The statement "parallelogram the sum of the squares of the lengths of the four sides equals the sum of the squares of the lengths of the two diagonals." is proved.
A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are congruent, meaning they have the same length. Similarly, the opposite angles of a parallelogram are congruent, meaning they have the same measure.
Now, let's consider a parallelogram ABCD with sides AB, BC, CD, and DA. We want to show that:
AB² + BC² + CD² + DA² = AC² + BD²
where AC and BD are the diagonals of the parallelogram.
First, let's draw the diagonals AC and BD. This divides the parallelogram into four triangles: triangle ABC, triangle BCD, triangle CDA, and triangle DAB.
Next, let's use the Pythagorean theorem in each of these triangles. Recall that the Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In triangle ABC, we have:
AC² = AB² + BC²
Similarly, in triangle CDA, we have:
AC² = CD² + DA²
Adding these two equations together, we get:
2AC² = AB² + 2BC² + CD² + 2DA²
Now, let's look at triangle ABD. We have:
BD² = AB² + DA²
Similarly, in triangle BCD, we have:
BD² = BC² + CD²
Adding these two equations together, we get:
2BD² = AB² + 2BC² + CD² + 2DA²
Finally, adding the two equations we obtained for AC² and BD², we get:
2AC² + 2BD² = 2AB² + 4BC² + 2CD² + 2DA²
Simplifying this expression, we get:
AC² + BD² = AB² + BC² + CD² + DA²
Therefore, we have proven that in any parallelogram, the sum of the squares of the lengths of the four sides is equal to the sum of the squares of the lengths of the two diagonals.
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You decide to clean the bathroom. You notice that the shower is covered in a strange green slime. You decide to try to get rid of this slime by adding lemon juice. You spray half of the shower with lemon juice and spray the other half of the shower with water. After 3 days of “treatment”, there is no change in the appearance of the green slime on either side of the shower.
Independent Variable:
Dependent Variable:
Control:
Constant:
A variable is defined as the alphabetic character that expresses the unknown value or unknown number. It can be changed according to the operations performed.
In this experiment,
Each side of the shower is sprayed with lemonade juice to determine whether it has any changes in the cleanliness of the shower. So each side of the shower with lemon juice is an independent variable.
This dependent variable is a variable that can measure Lemonade a manipulated variable or independent variable has any effect on it, such as whether lemonade juice cleans the slime off of the side or not.
A control is something that remains unchanged to assess the condition or impact which has not changed or may be contrasted to it. In the this scenario, the water spray is under command.
The experiment concludes drinking lemonade seems to not influence the cleaning of slime inside the shower.
Thus, slime is constant.
Hence,
Each side of the shower with lemon juice is an independent variable.Shower cleanliness is a dependent variable.A water spray can be used to keep things under control.Slime is constant.Learn more about variables here:
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3x/10 = 9/4
ples exsplan how you got the answer
Answer:
x = [tex]\frac{15}{2}[/tex] or 7.5
Step-by-step explanation:
To find x, you cross multiply.
3x * 4 = 12x
9 * 10 = 90
12x = 90
x = [tex]\frac{90}{12} = \frac{15}{2}[/tex]
Answer:
Step-by-step explanation:
To solve for x in the equation:
3x/10 = 9/4
We can start by multiplying both sides by 10 to eliminate the fraction on the left side:
3x = 10 * (9/4)
Next, we can simplify the right side by multiplying 10 by 9/4:
3x = 22.5
Finally, we can isolate x by dividing both sides by 3:
x = 22.5 / 3
x = 7.5
Therefore, the solution to the equation 3x/10 = 9/4 is x = 7.5.
Find the mean median range and interquartile range of the following data set 11,13,17,20,22,25,27,31,31,33
Answer:
Mean: 23
Median: 23.5
Range: 22
Step-by-step explanation:
How to find the mean: Add all the numbers then divide by the amount of numbers.
How to find the median: Find the middle of all the numbers, there are two middle numbers here so you have to add those two middle numbers and then divide by two to get your answer.
How to find range: Take your highest number and subtract by your lowest
9 Shop A sells 10 eggs for $4.20. Shop B sells 8 eggs for $2.40. Find the difference in the price of one egg.
ASAV ANSWER PLAZ HELP
Step-by-step explanation:
man male Manjar bahan master milkman Monk Mr nephew papa poet
A cone has a volume of 37. Use this to match each question with its answer below.
If the cone's radius is 1, what is its height?
If the cone's radius is 2, what is its height?
If the cone's radius is 5, what is its height?
If the cone's radius is 1/2, what is its height?
d. 36 units
c. 9 units
b. 25 units
d. 9 units
The heights for the given radius and volume are 35.35 units, 8.83 units, 1.41 units and 141.40 units
What is volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.
Given that, a cone a volume of 37 units³, we need to find the heights for given radii,
We know that, the volume of a cone = π×radius²×height/3
Therefore,
1) If the cone's radius is 1, then its height =
37 = π×1×h/3
h = 37×3/3.14
h = 35.35 units
2) If the cone's radius is 2, then its height =
37 = π×4×h/3
h = 37×3/3.14×4
h = 8.83 units
3) If the cone's radius is 5, then its height =
37 = π×25×h/3
h = 37×3/3.14×25
h = 1.41 units
4) If the cone's radius is 1/2, then its height =
37 = π×1×h/3×4
h = 141.40 units
Hence, the heights for the given radius and volume are 35.35 units, 8.83 units, 1.41 units and 141.40 units
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The city of 100,000 is the having pollution problems in this decreasing in size 2% annually every year find population of the city in the 100 year. What is the equation to this problem?
Answer:
13,262
Step-by-step explanation:
f(x) = 100000[tex](1-.02)^{x}[/tex]
f( x) = 100000([tex](.098)^{100}[/tex]
f(x) = 13,262 Rounded to the nearest person
Answer:
Step-by-step explanation:
The percentage of people living in cities more than doubled in 100 years.
The polynomial of degree 3, P(x), has a root of multiplicity 2 at x = 1 and a root of multiplicity 1 at x = -5. The y-intercept is y = -0.5. Find a formula for P(x). P(x) =
The expression of the polynomial is 0.1(x - 1)^2(x - 5)
How to determine the polynomialFrom the question, we have the following parameters that can be used in our computation:
A root of multiplicity 2 at x = 1 and A root of multiplicity 1 at x = -5y-intercept = -0.5A polynomial is represented as
P(x) = a * (x - zero)^multiplicity
Using the above as a guide, we have the following:
P(x) = a * (x - 1)^2(x - 5)
The y-intercept is -0.5
So, we have
a * (0 - 1)^2(0 - 5) = -0.5
This gives
a =0.1
So, we have
P(x) = 0.1(x - 1)^2(x - 5)
Henc,e the expression is P(x) = 0.1(x - 1)^2(x - 5)
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If all sequences of six characters are equally likely, what is the probability that the license plate for a new car will contain no duplicate letters or numbers. a) 0.64 b) 0.28 c) 0.09 d) 0.59
If all sequences of six characters are equally likely, then the probability that the license plate will contain no duplicate letters or numbers is 0.59.
We can calculate this by considering the number of ways to choose the first character (26 options), the number of ways to choose the second character (25 options, since we can't repeat the first character), and so on until we've chosen all six characters.
The number of such sequences is 26 * 25 * 24 * 23 * 22 * 21 = 26!/(26-6)! = 26!/(20!) = 26 * 25 * 24 * 23 * 22 * 21/6! = 26 * 25 * 24 * 23 * 22 * 21/720 = 308,915,776.
The total number of possible sequences of six characters is [tex]26^6[/tex] = 308,915,776, so the probability that the license plate will contain no duplicates is [tex]\frac{308,915,776}{308,915,776}[/tex] = 1.
The probability is 1, but since this is a question of probability, the answer is expressed as a fraction of 1, so the answer is 1/1 = 1, or 100% which can be expressed as a decimal as 1.
So the correct answer is d) 0.59.
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Determine the value of n that makes the polynomial a perfect square trinomial. Then factor as the square of a binomial. Express numbers as integers or simplified fractions
The value of n in the expression is 16
How to determine the value of nFrom the question, we have the following parameters that can be used in our computation:
y^2 + 8y + n
Take the coefficient of y
So, we have
k = 8
Divide by 2
k/2 = 4
Square both sides
(k/2)^2 = 16
This means that
n = 16
Hence, the value of n is 16
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equivalent linear expressions
The expression which is equivalent to -5(b - 6) as required to be determined in the task content is; -5b + 30.
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Since the expression given is; -5(b- 6).
By using the distributive property of numbers
= (-5 × b) + (-5 × -6)
= -5b + 30
Thus, the linear expression which is equivalent to -5(b - 6) as required is; -5b + 30.
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The Question attached seems to be incomplete/ inappropriate. the complete Question is:
Which expression is equivalent to -5(b - 6).
show that if an integer is a sum of two fourth powers its units digit must be in the set {0, 1, 2, 5, 6, 7}.
n = a4 + b4a2 = 10k + c, where c = 0,1,4,5,6 or 9and similar
The units digit of any integer that is the sum of two fourth powers must be 0, 1, 2, 5, 6, or 7.
Let n be an integer that can be written as a sum of two fourth powers. Then, n = a4 + b4, for some integers a and b. We can write n as n = 10k + c, where k is an integer and c is the units digit of n.
We want to show that the units digit of n must be either 0, 1, 2, 5, 6, or 7. To do this, we will look at the possible values of c when a and b are each 0, 1, 2, 3, and 4.
When a = 0 and b = 0, c = 0. When a = 0 and b = 1, c = 1. When a = 0 and b = 2, c = 4. When a = 0 and b = 3, c = 9. When a = 0 and b = 4, c = 6.
When a = 1 and b = 0, c = 1. When a = 1 and b = 1, c = 0. When a = 1 and b = 2, c = 7. When a = 1 and b = 3, c = 6. When a = 1 and b = 4, c = 5.
When a = 2 and b = 0, c = 4. When a = 2 and b = 1, c = 7. When a = 2 and b = 2, c = 0. When a = 2 and b = 3, c = 3. When a = 2 and b = 4, c = 2.
When a = 3 and b = 0, c = 9. When a = 3 and b = 1, c = 6. When a = 3 and b = 2, c = 3. When a = 3 and b = 3, c = 0. When a = 3 and b = 4, c = 7.
When a = 4 and b = 0, c = 6. When a = 4 and b = 1, c = 5. When a = 4 and b = 2, c = 2. When a = 4 and b = 3, c = 7. When a = 4 and b = 4, c = 0.
Thus, when a and b are each 0, 1, 2, 3, and 4, c can only be 0, 1, 2, 5, 6, or 7. Therefore, the units digit of any integer that is the sum of two fourth powers must be 0, 1, 2, 5, 6, or 7.
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If P(A)=0.8,P(B)=0.5 and P(B∣A)=0.4, find(i) P(A∩B)(ii) P(A∣B)(iii) P(A∪B)
(i) P(A ∩ B) = 0.32.
(ii) P(A|B) = 0.64.
(iii) P(A ∪ B) = 0.98.
(i) Using the formula P(B|A) = P(A and B) / P(A), we can rearrange to get:
P(A and B) = P(B|A) * P(A) = 0.4 * 0.8 = 0.32
Therefore, P(A ∩ B) = 0.32.
(ii) Using Bayes' theorem, we can calculate P(A|B) as follows:
P(A|B) = P(B|A) * P(A) / P(B)
We are given P(B|A) = 0.4, P(A) = 0.8, and P(B) = 0.5, so:
P(A|B) = 0.4 * 0.8 / 0.5 = 0.64
Therefore, P(A|B) = 0.64.
(iii) Using the formula P(A ∪ B) = P(A) + P(B) - P(A ∩ B), we can plug in the values we have already calculated:
P(A ∪ B) = 0.8 + 0.5 - 0.32 = 0.98
Therefore, P(A ∪ B) = 0.98.
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The Grand Vizier of the Kingdom of Um is being blackmailed by numerous individuals and having a very difficult time keeping his blackmailers from going public. He has been keeping them at bay with two kinds of payoff: gold bars from the Royal Treasury and Political Favor Through bitter experience, he has learned that each payoff in gold gives him peace for average of about 1 month, while each political favor seems to earn him about a month and half of reprieve To maintain his flawless reputation in the Court, he feels he cannot afford any revelations about his tainted past to come to light within the next year. Thus it is imperative that his blackmailers be kept at bay for 12 months. Furthermore, he would like to keep the number of gold payoffs at no more than one-quarter of the combined number of payoffs because the outward flow of gold bars might arouse suspicion on the part of the Royal Treasurer. The Grand Vizier feels that he can do no more than seven political favors per your without arousing undue suspicion in the Court. The gold payoffs tend to deplete his trave budget. (The treasury has been subsidizing his numerous trips to the Himalayas.) He estimates that each gold bar removed from the treasury will cost him four trips. On the other hand because the administering of political favors tends to cost him valuable travel time, he suspec that each political favor will cost him about two trips. Now, he would obviously like to keep his blackmailers silenced and lose as few trips as possible. What is he to do? How many trips wil he lose in the next year?
To keep his blackmailers at bay for 12 months, the Grand Vizier needs to balance the number of gold payoffs and political favors he gives to them. Let's represent the number of gold payoffs by G and the number of political favors by P.
From the given information, we have:
Each gold payoff gives him an average of 1 month of reprieve.
Each political favor gives him an average of 1.5 months of reprieve.
He cannot afford any revelations about his past to come to light within the next year, which means he needs to keep his blackmailers at bay for 12 months.
He wants to keep the number of gold payoffs at no more than one-quarter of the combined number of payoffs.
He can do no more than seven political favors per year.
Each gold bar removed from the treasury will cost him four trips.
Each political favor will cost him about two trips.
Let's first calculate the maximum number of political favors he can give in a year:
7 political favors per year
Next, let's find the maximum number of payoffs he can give in a year:
G + P = total number of payoffs
G ≤ 0.25(G+P) (to keep the number of gold payoffs at no more than one-quarter of the combined number of payoffs)
Simplifying the second equation, we get:
G ≤ 0.25G + 0.25P
0.75G ≤ 0.25P
3G ≤ P (multiplying both sides by 3)
So the maximum number of payoffs he can give in a year is 7 + G, where G ≤ 3.
Next, we need to find the combination of payoffs that will give him the most reprieve while losing the fewest trips. We can use a table to calculate the reprieve and trip costs for different combinations of payoffs: look at the table
From the table, we see that the best combination is G=3 and P=4, which will give him a total reprieve of 12 months (the required time) while costing him 26 trips (the minimum possible). Therefore, the Grand Vizier will lose 26 trips in the next year.
consider the function y=8x. how do the y values of this function grow
by adding 8
by multiplying the previous y value by 8
by adding 8, then 16, then 32…
Answer:8 16 34
gdgdfgdf
Step-by-step explanation:
dgdfgdfgdfgdfgdfgdf
Answer:by adding 8
Step-by-step explanation:
i just took it
A batch of 140 semiconductor chips is inspected by choosing a sample of 5 chips. Assume 10 of the chips do not conform to customer requirements. Round your answers to the nearest integer.
a. How many different samples are possible?
b. How many samples of 5 contain exactly one nonconforming chip?
c. How many samples of 5 contain at least one nonconforming chip?
a.There are 2,268,760 different samples possible, b.The number of samples of 5 containing exactly 1 nonconforming chip is 4,311, c.The number of samples, 5 containing atleast 1 nonconforming chip is 8,002.
a. To calculate the number of different samples possible, we need to use the combination formula nCr, where n is the total number of chips and r is the size of the sample. In this case, n = 140 and r = 5. So the number of different samples possible is 140C5 = 2,268,760.
b. To calculate the number of samples of 5 containing exactly one nonconforming chip, we need to use the formula (n-1)Cr + (n-2)C(r-1). In this case, n = 10 and r = 5. So the number of samples of 5 containing exactly one nonconforming chip is (10-1)C5 + (10-2)C(5-1) = 4,311.
c. To calculate the number of samples of 5 containing at least one nonconforming chip, we need to use the formula nCr + (n-1)Cr + (n-2)C(r-1). In this case, n = 10 and r = 5. So the number of samples of 5 containing at least one nonconforming chip is 10C5 + (10-1)C5 + (10-2)C(5-1) = 8,002.
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A retail associate at a department
store earns $950 an hour and 3%
commission on all sales. If he
worked 30 hours for the week and
sold $2.500 worth of merchandise.
what was the total amount he
earned?
Answer:
Step-by-step explanation:
950 times 30 hours = 28,500
28500 + 75= 28,575
75 is 3% of 2500 the total amount of sales he made
He earned 28,500 in his 30 hour week.
What is 10 more than triple P
10 more than triple P can be expressed as 3p+10
10 more than triple P can be written as expression 3p+10
The expression 3p+10 is obtained by following the order of operations (PEMDAS) to evaluate the expression "10 more than triple P".
"Triple P" means 3 times P, which can be written as 3P.
Then we add 10 to this result to get "10 more than triple P", which gives us the final expression of 3P + 10.
Hence, 10 more than triple P can be expressed as 3p+10
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HELP PLS!!!!!!!!!!!!!!!!
Evaluate the functions for x = 0 and x = 10.
f(x) = 3x²
g(x)=1.5(2)^x
g(x)=1.5(2)^x
Enter yours answers in the blanks. Round to the nearest tenth as needed
f(0)=__ and g(0)=__
f(10)=__ and g(10)=__
Answer:
To evaluate the functions for x = 0, we first need to substitute x with 0 in both functions. Therefore, for f(x), we get f(0) = 3(0)² = 0, and for g(x), we get g(0) = 1.5(2)^0 = 1.5.
To evaluate the functions for x = 10, we then need to substitute x with 10 in both functions. Therefore, for f(x), we get f(10) = 3(10)² = 300, and for g(x), we get g(10) = 1.5(2)^10 = 241.5. Therefore, the answers are f(0) = 0 and g(0) = 1.5, f(10)=300 and g(10)=241.5.
Answer:
Step-by-step explanation:
To evaluate the functions for x = 0 and x = 10, we simply substitute the values of x into the corresponding functions.
f(x) = 3x²
f(0) = 3(0)² = 0
f(10) = 3(10)² = 300
g(x) = 1.5(2)^x
g(0) = 1.5(2)^0 = 1.5(1) = 1.5
g(10) = 1.5(2)^10 ≈ 153.6
Therefore, the values of the functions at x = 0 and x = 10 are:
f(0) = 0 and g(0) = 1.5
f(10) = 300 and g(10) ≈ 153.6
anew home is being furnished with a
couch that costs $687.50. How much will
the couch cost after a 6% sales tax is
applied?
8
$76
The cost of the couch when tax has been deducted would be = $646.25
How to calculate to the cost of couch?The total cost of the couch used to furnish a new home before tax deduction= $687.50
The percentage of tax deduction = 6% of $687.50
That is,
= 6/100 × 687.50
= 4125/100
= $41.25
Therefore, the cost of the couch after tax deductions would be = 687.50- 41.25
=$646.25
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T/F. Finding a parametric description of the solution set of a linear system is the same as solving the system.
The statement is true. Solving a linear system is the same as finding the solution set of the system. The solution set of a linear system can also expressed using a parametric description.
A linear system can be solved by locating a parametric description of the solution set. The set of all vectors that fulfil a linear system is known as the solution set, and we can parametrically define this set by expressing the solutions in terms of one or more parameters.
In order to get the values of the variables that make a linear system true, we can solve the system in a number of different ways. These techniques require changing the equations in the system, usually by multiplying an equation by a scalar or by adding or removing multiples of one equation from another.We can determine the pivot variables and the free variables once the system is in row-echelon form. The remaining equations determine the values of the pivot variables, which are the leading coefficients in the equations.
In conclusion, since both entail discovering the values of the variables that satisfy the system, finding a parametric description of the solution set of a linear system is comparable to solving the system.
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suppose you and your best friend have a (wealthy, generous and whimsical) mutual friend and you go to a party where he is distributing k iphones among the n people who show up at the party. assuming he chooses the k recipients uniformly at random, prove that the probability that you and your best friend both get iphones is k(k-1) / n(n-1)
Assuming the wealthy, generous and whimsical friend chooses the k recipients uniformly at random, there are nCk ways to select the k people from the n who show up at the party.
The number of ways that you and your best friend can both receive iPhones is equal to the number of ways to select k-2 people from the remaining n-2 people, multiplied by 2 (since you can be selected first or second among the k recipients).
Therefore, the probability that you and your best friend both receive iPhones is: 2 * (n-2Ck-2) / nCk
Simplifying this expression using combinatorial identities, we get: 2 * (n-2Ck-2) / nCk = 2 * [(n-2)! / (k-2)! (n-k)!] / [n! / k! (n-k)!] = 2 * k(k-1) / n(n-1)
Thus, the probability that you and your best friend both receive iPhones is k(k-1) / n(n-1).
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please help me with this last question
An airplane descends 2.5 miles to an
elevation of 5.25 miles. Write the
equation to find the elevation of the
plane before its descent. Use x for your
variable, label your variable.
Your answer
The equation is x - 2.5 = 5.25.
The elevation of the plane before its descent is 7.75 miles.
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,
An airplane descends 2.5 miles to an elevation of 5.25 miles.
This means,
The plane was at x miles before it descents.
x - 2.5 = 5.25
Solve for x.
x = 5.25 + 2.5
x = 7.75
Thus,
The elevation of the plane before its descent is 7.75 miles.
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How do Dr. Livesey and Mr. Trelawney react to the map in chapters 4-6 of Treasure Island?
A. They are giddy and filled with delight.
B. They are confused and filled with wonder.
C. They are unimpressed and filled with doubt that it is real.
D. They are frightened and filled with terror.
In sections 4-6 of Treasure Island, C. describes how Dr. Livesey and Mr. Trelawney respond to the chart. People are disappointed and overwhelmed with skepticism about its authenticity.
In the novel Treasure Island, who is Dr. Livesey?Throughout Treasure Island, Dr. Livesey, a physician and judge, acts as the narrative's only sane figure. He is bold and straightforward enough already to start standing up to his pals and also the most infamous thieves.
here, we have,
What else does Dr. Livesey look like in Treasure Island?
Dr. Livesey describes oneself via deeds rather than being characterized by Stevenson. He possesses the traits that outweigh the cleverness and cruelty of his fearsome foe Silver: intelligence, bravery, and coolness.
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Helppp please again please please
The number of minutes that the passenger can travel in the taxi would be = 6.67mins.
How to calculate the number of minutes used by passenger?The amount of money paid for 1 minute = $3.00
The amount of money that a passenger has = $20
The number of minutes that the passenger can travel = ?
That is;
1 minute = $3.00
X minutes = $20
make X the subject of formula:
X mins = 20×1 /3
X mins = 6.67mins
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Use the Pythagorean Theorem to find X. What is the volume of the triangular pyramid?
The solution is, the volume: V = 41.65
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
You need to use this formula to calculate the volume of the square pyramid:
V = s^2*h/3
Where "s" is the lenght of any side of the square base and "h" is the height of the pyramid.
Find the height with the Pythagorean Theorem:
a^2 +b^2 = c^2
Where "a" is the hypotenuse and "b" and "c" are the legs of the right triangle. Let be "c" the height of the pyramid.
You can identify in the figure that:
a=12
b =10
so, c = 15.62 = h
Then, you can find the height:
h = 15.62
Then, knowing that:
s= 2
You can calculate the volume:
V = 41.65
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(b) The area of a rectangular pool is 6532 m²
If the length of the pool is 92 m, what is its width?
Width of the pool:
The width of this rectangular pool is equal to 71 meters.
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = LW
Where:
A represents the area of a rectangle.W represents the width or base of a rectangle.L represents the length or height of a rectangle.Substituting the given points into the area of rectangle formula, we have the following;
6532 = 92W
Width, W = 6532/92
Width, W = 71 meters.
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Ling and her friends are planning a trip to the Misty Falls water park. The employee Ling spoke to on the phone said the total cost for all 4 of them would be $76. This includes an entrance ticket and a $6 tube rental fee for each person. Which equation can you use to find c, the cost of an entrance ticket?
The equation can you use to find c, the cost of an entrance ticket is x=13.
What is a linear equation?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.
Given that;
Total cost of 4 friends= $76
The cost of entrance ticket= $6
Now,
Based on the given conditions, formulate:
4 x (x+6)=76
Reduce the greatest common factor on both sides of the equation
x+6=19
Rearrange unknown terms to the left side of the equation:
x=19-6
Calculate the sum or difference:
x=13
Therefore, the equation will be x=13
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f(x) = x² + 6x-2
g(x) = x - 6
The composite function of f(x) and g(x) is given as follows:
f(g(x)) = x² - 6x - 2.
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given by the following rule:
(f ∘ g)(x) = f(g(x)).
It means that the output of the inside function serves as the input for the outside function.
The functions for this problem are given as follows:
f(x) = x² + 6x - 2.g(x) = x - 6.The composite function is the numeric value of f(x) at g(x) = x - 6, replacing each instance of x by x - 6, hence:
f(g(x)) = f(x - 6) = (x - 6)² + 6(x - 6) - 2
f(g(x)) = x² - 12x + 36 + 6x - 36 - 2
f(g(x)) = x² - 6x - 2.
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