Explain the Pythagorean Theorem, and provide two additional examples (other than football) of how it can it apply to sports
Answers
Given:
The objective is to explain Pythagorean Theorem with two examples by applying it to sports.
Explanation:
The Pythagorean Theorem states that. in a right triangle the sum of the squares of a two perpendicular legs will be equal to the square of the largest side of the triangle.
Consider a right triangle ∆ABC right angled at B.
By applying the Pythagorean Theorem to the above right triangle,
[tex]AC^2=AB^2+BC^2\text{ . . . . . .(1)}[/tex]Example 1:
Consider a tennis player standing striking the ball to the service line of opponent field.
Let the height of the tennis player will be h = 3m.
The distance between the tennis player and the opponent service line is x = 18m.
Then, the distance at which the tennis player strikes the ground can be calculated as,
From the above diagram the distance d can be calculated using equation (1) as,
[tex]d^2=h^2+x^2\text{ . . . . . . (2)}[/tex]On plugging the values in equation (2),
[tex]\begin{gathered} d^2=3^2+18^2 \\ d^2=9+324 \\ d=\sqrt[]{333} \\ d\approx18.25m \end{gathered}[/tex]Example 2:
Consider a basket ball player ready to take a free throw standing at a horizontal distance of 20 ft from the ring and holding the ball at with distance of 10ft below the ring.
Then, the hypotenuse distance of the ring can be calculated using equation (1) as,
[tex]\begin{gathered} x^2=10^2+20^2 \\ x^2=100+400 \\ x=\sqrt[]{500} \\ x\approx22.36ft \end{gathered}[/tex]Hence, the explanation for Pythagorean Theorem with two examples are provided.
Related Questions
what are the points that are on the graph of the line 2x + 4y = 20
Answers
Answer:
The points are 10 on the x-axis, and 5 on the y-axis
Explanation:
Given the line:
2x + 4y = 20
The values that satisfy this equation are x = 10, y = 5
The points are 10 on the x-axis, and 5 on the y-axis
Look at the graph of the line below:
The line intersects the x-axis at point 10, and the y-axis at point 5
Which phrase represents the algebraic expression below? 8 + 9x O A. the sum of nine and the quotient of a number x and eight O B. the product of eight and nine less than a number x O C. the product of nine, a number x, and eight OD. the sum of eight and the product of nine and a number x 11
Answers
Given data:
The given expression is 8+9x.
The given expression can be read as sum of 8 and product of nine times the number.
You spin the spinner twice.678What is the probability of landing on an odd number and then landing on a 6?Simplify your answer and write it as a fraction or whole number.
Answers
We are asked to determine the probability of landing on an odd number and then landing on a 6.
To do that we will use the product rule of probabilities:
[tex]P(AandB)=P(A)P(B)[/tex]Where:
[tex]\begin{gathered} A=\text{ landing on an odd number} \\ B=\text{ landing on a 6} \end{gathered}[/tex]To determine the value of the probability of A we need to have into account that there is only 1 odd number (7) out of 3 possible numbers, therefore, the probability is:
[tex]P(A)=\frac{1}{3}[/tex]Now, to determine the value of the probability of "B" we need to have into account that there is only one number 6 out of 3 numbers therefore, we have:
[tex]P(B)=\frac{1}{3}[/tex]Now, we substitute the values:
[tex]P(AandB)=(\frac{1}{3})(\frac{1}{3})[/tex]Now, we solve the operations:
[tex]P(AandB)=\frac{1}{9}[/tex]Therefore, the probability is 1/9
Is AABC - ADEF? Explain your reasoning. B E 6 units US Enter your altswer and explanation. 1 polie
Answers
SAS Similarity Theorem
If two sides of one triangle are proportional to two sides of another triangle and the included angle in both are congruent, then the triangles are similar by the SAS theorem.
We need to check if the conditions are met in the triangles given in the question.
First, let's test the proportionality of the sides.
In triangle ABC, side AB has a measure of 9 units
In triangle DEF, side DE has a measure of 6 units.
The proportion is 9/6 = 1.5. This is the scale factor.
Now check the other given sides.
In triangle ABC, side CA has a measure of 6 units
In triangle DEF, side FD has a measure of 4 units.
Proportion is 6/4 = 1.5
Given the scale factor is identical for both triangles, the first condition is met.
Now we can see the included angles BAC and EDF are congruent because they have the same measure of 40°.
Since both conditions are met, we conclude the triangles are similar by the SAS theorem
What percent is 12 of 407
Answers
To find the percent, we just have to divide.
[tex]\frac{12}{407}=0.0295[/tex]Then, we multiply by 100 to express it in percentage.
[tex]0.0295\cdot100=2.95[/tex]Hence, 12 represents 2.95% of 407.Kiran read for x minutes, and Andre read 5/8 more than that. Write an equation that relates the number of minutes Kiran read with Y ,the number of minutes Andre read. "Use decimals in the equation.DO NOT ROUND"
Answers
The time for which Kiran read is x minutes.
Determine the time for which Andre read.
[tex]\begin{gathered} Y=x+\frac{5}{8}\cdot x \\ =x+0.625x \\ =\text{1}.625x \end{gathered}[/tex]Thus answer is Y = 1.625 x.
6- 5 and 1/2 pls help
Answers
First, express the mixed number as a fraction:
[tex]5\frac{1}{2}=\frac{\lbrack(5\times2)+1\rbrack}{2}=\frac{11}{2}[/tex][tex]6-\frac{11}{2}[/tex]multiply 6 by (2/2)
[tex]6\times\frac{2}{1}-\frac{11}{2}=\frac{12}{2}-\frac{11}{2}=\frac{1}{2}[/tex]It takes approximately 4.65 quarts of milk to make a pound of cheese. Express this amount as a mixed number in simplest form.
Answers
The mixed number in simplest form would be 4 and 13/20.
How to convert decimals into mixed fractions?Separate the whole part from the number at the decimal point.The number behind the decimal point becomes the numerator of the fraction.Find the place value of the decimal part. This is the denominator of the fraction.Write the whole part of the number followed by the numerator over the denominator of the fraction.If possible, simplify the fractional part using common factors.Convert 3.4 to a mixed number
The whole part of the number is 3.
The numerator of the fraction is 4.
The place value of the decimal part is tenths, so the denominator of the fraction is 10.
The mixed number is 3*4/10
To learn more about mixed fractions refer to:
https://brainly.com/question/26836561
#SPJ1
Estimate the local minimum of y = −³ − 5x² − 3x + 9.-OA. (1.5,-10.25)OB. (-3,0)C. there is no local minimumOD. (-0.33,9.48)Reset Selection
Answers
Given: The function below
[tex]y=-x^3-5x^2-3x+9[/tex]To Determine: The local minimum
Solution
The graph of the function is as shown below
Hence, the local minimum from the graph above is (- 3, 0), OPTION B
21. What is the probability of getting an odd number? a.1/3b.2/3c.1/4d.1/5
Answers
The probability of getting an odd number from 1-10 is 1/5.
Given, we have numbers from1-10
The odd numbers ranging from 1-10 are 5
Hence we know the probability formula = Number of favourable outcomes/ totall number of outcomes.
Probability of getting an odd number = 1/5
Hence we get the answer as 1/5.
Learn more about Probability here:
brainly.com/question/24756209
#SPJ9
A ball is thrown upward and outward from a height of 6 feet. The height of the ball, f(x), in feet, can be modeled byf(x)=−0.6x2+2.7x+6where x is the ball's horizontal distance, in feet, from where it was thrown. Use this model to solve parts (a) through (c).a. What is the maximum height of the ball and how far from where it was thrown does this occur?The maximum height is 1010 feet, which occurs 22 feet from the point of release.
Answers
We need to find the vertex of the parabola
Vertex (h,k) is given by the following formula:
[tex]\begin{gathered} (h,k) \\ h=-\frac{b}{2a} \\ k=f(h) \end{gathered}[/tex]Where, a and b are coefficients of the quadratic equation
[tex]f(x)=ax^2+bx+c[/tex]in this example:
[tex]f(x)=-0.6x^2+2.7x+6[/tex]Therefore,
a = 0.6
b = 2.7
Now, we know that, we can find vertex (h,k)
[tex]h=-\frac{2.7}{2\cdot(-0.6)}=2.25[/tex]now, let's determine k
[tex]\begin{gathered} k=f(h)=f(2.25)=-0.6\cdot(2.25)^2+2.7\cdot(2.25)+6 \\ k=9.0375 \end{gathered}[/tex]So, the vertex of the parabola is the point (2.25 , 9.0375)
This means that the maximum height of the ball is k = 9.0375 ft and it occurs h = 2.25 ft from where it was thrown
Very confused on question 5 need help as soon as possible
Answers
To solve this, we can use the remainder theorem.
The theorem says:
Given a polynomial P(x), the remainder of
[tex]\frac{P(x)}{x-a}[/tex]Is equal to P(a)
This means, that we are looking for a value of x such as P(a) = 0
We need to find the roots of the polynomial. We can do this, by trying values of x.
Let's use:
x = 0, 1, 2, 3
[tex]x^3+3x^2-16x-48[/tex]Then:
[tex]\begin{gathered} x=0\Rightarrow0^3+3\cdot0^2-16\cdot0-48=-48 \\ x=1\Rightarrow1^3+3\cdot1^2-16\cdot1-48=1+3-16-48=-60 \\ x=2\Rightarrow2^3+3\cdot2^2-16\cdot2-48=8+12-32-48=-60 \\ x=3\Rightarrow3^3+3\cdot3^2-16\cdot3-48=27+27-48-48=-42 \end{gathered}[/tex]Let's try negative values,
x = -1, -2, -3
[tex]\begin{gathered} x=-1\Rightarrow(-1)^3+3(-1)^2-16(-1)-48=-1+3+16-48=-30 \\ x=-2\Rightarrow(-2)^3+3(-2)^2-16(-2)-48=-8+12+32-48=-12 \\ x=-3\Rightarrow(-3)^3+3(-3)^2-16(-3)-48=-27+27+48-48=0 \end{gathered}[/tex]We have found that the polynomial evaluated in x = -3 is equal to zero, which means:
[tex]\frac{x^3+3x^2-16x-48}{x+3}[/tex]has remainder zero.
The answer is (x + 3)
PLEASE HELP ANSWER THESE 3 VERY IMPORTANT QUESTIONS!!!
1. The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 98° is added to the data, how does the mean change?
2. The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 48° is added to the data, how does the median change?
3. The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 80.8° is added to the data, how does the range change?
Answers
If a value of 98° is added to the data, then the mean change is 1.35, if a value of 48° is added to the data, then the median change from the 6th number to the 7th number but the value still same, if a value of 80.8° is added to the data then the range still same.
In the given question we have to find the change in mean, median and range after the addition of another value.
(1) The list of average high temperatures in degrees for a city is
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
So the mean is find as the sum of value divided by the total number of values.
As we see that the total number of values are 12.
Now the sum of values
∑x=58+61+71+77+91+100+105+102+95+82+66+57
∑x=965
Mean = ∑x/n
Mean = 965/12
Mean = 80.42
If a value of 98° is added to the data, then the sum of values will be
∑x'=58+61+71+77+91+100+105+102+95+82+66+57+98
∑x'=1063
The total number of values = 13
So the
Mean'=∑x'/n'
Mean'=1063/13
Mean'=81.77
Now the change in mean=Mean'−Mean
change in mean=81.77−80.42
change in mean=1.35
(2) The list of average high temperatures in degrees for a city is
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
So the median is find after arranging the values in ascending order.
57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105
Total number=12
Meadian=n/2 th number
Meadian=12/2 th number
Meadian=6 th number
Meadian= 77
If a value of 48° is added to the data.
So the ascending order of the number is
48, 57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105
Total number=13
Meadian=(n+1)/2 th number
Meadian=13+1/2 th number
Meadian=14/2 th number
Meadian=7 th number
Meadian=77
Now the range changes from the 6th number to the 7th number but the value still same.
(3) The list of average high temperatures in degrees for a city is
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
So the range is find after subtracting the greatest number to the smallest number.
So the range=Greatest Number−Largest Number
range=105−57
range=48
If a value of 80.8° is added to the data then the range still same because the added value is between the largest and smallest number.
To leran more about mean, median and range link is here
brainly.com/question/9026799
#SPJ1
At a bowling alley, the cost of shoe rental is $2.55 and the cost per game is $3.75. If f (n) represents the total cost of shoe rental and n games, what is the recursive equation for f (n)? f (n) = (2.55 + 3.75)n, n > 0 f (n) = 2.55 + 3.75n, n > 0 f (n) = 2.55 + 3.75 + f (n − 1), f (0) = 2.55 f (n) = 3.75 + f (n − 1), f (0) = 2.55
Answers
To find the recursive function we need to take into account that shoe rental doesn't depend on the number of games you play. You rent a pair of shoes and you pay for it just once, but the cost per game does depend on the number of games (n), then the total cost of shoe rental and n games will be:
[tex]\begin{gathered} f(n)=\cos t\text{ of shoe rental + cost per game x number of games} \\ f(n)=2.55+3.75n,n>0 \end{gathered}[/tex][tex]4112 \div 5 = 822 remainder 2[/tex]drag each expression to a box to show whether it is a correct way to check the answer to this equation
Answers
given that
4112/5 = 822 remainder 2
to get the correct way and incorrect way.
so
For,
822 x 5 = 4110
For,
822 x 2 + 5 = 1649
For,
822 x 5 + 2 = 4112
therefore,
The correct way to check The incorrect way to way to check
822 x 5 + 2 822 x 5
822 x 2 + 5
Joseph deposited $60 in an account earning 10% interest compounded annually.To the nearest cent, how much will he have in 2 years?Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answers
Solution:
Using;
[tex]\begin{gathered} B=p(1+r)^t \\ \\ \text{ Where }p=60,r=10\text{ \%}=0.1,t=2 \end{gathered}[/tex][tex]\begin{gathered} B=60(1+0.1)^2 \\ \\ B=72.6 \end{gathered}[/tex]ANSWER: $72.6
Write the number 0.2 in the form a over b using integers
Answers
We can express 0.2 in the form:
[tex]\frac{2}{10}[/tex]I just don't know how to indicate values on ration equations
Answers
Solving the equation we have:
[tex]\begin{gathered} \frac{x+3}{x-3}=\frac{12}{3} \\ \frac{x+3}{x-3}=4\text{ (Simplifying the fraction)} \\ x+3=4(x-3)\text{ (Multiplying x-3 on both sides of the equation)} \\ x+3=4x-12\text{ (Distributing)} \\ x+3+12=4x\text{ (Adding 12 to both sides of the equation)} \\ 3+12=4x-x\text{ (Subtracting x from both sides of the equation)} \\ 15=3x\text{ (Adding)} \\ \frac{15}{3}=x\text{ (Dividing by 3 on both sides of the equation)} \\ 5=x\text{ } \end{gathered}[/tex]The solution is x=5 and it is valid as the result of replacing it in the denominator is not zero. ( 5 - 3 ≠ 0)
15. Find the missing sides/angles.i=94jk=42k
Answers
From the figure given,
[tex]\begin{gathered} j=\text{opposite}=\text{?} \\ k=adjacent=\text{?} \\ hypotenuse=94 \\ \theta=42^0 \end{gathered}[/tex]Let us solve for 'j'
To solve for j, we will employ the method of Sine of angles.
[tex]\begin{gathered} \text{ Sine of angles=}\frac{opposite}{\text{hypotenuse}} \\ \sin \theta=\frac{j}{hypotenuse} \end{gathered}[/tex][tex]\begin{gathered} \sin 42^0=\frac{j}{94} \\ \text{cross multiply} \\ j=94\sin 42^0 \\ j=94\times0.6691 \\ j=62.8954\approx62.9units(nearest\text{ tenth)} \end{gathered}[/tex]Let us solve for k
To solve for k, we will employ the method of Cosine of angles.
[tex]\begin{gathered} \text{ Cosine of angles=}\frac{k}{\text{hypotenuse}} \\ \cos \theta=\frac{k}{hypotenuse} \\ \cos 42^0=\frac{k}{94} \\ \text{cross multiply} \\ k=94\cos 42^0 \\ k=94\times0.7431 \\ k=69.8514\approx69.9units(nearest\text{ tenth)} \end{gathered}[/tex]Hence, the value of j=62.9units,
k=69.9units.
Find the slope of the function 8x - 2y = 10.
Answers
Solve the equation in terms of y, so that it is in the slope-intercept form
[tex]\begin{gathered} 8x-2y=10 \\ -2y=10-8x \\ \frac{-2y}{-2}=\frac{10-8x}{-2} \\ y=-5+4x \\ y=4x-5 \end{gathered}[/tex]Since it is already in the slope-intercept form y = mx + b, where m is the slope. We find that m = 4.
Therefore, the slope of the function is equal to 4.
[tex](x + 4)x + 5)[/tex]write the equivalente expression
Answers
given that (x+4) (x+5) and they are asking for equivalent form.
at first both terms are in multiplication form,so multiply x with (x+5) so we get that
[tex](x+4)(x+5)=x^2+5x+4x+20=x^2+9x+20[/tex]A batting average of 0.250 in baseball means a player, on average gets 25 hits in 100 times at bat. How many hits would he expect to get in 360 times at bat
Answers
From the given information:
Batting average of the player = 0.25.
This means that, on average, the player gets 25 hits in 100 times at-bat.
Therefore:
The number of hits which he would expect to get in 360 times at-bat
= Batting Average X Number of Times at-bat
[tex]\begin{gathered} =0.25\text{ x 360} \\ =90 \end{gathered}[/tex]The baseball player would expect to get 90 hits in 360 times at-bat.
Another approach is to use ratio.
[tex]\frac{25\text{ Hits}}{100\text{ times at bat}}=\frac{x\text{ Hits}}{360\text{ times at bat}}[/tex]Cross multiply
[tex]\begin{gathered} 100x=25\text{ }\times\text{ 360} \\ 100x=9000 \end{gathered}[/tex]Divide both sides by 100 to solve for x
[tex]x=90[/tex]Therefore, the baseball player would expect to get 90 hits in 360 times at-bat.
One month Chris rented 8 movies and 4 video games for a total of 49$.The next month he rented 3 movies and 2 video games for a total of 21$.Find the rental cost for each movie and each video game.
Answers
Given
One month Chris rented 8 movies and 4 video games for a total of 49$.The next month he rented 3 movies and 2 video games for a total of 21$. Find the rental cost for each movie and each video game.
Solution
Step 1
Let m represent the movies
And let v represent the video
Therefore,
[tex]\begin{gathered} 8m+4v=\text{ \$49}\ldots Equation\text{ 1} \\ 3m+2v=\text{ \$ 21 }\ldots Equation\text{ 2} \end{gathered}[/tex]Step 2
Train A travels 30 miles in 20 minutes at a constant speed. Train B travels 20 miles in 15 minutes at a constant speed. Redo Which train is going faster? Circle your answer and show how you figured it out below, Train A Train B
Answers
Find the equation of the line through the followingpair of points: (2, -10) and (4, -7).
Answers
Lets find the slope first:
Slope (m) is change in y's by change in x's
Change in y: -7 - - 10 = -7 + 10 = 3
Change in x: 4 - 2 = 2
Slope = 3/2 (this is m)
So, the equation is:
[tex]\begin{gathered} y=mx+b \\ y=\frac{3}{2}x+b \end{gathered}[/tex]b is the y-intercept.
We can get it by plugging in any point. Let's put (2, -10). So we have:
[tex]\begin{gathered} y=\frac{3}{2}x+b \\ -10=\frac{3}{2}(2)+b \\ -10=3+b \\ b=-10-3 \\ b=-13 \end{gathered}[/tex]Final equation is:
[tex]\begin{gathered} y=\frac{3}{2}x+b \\ y=\frac{3}{2}x-13 \end{gathered}[/tex]Learning Diagnostic Analytics Recommendations Skill plans Social stu La Language arts All Science Math Eighth grade ) T.11 Volume of cones YYR A cone has a height of 14 meters and a diameter of 12 meters. What is its volume? Use A 3.14 and round your answer to the nearest hundredth. cubic meters Submit
Answers
The volume of a cone is calculated as follows:
[tex]V=\pi\cdot r^2\cdot\frac{h}{3}[/tex]where r is the radius and h is the height of the cone.
Given that the diameter of the cone is 12 meters, then its radius is 12/2 = 6 meters
Substituting into the equation with h = 14 m, and r = 6 m, we get:
[tex]\begin{gathered} V=3.14\cdot6^2\cdot\frac{14}{3} \\ V=3.14\cdot36\cdot\frac{14}{3} \\ V=527.52m^3 \end{gathered}[/tex]In the diagram below, ALMK - APMN. Based on the relationship between the triangles, which of the following proportions is true? KA d.
Answers
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional
In this problem
triangle LMK and triangle PMN are similar
that means
LM/PM=MK/MN=LK/PN
therefore
answer is
option ay (-3 - 8x) how can i expand this expression with a variable?
Answers
Statement Problem: Expand the expression;
[tex]y(-3-8x)[/tex]Solution:
We would multiply the variable with each of the term.
[tex]\begin{gathered} y(-3-8x) \\ (y\times-3)+(y\times-8x) \\ -3y-8xy \end{gathered}[/tex]Need to write the formula and then make a graph for the following problem. Number of tablespoons T = the number of teaspoons X divided by3
Answers
Given:
The number of tablespoon is T.
The number of teaspoon is X.
The objective is to write formula and make a graph for the statement, Number of tablespoons T = the number of teaspoons X divided by 3.
Explanation:
The equation can be written as,
[tex]T=\frac{X}{3}[/tex]To plot the graph:
Consider 3 values of X -3, 0, 3.
Substitute the values of X in the obtained equation to find the value of T.
At X = -3,
[tex]\begin{gathered} T=\frac{-3}{3} \\ T=-1 \end{gathered}[/tex]Thus, the coordinate is (-3,-1).
At X = 0,
[tex]\begin{gathered} T=\frac{0}{3} \\ T=0 \end{gathered}[/tex]Thus, the coordinate is (0,0).
At X = 3,
[tex]\begin{gathered} T=\frac{3}{3} \\ T=1 \end{gathered}[/tex]Thus, the coordinate is (3,1).
On plotting the coordinates in the graph,
Hence, the required equation is T = (X/3) and the graph of the equation is obtained.
A bag contains:• 3 red marbles• 2 orange marbles• 1 yellow marble• 4 green marblesRico will randomly choose a marble. Then he will put itback and randomly choose another marble. What isthe probability that he will choose a red and then anorange marble?
Answers
The probability is given by the following formula:
Probability = number of favorable outcomes / total number of outcomes
The total number of outcomes is 10, 3 of the initial number of marbles are red and 2 of them are orange.
The probability of getting a red marble in the first draw is:
Probability = 3/10
The probability of getting an orange marble in the second draw is:
Probability = 2/10 = 1/5
the probability that he will choose a red and then an orange marble can be calculated by multiplying the probabilities that we found, then we get:
Probability = 3/10 × 1/5 = 3/150 = 1/50
Then, the answer is 1/50