Nasim is flying a kite, holding his hands a distance of 2.5 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be 28 degrees
. If the string from the kite to his hand is 105 feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary.
Step-by-step explanation:
this creates a right-angled triangle 2.5 ft above the ground.
the string is the Hypotenuse (the side opposite to the 90° angle). the air distance to the height of the kite is one leg, and the height of the kite minus the 2.5 ft is leg 2.
in the trigonometric triangle the up/down side is sine (multiplied by the Hypotenuse or radius of the circle) of the angle at the center of the circle. and the left/right side is cosine (again multiplied by the Hypotenuse or radius) of the angle.
so, the height of the kite above ground is
105×sin(28°) + 2.5 = 51.79451409... ≈ 51.79 ft.
Let f(x) = 3x2 – 2x + 6 and g(x) = 7x – 4. Identify the rule for f + g.
The sum between the functions:
f(x) = 3x² - 2x + 6
g(x) = 7x - 4
is (f + g)(x) = 3x² + 5x + 2
How to add the two functions?Here we have two functions which are:
f(x) = 3x² - 2x + 6
g(x) = 7x - 4
And we want to add these to get f + g, so we only need to add the two functions, we will get:
f(x) + g(x) = (3x² - 2x + 6) + (7x - 4)
Grouping like terms we will get:
(3x² - 2x + 6) + (7x - 4) = (3x²) + (-2x + 7x) + (6 - 4)
And now we can simplify that to get:
(3x²) + (-2x + 7x) + (6 - 4) = 3x² + 5x + 2
The sum is:
(f + g)(x) = 3x² + 5x + 2
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Factorise the following expression
please
The factorization of the given expression is p(4p-12q+qp).
What is factorization?The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.
The given expression is 4p²-12pq+qp².
Group and factor out the greatest common factor (GCF), then combine.
Here, the greatest common factor of the terms is p
Now, p(4p-12q+qp)
Therefor, the factorization of the given expression is p(4p-12q+qp).
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How to solve image. (solving rational expressions) and check for extraneous solutions
The evaluation of the equation to find the value of n in the rational function [tex]\frac{1}{n^2} + \frac{1}{n} = \frac{1}{2\cdot n^2}[/tex] is; n = -1/2
What is a rational function?A rational function is a function that contains rational fractions, such that the dividend and the divisor are polynomial expressions.
2) The specified rational equation or function can be presented as follows;
1/(n²) + 1/n = 1/(2·n²)The above equation consists of rational expressions. The expressions can be resolved by collecting like terms as follows;
The like terms are terms that can be resolved by simple addition or subtraction.
1/n = 1/(2·n²) - 1/(n²) = (1 - 2)/(2·n²) = -1/(2·n²)
1/n = -1/(2·n²)
Multiplying both sides by n, we get;
(1/n) × n = (-1/(2·n²)) × n
(1/n) × n = 1 = (-1/(2·n))
1 = (-1/(2·n))
Multiplying both sides by n, we get;
1 × n = (-1/(2·n)) × n
n = -1/2
The value of n in the equation, 1/(n²) + 1/n = 1/(2·n²), is -1/2Learn more on rational functions here: https://brainly.com/question/29185109
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What is the ordered pair that represents the point (−4, −7) after a reflection over the x-axis?
(4, 7)
(−4, 7)
(7, −4)
(−7, −4)
After reflection over the x-axis the ordered pair is at (-4, 7).
What is the reflection?When two different media come together at an interface, a wavefront might change direction so that it returns to the first medium, which is known as reflection.
When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the x-axis is (x, -y).
Here,
The reflection of point (-4, 7) across the x-axis is (-4, -7).
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how do i find the missing angles?! please help this is due today! please and thxx!
The measure of each angle are
<1 =46<2=164<3= 46<5= 46<6= 164<7= 46<8= 134What are Parallel lines?The fundamental characteristics listed below make it simple to recognise parallel lines.
Straight lines that are always the same distance apart from one another are called parallel lines.No matter how far apart they are from one another, parallel lines can never intersect.Given:
<4 = 134
So, <4 = <2 = 134 (Vertical opposite angle)
<4= <8= 134 (Corresponding Angle)
<1 + <4 = 180 (Linear Pair)
<1 = 180-134
<1 = 46
<1 = <3= 46 (Vertical opposite angle)
<2= <6= 164 (Corresponding Angle)
<3= <7 (Corresponding Angle)
<1= <5 (Corresponding Angle)
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Select all the true statements about the table.
x y
2 7
6 21
8 28
14 49
The slope is 3.5.
There is a proportional relationship between the variables x and y.
The slope is 7.
There is a linear relationship between the variables x and y, but not a proportional relationship.
The graph does not pass through the point (0, 0).
Answer:
Slope is 3.5
There is a proportional relationship between the variables x and y
The other statements are false.
The slope is 3.5, not 7
A linear relationship is the same a proportional relationship so statement 4 is always false
The graph does pass through (0, 0)
Step-by-step explanation:
Consider the first 2 pairs of coordinates, (2, 7) and (6, 21);
The increase in x is from 2 to 6, i.e. an addition of 4, the increase in y is from 7 to 21, i.e. an addition of 14;
Now consider the the 2nd and 3rd pairs of coordinates, (6, 21) and (8, 28);
The increase in x is from 6 to 8, i.e. an addition of 2, the increase in y is from 21 to 28, i.e. an addition of 7;
So, with the first 2 pairs of coordinates, an increase of 4 in x resulted in an increase of 14 in y and with the second 2 pairs of coordinates, an increase of 2 in x resulted in an increase of 7 in y, i.e. (+4, +14) and (+2, + 7);
2 × (+2, +7) = (+4, 14)
Or:
(+4, +14) ÷ 2 = (+2, +7)
This means a line from the 1st point to the 2nd point and a line from the 2nd point to the 3rd point will have the same gradient:
To find the slope simple, find the increase in y resulting from an increase of 1 in x, so:
(+2, +7) ÷ 2 = (+1, +3.5)
The gradient (or slope) is 3.5;
If there is a line with a fixed gradient that passes through all the points, then the relationship is proportional, also linear;
This is the case for this question;
If we follow the pattern backwards as well, so the point:
(2, 7) - (+2, +7) = (0,0)
This means (0,0) lies on the line.
(0,0), (2, 7), (4, 14), (6, 21), (8, 28), (10, 35), (12, 42), (14, 49), etc.
All these points would lie on the line, just add 2 to x, add 7 to y;
You would find the same points plus others by the rule, add 1 to x, add 3.5 to y.
For events A, B, and C we have that
P(A)=0.24,
P(B)=0.26,
P(A n B)=0.05,
P(A n C)=0.05,
P(B n C)=0.05,
P(A n B n C)=0.02 and P((A u B uC)^/)=0.33,
find P(C)
How should i go about this
Answer:
give me brainlist please
Step-by-step explanation:
We can use the formula for conditional probability and the formula for the probability of the union of events to find P(C).
Using the formula for conditional probability, we can find P(A|B) = P(A n B) / P(B) = 0.05 / 0.26 = 0.192
Using the formula for conditional probability again, we can find P(A|C) = P(A n C) / P(C) = 0.05 / P(C)
Since A and C are independent events, we know that P(A|C) = P(A), so we can write:
0.05 / P(C) = 0.24
Solving for P(C) we get P(C) = 0.05/0.24 = 0.208
Alternatively, we can use the formula for the probability of the union of events:
P(A u B u C) = P(A) + P(B) + P(C) - P(A n B) - P(A n C) - P(B n C) + P(A n B n C)
We know that P(A u B u C) = 1 - P((A u B u C)^/) = 1 - 0.33 = 0.67
and we know the values of P(A), P(B), P(A n B), P(A n C), P(B n C), P(A n B n C)
We can substitute these values into the above equation to find P(C)
P(C) = 0.67 - 0.24 - 0.26 + 0.05 + 0.05 + 0.05 - 0.02 = 0.208
So P(C) = 0.208
Consider this series.
16+32/3 +64/9 +128/27 +...
Does the series converge or diverge?
Select answers from the drop-down menus to correctly complete the statements.
The series Choose... You know this because the series is
Choose....
The series converges to 16 * 3 = 48
What is a series?A number series is a continues chain of number identical of non-identical depending on the logic behind the series. It can contain letters, number, variable, fraction, and numbers with power or exponents.
How to find the series coverage?The series converges.
This series is in the form of 16 * (1 + 1/3 + 1/9 + 1/27 + ...)
The series 1 + 1/3 + 1/9 + 1/27 + ... is a geometric series with a common ratio of 1/3.
A geometric series converges if |r| < 1, where r is the common ratio. In this case, |1/3| < 1, so the series converges to lim (1/(1-1/3)) = 3.
So the series converges to 16 * 3 = 48
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which inequality represents the graph??
Answer:
C
Step-by-step explanation:
8x+10y=-30 into slope intercept form, simplifying all fractions
A conversion of this equation in standard form to slope-intercept is y = 4x/5 - 3.
What is the slope-intercept form?In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:
y = mx + c
Where:
x and y represents the data points.m represents the slope of a line.c represents the y-intercept of a line.Based on the information provided about the line, it is represented by this equation;
8x + 10y = -30
Making y the subject of formula in the above equation, we have the following:
10y = 8x - 30
y = 8x/10 - 30/10
y = 4x/5 - 3
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Find the inverse of this function question (i) only please
The inverse of the function will be x=(4y-2)/(y+2) where x is the inverse of the function given in i.
What is a function?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).
There are several types of functions in math. Some important types are:
Injective function or One to one function: When there is mapping for a range for each domain between two sets.
Surjective functions or Onto function: When there is more than one element mapped from domain to range.
Polynomial function: The function which consists of polynomials.
Inverse Functions: The function which can invert another function.In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x.
Now,
As given
f(x)=2(x+1)/4-x
from here x will be inverse of the function
Therefore
y(4-x)=2x+2
4y-yx=2x+2
4y-2=x(y+2)
x=(4y-2)/(y+2)
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K travels 1 mile north, then 2 miles east, then 3 miles north again, and then once more east for 4 miles.
How far is she from her starting point when she arrives? Round to the nearest hundredth
The total distance from the starting point is 7.21 miles
Now, According to the question:
The movements are represented as:
[tex]N_1= 1miles\\E_1= 2miles\\\\N_2 =3 miles\\\\E_2 = 4miles[/tex]
To find the distance from the starting point.
First, calculate the total distance towards North.
[tex]N = N_1+N_2[/tex]
N = 1 + 3
N = 4 miles
Next, calculate the total distance towards East
[tex]E = E_1+E_2[/tex]
E = 2 + 4
E = 6 miles
The total distance from the starting point is calculated using Pythagoras theorem.
[tex]D^2=N^2+E^2[/tex]
[tex]D^2[/tex] = [tex]4^2+6^2[/tex]
[tex]D^2[/tex] = 16 + 36
[tex]D^2 =[/tex] 52
[tex]D = \sqrt{52}[/tex]
D = 7.21
Hence, The total distance from the starting point is 7.21 miles
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in a randomly selected 100 students in a large college, 20 of them had at least one sibling. does this provide strong evidence that more than 15% of college students in america have at least one sibling? test using
Answer:
No
Step-by-step explanation:
It could only represent large colleges, not all colleges. Sampling requires similar characteristics to represent the entire population of testing.
Need answer of number 3,4,5
A linear equation - y = 5x -7 is a slant line with intercepts for linear equations. A vertical line is x = 2. A line that runs through the origin is y = 3/4x.
A slant line with intercepts is y = 1/2x + 3. A horizontal line is y = 9. The line x = -1 runs vertically.
A linear equation is what?A direct condition is one that has a level of 1 as its most extreme worth. As a result, there is no variable in a linear equation with an exponent greater than 1. The graph of a linear equation will always be straight.
y = 5x -7 is the first line equation.This line is not horizontal or vertical when the equation is graphed; rather, it is slant.
Additionally, this line does not traverse the origin. As a result, this equation has intercepts and slant lines.
x = 2 is the second line equation.Since there is no y-intercept in this equation, it will be a vertical line that runs parallel to the y-axis.
Additionally, this line does not traverse the origin. As a result, this equation has a line that runs vertically.
y = 3/4x is the third equation for the line.This line is not horizontal or vertical when the equation is graphed; rather, it is slant.
Additionally, this line actually traverses the origin. As a result, the origin of this equation is traversed by slant lines.
y = 1/2x + 3 is the fourth equation for a line.This line is not horizontal or vertical when the equation is graphed; rather, it is slant.
Additionally, this line does not traverse the origin. This equation is therefore a slant line with intercepts.
y = 9 is the fifth line equation.Since there is no x-intercept in this equation, it will be a horizontal line that runs parallel to the x-axis.
Additionally, this line does not traverse the origin. As a result, there is a horizontal line in this equation.
x = -1 is the sixth line equation.Since there is no y-intercept in this equation, it will be a vertical line that runs parallel to the y-axis.
Additionally, this line does not traverse the origin. As a result, this equation has a line that runs vertically.
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Express tan Y as a fraction in simplest terms.
Answer 8 and 9.
Find the measure of an arc from the central angle.
8) The Length of major arc MQN is; ⁵/₄πr
Length of minor arc MPN is; ³/₄πr
9) Length of major arc HJK is; ¹³/₁₅πr
Length of minor arc MPN is; ⁴/₁₅πr
How to find the length of an arc?The formula that is used to find the length of an arc is;
L = (θ/360) * 2πr
where;
L is length of arc
θ is central angle
r is radius
8) We are not given the radius and as such;
Length of major arc MQN = (225/360) * 2πr
= ⁵/₄πr
Length of minor arc MPN = ((360 - 225)/360) * 2πr
= ³/₄πr
9) Length of major arc HJK = (312/360) * 2πr
= ¹³/₁₅πr
Length of minor arc MPN = ((360 - 312)/360) * 2πr
= ⁴/₁₅πr
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Write a real-world problem that you could represent with the equation 20 2n5 4. Solve the equation to find the answer to your problem
The solution of the given equation is 1.6. It has been represented and solved as a real-world problem below.
The given equation is = - 20 + 2x5 = 4
We can rewrite this equation as = - 4 + 2x5 = 20
Let us suppose that person A has x number of bananas that they have taken out from a stock full of bananas. They continue taking x number of bananas two more times. They then stop and see that person B has already taken 4 bananas from the stock. We can write this equation as -
= 4 + 2x
Person A saw knew that there were 20 bananas in total. So, we can write it as -
= 4 + 2x = 20
Person A then resumed and took x number of bananas again 5 more times. We can rewrite this as -
= 4 + 2x5 = 20
Solving this equation, we get -
= 4 + 10x = 20
= 10x = 20-4 = 16
= x = 16/10
= x = 1.6
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What is the product of the polynomials?
Answer:
Multiply all of the terms of each polynomial and then combine like terms. Example: Multiply: ( 2 x 2 + x − 3 ) ( x 2 − 2 x + 5 ) . Solution: Multiply each term of the first trinomial by each term of the second trinomial and then combine like terms.
the meaure of the exterior angel of a hexagon are x,3x,,4x,5x,8x, and 9x find the meaure of the larget exterior angel
The largest exterior angle of hexagone is 108°.
Given that exterior angle of a hexagon are x, 3x, 4x, 5x, 8x and 9x.
Exterior angles are those that run parallel to a polygon’s inner angles but are located outside of polygon.
We know that sum of exterior angle of any polygon is 360°.
So, sum of exterior angle of hexagon will be 360°.
x + 3x + 4x + 5x + 8x + 9x = 360°
30x = 360°
x = 360° / 30
x = 12°
Now the largest angle = 9 * 12 = 108°
Therefore, the largest angle of hexagon is 108°.
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Which are solutions for the inequality k≤12
? (Select all that apply)
The negative values, zero and the positive numbers lesser than 12 and equal to twelve are solutions of inequality.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
We need to find the solutions for the inequality k≤12
k lesser than or equal to twelve.
Which means the solution of the inequality are the values which are lesser than or equal to 12.
The solution of the inequality k≤12 is (-∞, 12]
All the negative values, zero and the positive numbers lesser than 12 and equal to twelve are solutions of inequality.
Hence, the negative values, zero and the positive numbers lesser than 12 and equal to twelve are solutions of inequality.
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The ratio of boys to girls in Mandy’s mathematics class is 3 to 12.
This ratio is the same in Mandy’s science class, in which there are 20 girls. How many boys are there in Mandy’s science class? Show your work
Number of boys in Mandy’s science class is 5.
Now, According to the question:
The ratio of boys to girls in Mandy’s mathematics class is 3 to 12.
This ratio is the same in Mandy’s science class,
There are 20 girls.
To find the how many boys are there in Mandy’s science class?
Based on the given condition:
Let the ratio be 3x and 12x
Now, According to the statement:
12x = 20
x = 20/12
x = 5/3
So, Number of boys = 3 × 5/3 = 5
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An experimental plant has an unusual growth pattern. On each day. The plant doubles its height of the previous day. On the first day of the experiment, the plant grows to twice, or 2 times, its original height. On the second day, the plant grows to 4 times its original height. On the third day, the plant grows to 8 times its original height.
A. How many times its original height does the plant reach on the sixth day? On the nth day?
A. On the sixth day, the plant grows to 64 times its original height.
B. On the nth day, the plant would [tex]2^n[/tex] time its original height.
A. From the given condition we can that the growth of the plant shows a geometric progression with a first term of 2 and a common ratio of 2.
On the first day, the plant grows to [tex]2^1[/tex] = 2 times its original height.
On the second day, the plant grows to [tex]2^2[/tex] = 4 times its original height.
Similarly, on the sixth day, the plant grows to [tex]2^6[/tex] = 64 times its original height.
B. The nth term of the progression can be calculated by multiplying the first term by the common ratio raised to the power of n-1.
In this case, the first term is 2 and the common ratio is 2. So the nth term is [tex]2 * 2^{n-1} = 2^n[/tex]
Hence, on the nth day, the plant grows to [tex]2^n[/tex] times its original height.
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To be a member at Sal's gym, there is a one-time sign-up fee plus a monthly fee for each month of membership. The table shows the total cost to be a member of the gym for different numbers of months.
Number of Months Total Cost
3 $53. 97
6 $77. 94
12 $125. 88
Create a function that gives the total cost,
C
C
, in dollars, to be a member of the gym given the number of months,
m
m
, of membership.
Enter your function in the space provided
A function that gives the total cost, C in dollars, to be a member of the gym given the number of months, m is C = 7.99m + 30
The table that shows the total cost to be a member of the gym for different numbers of months is:
Number of Months Total Cost
3 $53. 97
6 $77. 94
12 $125. 88
The rate of change of total cost per month would be,
m = [tex]\frac{77. 94-53. 97}{6-3}\\\\[/tex]
m = 7.99
so, the function for the total cost would be,
C = 7.99m + d .......(1)
where d is the fixed cost of the gym
For m = 3, C = 53.97
53. 97 = 7.99m + d
53. 97 = 7.99(3) + d
d = 30
So, function (1) would be,
C = 7.99m + 30
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Mock June 22 1F Overview Question Progress Exam Paper Progress 42/80 Marks 10 Eric throws a biased coin 10 times. He gets 3 Tails. Sue throws the same coin 50 times. She gets 20 Tails. 10 Grade For This Paper U 3 Aadi is going to throw the coin once. (i) Which one of the following statements is correct about the probability of Aadi getting Tails? 2/5 (ii) Use Eric's and Sue's results to work out an estimate for the probability that Aadi will get Tails. Write your fraction in the form a/b 13 A Sue's estimate is best because she throws it 50 times. B Sue's estimate is best because she gets more Tails. C Sue's estimate is best because she throws it more times than Eric (1) (1) 15 Total marks: 2 16 17
The best estimate for the probability of getting tails is given as follows:
C Sue's estimate is best because she throws it more times than Eric.
How to obtain the probabilities?A probability is obtained as the division of the number of desired outcomes by the number of total outcomes.
For this problem we calculate an experimental probability, as the outcomes are obtained from the previous trials of Eric and Sue.
The higher the number of trials, the closer the experimental probability is to the theoretical probability, meaning that the correct option is given by option C.
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the sum of the cube of a number and the product of the number and twelve is equal to seven times the square of the number. find the number.
Answer:
4 or 3
Step-by-step explanation:
X³+12X=7X²
X³-7X²+12X=0
X(X²-7X+12)=0
SOLVING THE QUADRATIC EQUATION
you have X=3 or X=4
3. Two apples and 3 pears cost $2.40. Five times the cost of an apple less three times the
cost of a pear is 65 ¢. What is the unit cost of an apple and a pear?
The unit cost of an apple and a pear are $1.27 and $1. 98 respectively.
What are algebraic expressions?Algebraic expressions are defined as expressions that comprises of variables, factors, constants, terms and coefficients.
They are also made up of arithmetic operations like;
Floor divisionMultiplicationAdditionSubtractionBracketParenthesesDivisionFrom the information given, we have that;
Let the apples be x
Let the pears by y
2x + 3y = 2.40
5x - 3y = 6.5
Let's solve the simultaneous equation
-1(2x + 3y = 2.40)
-2x - 3y = -2. 40
5x - 3y = 6.5
-2x - 5x = -2. 40 - 6.5
-7x = -8.9
x = $1.27
substitute the value for y
-2y -5(1.27) = -2.40
y = $1. 98
Hence, the values are $1.27 and $1. 98
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Help pls I really need help
Answer:
b
Step-by-step explanation:
Some animal become endangered and a trict law ha to be
implemented to protect them. What will you do to protect and help
them?
One of the most important things to do to protect endangered animals is to reduce the amount of habitat destruction caused by human activities.
This can be done by creating protected areas and limiting or banning activities like logging, mining, or development in sensitive areas. Additionally, it is important to reduce over-hunting and poaching of these animals. This can be accomplished by establishing quotas and strict regulations on allowable hunting and fishing, as well as increasing enforcement efforts to catch violators. It is also important to understand the life cycles and behaviors of the threatened species so that we can better protect them. This can be done through field research, monitoring, and analyzing population trends. Finally, it is important to develop conservation plans and strategies to protect the species. These could include habitat restoration, reintroduction programs, captive breeding, and other measures to ensure their survival.
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Select the procedures that cannot be used to show the converse of the Pythagorean theorem using side lengths chosen from 3 cm, 4 cm, 5 cm, and 6 cm.
A.
Knowing that 3² + 4² = 5², draw any two sides with a right angle between them. The third side will fit to form a right triangle.
B.
Knowing that 3 + 4 > 5, draw the 3 cm side and the 4 cm side with a right angle between them. The 5 cm side will fit to form a right triangle.
C.
Knowing that 3 + 5 > 6, draw the 3 cm side and the 5 cm side with a right angle between them. The 6 cm side will fit to form a right triangle.
D.
Knowing that 3² + 4² = 5², draw the 3 cm side and the 4 cm side with a right angle between them. The 5 cm side will fit to form a right triangle.
The procedure that cannot be used are:
A. Knowing that 3² + 4² = 5², draw any two sides with a right angle between them. The third side will fit to form a right triangle.
B.
Knowing that 3 + 4 > 5, draw the 3 cm side and the 4 cm side with a right angle between them. The 5 cm side will fit to form a right triangle.
C.
Knowing that 3 + 5 > 6, draw the 3 cm side and the 5 cm side with a right angle between them. The 6 cm side will fit to form a right triangle.
What is the Pythagorean theorem?The Pythagorean theorem states that the result obtained by squaring the value of the hypotenuse of a right angled triangle is equal to the sum of the squares of the values other two sides of the triangle.
The hypotenuse of a a given triangle is usually longer that the other two sides.
Therefore, the correct procedure when lengths such as 3 cm, 4 cm, 5 cm, and 6 cm should be knowing that 3² + 4² = 5², draw the 3 cm side and the 4 cm side with a right angle between them. The 5 cm side will fit to form a right triangle.
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