The midpoint of KL is M(8, 3). One endpoint is L(8, 0). Find the coordinates of the other
endpoint K.
Answers
Answer: K(8,6)
Step-by-step explanation:
M(8,3) - the midpoint of KL L(8,0) K(x,y)=?
\(\displaystyle\\Mx=\frac{Kx+Lx}{2}\)
Multiply both parts of the equation by 2:
\(2Mx=Kx+Lx\\2Mx-Lx=Kx+Lx-Lx\\2Mx-Lx=Kx\\Mx=8\ \ \ \ Lx=8\\Hence,\\2(8)-8=Kx\\16-8=Kx\\8=Kx\\\\2My-Ly=Ky\\My=3\ \ \ \ Ly=0\\Hence,\\2*(3)-0=Ky\\6-0=Ky\\6=Ky\\Thus,\\K(8,6)\)
Related Questions
Simplify: 12 + 2 x 3 + ( 43 - 12)
68
54
70
18
Answers
What will be the coordinates of N after a 90° counterclockwise rotation around the origin?
A. (-7,-3)
B. (-7,0)
C. (3,7)
D. (-3,-7)
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Answer:
A. (-7,-3)
D.(-3,-7) If clockwise
–2 over 5 (15 – 20d).
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Which system of inequalities is shown?
Answers
Answer:
the answer is D
Step-by-step explanation:
y>4 : the shaded region is above the line
y>x : the shaded region is above the line
PLEASE HELP!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
x= -3
y=2
Step-by-step explanation:
help?! Will mark brainliest
Answers
Answer(s):
3. Option B
4. Option D
Step-by-step explanation:
Question 3:
2/3 = 1.2/x=> 2 × x = 1.2 × 3=> 2x = 3.6=> x = 3.6/2=> x = 1.8 [Option B]Question 4:
8/15 = 24/x=> 8 × x = 24 × 15=> 8x = 3 × 8 × 3 × 5=> 8x = 9 × 40=> 8x = 360=> x = 360/8=> x = 45 [Option D]Let (Xi, y), i = 1, 2, 3, 4, 5 be a set of five distinct points with integer coordinates in the xy plane. Show that the midpoint of the line joining at least one pair of these points has integer coordinates. Multiple Choice A. By the pigeonhole principle, the coordinates of the midpoint of the line joining one pair of these points must be integers; because the coordinates of the five points are all integers. B. By the pigeonhole principle, there are 10 numbers and it is always possible for the midpoint of the line joining one pair of these points to have integer coordinates. C. By the pigeonhole principle, if we have 5 points, then at least two of these points will have the same parity (both odd or both even). The midpoint of the segment joining these two points will therefore have integer coordinates. D. By the pigeonhole principle, if we have 5 points, then exactly two of these points will have the same parity (both odd or both even). The midpoint of the segment joining these two points will therefore have integer coordinates.
Answers
The correct answer is (C) by the pigeonhole principle, if we have 5 points, then at least two of these points will have the same parity (both odd or both even). The midpoint of the segment joining these two points will therefore have integer coordinates
The statement that at least one pair of the five distinct points with integer coordinates in the xy plane has a midpoint with integer coordinates can be proven using the pigeonhole principle.
Assume that we have five distinct points with integer coordinates, (X1, Y1), (X2, Y2), (X3, Y3), (X4, Y4), and (X5, Y5) in the xy plane. To find the midpoint of the line joining two points, we take the average of their x-coordinates and the average of their y-coordinates. Thus, the x-coordinate of the midpoint of the line joining two points (Xi, Yi) and (Xj, Yj) is (Xi + Xj)/2, and the y-coordinate is (Yi + Yj)/2.
Consider the x-coordinates of the five points. These are integer values, and there are only five of them. Therefore, at least two of them must be equal, by the pigeonhole principle. Without loss of generality, let us assume that X1 = X2.
Now, consider the midpoint of the line joining (X1, Y1) and (X2, Y2). Its x-coordinate is (X1 + X2)/2 = X1, which is an integer. Therefore, we have found a midpoint with an integer x-coordinate.
Alternatively, consider the parity (even or oddness) of the x-coordinates of the five points. There are only two possible parities, and there are five points. Therefore, at least two points must have the same parity, by the pigeonhole principle. Without loss of generality, assume that (X1, Y1) and (X2, Y2) have the same parity. Then, the midpoint of the line joining these two points has an integer x-coordinate, since the sum of two even (or two odd) integers is even.
Therefore, we have shown that at least one pair of the five distinct points with integer coordinates in the xy plane has a midpoint with integer coordinates. The correct answer is (C) by the pigeonhole principle, if we have 5 points, then at least two of these points will have the same parity (both odd or both even). The midpoint of the segment joining these two points will therefore have integer coordinates.
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Ex: Solve by reduction of order: 1) y ′′
+16y=0 given y 1
=cos4x
Answers
The general solution to the differential equation y'' + 16y = 0 is y(x) = (c₁ + c₂) * cos(4x)
To solve the differential equation y'' + 16y = 0 using reduction of order, we'll assume a second solution of the form y₂(x) = u(x) * y₁(x), where y₁(x) is a known solution and u(x) is an unknown function.
Given y₁(x) = cos(4x), we'll differentiate it to find y₁'(x) and y₁''(x):
y₁'(x) = -4sin(4x)
y₁''(x) = -16cos(4x)
Now we substitute y₂(x) = u(x) * y₁(x) into the original differential equation:
y'' + 16y = 0
(-16cos(4x)) + 16(u(x) * cos(4x)) = 0
Simplifying the equation:
-16cos(4x) + 16u(x) * cos(4x) = 0
cos(4x)(-16 + 16u(x)) = 0
For this equation to hold for all values of x, we must have (-16 + 16u(x)) = 0.
Solving for u(x):
-16 + 16u(x) = 0
16u(x) = 16
u(x) = 1
Now we have the second solution:
y₂(x) = u(x) * y₁(x)
y₂(x) = 1 * cos(4x)
y₂(x) = cos(4x)
Therefore, the general solution to the differential equation y'' + 16y = 0 is:
y(x) = c₁ * y₁(x) + c₂ * y₂(x)
y(x) = c₁ * cos(4x) + c₂ * cos(4x)
y(x) = (c₁ + c₂) * cos(4x)
Where c₁ and c₂ are arbitrary constants.
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how many simple random samples of size 3 can be selected from a population of size 8?
Answers
In a population of size 8, there are 56 different simple random samples of size 3 that can be selected using permutation combination.
To determine the number of simple random samples of size 3 that can be selected from a population of size 8, we can use the combination formula. The combination formula calculates the number of ways to choose a subset of a given size from a larger set without considering the order of the elements. In this case, we want to choose 3 elements from a population of 8.
Using the combination formula, the number of simple random samples of size 3 can be calculated as \(\[C(8, 3) = \frac{{8!}}{{3! \cdot (8-3)!}} = 56\]\). Here, "C" represents the combination operator and the numbers inside the parentheses denote the values for the formula. The factorial symbol (!) indicates the product of all positive integers less than or equal to the number.
Therefore, in a population of size 8, there are 56 different simple random samples of size 3 that can be selected. Each sample consists of 3 elements chosen from the population without replacement, meaning that once an element is chosen, it is not replaced before selecting the next element.
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I am confused. I believe it is 5(x^2+2)=45
Here is the problem: 5 times the square of a number and 2 is 45.
Answers
seen previously. i have 18 distinguishable socks in my drawer: 8 white, 6 brown, and 4 blue. in how many ways can i choose a pair of socks, provided that i get two socks of the same color?
Answers
The number of possible ways to choose a pair of socks, then, is 18 x 2 = 36.
What is pair?Pair is a set of two related items, usually of the same type. For example, a pair of shoes, a pair of gloves, a pair of socks, a pair of jeans, a pair of scissors, or a pair of sunglasses. Pairs are often used in mathematics and statistics, where the two elements are usually referred to as X and Y.
There are 18 possible ways to choose a pair of socks from your drawer: 8 possibilities for choosing a pair of white socks, 6 for brown, and 4 for blue. Given that you have to choose two socks of the same color, you can only choose a pair of socks from one of the three colors, so the total number of ways to choose a pair of socks is 8 + 6 + 4 = 18.
In each case, you have two options to choose from: either choose a matching pair of socks, or choose two different socks of the same color. The number of possible ways to choose a pair of socks, then, is 18 x 2 = 36.
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what is the slope of the line on this graph
Answers
Answer:
m = 1/2
Step-by-step explanation:
Look at the points on the graph and determine what the slope would be using the slope formula. y2-y1 / x2-x1.
2 - 0 / 0 - (-4)
2/4
1/2
Answer:
the slope of the line is 2
Step-by-step explanation:
use the formula for the slope of a line: y2-y1/x2-x1
this will give you 2-0/0-(-4) = 2/4
simplified to 2 for the slope.
if the answer you need is just the slope ten it would be 2
if you're looking for the equation of the line it would be y=2x+2
z scores: first aid course the college physical education department offered an advanced first aid course last semester. the scores on the comprehensive final exam were normally distributed, and the z scores for some of the students are shown below: robert, 1.10 juan, 1.70 susan, 2.00 joel, 0.00 jan, 0.80 linda, 1.60 (a) which of these students scored above the mean? (b) which of these students scored on the mean? (c) which of these students scored below the mean? (d) if the mean score was m 5 150 with standard deviation s 5 20, what was the final exam score for each student?
Answers
Robert, Juan, Susan, and Linda scored above the mean, Joel scored on the mean, and Jan scored below the mean on the advanced first aid course's final exam based on their z-score. Their final exam scores were 172, 184, 190, 150, 166, and 182, respectively.
The students with positive z-scores scored above the mean. So, Robert, Juan, Susan, and Linda scored above the mean. The student with a z-score of 0.00 scored on the mean. So, Joel scored on the mean. The student with a negative z-score scored below the mean. So, Jan scored below the mean.
To find the final exam score for each student, we can use the formula:
z = (x - m) / s
where z is the z-score, x is the final exam score, m is the mean score, and s is the standard deviation.
Rearranging the formula, we get:
x = z * s + m
Using the given values of z, s, and m, we can find the final exam score for each student:
Robert: x = 1.10 * 20 + 150 = 172
Juan: x = 1.70 * 20 + 150 = 184
Susan: x = 2.00 * 20 + 150 = 190
Joel: x = 0.00 * 20 + 150 = 150
Jan: x = 0.80 * 20 + 150 = 166
Linda: x = 1.60 * 20 + 150 = 182
So, the final exam scores for Robert, Juan, Susan, Joel, Jan, and Linda are 172, 184, 190, 150, 166, and 182, respectively.
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Find the sum of 4x2 - 4x + 10 and 2x2 + 5x – 8.
Answers
Step-by-step explanation:
\( {4x}^{2} - 4x + 10\)
\( {2x}^{2} + 5x - 8\)
\( {6x}^{2} + x + 2\)
Answer:
6x^2 +x +2
Step-by-step explanation:
Line up the terms
4x^2 - 4x + 10
+2x^2 + 5x – 8
----------------------------
6x^2 +x +2
The length of a rectangle is 5cm longer than its width.
If the perimeter of the rectangle is 62 cm , find its length and width.
Answers
Answer:
length = 18 cm & width= 13 cm
Step-by-step explanation:
w+w+5+w+w+5=62
4w+10=62
4w=52
w=13
w+5=13+5 = 18 cm
Given y = x^a + x^-b, find positive integers a and b such that x^2y’’ + 2xy’
Answers
The positive integers a and b such that x^2y’’ + 2xy’=12y is
a=6b=3What are integers?To find the second derivative of y, we can use the power rule for differentiation:
\($$y^{\prime \prime} = a(a-1)x^{a-2} - b(b+1)x^{-b-2}$$\)
Substituting this expression into the given equation, we get:
\($$x^2 (a(a-1)x^{a-2} - b(b+1)x^{-b-2}) + 2x(ax^{a-1} - bx^{-b-1}) = 12(x^a + x^{-b})$$\)
This simplifies to:
\($$x^2 a(a-1) - x^2 b(b+1) + 2ax - 2bx = 12x^a + 12x^{-b}$$\)
Matching powers of x on both sides, we get the following system of equations:
\($$\begin{cases} 2a = 12 & \text{for } x^0 \ a(a-1) - b(b+1) + 2 = 0 & \text{for } x^1 \ -2b = 12 & \text{for } x^{-1} \end{cases}$$\)
Solving this system of equations, we find that the positive integer solutions are a=6 and b=3.
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Jane takes out a loan for $100,000.00 over 10 years
and agrees to pay interest only at an annual rate of
8%. What will her monthly payment be?
Answers
$1799.10
Step-by-step explanation:Each year, the amount of money in the account is increased by 8%. This is the same as multiplying by 1.08 each year.
For 10 years, you multiply the original $100,000 by 1.08 a total of 10 times.
This tends to be simplified to:
\(100,000 * 1.08^{10}\)
This gives $215892.4997.
This is paid back over 10 years, which is 10 x 12 months, or 120 months.
Divide the $215892.4997 by 120 to get the monthly payment of:
$1799.10 (round to 2 decimal places as it is a currency)
Consider the following function ou the interval | 8, 27)
f(x) = 3x^2/3 - x
Find the critical point
Answers
The critical point of the function f(x) on the interval (8, 27) is x = 1/8.
How to find the critical points of a function?To find the critical points of a function, we need to find the values of x where the derivative of the function is zero or undefined.
The derivative of the function \(f(x) = 3x^(2/3) - x\) is:
\(f'(x) = 2x^(-1/3) - 1\)
To find the critical point, we set the derivative equal to zero and solve for x:
\(2x^(-1/3) - 1 = 0\)
\(2x^(1/3) = 1\)
\(x^(1/3) = 1/2\)
\(x = (1/2)^3\)
x = 1/8
So the critical point of the function f(x) on the interval (8, 27) is x = 1/8.
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Find the area of the resulting slick, assuming that it is one molecule thick, and that each molecule occupies a cube 0.50 μm on a side.
Answers
The area of the resulting slick is 1. 5 μm²
What is the area?
The formula for area of a cube is expressed as;
Area = 6 a²
Where,
a = length of its side
From the information given, we have that;
a = 0.50 μm
Substitute into the formula
Area = 6 × (0.50)²
Area = 6 × 0. 25
Area = 1. 5 μm²
Thus, the area of the resulting slick is 1. 5 μm²
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A nature center charges $35.25
for a yearly membership and $6.25 for a single
admission. Last
veek it sold a combined total of 50 yearly memberships and single
admissions for $660.50. How many memberships and how many single admissions
were sold?
Answers
Answer: 12 yearly admissions and 38 single admissions
Step-by-step explanation:
Let x be yearly membership
Let y be single admission
x+y=50 --> # of tickets sold
35.25x+6.25y=660.50 --> $ of tickets
Use elimination method to solve (multiply equation 1 by -3525 and equation 2 by 100)
-3525x-3525y=-176250
+ 3525+625y=66050
-----------------------------------
-2900y=-110200
y=38
Substitute y=38 into equation 1
x+38=50
x=12
Therefore, 12 yearly admissions and 38 single admissions were sold
There are 12 balls in a box. 3 are red and 9 are blue. A ball is chosen, and without replacement, another ball is chosen. What is the probability of getting two balls of the same color. Answer with a fraction.
Answers
The probability of getting two balls of the same color is 13/22.
How to calculate the probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true
Since there are 12 balls in a box and 3 are red and 9 are blue. The probability of picking reds will be:
= P(red) × P(red)
= 3/12 × 2/11
= 1/22
The probability of picking blues will be:
= P(blue) × P(blue)
= 9/12 × 8/11
= 6/11
Therefore, the probability of getting two balls of the same color will be:
= P(reds) + P(blues)
= 1/22 + 6/11
= 13/22
The probability is 13/22.
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Which expression is equivalent to 4 √10 ?
(૧/x
0 x ²
022
○ +³² (+ √/x)
0 +5
Answers
Unit 11 volume and surface area
homework 3: area of composite figures.
find the area of the figures. The figures with the shaded areas: find the area of the shaded object
Answers
To find the area of a shaded object within a composite figure, we need specific information or a visual representation of the figure. Without those details, it is not possible to provide an accurate calculation for the area of the shaded object.
The area of a composite figure is calculated by finding the sum of the areas of its individual components. However, the specific dimensions and arrangement of the figures in question are not provided. Consequently, without knowing the measurements or having a visual representation of the figures, it is impossible to determine the area of the shaded object accurately. To find the area of a shaded object within a composite figure, we would need to identify the individual components and their dimensions. This could involve breaking down the figure into simpler shapes, such as rectangles, triangles, circles, etc., and calculating their respective areas. Once the areas of the individual components are determined, we can sum them to find the total area of the composite figure. However, without specific information or a visual representation, it is not possible to calculate the area of the shaded object within the given composite figures.
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Does anyone know the answer? (8x+2) What does X equal?
Answers
Answer:
It would be 10x until you found what x is then u do the rest on yur own
Step-by-step explanation:
please help this is for my study guide thanks! (Find volume)
Answers
The formula to calculate the volume of a sphere is:
\(V=\frac{4}{3}\pi\cdot r^3\)Start by finding the radius using the diameter and dividing it by 2
\(\begin{gathered} r=\frac{D}{2} \\ r=\frac{2}{2} \\ r=1ft \end{gathered}\)then, replace the radius in the formula and find the volume
\(\begin{gathered} V=\frac{4}{3}\cdot\pi\cdot r^3 \\ V=\frac{4}{3}\cdot\pi\cdot(1)^3 \\ V=\frac{4\pi}{3} \end{gathered}\)elijah factors the polynomial p(x)=x^2 - 2x "-48" to find its zeroes are "-8" and 6. is elijah correct, and why?
Answers
Answer: Elijah is incorrect
Step-by-step explanation:
The factor of the polynomial is (x+6)(x-8). To find the zeroes, you must set each quantity to 0 so (x+6) = 0, get x alone, so x = -6, and (x-8) = 0 so x = 8. The zeroes are -6 and 8, not 6 and -8.
This is the same dilation that you use in question 3. What scale factor was used to create the dilated triangle MSV’? In your answer, keep the scale factor that was used in explain how you calculated.
Answers
From the information given, triangle M'S'V' was dilated to give triangle MSV. Since triangle MSV is an enlargement of triangle M'S.V, it means that the scale factor is greater than 1. To find the scale factor, we would find the ratio of the x and y coordiantes. We have
Scale factor = M/M' = - 3/- 2 = 3/2 = 1.5
Scale factor = 1.5
Taking a shower accounts for about 20% of your daily water usage. You use 60 gallons of water daily for other purposes. How many gallons of water do you use daily while taking a shower?
(How we are expected to do it is in the photo)
Answers
12/1 - 0.2
12/0.8
Rewrite the fraction
120/8
Simply into 15
The number of gallons of water you use daily while taking a shower is 12 gallons and the value of m in equation 8m + 5 = 6m + 1 is 2.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
As we know, the percentage is the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
For the percentage problem:
A number of gallons of water you use daily while taking a shower:
= 20% of 60
= (20/100)60
= 12 gallons
For the linear equations:
We have:
8m + 5 = 6m + 1
8m - 6m = 1 - 5
-2m = -4
m = 2
Similarly, we can solve any linear equation.
Thus, the number of gallons of water you use daily while taking a shower is 12 gallons and the value of m in equation 8m + 5 = 6m + 1 is 2.
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There are 15 squares and 6 triangles. What is the simplest ratio of triangles to total shapes?
Answers
Answer: 2:7
Step-by-step explanation:
\(\displaystyle\\\frac{6}{15+6} =\\\\\frac{6}{21} =\\\\\frac{2(3)}{7(3)} =\\\\\frac{2}{7} =\\\\2:7\)
The ratio of triangles to total shapes in simplest form is 2 : 7.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, There are 15 squares and 6 triangles.
Therefore, The total number of shapes is (15 + 6) = 21.
So, The ratio of triangles to total shapes is,
triangle/total shapes = 5/15 + 6.
triangles/total shapes = 6/21.
triangles : total shapes = 6 : 21 = 2 : 7
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name four fractions whose values are between 1/4 and 3/4
Answers
Answer:
ok don't panic it's organic
Answer:
\(\frac{1}{3} , \frac{1}{2} , \frac{3}{8} , \frac{5}{8}\)
Step-by-step explanation: