Right angled triangle is formed by the points (3, 2), (-2, -3) and (2,3).
Let the given points be,
A = (3, 2), B = (-2, -3) and C = (2, 3)
The formula for the distance between two points:
The length of the line segment bridging two points on a plane is known as the distance between the points.
The formula to find the distance between the two points is usually given by [tex]D = $$\sqrt{\left(X_2-X_1\right)^2+\left(Y_2-Y_1\right)^2}$$[/tex].
Therefore,
A = [tex](x_{1} , y_{1} )[/tex] = (3, 2), B = [tex](x_{2} , y_{2} )[/tex] = (-2, -3)
[tex]& \mathrm{AB}=\sqrt{(3+2)^2+(2+3)^2}=\sqrt{50}=5 \sqrt{2}[/tex] units
B = [tex](x_{1} , y_{1} )[/tex] = (-2, -3), C = [tex](x_{2} , y_{2} )[/tex] = (2, 3)
[tex]& \mathrm{BC}=\sqrt{(-2-2)^2+(-3-3)^2}=\sqrt{52}=2 \sqrt{13}[/tex] units
A = [tex](x_{1} , y_{1} )[/tex] = (3, 2), C = [tex](x_{2} , y_{2} )[/tex] = (2, 3)
[tex]& \mathrm{AC}=\sqrt{(3-2)^2+(2-3)^2}=\sqrt{2}[/tex] units
By using the Pythagorean theorem:
According to Pythagoras's Theorem in a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides.
Now, we can see that,
[tex]& (2 \sqrt{13})^2=(5 \sqrt{2})^2+(\sqrt{2})^2 \\[/tex]
[tex]& \mathrm{BC}^2=\mathrm{AB}^2+\mathrm{AC}^2[/tex]
Therefore, the given triangle is a right angled triangle.
Therefore, option(A) s correct.
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What type of triangle do the points (3, 2), (-2, -3) and (2,3) form a triangle? If so, name the type.
A. right triangle
B. equilateral triangle
C. isosceles triangle
D. none of these
2. If Sarah makes $11 per hour at her part time job and she works 20 hours in a week. How much is her weekly grass
pay?
A. $440
B. $110
C. $220
D. $200
Answer:
C. $220
Step-by-step explanation:
11 x 20 = 220
can the vertex also be a solution of a graphed parabola?
a) A designer has a circular tablecloth with radius 0.5 m. He wants to sew a fringe around the cloth. The fringe is sold by the tenth of a meter.
(i) What length of fringe is needed?
(ii) One meter of fringe costs $4.70. How much will the fringe cost?
b) A semicircular mat has a diameter of 18 m. What is the area of the mat?
Solve the differential equation by variation of parameters.
y'' + y = sin2 x
The solution to the differential equation y'' + y = sin2x is y = -2sin2x + (Acos2x + Bsin2x).
This differential equation can be solved by the method of variation of parameters. This method involves finding two arbitrary functions, U and V, such that U' = V and V' = -U + sin2x, so that the general solution of the differential equation is y = U + V. Solving the two equations yields U = Acos2x + Bsin2x and V = -2sin2x, where A and B are arbitrary constants. Substituting U and V into the general solution of the differential equation yields the final solution y = -2sin2x + (Acos2x + Bsin2x).
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A book is 6 inches wide and 9 inches tall.
A rectangle is shown. The length of the rectangle is labeled 6 inches. The width of the rectangle is labeled 9 inches.
A publisher wants to use a scale factor of 1.5 to enlarge a book. What will the area of the front of the book be after the book is enlarged? (5 points)
a
54 in2
b
81 in2
c
121.5 in2
d
78.75 in2
The area of the front of the book after it has been enlarged would be = 121.5 in². That is option C.
What is a rectangle?A rectangle is defined as the type of quadrilateral which has two opposite sides that are equal and parallel and with four angles that are equal to 90°.
The length of the rectangular book= 6 inches
The width of the rectangular book = 9 inches
Using the scale factor of 1.5 the new length and width is thus:
length = 6 × 1.5 = 9 inches
9× 1.5 = 13.5
Therefore area of the book = l×W = 9 × 13.5 = 121.5 in².
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Can someone please help me with this? and also help me understand how to do it I have a test this Friday.
Answer:
Refer to the image attached. If you have ANY questions about what I did/how I did it, please ask in the comments. I will be happy to help you understand! :)
Step-by-step explanation:
Which data set has a relatively low mean and variability when compared with a data set that has a mean of 20 and a MAD of 3.1? A. Mean: 5 and MAD: 4.6 B. Mean: 25 and MAD: 6.5 C. Mean: 41 and MAD: 0.9 D. Mean: 8 and MAD: 1.2
Answer:
Mean: 8 and MAD: 1.2
Step-by-step explanation:
Given a data with :
Mean = 20 ; mean absolute deviation (MAD) = 3.1
DATA with a low mean and variability Than The above from the options given :
The most appropriate option is : Mean: 8 and MAD: 1.2 ; because both values of the mean and mean absolute deviation are lesser than the value given.
20 points help asap!!!
Find B n C Given
B
Answer:
Step-by-step explanation:
Sets B and C have nothing in common and therefore B ∩ C = empty set
There are 20 gloves in a drawer: 5 pairs of black gloves, 3 pairs of brown,
and 2 pairs of gray. You select the gloves in the dark and can check them
only after a selection has been made. What is the smallest number of gloves
you need to select to guarantee getting the following?
(a) At least one matching pair
(b) At least one matching pair of each color
The number of gloves selected for each cases is 11 and 19 gloves respectively.
How is selection done?
In mathematics, most of the times selection is done using permutation and combination.
Putting things or numbers in order is known as a permutation.
Combinations are a means to choose items or numbers from a collection of items or groups of items without regard to their order.
Given,
Total black gloves = 5 left hand+ 5 right hand
Total brown gloves = 3 left hand + 3 right hand
Total gray gloves = 2 left hand + 2 right hand
Now to find the least number of gloves for the given conditions, we start with the worst condition.
a) To get at least one matching pair, we first consider no matching pair, which is (5 +3+2) gloves of only left only or right only hand of each colour.
Now to make one pair, we need to select only one glove of the opposite hand of any colour.
Therefore to get atleast one matching pair, smallest number of gloves to be selected = 5 + 3 + 2 + 1 = 11 gloves
b) In this case also we start with worst case.
For no matching pair of each colour we have to take 10 black gloves, 6 brown gloves and 2 gray gloves of any one hand.
Therefore to get matching pair of each colour, we have to take one more gray glove.
Therefore to get atleast one matching pair of each colour, smallest number of gloves to be selected = 10 + 6 + 2 + 1 = 19 gloves.
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Item 8 You put $400 in an account. The account earns $18 simple interest in 9 months. What is the annual interest rate? The annual interest rate is %.
Answer:
6%
Step-by-step explanation:
$18/9=$2 interest per month
$2 x 12 = $24 annual interest.
24/400=6%
This is just for fun...
Explain why every number to the digit 0 is 1 by using an algebraic formula (of sorts).
For example like (a and b or x and y for the substitutes of this and that to the power of 0)
Answer:
y is for genius factor
a is for angles
b are absoulutely for divides and multiply from the sides of heptagon
X are like EQUAL to 7 tables for example D% 72*(09 1/2 its just like this!!
and Deciamals are apart like 22 . 27 its just like that!!
Step-by-step explanation:
Does this help? let me know!!
Identify the two x values?
When the points are (4, 2) and (6, 5), the slope is 3/2. The slope of a line determines its direction and degree of steepness.
what is slope ?A line's steepness and direction are determined by the slope of the line. The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. While there has been no net change in the x coordinate, there has been no net change in the y coordinate. hence, the shift in the y coordinate in relation to the shift in the x coordinate. The slope of a line is the rise to run ratio, or the rise divided by the run. It gives information about a line's slope in the coordinate plane. Any two clearly separated points on a line can be used to calculate the slope of any line.
given
slope = [tex]m = \frac{y2 - y1}{x2 - x1}[/tex]
points are ( 4, 2 ) and ( 6, 5)
[tex]\frac{5 - 2}{6 - 4} \\= \frac{3}{2}[/tex]
hence the slope is 3 / 2 .
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The sample points of a sample space are a equally likely events. b equally unlikely events. c simple events. d complex events.
The correct option is option A , the sample points of a sample space are equally likely events.
In probability when two the occurrence of two events are having a 50 - 50 possibility then those two events are said to be equally likely events. Example , on tossing a coin the probability of getting a H or a tail is 1/2 . Therefore, these events are said to be equally likely events.
Probability is a field of mathematics which tells us about the possibility of occurrence of an event. P = number of favorable outcomes / total number of outcomes , is the formula to calculate probability.
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Help PlSss there’s people not helping I really need to bring my grades up
Answer:
center: P
Radius: 12cm
# of radii: 5
Diameter: 24cm
# of diameters: 2
Circumference: 75.36cm
Step-by-step explanation:
the center is labeled with the point p
radius is the distance from the center to the circumference of a circle
diameter is the distance from one point on a circle through the center to another point on the circle. (and twice the radius)
circumference is 2(pi)r
pi can be rounded to 3.14
Jeff bought a 5-gallon bucket of paint. He used 1.25 gallons to paint his bedroom, then he used two-thirds of the remaining paint for his living room. How many gallons of paint did he use to paint his living room?
Answer:
2.5 gallons
Step-by-step explanation:
5-1.25=3.75
3.75/3=1.25
1.25*2=2.50
Answer:
2.5, or 2 1/2 gallons
Step-by-step explanation:
The quotient of 18 and the number is three what is the number
Answer:
Step-by-step explanation:
Divide: 18 ÷3=?
The answer is 6
A community hall is in the shape of a cuboid.
Total cost of Painting and tileing is for the cuboidical community hall is $2172.
What is a Cuboid ?A three-dimensional form called a cuboid contains six faces, twelve edges, and eight vertices. It differs from a cube in that a cuboid's faces are entirely rectangular in shape whereas a cube's faces are square. A cuboid has three dimensions: length, breadth, and height.
Properties of a Cuboid are :
There are 6 faces, 12 edges, and 8 vertices on a cuboid.
All of the cuboid's faces have rectangular shapes.
The cuboid's opposing edges are parallel to one another.
The dimensions of a cube are length, breadth, and height.
All of the angles created at the cuboid's vertices are 90 degrees.
Surface area of 4 walls and Ceiling is = 40*3*2 + 15*3*2 + 40*15 = 930
Surface area of the floor is 40 *15 = 600
10 lt of tin covers 25
1 can be covered by 10/25 lt
930 can be covered by (10/25) * 930 = 372 lt.
Total cost of Painting is $372.
1 of floor tiles cost $3
600 of floor tiles will cost 3*600 = $ 1800
Total cost of Painting and tileing is for the cuboidical community hall is $ 372 + 1800 = $2172.
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The average scores on Mrs. Wilson's test and Mr. Lewandowski's test were normally distributed on the last Algebra 2 test they gave. The average in my class Mrs. Wilson's class, was 86 with a standard deviation of 2. The average in my friend's class, Mr. Lewandowski's class was an 82 with a standard deviation of 2. If I made an 88 on the test and my friend made an 85 on their test, who had the better score relative to the rest of their class?
You had a better score relative to the rest of your class.
To compare the scores of you and your friend relative to the rest of their classes, we need to calculate the standard deviation of your score and your friend's score from the average of their respective classes.
A standard deviation of 2 means that 68% of the scores in the class fall within 1 standard deviation of the mean, or between 84 and 88 in the case of Mrs. Wilson's class. Since 88 is greater than 86 (the mean) and less than 2 standard deviations away (88-86 < 2*2=4) , so your score of 88 is better than the average score in your class.
On the other hand, 85 is less than 82 (the mean) and more than 1 standard deviation away (85-82 > 2) so your friend's score of 85 is less than the average score in their class.
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there are 32 students who studied maths and 28 geography and 26 social science if there are total 40 students in school if they all studies one subject atleast then find maximum number of students who studied all subjects
The maximum number of students who studied all subjects is 6.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Total students = 40
Number of students who studied maths = 32
Number of students who studied geography = 28
Number of students who studied social science = 26
The maximum number of students who studied all subjects.
= Highest number of students who studied one subject - Least number of students who studied a subject
= 32 - 26
= 6
Thus,
6 is the maximum number of students who studied all subjects.
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Solve for x.
-10 <-2x +4≤8
Enter your answer, as one inequality, in the box.
The solution of the inequality is x < 7 and x >= -2.
What is linear inequality?
An inequality is a mathematical statement comparing two values or expressions, usually involving one of the following relational operators: < (less than), > (greater than), <= (less than or equal to), >= (greater than or equal to), or != (not equal to). The solution to inequality is a set of values that make the inequality true.
To solve the inequality -10 < -2x + 4 ≤ 8, we have to solve the inequality twice because of the less than or equal to symbol and greater than or equal to symbol.
First we have to solve -10 < -2x + 4
-2x + 4 > -10
-2x > -14
x < 7
Second, we have to solve -2x + 4 <= 8
-2x + 4 <= 8
-2x <= 4
x >= -2
Hence, the solution of the inequality is x < 7 and x >= -2. This solution is represented by all the values of x that are less than 7 and greater than or equal to -2.
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1. What is a stock? a. A bank account b. A type of bank c. Shares that are given to only rich people who own companies d. Shares people buy and it gives them a small ownership of that company
Answer:
D
Step-by-step explanation:
Stocks represent ownership in companies. Anyone can purchase publicly traded stock shares.
It’s midnight and I’m so confused someone please help or I’m going to summer school lol
Chose the best 3 options
The beat three options are: The slope of the line is 1/5, (2) The possible equation if the line is y=1/5x, (3) The slope and the y intercept are the same
What is slope of a line?Lope is the rate of change of y with respect to x. slope is also the increase in y over increase in x vice versa
Slope is denoted by rise/run
The Possible solutions from the graph are:
The slope and y-intercept are the sameThe possible equation of the line is y=1/5xThe slope of the line is 1/5Taking any two points on the graph : (4, 1) and -4, -1,)
We can find the slope as (1--1)/4--4
Therefore, the Slope = 2/3≡1/5
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[tex] \frac{1}{5} + \frac{3}{4} [/tex]
Answer:
19/20
Step-by-step explanation:
the answer is 19/20 <3
Step-by-step explanation:
<3
<3
<3
<3
hope you have a good day ^^<3
Find the mean and standard deviation for the set of data.
{31,12,21,6,28,5,26,23,19}
A. mean: 19; standard deviation: 8.87
B. mean: 19; standard deviation: 9.24
C. mean: 20; standard deviation: 8.87
D. mean: 20; standard deviation: 9.24
Answer:
if it says bit .ly etc don't click it
PLEASE ASAP ILL GIVE BRAINLIEST.
Answer:
12 km/h
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
we don’t know if it would change any other way so i would say D, because 1.5 hours, that’s just divide 18 by 3 (6) to get the half hour. then you figure out that 12 km/h (north?) since the half brings it to 18. sorry if that’s confusing i’m bad with explaining
The circumference of a circle is C centimeters. The diameter of the circle is 13 centimeters.
Which expression best represents the value of pi?
A. C/6. 5
B. 6. 5/C
C. C/13
D. 13/C
The diameter of the circle C/13
The formula provides the circumference of a circle.
The circumference of any shape in mathematics designates the path or limit that surrounds the shape. In other words, the circumference, sometimes referred to as the perimeter, aids in figuring out how long the contour of a shape is. The size and perimeter of a circle are, as we all know, its two most important properties.
C = pi * d, where d is the diameter and c is the circumference.
C = pi * 13 gives the diameter as 13.
Subtract 13 from each side, C/13 = d.
Dimensions are C/13.
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Find the geometric mean of 14 and 20. Answer in simplest form
The Geometric Mean (GM) is the average value or mean that, in mathematics, represents the centre tendency of a group of numbers by calculating the product of their values.
What is geometric mean?The Geometric Mean (GM) in mathematics is the average value or mean that represents the centre tendency of the group of numbers by calculating the product of their values. Basically, n is the entire amount of data values, and we multiply the numbers collectively before taking their nth root.
The geometric mean can be calculated in two steps: To obtain their product, multiply all values collectively. Calculate the product's nth root (n is the number of values).
The geometric mean of 14 and 20 must be determined. Let's see the numbers:
a = 14 and b = 20
For two numbers, the geometric mean is calculated as follows:
[tex]$M=\sqrt{a b}$[/tex]
Filling in the values as shown in the formula above:
[tex]$M=\sqrt{14 \times 20}$$M=\sqrt{7 \times 2 \times 5 \times 4}$$M=16.73$[/tex]
Therefore, the answer is 16.73.
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The required geometric mean of 14 and 20 is 16.73.
What is geometric mean?The Geometric Mean (GM) in mathematics is the average value or mean that represents the centre tendency of the group of numbers by calculating the product of their values. Basically, n is the entire amount of data values, and we multiply the numbers collectively before taking their nth root.
The geometric mean can be calculated in two steps: To obtain their product, multiply all values collectively. Calculate the product's nth root (n is the number of values).
The geometric mean of 14 and 20 must be determined. Let's see the numbers:
a = 14 and b = 20
For two numbers, the geometric mean is calculated as follows:
G.M = [tex]\sqrt{ab}[/tex]
Filling in the values as shown in the formula above:
G.M = [tex]\sqrt{14(20)}[/tex]
G.M = [tex]\sqrt{280}[/tex]
Therefore, the answer is 16.73.
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Help, please!!! I'll mark brainliest!!
Answer:
Step-by-step explanation:
okkkkkkk
Jim's marble collection contains 20 marbles, including 4 pink marbles. What is the probability that a randomly selected marble will be a pink marble? Write your answer as a fraction or whole number.
Answer: 20%
Step-by-step explanation:
The probability that a randomly selected marble will be pink can be found by the formula:
= Number of pink marbles / Number of total marbles
= 4 / 20
= 20%
There is a 20% chance that if you pick a marble, it will be pink.