The endpoints of (MP)are M(2,1) and P(12,6). If point K partitions (MP) in a ratio of MK:KP = 3:2, what are the coordinates of K?
Answers
Answer:
K(8, 4)
Step-by-step explanation:
Given:
M(2, 1), P(12, 6)
MK:KP = 3:2
Required:
Coordinates of K
SOLUTION:
Coordinates of K can be determined using the formula below:
[tex] x = \frac{mx_2 + nx_1}{m + n} [/tex]
[tex] y = \frac{my_2 + ny_1}{m + n} [/tex]
Where,
[tex] M(2, 1) = (x_1, y_1) [/tex]
[tex] P(12, 6) = (x_2, y_2) [/tex]
[tex] m = 3, n = 2 [/tex]
Plug in the necessary values to find the coordinates of K:
[tex] x = \frac{mx_2 + nx_1}{m + n} [/tex]
[tex] x = \frac{3(12) + 2(2)}{3 + 2} [/tex]
[tex] x = \frac{36 + 4}{5} [/tex]
[tex] x = \frac{40}{5} [/tex]
[tex] x = 8 [/tex]
[tex] y = \frac{my_2 + ny_1}{m + n} [/tex]
[tex] y = \frac{3(6) + 2(1)}{3 + 2} [/tex]
[tex] y = \frac{18 + 2}{5} [/tex]
[tex] y = \frac{20}{5} [/tex]
[tex] y = 4 [/tex]
The coordinates of K = (8, 4)
Related Questions
Solve the equation 15.6 + (-1.8) =
Answers
Since +(-) becomes (-) we can write the given problem as
15.6-1.8
Subtraction gives us 13.8
:)
8 plus 78 oooooooooooooooooooooooooooooooooooooooooooooo
Answers
Answer:
86 ✌️
Step-by-step explanation:
just get a calculator
The admission fee at an amusement park is 20$ for children and 35$ adults. On a certain, day 264 people entered the park, and the admission fees collected totaled $6780. How many children and how many adults were admitted?
Answers
Answer:
100 Adults and 164 Children
Step-by-step explanation:
To solve this we will need to write two equations to solve for the two unknowns. Firstly, we know that tickets are 20 for children and 35 for adults, and that the total price was 6780. We can write an expression to represent this. 6780 is the total price, this also means it is the price of all the adults + the price of all the children. The total price of the adults tickets is the price of each ticket multiplied by the number of adults, so the total price of adult tickets can be represented by: 35A, 35 being the ticket price per adult, and A being the number of adults. Similarly the total children's price can be expressed as such: 20C, 20 being the price per child, and C being the number of children. Since we know that these two values total to 6780, we can now form an equation:
35A (total adult price) + 20C (total children price) = 6780
35A+20C=6780
Now we need another expression so we can substitute for one of the values. The other piece of information we are given, is that a total of 264 people entered the park. This means that the total number of adults + the total number of children = 264. Since we already have variables for the numbers of adults and children we now have our second equation:
A (number of adults) + C (number of children) = 264
A+C=264
Now we can use this second equation to substitute for one of the values in the first equation. Let's substitute for children:
If we rearrange the second expression we will get:
A+C-A=264-A
C=264-A
So now we substitute this expression into our first formula:
35A+20C=6780
C=264-A
35A+20(264-A)=6780
Now since we only have one unknown, we can simplify, expand and solve!
35A+20*264-20*A=6780
35A+5280-20A=6780
35A-20A+5280-5280=6780-5280
15A=1500
15A/15=1500/15
A= 100
A total of 100 adults were admitted.
Now we can use the number of adults to find the number of children using our second formula:
C=264-A
C=264-100
C=164
And there we are! A total of 100 adults and 164 children were admitted.
Hope this helped!
Which of the following relations is a function?
OA. (-7, 1), (0, -5), (1,5), (5, 1)
OB. (-7, 4), (0, 6), (-7, 3), (5,2)
C. (1, 1), (0, 4), (-7, 1), (1,-5)
OD. (-7,1), (0,4), (1,-5), (0, 6) ting
Answers
Answer:
A
Step-by-step explanation:
It would be "a" because the x points are all different, as seen on the others they all have at least one similar x.
1 added by 1 is
A. 2
B. 3
C. 5
D. 11
Explain your answer
Answers
Answer:
A. 2
Step-by-step explanation:
When adding two numbers, you are combining their values.
In this problem, you are combining the value of 1 with the value of 1. When you combine them, you are saying that you have two 1's. So in this problem, you combine both ones and get a final answer of 2.
The brain volumes (cm3) of 20 brains have a mean of 1162.5 cm3 and a standard deviation of 126.7 cm3. Use the given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For such data, would a brain volume of 1405.9 cm3 be significantly high?
Answers
Answer:
No, the brain volume of 1405.9cm³ would not be significantly high.
Step-by-step explanation:
We would use the Empirical rule to determine the answer for this question.
The empirical rule - formula states that:
a) 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ
b) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ
The question asks us to use the given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or significantly high.
The range rule of thumb tells us that the range is four times the standard deviation. So we say that the usual values will be 2 standard deviations away from the mean of the data distribution.that the values are usually within 2 standard deviations from the mean.
Hence, μ = mean =1162.5 cm³
σ = Standard deviation = 126.7 cm³
μ – 2σ
1162.5 cm³ - 2(126.7 cm³)
= 1162.5 cm³ - 253.4 cm³
= 909.1cm³
μ + 2σ
1162.5 cm³ + 2(126.7 cm³)
= 1162.5 cm³ + 253.4 cm³
= 1415.9cm³
From the calculation above, we can see that for such data, 1405.9 cm³ is within the lower limits of 909.1 cm³ and the higher limits of 1415.9 cm³. Therefore the brain volume of 1405.9 cm³ would not be significantly high.
I need help on the value of X
Answers
I did 24 hours on my speed paint if i did it for 4 more days how many minutes would that be?
Answers
Answer:
7,200 minutes.
Step-by-step explanation:
5 days * (24 hours / 1 day) = 5 * 24 hours = 120 hours
120 hours * (60 minutes / 1 hour) = 120 * 60 minutes = 7,200 minutes.
Hope this helps, and I love your art!
Answer:
7,200
Step-by-step explanation:
Phyllis, Kelly, Erin, and Renee bought a gift for their dance instructor. The total cost of the gift, 1 including tax, was $55.80. Erin paid $14, Kelly paid of the cost, Renee paid 25% of the cost, and Phyllis paid the remaining cost. What amount did Phyllis pay? $41.80
Answers
Answer:27.85
divide 55.8 by 100 and you get 0.558 and then multiply that by 25 which is 13.95 and then add that with 14 dollars.That equals 27.95 dollors for kelly and renee and then lastly subtract the 27.95 dollars from the total amount of the price to get phyllis's price
A negative number multiplied by a negative number will result in a ___ product.
Answers
Answer:
Positive product
Step-by-step explanation:
[tex] \sqrt{3969} [/tex]
Answers
Answer:
63
Step-by-step explanation:
The result of accounting root is a fortified number
63²= 3969
Determine whether the given segments have the same length. Complete the justification of your answer,
AB and BC
The length of AB is
length
The length of BC is /
.So, AB and BC (select)
the same length
Answers
Answer:
No does not contain the same length
Step-by-step explanation:
Given that
A(-4,2) , B (1,4), C (2, -1)
Now
AB would be
= [tex]\sqrt{(1-(-4))^2 + (4-2)^2} \\\\= \sqrt{29}[/tex]
And, BC is
[tex]= \sqrt{(2-1)^2 + 1-(-4))^2} \\\\= \sqrt{26}[/tex]
As we can see that the AB and BC are not equaled
So,
AB ≠ BC
Due to the different length
Therefore they do not contains the same length
We simply applied the distance formula due to which the length could be determined and the same is to be considered
Find the measure of x
Answers
use the point slope form to find the linear equation of a line that passes through the points 2,-1 and 10,7
Answers
Answer:
Step-by-step explanation:
Y2-y1 , x2-x1
7-3=5
10-(-1=11
5/11 so y=5/11x is the answer
Answer:
Y= 1x+-3
Step-by-step explanation:
Use the given conditions to write an equation in point-slope form. Keep parenthesis in point-slope form. slope = 7, passing through (1,-3)
Answers
Answer:
Step-by-step explanation:
y + 3 = 7(x - 1)
y + 3 = 7x - 7
y = 7x - 10
Which problem can be solved with the equation 1.75+(-1.75)=0?
Answers
Answer:
bank account one is the answer
Step-by-step explanation:
bank account one is the answer
Hope it helps
Pls mark as brainliest
Problem number 4 is solved by the equation 1.75 + (-1.75).
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
In problem number 4, the question is the number Sam deposited in the amount of $1.75 and then purchased a movie ticket for $1.75.
The account balance will be represented by the equation.
Account = 1.75 + (-1.75)
The actual account balance will become zero.
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which value is a solution to the inequality 9-y>12?
Answers
Hey there!
[tex]Answer:\boxed{y<-3}[/tex]
[tex]Explanation:[/tex]
[tex]9-y>12[/tex] Inequality
Let's start by simplifying both sides of the inequality.
[tex]-y+9>12[/tex]
Now subtract 9 from both sides.
[tex]-y+9-9>12-9\\-y>3[/tex]
Now divide both sides by -1.
[tex]\frac{-y}{-1}>\frac{3}{-1}[/tex]
[tex]y<-3[/tex]
Hope this helps!
what is the least common multiple of 6, 12 , and 15
Answers
Answer:
It's 3.
Step-by-step explanation:
3x2=6
3x4=12
3x5=15
An arhitect wants to draw a rectangle with a diagonal of 20 inches. The length of the rectangle is to be 8 inches more than twice the width.what dimensions should she make the rectangle
Answers
The diagonal of a rectangle = sqrt(w^2 + l^2)
w = width
l = length
In this problem,
The diagonal = 20 in
w = x
l = 2x + 8
Let's plug our numbers into the formula above.
20in = sqrt((x)^2 + (2x + 8)^2)
Let's simplify the inside of the sqrt
20 in = sqrt(5x^2 + 32x + 64)
Now, let's square both sides.
400 = 5x^2 + 32x + 64
Subtract 400 from both sides.
0 = 5x^2 + 32x - 336
Factor
0 = (5x - 28)(x + 12)
Set both terms equal to zero and solve.
x + 12 = 0
Subtract 12 from both sides.
x = -12
5x - 28 = 0
Add 28 to both sides.
5x = 28
Divide both sides by 5
x = 28/5
The width cant be a negative number so now we know that the only real solution is 28/5
Let's plug 28/5 into our length equation.
Length = 2(28/5) + 8 = 56/5 + 8 = 96/5
In conclusion,
Length = 96/5 inches
Width = 28/5
Find the 9th term of the geometric sequence 4, 16, 64, ...
Answers
Answer: Just keep multiplying by 4 after 64 like multiply 64 times 4 and do that number times and keep doing that until its the 9th answer :)
Step-by-step explanation:
A geometric series is the sum of an unlimited number of terms with a fixed ratio between them. The 9th term of the geometric sequence 4, 16, 64, ... is 262,144.
What is geometrical series?A geometric series is the sum of an unlimited number of terms with a fixed ratio between them.
The first term of the series is 4, while the ratio of the geometric sequence:
[tex]\rm Ratio, r = \dfrac{16}{4} = 4[/tex]
Thus, the 9th term of the geometric series can be written as,
[tex]a_n = a_1 \times r^{(n-1)}\\\\a_9 = 4 \times 4^8\\\\a_9 = 262,144[/tex]
Hence, the 9th term of the geometric sequence 4, 16, 64, ... is 262,144.
Learn more about Geometrical Series:
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Anurak has nickels, dimes, and pennies in his pocket. The coins in Anurak's pocket have a total value of 75 cents. He has three more nickels than dimes and five times as many pennies as dimes. How many coins of each type does Anurak have?
Answers
Answer:
Anurak has 15 pennies, 6 nickels and 3 dimes.
Step-by-step explanation:
We must have these informations in mind:
1) A penny is a 1-cent coin.
2) A dime is a 10-cent coin.
3) A nickel is a 5-cent coin.
Let be [tex]x[/tex], [tex]y[/tex], [tex]z[/tex] the quantities of pennies, nickels and dimes, respectively. From statement we get that to value in Anurak's pocket is represented by this mathematical expression:
[tex]0.01\cdot x + 0.05 \cdot y + 0.10\cdot z = 0.75[/tex] (Eq. 1)
In addition, we get the following identities:
i) He has three more nickels than dimes
[tex]z + 3 = y[/tex] (Eq. 2)
ii) And five times as many pennies as dimes
[tex]x = 5\cdot z[/tex] (Eq. 3)
The system of linear equations is now reduced: (Eqs. 2, 3) in (Eq. 1)
[tex]0.05\cdot z +0.05\cdot z + 0.15 + 0.10\cdot z = 0.75[/tex]
[tex]0.20\cdot z = 0.60[/tex]
[tex]z = 3[/tex]
The remaining variables are [tex]y = 6[/tex] and [tex]x = 15[/tex].
Anurak has 15 pennies, 6 nickels and 3 dimes.
Answer:
Anurak has 15 pennies, 6 nickels and 3 dimes.
Step-by-step explanation:
Round 3,760 to the nearest hundred.
Answers
Answer:
3,800
Step-by-step explanation:
Rounding something means going up or down basically. To the nearest hundred means rounding up or down until the number is exactly 100, 200, 300, etc.. If it's 50 or higher it'll always be rounded up. so 760 is rounded to 800 as "60" is higher than "50."
Hope this helps and have a nice day!
Answer:
3,800
I hope this helps!
What is the mid point between (0,0) and (3,4)
Answers
Answer:
Midpoint of a line segment
(xM,yM) = (4, 5).
Answer:
I think it's point (1.5,2).
Step-by-step explanation:
3 ÷ 2 = 1.5
4 ÷ 2 = 2
Please help
Using the mileage chart below, find the distance between Spearfish and
Madison
sus
Huron
Η
22.223 Mehellye
O A. 191 miles
O B. 45 miles
O C. 123 miles
O D. 390 miles
Answers
The distance between Spearfish and Madison is 390 miles.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is a mileage chart.
Assume that the distance between Spearfish and Madison is [x] miles.
Then the point of intersection of Spearfish row and Madison column would give the distance between both of them as 390 miles. So, we can write -
x = 390 miles
Therefore, the distance between Spearfish and Madison is 390 miles.
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I can’t find the answer please help
Answers
Answer:
5.4 & 5.4
Step-by-step explanation:
CD²=5²+2²=29
CD=AB=5.4
Answer:
C) 5.4 and 5.4
Step-by-step explanation:
CD: 5²+2²=c² = 25+4=c² = 29=c² = c=√29 = 5.4
AB: 5²+2²=c² = 25+4=c² = 29=c² = c=√29 = 5.4
-i+5=t-19 please help!!
Answers
Answer: t=24−i
Step-by-step explanation:
Truffles cost $3 each and caramels cost $2 each. If t represents the number of truffles and c represents the number of caramels, explain what each of the following expressions represents. Explain your reasoning for each. a) t +c b) 3t +2c
Answers
Answer:
a) Combined amount of truffles and caramels bought
b) Amount of money spent in total on both truffles and caramels
Elizabeth is a manager at a nursery and is in charge of displaying potted trees in a row Elizabeth has 150 citrus trees and 180 Palm trees she wants to make rows of trees so that each row has the same number of trees and each tree is in the same row. if the citrus trees and the palm trees must not be mixed in the rows what is the largest number of trees she can have in a row
Answers
Answer: the greatest number of trees that ElizaBeth can have in a row is 30
Step-by-step explanation:
given data:
citrus trees = 150
palm trees = 180
As we have to find the greatest number of trees that Elizabeth can have in a row, we will find the GCF or greatest common factor.
150 = 2 x 3 x 5 x 5
180 = 2 x 2 x 3 x 3 x 5
Greatest common factor is = 2 x 3 x 5 = 30
Therefore, the largest number of trees that ElizaBeth can have in a row is 30.
7x + 15 - 9x = 5 plz help
Answers
Answer:
x =5
Step-by-step explanation:
[tex]7x + 15 - 9x = 5\\\\\mathrm{Group\:like\:terms}\\7x-9x+15=5\\\\\mathrm{Add\:similar\:elements:}\:7x-9x=-2x\\-2x+15=5\\\\\mathrm{Subtract\:}15\mathrm{\:from\:both\:sides}\\-2x+15-15=5-15\\\\Simplify\\-2x=-10\\\\\mathrm{Divide\:both\:sides\:by\:}-2\\\frac{-2x}{-2}=\frac{-10}{-2}\\\\Simplify\\x = 5[/tex]
State how many solutions, 3 + 2x + 1 = 2x + 3
Answers
Answer:
Step-by-step explanation:
3 + 2x + 1 = 2x + 3
2x + 4 = 2x + 3
4 ≠ 3
no solution