Answer:
The distributive property is used when finding the product of two polynomials by distributing one polynomial to each term of the other polynomial. For example, if we wanted to multiply (3x - 4)(2x + 5), we would use the distributive property by first multiplying 3x(-4) and 2x(5) and then adding the results together.
Polynomials are closed under multiplication, meaning that when two polynomials are multiplied together, the result is always another polynomial. This is true because a polynomial is a combination of constants and variables raised to non-negative integer powers, and when two polynomials are multiplied, the result is a combination of constants and variables raised to non-negative integer powers, which is a polynomial.
QUESTION: LetP=[72753231]. Answer the following: 1. (1 mark) Explain (briefly) whyPis a regular transition matrix. 2. (2 marks) Given the initial state vectorx0=[103107]T, find the state vectorx2. 3. (3 marks) Calculate the steady state vector. SHOW YOUR WORK!
1. A transition matrix is regular if there is a positive integer k such that P^k has all positive elements.
2. The value of x2 = [128,295, 44,557]T.
3. The value of x = [0.701, 0.299, 0]T .
1. P is a regular transition matrix because it has all positive elements, meaning that it is possible for any state to transition to any other state.
2. To find the state vector x2, we need to multiply the initial state vector x0 by the transition matrix P twice:
x2 = P^2 * x0
= P * P * x0
= P * [72 * 10 + 75 * 7, 32 * 10 + 31 * 7]T
= P * [945, 457]T
= [72 * 945 + 75 * 457, 32 * 945 + 31 * 457]T
= [128,295, 44,557]T
3. To find the steady state vector, we need to solve the equation Px = x for x. This means that we need to find the eigenvector of P corresponding to the eigenvalue
1. We can do this by finding the null space of (P - I), where I is the identity matrix:
(P - I)x = 0
=> [71 -75 0, -32 30 0, 0 0 -1]x = 0
=> x = c[75, 32, 0]T, where c is a constant.
To find the steady state vector, we need to normalize this eigenvector so that it sums to 1:
x = [75/107, 32/107, 0]T
= [0.701, 0.299, 0]T
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Question 15 Solve the compound inequality and give your answer in interval notation. 8x+7>55 OR -5x-1>=-26 Submit Question
To solve the compound inequality, we need to solve each inequality separately and then combine the solutions using the word "OR."
For the first inequality, 8x+7>55, we can isolate the variable on one side of the inequality by subtracting 7 from both sides:
8x > 48
Next, we can divide both sides by 8 to solve for x:
x > 6
For the second inequality, -5x-1>=-26, we can isolate the variable on one side of the inequality by adding 1 to both sides:
-5x >= -25
Next, we can divide both sides by -5 to solve for x. Remember that when we divide or multiply both sides of an inequality by a negative number, we need to reverse the inequality sign:
x <= 5
Now we can combine the solutions using the word "OR." In interval notation, this would be (-∞, 5] U (6, ∞). This means that the solution includes all values of x less than or equal to 5 or greater than 6.
So the final answer is:
x ∈ (-∞, 5] U (6, ∞)
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Find the total cost of tiling a triangular area having a base
length of 3 meters and a height of 9 meters if it costs $9.71 to
tile one square meter. Round to the nearest cent
The total cost of tiling a triangular area having a baselength of 3 meters and a height of 9 meters is $131.29.
Given base length of triangular area is 3 metersHeight of triangular area is 9 metersCost of tiling one square meter = $9.71 We need to find the total cost of tiling the triangular area. The area of a triangle is given by the formula as shown below,
Area of a triangle = 1/2 × base length × height, Therefore, Area of the given triangle = 1/2 × 3 meters × 9 meters= 13.5 square meters. Now, the total cost of tiling the triangular area can be found by multiplying the area by the cost per square meter. Total cost of tiling triangular area = 13.5 square meters × $9.71/square meter = $131.29 (approx)
Hence, the total cost of tiling a triangular area having a baselength of 3 meters and a height of 9 meters is $131.29.
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Polling agency is investigating the voter support for_ regions have equal number of voters ballot measure in an upcoming city election The City is divided in two in them: The agency will select _ random regions Region A and region B. Both population proportion of voters who would sample of 500 voters from one region, Region A of the city Assume that support the ballot measure in Region A is 0. 47. The What is the probability that the proportion of voters in the sample of Region who support the ballot measure greater than 0. 50 ? The polling agency will take another sample from different region, Region B, of the city: The the population proportion of voters who would agency plans to select random sample of 400 voters. Assume that support the ballot measure in Region B is 0. 51 What is the probability that , measure might pass?
The probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50 is approximately 0.1736 or 17.36%. The probability that the ballot measure might pass in Region B can be calculated using a confidence interval approach.
The confidence interval for the population proportion of voters who support the ballot measure in Region B:
CI = p ± z × SE
where p is the sample proportion, z is the critical value for the desired confidence level (e.g., z=1.96 for 95% confidence), and SE is the standard error of the sample proportion.
the standard error of the sample proportion:
SE = [tex]sqrt [p ×\frac{(1-p)}{n} ][/tex] = [tex]sqrt[0.51 ×\frac{(1-0.51)}{400} ][/tex] = 0.025
where p is the sample proportion and n is the sample size.
the confidence interval using a 95% confidence level:
CI = 0.51 ± 1.96 0.025 = (0.46, 0.56)
Therefore, we can be 95% confident that the true population proportion of voters who support the ballot measure in Region B falls within the range of 0.46 to 0.56. Since the lower bound of the confidence interval is above 0.50, there is a possibility that the ballot measure might pass in Region B. However, the exact probability would depend on the actual population proportion and the sample size.
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How to solve probability?
The runner should choose the second cooler, because the probability of selecting a sports drink and a water from the first cooler is about 24.98% and the second cooler is about 25.86%.
To calculate the probability of selecting a sports drink and a water bottle from each cooler, we need to use the following formula:
Probability of selecting a sports drink and a water bottle = (number of sports drinks / total number of bottles) x (number of water bottles / (total number of bottles - 1))
For the first cooler, the probability of selecting a sports drink and a water bottle is:
(19/39) x (20/38) = 0.2498, or about 24.98%
For the second cooler, the probability of selecting a sports drink and a water bottle is:
(14/29) x (15/28) = 0.2586, or about 25.86%
Therefore, the runner should choose the second cooler, because it has a slightly higher probability of selecting a sports drink and a water bottle.
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Two brothers, Joe and Keith, saved $45 total in one week. Joe saved $15.
a. What is the ratio of the amount Joe saved to the amount Keith saved?
Represent the ratio in simplest form.
The ratio of the amount Joe saved the money against Keith is 1:2.
What is the ratio?A ratio in mathematics demonstrates how many times one number is present in another.
For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.
Ratios contrast two figures by ordinarily dividing them.
A/B would be your formula if you were comparing one data point (A) to another data point (B).
This indicates that you are multiplying information A by information B.
For instance, your ratio will be 5/10 if A is 5 and B is 10.
So, the total money saved is $45.
Joey saved $15.
Then, Keith saved:
45 - 15 = 30
The ratio would be:
15/30
1/2
1:2
Therefore, the ratio of the amount Joe saved the money against Keith is 1:2.
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Which expression is equivalent to |a|≤5 ?
Responses
a ≥ –5 and a ≤ 5
a ≥ –5 and a ≤ 5
a ≥ –5 or a ≤ 5
a ≥ –5 or a ≤ 5
a ≤ –5 or a ≥ 5
a ≤ –5 or a ≥ 5
a ≤ –5 and a ≥ 5
the values of a that satisfy the inequality |a|≤5 are those that satisfy both a ≤ 5 and a ≥ -5. This is why the expression equivalent to |a|≤5 is a ≥ –5 and a ≤ 5.
What is expression ?
In mathematics, an expression is a combination of numbers, variables, and operators that can be evaluated to produce a value. It can be as simple as a single number or variable, or as complex as a long sequence of operations involving multiple variables and operators.
The expression |a|≤5 means that the absolute value of a is less than or equal to 5. The absolute value of a number is its distance from zero on the number line, regardless of whether the number is positive or negative.
So, if |a|≤5, then a must be between -5 and 5, including both.
To see why this is true, consider two cases:
If a is greater than or equal to zero, then |a| = a, and so we have a ≤ 5.
If a is less than zero, then |a| = -a, and so we have -a ≤ 5, which is equivalent to a ≥ -5.
Therefore, the values of a that satisfy the inequality |a|≤5 are those that satisfy both a ≤ 5 and a ≥ -5. This is why the expression equivalent to |a|≤5 is a ≥ –5 and a ≤ 5.
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Answer:
the values of a that satisfy the inequality |a|≤5 are those that satisfy both a ≤ 5 and a ≥ -5. This is why the expression equivalent to |a|≤5 is a ≥ –5 and a ≤ 5.
Step-by-step explanation:
What is expression ?
In mathematics, an expression is a combination of numbers, variables, and operators that can be evaluated to produce a value. It can be as simple as a single number or variable, or as complex as a long sequence of operations involving multiple variables and operators.
According to the given conditions :
The expression |a|≤5 means that the absolute value of a is less than or equal to 5. The absolute value of a number is its distance from zero on the number line, regardless of whether the number is positive or negative.
So, if |a|≤5, then a must be between -5 and 5, including both.
To see why this is true, consider two cases:
If a is greater than or equal to zero, then |a| = a, and so we have a ≤ 5.
If a is less than zero, then |a| = -a, and so we have -a ≤ 5, which is equivalent to a ≥ -5.
Therefore, the values of a that satisfy the inequality |a|≤5 are those that satisfy both a ≤ 5 and a ≥ -5. This is why the expression equivalent to |a|≤5 is a ≥ –5 and a ≤ 5.
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Find the \( x \)-intercept(s) of the following function. \[ f(x)=x^{2}+5 x-14 \] Give your answer as ordered pairs separated by commas, if necessary. For example, your answer might take the form \( (a
To find the \( x \)-intercepts of a function, we need to set the function equal to 0 and solve for \( x \). This will give us the values of \( x \) where the function crosses the \( x \)-axis. In this case, we have:
\[ f(x)=x^{2}+5 x-14=0 \]
We can solve this quadratic equation using the quadratic formula:
\[ x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a} \]
Plugging in the values of \( a=1 \), \( b=5 \), and \( c=-14 \), we get:
\[ x=\frac{-(5)\pm\sqrt{(5)^{2}-4(1)(-14)}}{2(1)} \]
Simplifying, we get:
\[ x=\frac{-5\pm\sqrt{25+56}}{2} \]
\[ x=\frac{-5\pm\sqrt{81}}{2} \]
\[ x=\frac{-5\pm9}{2} \]
This gives us two solutions for \( x \):
\[ x=\frac{-5+9}{2}=\frac{4}{2}=2 \]
\[ x=\frac{-5-9}{2}=\frac{-14}{2}=-7 \]
So the \( x \)-intercepts of the function are \( (2,0) \) and \( (-7,0) \).
Answer: \[ (2,0),(-7,0) \]
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Using a formula estimate the body surface area of a person whose height is 166cm and weighs 100kg. A. 2.29m^(2) B. 2.15m^(2) C. 55.9m^(2) D. 5.44m^(2)
The correct answer is B. 2.15m^(2). The estimated body surface area of the person is 2.15m^(2).
To estimate the body surface area of a person, we can use the Mosteller formula:
BSA = square root of [(height in cm x weight in kg)/3600]
Plugging in the given values for height and weight:
BSA = square root of [(166cm x 100kg)/3600]
BSA = square root of 1660000/3600
BSA = square root of 461.11
BSA = 2.15m^(2)
Therefore, the estimated body surface area of the person is 2.15m^(2). Hence, B is the correct answer.
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Work the problem using the three-step method. Show your work.
The sum of three consecutive integers is 18. Find the integers.
WRITER
Answer:
5,6 and 7.
Step-by-step explanation:
I am not sure what the three step method is, but here is how I solved it.
Consecutive integers means integers in a row. For example, 5,6 7 are consecutive integers or -4,-3,-2 are consecutive integers.
Integers are all the whole numbers (0,1,2,3...) and their opposites (..., -3, -2, -1) 1/2 or -.23 are not integers.
Let x = the first number
Let x + 1 = the second number
Let x + 2 = the third number
x + (x + 1) + (x + 2) = 18 I do not need the parentheses, but I want you to see that the first number, plus the second number, plus the third number equals 18.
x + x + 1 + x + 2 = 18 Combine like terms
3x + 3 = 18 Subtract 3 from both sides of the equation
3x + 3 - 3 = 18 - 3
3x = 15 Divide both sides by 3
[tex]\frac{3x}{3}[/tex] = [tex]\frac{15}{3}[/tex]
x = 5
The first number is 5. The second number is 6 and the last number is 7.
Check:
5 + 6 + 7 = 18
18 =18 Checks.
Helping in the name of Jesus.
I. Linear functions - Complete the table by writing the Slope-Intercept form, identifying the slope, and finding the
y
-intercept for each equation given. Indicate if an answer does not exist.
Equation Slope-Intercept Form Slope y-Intercept
y = 2x + 5 y = 2x + 5 2 5
4x - 3y = 12 y = (4/3)x - 4 4/3 -4
x = 7 Does not exist Does not exist Does not exist
3y = 9 y = 3 0 3
For the first equation, y = 2x + 5, it is already in slope-intercept form. The slope is the coefficient of x, which is 2, and the y-intercept is the constant term, which is 5.
For the second equation, 4x - 3y = 12, we can rearrange it to get it in slope-intercept form by isolating y on one side of the equation. We can do this by subtracting 4x from both sides and then dividing by -3: 4x - 3y = 12 -3y = -4x + 12 y = (4/3)x - 4
The slope is the coefficient of x, which is 4/3, and the y-intercept is the constant term, which is -4. For the third equation, x = 7, there is no y term, so it cannot be written in slope-intercept form and the slope and y-intercept do not exist.
For the fourth equation, 3y = 9, we can rearrange it to get it in slope-intercept form by dividing both sides by 3: 3y = 9 y = 3 The slope is 0, since there is no x term, and the y-intercept is the constant term, which is 3.
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By what will the product of 2 numbers decrease if one of the numbers is decreased by 25% and the other number is decreased by 50%
Answer:
62.5%
Step-by-step explanation:
the product of the two numbers=xy
the product of the altered numbers=(0.75x)(0.5y) OR 0.375xy
finally you subtract this from one to get your decrease: 1-0.375=0.625
then simply convert that to a percent, leaving you with 62.5%. hope this helps!
Please help me i need the answer asap
The required slope of the line shown in the graph is 4/3, and the lines representing the rise and run are shown in the graph.
What is the slope of the line?The slope of a line is a measure of how steeply the line is inclined with respect to the horizontal axis.
Here,
To calculate the slope of a line from the rise and run values, we use the formula:
slope = rise/run
In this case, rise = 6 and run = 4.5. Substituting these values into the formula, we get:
slope = 6 / 4.5
Simplifying the fraction by dividing both the numerator and denominator by 1.5,
slope = 4/3
Therefore, the slope of the line is 4/3.
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By completing the square, the expression x^(2)+10x+140 equals (x+A)^(2)+B where A= and B
By completing the square, the expression x²+10x+140 can be rewritten in the form (x+A)²+B. Where A=5 and B=-115.
To do this, we need to find the values of A and B.
Start with the original expression: x²+10x+140
Move the constant term to the right side of the equation: x²+10x = -140
Take half of the coefficient of the x term and square it: (10/2)²= 25
Add this value to both sides of the equation: x²+10x+25 = -140+25
Simplify the right side of the equation: x²+10x+25 = -115
Factor the left side of the equation: (x+5)² = -115
Therefore, the expression x²+10x+140 can be rewritten as (x+5)²-115, where A=5 and B=-115.
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Giving Brainlist
Please show the steps :)
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Let
f(x)=−2x+4 and g(x)=−6x -7. Find f(x)−g(x).
A local theater is putting on the musical "peter pan." Tickets for adults cost $20, while tickets for children up to age 12 cost $10. On opening night a total of 140 people are in attendance and the theater earns $2270.
a. Define the variables for this problem.
b. Write a system of equations that represents this situation. DO NOT SOLVE.
a. The variables for this problem is x + y = 140
b. a system of equations that represents this situation is 20x + 10y = 2270
What are variables?An attribute οr phenοmenοn that may be quantified as a variable and that changes in value οver time. As a result, a variable is a quantity that can be calculated and is subject tο change.
Bοth discrete and cοntinuοus variables are pοssible.
a. Tο sοlve this questiοn we will need twο variables x and y.
Let number οf adults be x and number οf kids be y then we get,
x + y = 140
b. Tο write a system fοr sοlving this questiοn we are given the price οf tickets.
20x + 10y = 2270
and, x + y = 140
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Find the percent of change 4/3 to 3/5
The percent of change from 4/3 to 3/5 is 6.1%
How to determine the percentage changeTo find the percent of change from 4/3 to 3/5, we'll use the following formula:
Percent change = ((Old value - New value) / old value) x 100%
First, we'll identify which value is the old value and which is the new value.
The old value is 4/3 and the new value is 3/5.
Substitute the known values in the above equation, so, we have the following representation
Percent change = ((4/3 - 3/5) / 4/3) x 100%
Evaluate
Percent change = 6.1%
Hence, the percent change is 6.1%
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Si tengo un cubo de 3600 m³ cuantos kilo litros caben?
If you have a 3600 m³ cube, then you can fit 3600 kiloliters in the cube.
A kiloliter (kL) is defined as a unit of volume which is used to measure liquids. It is equal to 1,000 liters, and it is used to measure large volumes of water, oil, and other liquids.
We know that 1 cubic meter is equal to 1 kiloliter,
We have to convert 3600 meter cube to Kiloliter,
So , we multiply by 3600,
On multiplying,
We get,
⇒ 3600 meter cube = 3600 × 1 Kiloliter,
⇒ 3600 meter cube = 3600 Kiloliter,
Therefore, 3600 Kiloliter can fill in the cube having the volume as 3600 meter cube.
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Please help! I'm being timed!
Answer:1 4/10
Step-by-step explanation:
We can reduce this to lowest terms by dividing the numerator and denominator or 4/10 by 2 to get the equivalent fraction 1 and 2/5
Shan used a surveying tool to map a region of land for his science class. To determine the height of a vertical rock formation, he measured the distance from the base of the formation to his position and the angle between the ground and the line of sight to the top of the formation. The distance was 43 meters, and the angle was 36°. What is the height of the formation to the nearest meter?
The height of the formation is [tex]31meter[/tex], to the nearest meter.
How is height defined?Height, altitude, and elevation all refer to the vertical distance between something's top and bottom or its base but something above it. Height is used to describe everything that may be measured vertically, high or low.
What types of heights are there?In essence, height relates to elevation, which is the height above a certain level. Furthermore, height refers to any quantifiable distance above a particular level as well as extend upwards (as it is from foot to head). For instance, the elevation of a tower, tree, person, mountain, etc.
We can use the tangent function to calculate the formation's height.
[tex]tan(36^{0} )=\frac{h}{3}[/tex]
Here, we have to multiply both sides by [tex]43[/tex] we get,
[tex]43tan(36^{0} )=h[/tex]
[tex]h=31meter[/tex]
Therefore, the height of the formation to the nearest meter is [tex]31meter[/tex].
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Quadrilateral MATH is dilated by a scale factor of 2.5 centered at (1, 1) to create quadrilateral M'ATH: Select all the statements that are true about the dilation.
M'A' will overlap MA
The area of M'A'T'H' is equal to 2.5 times the area of MATH
ΜΑΣ Μ' Α'
AT' will overlap AT
The slope of HT is equal to the slope of HT
M' A'T" H' is (1,1) and (2.5) equals 3.6 to form a quadrilateral. A two-dimensional shape with four sides, four vertices, and four angles is referred to as a quadrilateral.
What is meant by scale factor of quadrilateral?The scale factor is the ratio of one figure's side length to the other figure's corresponding side length.The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger.The scale factor is the ratio of one figure's side length to the other figure's corresponding side length.A scale factor is the amount by which an object is multiplied to produce a second object of different size but with the same appearance. Just a larger or smaller version of the original is created, not an exact copy.Let the scale factor of quadrilateral is center at 2.5 at (1, 1) then
(1,1) and (2.5) equals 3.6
(1,1) + (2.5) = 3.6
Therefore, the statement exists true about the dilation is
D. [tex]\frac{}{A'T'}[/tex] will overlap [tex]\frac{}{AT}[/tex]
A. [tex]\frac{}{M'A'}[/tex] will overlap [tex]\frac{}{MA}[/tex]
E. The slope of [tex]\frac{}{HT}[/tex] is equal to the slope of [tex]\frac{}{H'T'}[/tex]
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Срочно помогите про практической задание сделать)
Найти решение уравнения x^3+2x+4=0 c точностью Ɛ=0,01 методом деления отрезка пополам.
Answer:
Для применения метода деления отрезка пополам нужно использовать тот факт, что функция x^3 + 2x + 4 непрерывна на всей числовой оси. Кроме того, нужно заметить, что функция монотонно возрастает на всей числовой оси, так как ее производная 3x^2 + 2 всегда положительна.
Начнем с интервала [a, b], где a = -2 и b = 0. Тогда значение функции в точке a равно -4, а значение функции в точке b равно 4. Значит, на этом интервале есть хотя бы один корень уравнения x^3 + 2x + 4 = 0.
Посередине интервала [a, b] находим точку c = (a + b) / 2 = -1. Значение функции в точке c равно 1, то есть на интервале [c, b] нет корней уравнения.
Затем выбираем интервал [a, c] и повторяем процесс. Находим точку d = (a + c) / 2 = -1.5. Значение функции в точке d равно -1.375, то есть на интервале [d, c] есть корень уравнения.
Продолжаем делить отрезки пополам и находить корни, пока не достигнем требуемой точности. Например, следующая точка будет e = (d + c) / 2 = -1.25. Значение функции в точке e равно 0.234375, то есть на интервале [e, c] есть корень уравнения.
Таким образом, метод деления отрезка пополам дает корень уравнения x^3 + 2x + 4 = 0 на интервале [-1.25, -1.125], который можно записать в виде x ≈ -1.1875 (с точностью до Ɛ=0,01).
50x8+25 take away what equals 225?
Answer:
1.8 i think
Step-by-step explanation:
i used a calculator
PLEASE HELPP WILL GIVE BRAINLIEST!!!!
image of proof attached !!!
line e is parallel to line m because angle 1 + angle 2 = 180°
What are angles on parallel lines?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.
Represent the adjascent angle to angle 2 by x and adjascent angle to angle 1 by y
therefore ;
2 = y ( corresponding angles are equal)
1 = x ( corresponding angles are equal)
angle 1+y = 180 ( angle on a straight line)
angle 2 + x = 180
<1= 180-y
<2 = 180 -x
and both equations
< 1 +<2 = 180
therefore since < 1 +<2 = 180, then line e is parallel to line m
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I need help pls pls pls help quickly.
The lateral surface area of the cylinders {W} and {Y} are same.
What is volume?Volume is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write -
V = ∫∫∫ F(x, y, z) dx dy dz
Given are the dimensions of the cylinder as shown in the image.
The lateral surface area of the cylinder is -
L.S.A = 2πrh
{ 1 } -
L.S.A {W} = 2π x 3 x 9 = 54π
{ 2 } -
L.S.A {X} = 2π x 4 x 2 = 16π
{ 3 } -
L.S.A {Y} = 2π x 4.5 x 6 = 54π
Therefore, the lateral surface area of the cylinders {W} and {Y} are same.
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The map shows the distance in air miles from Houston to both Austin and San Antonio.What is the Least possible distance to Austin to san Antonio
a. The greatest possible distance from Austin to san Antonio is 335.77 mi, b. the Least possible distance to Austin to san Antonio is 120.03 mi.
Describe Distance?Distance refers to the physical length or space between two points or objects. It is an important concept in mathematics, physics, and everyday life. Distance can be measured in various units such as meters, feet, kilometers, miles, or light-years, depending on the context and scale of the measurement.
In mathematics, distance is often measured using the Euclidean distance formula, which calculates the distance between two points in a plane or in three-dimensional space. The formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
where d is the distance between the two points, (x1, y1) and (x2, y2).
In physics, distance is often used to describe the separation between two objects or particles. The distance between two objects can affect the strength of gravitational or electromagnetic forces between them. Distance is also an important concept in special relativity, where it is affected by the relative motion of observers and the distortion of spacetime.
a. Greatest possible distance from Austin to san Antonio= Distance from Austin →Houston → san Antonio.
Austin - Houston = 146.43 mi
Houston - San Antonio = 189.34 mi
Total distance= 146.43+ 189.34= 335.77 mi
b. Least possible distance to Austin to san Antonio= the shortest distance = x
By pythagoras theorem
(189.34)²= (146.43)²+ x²
x²= (189.34)²- (146.43)²
x²= 35849.63- 21441.744
x²= 14407.89
x=√14407.89
x= 120.03
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The complete question is:
Two  parallel lines, M and N Are cut by the transversal as shown suppose M1 equals 70 
The measure of angle 2 is 70° and the measure of angle 3 is also 70°°.
What is a transversal?We know when a transversal intersects two parallel lines at two distinct points,
Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.
From the given information ∠1 and ∠3 are pairs of alternate interior angles.
Therefore, m∠1 = m∠B = 70°.
We also know that the vertically opposite angles are equal,
Here ∠1 and ∠2 are vertically opposite angles,
Therefore, m∠1 = m∠2 = 70°.
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If f(a) > f(x) in an open interval containing a, x ≠ a, then the function value f(a) is a relative ..............of f.If f(b) < f(x) in an open interval containing b, x ≠ b, then the function value f(b) is a relative ............ of f.
The function is relative minima
If f(a) > f(x) in an open interval containing a, x ≠ a, then the function value f(a) is a relative maximum of f. If f(b) < f(x) in an open interval containing b, x ≠ b, then the function value f(b) is a relative minimum of f.
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the zeros and their multiplicities. Consider f(x)=2x^(5)+11x^(4)-2x^(3)-74x^(2)-60x+48
The zeros and their multiplicities of the function f(x)=2x^(5)+11x^(4)-2x^(3)-74x^(2)-60x+48 are:
x = -4, multiplicity 1
x = (-5 + √(41))/(2), multiplicity 1
x = (-5 - √(41))/(2), multiplicity 1
The zeros of a function f(x) are the values of x that make f(x) equal to 0. The multiplicity of a zero is the number of times that zero appears as a solution. To find the zeros and their multiplicities of the given function f(x)=2x^(5)+11x^(4)-2x^(3)-74x^(2)-60x+48, we can use synthetic division or factoring.
First, let's use synthetic division to find one of the zeros:
2x^(5)+11x^(4)-2x^(3)-74x^(2)-60x+48 = 0
Using synthetic division, we can find that x = -4 is a zero of the function:
(-4) | 2 11 -2 -74 -60 48
| 0 -8 20 88 104 -176
---------------------------
2 3 18 14 44 -128
Now we can divide the original function by (x+4) to find the remaining zeros:
f(x) = (x+4)(2x^(4)-x^(3)+14x^(2)+10x-32)
Using the quadratic formula, we can find the remaining zeros of the function:
x = (-b ± √(b^(2)-4ac))/(2a)
x = (-(10) ± √((10)^(2)-4(2)(-32)))/(2(2))
x = (-10 ± √(164))/(4)
x = (-10 ± √(4*41))/(4)
x = (-10 ± 2√(41))/(4)
x = (-5 ± √(41))/(2)
So the zeros of the function are x = -4, x = (-5 + √(41))/(2), and x = (-5 - √(41))/(2).
The multiplicity of each zero is 1, since each zero appears only once as a solution.
Therefore, the zeros and their multiplicities of the function f(x)=2x^(5)+11x^(4)-2x^(3)-74x^(2)-60x+48 are:
x = -4, multiplicity 1
x = (-5 + √(41))/(2), multiplicity 1
x = (-5 - √(41))/(2), multiplicity 1
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The manager of a coffee shop recorded the number of customers who put vanilla creamer or chocolate creamer in their coffee during one hour and classified them by age. The results are shown in the table. Coffee Creamer. Vanilla. Chocolate. Age 18 to 30. 2, 6. Age 31 plus. 4, 8 What percentage of these customers put chocolate creamer in their coffee during this hour?
The percentage of customers who put chocolate creamer in their coffee during the hour is 70%.
Finding the percentage of customers:To find the required percentage, find the number of customers that chose chocolate creamer and total the number of customers who came to choose the creamer in the hour.
Divide the number of customers that chose chocolate creamer by the total number of customers and multiply by 100.
Here we have
The manager of a coffee shop recorded the number of customers who put vanilla creamer or chocolate creamer in their coffee during one hour
The bale given is
Vanilla Chocolate
Age 18 - 30 2 6
Age 30 + 4 8
Here, number of customers = 2 + 4 + 6 + 8 = 20
No of customers that choose chocolate creamer = 6 + 8 = 14
The percentage of customers that put chocolate creamer
= [ 14/20 ] × 100 = 70%
Therefore,
The percentage of customers who put chocolate creamer in their coffee during the hour is 70%.
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Answer: 70%
Step-by-step explanation:
