The perimeter and area of triangle ABC are 22.15 units and 15 square units
How to find the perimeter and area of triangle ABCFrom the question, we have the following parameters that can be used in our computation:
A (-5, 2), B (-3, 5), C (5, 2), and D (-3, 2).
For the perimeter, we calculate the side lengths using the distance formula
So, we have
AB = √[(-5 + 3)² + (2 - 5)²] = √13
AC = √[(-5 - 5)² + (2 - 2)²] = 10
BC = √[(-3 - 5)² + (5 - 2)²] = √73
So, we have
Perimeter = √13 + 10 + √73
Evaluate
Perimeter = 22.15 units
For the area, we have
Area = 0.5 * | (x1 * y2 + x2 * y3 + x3 * y1) - (x2 * y1 + x3 * y2 + x1 * y3) |
Area = 0.5 * | (-5 * 5 + -3 * 2 + 5 * 2) - (-3 * 2 + 5 * 5 + -5 * 2) |
Area = 15 square units
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Which of the following is closest to the lateral surface area of a cylinder whose diameter is 18 cm and whose height is 28 cm
The lateral surface area of the cylinder is given by the equation
S = 1,583.36 cm²
What is a Cylinder?A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is
Volume of Cylinder = πr²h
Surface area of cylinder = 2πr ( r + h )
where r is the radius of the cylinder
h is the height of the cylinder
Given data ,
Let the surface area of the cylinder be represented as S
Now , the diameter of the cylinder d = 18 cm
So , the radius of the cylinder r = 18/2 = 9 cm
The height of the cylinder h = 28 cm
And , the lateral surface area of cylinder = 2πrh
Substituting the values in the equation , we get
The lateral surface area of cylinder = 2 ( 3.14 ) ( 9 ) ( 28 )
On simplifying the equation , we get
The lateral surface area of cylinder = 504π cm²
The lateral surface area of cylinder = 1,583.36 cm²
Hence , the lateral surface area is 1,583.36 cm²
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Page 1:
a. If two points on a line are A(-5, 7) and B(-2, 1), the rise is
so the slope of the line is
b. If two points on a line are A(10, -3) and B(12, 9), the rise is
run is
the run is
so the slope of the line is
c. If two points on a line are A(4, 6) and B(8,-8), the rise is
run is
Page 2:
so the slope of the line is
a. In the point-slope form of a line.
mix
the clon
and the
, and
and the
a) If two points on a line are A(-5,7) and B(-2,1), the rise -6, the run is of 3, and then the slope is of -2.
b) If two points on a line are A(10,-3) and B(12,9), the rise 12, the run is of 2, and then the slope is of 6.
c) If two points on a line are A(4,6) and B(8,-8), the rise -14, the run is of 4, and then the slope is of -3.5.
How to calculate the slope a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
For which the parameters are given as follows:
m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.As the slope represents the rate of change of the output relative to the input, it is calculated as the change in the output y divided by the change in the input x, that is, the rise divided by the run.
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A troop leader recorded whether the members of two troops prefer hiking or swimming. The troop leader plans to create a two-way table to display the results.
Which variables can the troop leader use as the row and column headings of the table?
The troop leader can use the two categories of preference (hiking or swimming) as the row and column headings of the table.
What is the linear relationship?A linear relationship is a connection that takes the shape of a straight line on a graph between two distinct variables - x and y. When displaying a linear connection using an equation, the value of y is derived from the value of x, indicating their relationship.
The troop leader can utilize the two preference categories (hiking or swimming) as the table's row and column headings.
The number of members who prefer each activity can be recorded in the cells of the table to show the distribution of preferences within each troop and the comparison between the two troops.
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2. The equation and the graph represent two functions. Use the equation y = 4 and the graph to answer the questions.
a) When x = 4, the function y = 4 has the greater numeric value.
b) The two equations have the same value for x = 6.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
For which the parameters are given as follows:
m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.From graph, when x = 0, y = 1, hence the intercept b is given as follows:
b = 1.
When x increases by two, y increases by one, hence the slope m is given as follows:
m = 1/2
m = 0.5.
Meaning that the function is given as follows:
y = 0.5x + 1.
When x = 4, the value is given as follows:
y = 0.5(4) + 1
y = 3 < 4.
The two functions will have the same value when:
0.5x + 1 = 4
0.5x = 3
x = 3/0.5
x = 6.
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what is the image of -6 -3 after a reflection over the line y =-x
Answer: i believe its -6, 3
(if im wrong pls inform me :3
A system of linear equations is given by the graph.
What is the system shown?
O
O
A. y=x
y=-3x - 5
B. y=-x
y =
C. y =
x - 5
x
y=-2 - 5
D. y=-x
y = x - 5
The system of equations is,
y = 2/3(x) and y = (-3/4)x -5.
The correct option is A.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given:
Two lines are intersecting each other.
Line 1 passes through two points (0, 0) and (3, 2).
The equation of the line is,
y = 2/3(x)
And line 2 passes through (0, -5) and (4, -2).
The equation of the line is,
y = (-3/4)x -5.
Therefore, the equations are y = 2/3(x) and y = (-3/4)x -5.
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Slope of the line perpendicular to the line
The slope of the perpendicular line is the inverse reciprocal of the line on which the line is perpendicular.
What is a slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, m = y/x can be used to express the change in the y coordinate with regard to the change in the x coordinate.
The slope of two parallel lines is such that the slope of one line is equal to the reciprocal of the negative slope of the other. The relationship between the slope of perpendicular lines can be represented by the formula m1 if the slopes of the two perpendicular lines are m1, m2.
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Beth is making fruit salad. She adds 5 grapes for every 2 strawberries. If she uses 14 strawberries, how many grapes will she use?
The number of grapes for 14 strawberries is 10
How to determine the number of grapesFrom the question, we have the following parameters that can be used in our computation:
She adds 5 grapes for every 2 strawberries.
So, we have the ratio to be
Grapes : Strawberries = 5 : 2
Multiply the ratio by 7
So, we have the following representation
Grapes : Strawberries = 10 : 14
This means that 10 grapes are required for 14 strawberries
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A student randomly draws a card from a standard deck of 52 cards. He records the type of card drawn and places it back in the deck. This is repeated 20 times. The table below shows the frequency of each outcome.
Outcome Frequency
Heart 7
Spade 3
Club 6
Diamond 4
Determine the experimental probability of drawing a spade.
0.15
0.25
0.35
0.50
The experimental probability of picking a spade is 0.15 (first option)
What is the experimental probability?Probability is used to determine how likely it is that a random event would happen. The odds that the event would happen has a probability value that lies between 0 and 1.
Experimental probability is based on the result of an experiment that has been carried out multiples times.
Experimental probability of picking a spade = number of times a spade was drawn / number of times the experiment was repeated
3/20 = 0.15
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and Bill collect coins. Karen has x coins. Bill has 6 coins fewer than two times the number of coins Karen has. Write and simplify an expression for the total number of coins Karen and Bill have.
Answer:
3x - 6
Step-by-step explanation:
Let's call the number of coins Karen has "x".
According to the information given, Bill has 6 coins fewer than two times the number of coins Karen has, so we can write the following expression for the number of coins Bill has:
Bill: 2x - 6
To find the total number of coins Karen and Bill have, we simply add the number of coins each person has:
Karen + Bill: x + (2x - 6) = 3x - 6
So the total number of coins Karen and Bill have is 3x - 6.
Answer: the total amount of coins Bill and Karen have can be found with the following equation: 3x-6
Step-by-step explanation:
Karen has x coins
Bill's coins are twice the x, so 2x, and he has 6 fewer than that.
The equation becomes x+2x-6 which can be simplified to 3x-6.
solve 5x + 30 > - 15
x>-9 is the solution of the inequality 5x + 30 > - 15
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
The given inequality is 5x+30>-15
Five times of x plus thirty greater than minus fifteen.
Subtract 30 on both sides
5x>-45
Divide both sides by 5
x>-9
Hence, x>-9 is the solution of the inequality 5x + 30 > - 15
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A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red 16
Blue 17
Green 5
Yellow 15
Purple 14
If the spinner is spun 200 more times, about how many times would you expect to land on blue? Round your answer to the nearest whole number.
The probability of having a blue in the spin is given as; 17/200.
How to calculate probability?Probability can be calculated as the ratio of the number of favorable outcomes to the number of possible outcomes in a given scenario. It is usually expressed as a decimal or a fraction between 0 and 1.
We know that in this case we are going to look at the table to see the number of times that we land a blue.
If the total number of the outcomes is 200 and the number of the expected outcomes is 17. We would have the probability as P(blue) = 17/200.
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Given the following table of values, what is the slope and y-intercept?
Answer:
Y- intercept= (0, -1)
Slope = 2/3
Step-by-step explanation:
Finding the Y-Intercept is pretty much finding the Y value when X is 0
Looking at this table, when x = 0, y is -1. Which means your y intercept is (0, -1)
To find slope, you take two points (x,y) and apply it to the slope formula. We'll do the bottom 4 since those are all nice looking numbers
[tex]slope = \frac{y2 - y1}{x2 - x1} [/tex]
plugging it in...
[tex]slope = \frac{3 - 1}{6 - 3} [/tex]
3-1 = 2 and 6-3 = 3
Keep that in fraction form
[tex]slope = \frac{2}{3} [/tex]
explain or show that we can approximate the area covered by mold in 8 weeks by multiplying a(7) by 1.01
The formula a(7) * 1.01 represents an exponential growth model, where a(7) is the area covered by mold at week 7, and 1.01 represents a growth rate of 1% per week.
The exponential growth model is represented by the formula a(7) * 1.01, where a(7) is the area covered by mould at week 7, and 1.01 indicates a weekly growth rate of 1%.
By multiplying the area at week 7 by 1.01, we can approximate the area covered by mold at week 8.
However, it's important to note that this model assumes that the growth rate remains constant and does not account for any limiting factors such as availability of food or changes in environmental conditions.
Additionally, this model may not accurately represent the actual growth of mold, as mold growth can be complex and affected by many variables.
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In the triangle below, angle BCA is obtuse.
Calculate angle BCA to 1 d.p
Answer:
56.27⁰
Step-by-step explanation:
a/sinA =b/sinB
35/sin 50⁰ = 38/sin B
cross multiply
35sinB = 38sin50⁰
sin B=29.1096/35
sinB=0.8317 find the inverse sine
angle BCA= 56.27⁰
-8 + n/2 = -13
Please help me I’m begging we just started to learn this today
Answer:
-10
Step-by-step explanation:
-8 + n/2 = -13
n/2 = -13 + 8
n/2 = -5
n = -5 * 2
n = -10
Hope it helps!
For a certain city, the high temperatures (in degrees Celsius) are plotted against the number of days after the new year.
The high temperature is a linear function of the number of days after the new year.
How to define a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
For which the parameters are given as follows:
m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.Three points on the graph are given as follows:
(1, -3), (3,1) and (10,15).
The slopes, calculated as the change in y divided by the change in x, for each of the intervals is given as follows:
(1, -3) to (3,1): m = 4/2 = 2.(1,-3) to (10, 15): m = 18/9 = 2.(3,1) to (10,15): m = 14/7 = 2.Due to the constant slopes, the relationship is in fact a linear function.
Missing InformationThe problem asks if the high temperature in this city a linear function of the number of days after the new year.
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what are some advantages of online surveys? multiple select question. they are generally readily available to survey responders. the data can be downloaded automatically into a spreadsheet. they deliver more accurate results than other types of surveys. the surveys can reach a very large number of respondents.
A, B, and D are some advantages of online surveys.
The advantages of online surveys are:
They are generally readily available to survey responders, as respondents can access the survey from anywhere with an internet connection.The surveys can reach a very large number of respondents, which can lead to a more representative sample.The data can be downloaded automatically into a spreadsheet, which makes it easier to analyze and process the data.They deliver more accurate results than other types of surveys, as online surveys can enforce skip patterns and provide immediate feedback to respondents.Online surveys are often less expensive than traditional surveys, as they do not require printing, postage, or interviewer time.To learn more about the online surveys, refer:-
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need help finding x y and z
Answer:
x= 67
y=40
z=40
Step-by-step explanation:
A=C B=D
67=X Y&?= Z&73
73+ x aka(67) = 140
180-140= y = 40
What is the measure of angle
XNM?
O 40
O 80
O 90
O 160
Check the picture below.
A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.
Number of Hours Total Number of Students
0 1
1 8
2 2
3 5
4 9
5 7
6 3
Determine the probability that a student studied for exactly 1 hour. Round to the nearest hundredth.
0.03
0.23
0.30
0.77
Based on the data provided, the probability that one student studied for exactly one hour is 0.22.
What is the probability in this case?When it comes to calculating the probability, we need to identify the frequency of a specific outcome (the probability a student studied for one hour) and compare it to the total outcome (total of students) as follows:
Total of students who studied for one hour: 8
Total of students: 1+8+2+5+9+7+3 = 35
Total of students who studied for one hour / total students
8/35 = 0.228 which can be rounded as 0.23 or 23% if expressed as a percentage.
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suppose that an usher randomly assigns the seats to the 7 people. find the probability that the three friends are next to each other.
The probability that the three friends are seated next to each other is 1/420
The total number of ways to seat the 7 people is 7! To find the number of ways to seat the three friends next to each other, we need to consider the number of ways to seat the other 4 people around them. So the number of favorable outcomes is 4!
The probability that the three friends are next to each other is then given by the ratio of the number of favorable outcomes to the total number of outcomes: (4!)/(7!) = 4!/5040 = 1/420.
So the probability that the three friends are seated next to each other is 1/420.
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Example 1) Suppose it is known that the height of all Canadians follows a normal distribution
with a mean of 160 cm and a standard deviation of 7 cm. What is the corresponding z score to the probability that the average height of Canadians is less than 157 cm?
The probability that the average height of Canadians is less than 157 cm is 0.337.
What is z-score?The relationship between a value and a set of values' mean is described by the statistical measurement known as the Z-score. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score. A value that is one standard deviation from the mean would have a Z-score of 1.0. Z-scores can be either positive or negative, with a positive number signifying a score above the mean and a negative value signifying a score below the mean.
Given that the standard deviation = 7cm and the mean = 160cm.
The z -score is given as:
z = x - mean / SD
z = 157 - 160/ 7
z = -3/7
z = - 0. 428
z = 0.337
P (X < 157) = P (z < -0.428)
P(X < 157) = 0.337
Hence, the probability that the average height of Canadians is less than 157 cm is 0.337.
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A right cone has a base with diameter 6 units. The volume of the
cone is 72π cubic units. What is the length of a segment drawn
from the apex to the edge of the circular base? Round to the
nearest tenth. This is a multi-step problem so DO NOT ROUND
UNTIL YOU GET TO YOUR FINAL ANSWER!!
HINT: DRAW A DIAGRAM!!
The segment drawn from the apex to the edge of the circular
base is____units.
The slant height of the right cone is 24.2 units, rounded to the nearest tenth.
The Pythagorean Theorem: What is it?A right triangle's hypotenuse, or side opposite the right angle, has a square length that, according to the Pythagorean theorem, is equal to the sum of the squares of the lengths of the other two sides.
The Pythagorean Theorem can be used to determine the slant height of a right cone. The circular base's radius is equal to its diameter times half, or 6/2 = 3 units.
The volume of the cone can be found using the formula:
V = (π/3)r²h
Where r is the radius, and h is the height of the cone. Plugging in the given values, we have:
72π = (π/3)r²h
72π = (π/3)3²h
72π = (π/3)9h
72π = 3πh
24 = h
Using the Pythagorean Theorem, we can find the slant height as follows:
c² = a² + b²
Where a and b are the height and radius of the cone, and c is the slant height. Plugging in the values we have:
c² = 24² + 3²
c² = 576 + 9
c² = 585
c = 24.2
Hence, the slant height of the right cone is 24.2 units, rounded to the nearest tenth.
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Number 8 please will give brainlist and tons of points
The value of x rounded to the nearest tenth is 10.2 units, this is found using trigonometric functions.
What are trigonometric functions?Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.
The triangle is a right-angles triangle and the given angle is 22 degrees.
Taking the cosine function, we have:
cos A = adjacent side/ hypotenuse
cos (22) = x / 11
0.927 = x/11
x = 10.2
Hence, the value of x rounded to the nearest tenth is 10.2 units, this is found using trigonometric functions.
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a company that manufactures video cameras produces a basic model and a deluxe model. over the past year, 32% of the cameras sold have been of the basic model. of those buying the basic model, 40% purchase an extended warranty, whereas 49% of all deluxe purchasers do so. if you learn that a randomly selected purchaser has an extended warranty, how likely is it that he or she has a basic model?
The probability that a randomly selected purchaser with an extended warranty has a basic model camera is approximately 0.0354
Denote S= Event that a purchase bought a basic camera, then P(S)=0.32
Denote D= Event that a purchase bought a deluxe camera, then
S and D are mutually exclusive.
P(D)=1-P(S)=0.68
P(W/S)=0.4
P(W/D)=4.9
We need to calculate the probability that a randomly selected purchaser who bought an extended warranty has a basic model. By notations, this is equivalent to finding P(S/W).
P(S/W)=P(W/S)*P(S)/P(W)
Since S and D are disjoint and P(S)+P(D)=1,
P(W)=P(W∩S)+P(W∩D)
P(W)=[0.4*0.32]+[4.9*0.68]
=3.61
Hence, our required probability is: P(S/W)=P(W/S)*P(S)/P(W)
[tex]=\frac{0.4*0.32}{3.61}\\=0.0354[/tex]
Hence, the probability that a randomly selected purchaser with an extended warranty has a basic model camera is approximately 0.0354
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Can you please help me
m is usually slope
lets analyze this problem
its a linear line, meaning a straight line
i see that y, the output, increases by 4 every time x goes up 2
slope, or m, is equal to the rise/run
rise is 4, run is 2
4/2 = 2
m = 2
this means that for every x, y goes up 2
or, for every 2 x, y goes up 4
hope this helps :)
-10v³ +50v² +40v
(Factor)
Answer:
-10v([tex]v^{2}[/tex] - 5v - 4)
Step-by-step explanation:
First, we have to find the GCF
The GCF is: -10v
We factor the GCF outside, and what is left we put in the ( )
-10v([tex]v^{2}[/tex] - 5v - 4)
what's something that I need to remember when classifying quadrilaterals
Answer:A quadrilateral is a polygon having four sides, four angles, and four vertices. The word 'quadrilateral' is derived from the Latin words 'quadri,' which means four, and 'latus', which means side. The above image is an example of a quadrilateral. AB, BC, CD, and DA are the four sides of the quadrilateral ABCD.
hope this helps alot<3
How many pounds are in 5 kilograms?
StartFraction 6 kilograms Over 13.23 pounds EndFraction = StartFraction 5 kilograms Over question mark pounds EndFraction
11.025 pounds
15.435 pounds
15.876 pounds
24.255 pounds
Answer:
A. 11.025
Step-by-step explanation:
1 Kilogram equals exactly 2.20462 pounds.
2.20462 multiplied by 5 is 11.025