dependent system, we need to find the value of 'a' that makes both equations equivalent or proportional.
Let's begin by rearranging the first equation so that it is in the standard form y = (2/3)x.
Now, let's substitute this expression for y in the second equation and simplify:
6y - a - 4x = 0
6(2/3)x - a - 4x = 0
4x - a = 0
We can see that if we choose 'a' to be equal to 4, then both equations will be equivalent. In other words, the system will become a dependent system with infinitely many solutions.
To see why, let's substitute 'a' as 4:
6y - 4 - 4x = 0
6y - 4x = 4
Now, if we compare this equation to the first one we wrote, y = (2/3)x, we can see that they are equivalent. Thus, any solution that satisfies the first equation will also satisfy the second equation, and vice versa. This means that we have infinitely many solutions to the system.
In conclusion, the value of 'a' that makes the given system a dependent system is 4.
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Health and safety guidelines set the highest sound intensity level in the workplace to 90. 0 db. One workshop with 32 similar machines produces a sound intensity level of 92. 0 db. How many of them must be shut down to bring the workshop into compliance with the guidelines?.
Answers
The sound intensity level should be decreased by 2 dB to carry the studio into consistency with the rules.
A decrease of 2 dB can be accomplished by one or the other by closing down a portion of the machines (since the sound intensity level declines by 6 dB for each splitting of the sound power) or by introducing sound-sealing materials.
Thus, to carry the studio consistent with the rules, 16 machines would need to be closed down.
It's vital to follow well-being and security rules in the working environment to guarantee the prosperity of representatives and forestall hearing harm. Decreasing the number of machines or introducing soundproofing materials can bring the studio into consistency.
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Given f(x)=-2x-1, what is the value of f(5)
Answers
Answer:
x=-11 this is right
1. Solve for the unknown in each triangle. Round each answer to the nearest tenth.
Answers
The values of the missing sides are;
a. x = 35. 6 degrees
b. x = 15
c. x = 22. 7 ft
d. x = 31. 7 degrees
How to determine the valuesTo determine the values, we have;
a. Using the tangent identity;
tan x = 5/7
Divide the values
tan x = 0. 7143
x = 35. 6 degrees
b. Using the Pythagorean theorem
x² = 9² + 12²
find the square
x² = 225
x = 15
c. Using the sine identity
sin 29= 11/x
cross multiply the values
x = 11/0. 4848
x = 22. 7 ft
d. sin x = 3.1/5.9
sin x = 0. 5254
x = 31. 7 degrees
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need help asap! look at the picture and let me know please
Answers
Answer:
y=-x+9
Step-by-step explanation:
help me pls working on quizizz :(
Answers
here your answer mate
3.25
hope it helps ☺️✌️
Answer:
3.25
Step-by-step explanation:
16/13 = 4/r
16 × r = 13 × 4
16r = 52
r = 52/16 = 3.25
What would the value of the exponent be?
Can someone tell me the answer? Thank you
❤️
Answers
Answer:
\( {11}^{7} \\
or\\19,487,171\)
Step-by-step explanation:
\((b)( {b}^{a} ) \\ plug \: a = 6 \: and \: b = 11 \\ \\ (b)( {b}^{a} ) \\ \\ = (11)( {11}^{6} ) \\ \\ = {11}^{6 + 1} \\ \\ = {11}^{7} \\\\= 19,487,171\)
HELPpppp
A standard deck of 52 playing cards contains 13 cards in each of four suits: hearts, diamonds, clubs, and spades. Four cards are drawn from the deck at random.
What is the approximate probability that exactly three of the cards are diamonds???
Answers
Answer:
0.25 is the probability
Step-by-step explanation:
If there are 13 diamonds in a deck of 52 cards, dividing 13 by 52 will get you 0.25. This is the probability of getting a diamond from the deck of 52 cards.
DeWayne stands on a rock that is (+10) feet compared to the surface of the water, as shown with the X below. What is the distance from where DeWayne is standing to (–10) feet below the surface of the water?
Answers
Answer:
Step-by-step explanation:
I do t k ow the answer
what are the slope and y-intercept of the line y=3x -4?
Answers
Slope = 3
Y-intercept = -4
===========================================================
This equation is written in slope-intercept form, which looks like so:-
\(\bigstar{\boxed{y=mx+b}\)
where
m is the slope
b is the y-intercept
Now, what is the slope?
Hint:- The slope is the coefficient of x, and the y-intercept is the constant.
That's right! The slope is 3, and the y-intercept is -4.
=========================================================
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)
Which property is 5+ a = a + 5 ?
Select one:
O a. Commutative Property of Addition
O b. Identity Property of Addition
O c. Commutative Property of Multiplication
O d. Inverse Property of Addition
Answers
Answer:
\(commutative \: property \: of \: addition \\ thank \: you\)
15. In a school, the ratio of boys and girls is 4:5, when 100 girls leave the school, the ratio becomes 6:7. How many boys are there in the school
Answers
Step-by-step explanation:
the ratio of boys and girls is equal to 4:5
let the number of boys be x
and the number of girls be y
so form 1st statement
x:y=4:5
now 2nd statements
x:y-100=6:7
Therefore solving equations 1 and 2
x=1200
y=1500
f(x)=2x^2+9
Find f(-5)
Answers
Answer:
59
Step-by-step explanation:
Given
f(x) = 2x² + 9
f ( -5) = 2 * ( -5)² + 9
= 25 * 2 + 9
= 50 + 9
= 59
════════ ∘◦❁◦∘ ════════
Answer = 59════════════════════
Knownf(x) = 2x² + 9
════════════════════
Questionf(-5) = ?
════════════════════
Way to do#as you the x inside the (x) changed into (-5) it means that you need to change the x into -5.
f(-5) = 2(-5)² + 9
= 2 × 25 + 9
= 50 + 9 = 59
#So f(-5) = 59
════════════════════
On january 14, edamame industries purchased supplies of $700 on account. the entry to record the purchase will include?
Answers
The entry to record the purchase will include: a debit to Supplies and a credit to Accounts Payable
What are supplies?Supplies are the small items, used in the company's overall operation. Supplies used during the period will be reported as supplies expense and the unused supplies will be reported in the balance sheet as an asset.Now, given: Purchased supplies = $500 (on account).
To find: What does entry to record the purchase include?
Now,
The supply asset will grow, which will cause a debit to be applied to it. It is believed to have been purchased on account, which increased (credited) the account for payments due.Hence, the entry to record the purchase will include: a debit to Supplies and a credit to Accounts Payable.
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A significance test about a proportion is conducted using a significance level of 0.05. The sample statistic is 0.12. The p-value is 0.03? a) If H0 were true, for what probability of a Type I error was the test designed?
b) What conclusion (reject or fail to reject) would you make for this test?
c) If this test resulted in a decision error, what type of error was it?
Answers
Answer: 28282
Step-by-step explanation:
I think
Find the area of the shaded segment of the circle
Answers
I need more info for your problem :
Maybe this could help you :Assume a sector having a radius
Assume a sector having a radius r and a central angle of a degrees.The sector's area will be \(A^{2}\) = (a / 360 °)* \(\pi\)*\(r^{2}\)
The area of an equilateral triangle having a side lenght a is A =( \(\sqrt{3}\)/4) * \(a^{2}\)