Answer:
The slope is 4/11.
Step-by-step explanation:
M = Y2 - Y1
X2 - X2
M = 6 - 2
4 - (-7)
M = 4
11
have two one-quart jars; the first is filled with water, and the second is empty. I pour half of the water in the first jar into the second, then a third of the water in the second jar into the first, then a fourth of the water in the first jar into the second, then a fifth of the water in the second jar into the first, and so on. How much water in quarts is in the first jar after the $10^{\textrm{th}}$ pour? Express your answer as a common fraction.
Answer:
water in quarts is in the first jar after 10th pour = 12/11
Step-by-step explanation:
Let X represent first jar and Y represents second jar.
have two one-quart jars; the first is filled with water, and the second is emptyLets give the initial value of 2 to the first jar which is filled with water. Lets say there are two liters of water in first jar.
Lets give the initial value of 0 to the second as it is empty.
So before any pour, the values are:
X: 2
Y: 0
pour half of the water in the first jar into the secondAfter first pour the value of jar X becomes:
Previously it was 2.
Now half of water is taken i.e. half of 2
2 - 1 = 1
So X = 1
The value of jar Y becomes:
The half from jar X is added to second jar Y which was 0:
After first pour the value of jar Y becomes:
0 + 1 = 1
Y = 1
a third of the water in the second jar into the firstAfter second pour the value of jar X becomes:
Previously it was 1.
Now third of the water in second jar Y is added to jar X
1 + 1/3
= (3 + 1)/3
= 4/3
X = 4/3
After second pour the value of jar Y becomes:
Previously it was 1.
Now third of the water in Y jar is taken and added to jar X so,
1 - 1/3
= (3 - 1)/3
= 2/3
Y = 2/3
a fourth of the water in the first jar into the secondAfter third pour the value of jar X becomes:
Previously it was 4/3.
Now fourth of the water in the first jar X is taken and is added to jar Y
= 3/4 * (4/3)
= 1
X = 1
After third pour the value of jar Y becomes:
Previously it was 2/3
Now fourth of the water in the second jar X is added to jar Y
= 2/3 + 1/4*(4/3)
= 2/3 + 4/12
= 1
Y = 1
a fifth of the water in the second jar into the firstAfter fourth pour the value of jar X becomes:
Previously it was 1
Now fifth of the water in second jar Y is added to jar X
= 1 + 1/5*(1)
= 1 + 1/5
= (5+1) / 5
= 6/5
X = 6/5
After fourth pour the value of jar Y becomes:
Previously it was 1.
Now fifth of the water in Y jar is taken and added to jar X so,
= 1 - 1/5
= (5 - 1) / 5
= 4/5
Y = 4/5
a sixth of the water in the first jar into the secondAfter fifth pour the value of jar X becomes:
Previously it was 6/5
Now sixth of the water in the first jar X is taken and is added to jar Y
5/6 * (6/5)
= 1
X = 1
After fifth pour the value of jar Y becomes:
Previously it was 4/5
Now sixth of the water in the first jar X is taken and is added to jar Y
= 4/5 + 1/6 (6/5)
= 4/5 + 1/5
= (4+1) /5
= 5/5
= 1
Y = 1
a seventh of the water in the second jar into the firstAfter sixth pour the value of jar X becomes:
Previously it was 1
Now seventh of the water in second jar Y is added to jar X
= 1 + 1/7*(1)
= 1 + 1/7
= (7+1) / 7
= 8/7
X = 8/7
After sixth pour the value of jar Y becomes:
Previously it was 1.
Now seventh of the water in Y jar is taken and added to jar X so,
= 1 - 1/7
= (7-1) / 7
= 6/7
Y = 6/7
a eighth of the water in the first jar into the secondAfter seventh pour the value of jar X becomes:
Previously it was 8/7
Now eighth of the water in the first jar X is taken and is added to jar Y
7/8* (8/7)
= 1
X = 1
After seventh pour the value of jar Y becomes:
Previously it was 6/7
Now eighth of the water in the first jar X is taken and is added to jar Y
= 6/7 + 1/8 (8/7)
= 6/7 + 1/7
= 7/7
= 1
Y = 1
a ninth of the water in the second jar into the firstAfter eighth pour the value of jar X becomes:
Previously it was 1
Now ninth of the water in second jar Y is added to jar X
= 1 + 1/9*(1)
= 1 + 1/9
= (9+1) / 9
= 10/9
X = 10/9
After eighth pour the value of jar Y becomes:
Previously it was 1.
Now ninth of the water in Y jar is taken and added to jar X so,
= 1 - 1/9
= (9-1) / 9
= 8/9
Y = 8/9
a tenth of the water in the first jar into the secondAfter ninth pour the value of jar X becomes:
Previously it was 10/9
Now tenth of the water in the first jar X is taken and is added to jar Y
9/10* (10/9)
= 1
X = 1
After ninth pour the value of jar Y becomes:
Previously it was 8/9
Now tenth of the water in the first jar X is taken and is added to jar Y
= 8/9 + 1/10 (10/9)
= 8/9 + 1/9
= 9/9
= 1
Y = 1
a eleventh of the water in the second jar into the firstAfter tenth pour the value of jar X becomes:
Previously it was 1
Now eleventh of the water in second jar Y is added to jar X
= 1 + 1/11*(1)
= 1 + 1/11
= (11 + 1) / 11
= 12/11
X = 12/11
After tenth pour the value of jar Y becomes:
Previously it was 1.
Now eleventh of the water in Y jar is taken and added to jar X so,
= 1 - 1/11
= (11-1) / 11
= 10/11
Y = 10/11
Answer:
6/11
Step-by-step explanation:
1/2 + (1/2)(2/11) = 6/11
sus
Given the original statement "If a number is negative, the additive inverse is positive,” which are true? Select three options. If p = a number is negative and q = the additive inverse is positive, the original statement is p → q. If p = a number is negative and q = the additive inverse is positive, the inverse of the original statement is ~p → ~q. If p = a number is negative and q = the additive inverse is positive, the converse of the original statement is ~q → ~p. If q = a number is negative and p = the additive inverse is positive, the contrapositive of the original statement is ~p → ~q. If q = a number is negative and p = the additive inverse is positive, the converse of the original statement is q → p.
Answer:
A. If p = a number is negative and q = the additive inverse is positive, the original statement is p → q.
B. If p = a number is negative and q = the additive inverse is positive, the inverse of the original statement is ~p → ~q.
D. If q = a number is negative and p = the additive inverse is positive, the contrapositive of the original statement is ~p → ~q.
Step-by-step explanation:
(not 100% sure if these are correct but if they are, then I hope they helped you!)
have a nice day/night!
Answer:
abd
Step-by-step explanation:
james is climbing a mountain. is the distance he travels to the top of the mountain a state function or a path function?
The distance he travels to the top of the mountain is a path function. It is because it depends on the distance that he traveled.
What is The path function?
Path function is a function that depends on the state that is taken from the initial state to the final state. A state function depends on the property, the initial value, and the final value like enthalpy and density,
From the question above, the initial state is the state that he started to traveled and the final state is the top of the mountain. So, the distance between those two is a path function.
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30 POINTS. Ally is given three different sums of the same sequence to calculate. If she completes the three problems in order do the sums increase or decrease in value. Why?
A) The sums decrease in value because you are subtracting.
B) The sums increase in value because even though you are multiplying and adding. There is no subtraction or division.
C) The sums increase in value because even though you subtract 7 from each term you are still increasing the positive number that is being multiplied so they will increase.
D) The sums decrease in value because even though you are increasing the positive number that is being multiplied you have to subtract 7 from each answer so they will decrease.
Answer:
check online for more information
percent.
7) A new social media site is increasing its
user base by a constant percentage per
month. If the user base grows from
29,130 users to 52,167 users over 10
months, at what monthly rate is the user base increasing?
Answer:
5. % increase in user base per month (g) = 10% Users at t0 (P) = 10000
Step-by-step explanation:
6. Thirty-five more than .8 times a number is the
same as 43 less than the
product of -7 and the
number.
The value of the given number is -10.
Here, we are given that Thirty-five more than 0.8 times a number is the same as 43 less than the product of -7 and the number.
Let the number be x
0.8 times x = 0.8
35 more than 0.8x = 35 + 0.8x
Thus, our left hand side of the equation is 35 + 0.8x
Now, the product of -7 and x = -7x
43 less than -7x = -7x - 43
Thus, we get the following equation-
35 + 0.8x = -7x - 43
we can solve this equation to find the value of x-
0.8x + 7x = -43 - 35
7.8x = -78
x = -78/ 7.8
x = -1/ 0.1
x = -10
Thus, the value of the given number is -10.
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Plz help me with this question
Answer:
The equation that models the population growth is y = 90,000(1.02)^x
Step-by-step explanation:
The formula of the exponential growth is y = a \((b)^{x}\), where
a is the initial valueb is the factor of growth ⇒ b > 1Let us solve the question
∵ At x = 0, the population y = 90,000
→ That means the initial value is 90,000
∴ a = 90,000
→ Substitute it in the form of the equation above
∴ y = 90,000 \((b)^{x}\)
→ To find b use any values from the table to substitute x and y
∵ At x = 1, y = 91,800
∵ 91,800 = 90,000 \((b)^{1}\)
∴ 91,800 = 90,000 b
→ Divide both sides by 90,000
∵ \(\frac{91,800}{90,000}\) = \(\frac{90,000b}{90,000}\)
∴ 1.02 = b
→ Substitute it in the equation above
∵ y = 90,000 \((1.02)^{x}\)
∴ The equation that models the population growth is y = 90,000(1.02)^x
Find a1 if a3=27 and a22=141
Find A. a=24,b=18, c=16
Find side c . A=42degrees , b=12,c=60degres
Find a . A=108 degrees ,b=8 , c=10
These are all different questions I need answers for. Thank you
The first term of the sequence is 15.
To find a1, we need to know the pattern of the sequence. From a3=27 and a22=141, we can find the common difference d using the formula a22=a1+21d.
Substituting the values, we get 141=a1+21d.
Similarly, a3=a1+2d. Substituting the value a3=27, we get 27=a1+2d.
Solving these two equations simultaneously, we get d=6 and a1=15.
It is important to note that there are different types of sequences, such as arithmetic, geometric, and others, and the method to find the missing term may vary depending on the type of sequence.
It is always important to identify the pattern and use the appropriate formula or method to find the missing term.
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Use SD and determine relationship
of polynomial and linear expression.
x³ + 9x²-16x-144 (division symbol) x +9
The polynomial expression x³ + 9x² - 16x - 144 can be factored as (x + 9)(x² - x - 16) with a remainder of -288 when divided by the linear expression x + 9.
To determine the relationship between the polynomial expression x³ + 9x² - 16x - 144 and the linear expression x + 9, we can use synthetic division (SD) to divide the polynomial expression by the linear expression.
The polynomial expression can be rewritten as:
x³ + 9x² - 16x - 144 = (x + 9)(x² - x - 16)
Using synthetic division, we divide the polynomial expression by x + 9:
-9 | 1 9 -16 -144
---------------------
1 0 -16 -288
The result of the division is 1x² + 0x - 16 with a remainder of -288.
Therefore, the relationship between the polynomial expression x³ + 9x² - 16x - 144 and the linear expression x + 9 is that the polynomial expression can be factored as (x + 9)(x² - x - 16) with a remainder of -288.
This means that the polynomial expression can be written as the product of the linear expression x + 9 and the quadratic expression x² - x - 16. The remainder -288 indicates that there is no perfect division, and there is a leftover term of -288.
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true false in the a/b/c classification of analytical queuing models, the term g refers to a general distribution with mean and variance.
In the a/b/c classification of analytical queuing models, the term g refers to a general distribution with mean and variance.[TRUE]
Common Queue Model Notation ( A / B / C );( D / E/ F )
Where :
A = distribution of time between arrivals (arrival distribution)
B = service time distribution
C = number of service channels/service facilities in the system (s = 1, 2, 3, … , ∞)
D = queuing discipline
E = size of population or resource
F = maximum number of consumers allowed in the system (in service plus waiting line)
Information :
1. For A and B, the following codes can be used:
M = Poisson distribution or exponential distribution (Markovian)
D = Degeneracy Distribution (constant time)
Ek = Erlang distribution
G = General distribution
2. For C, a positive integer is used which represents the number of services.
3. For D, use the replacement codes FIFO, LIFO, or SIRO.
4. For E and F, use the code:
N = Limited quantity
∞ = Infinity
For example, queuing system M/M/1 means Poisson distribution for arrival and Exponential distribution for service time and one server. Queuing system M/M/2 has customers arrive according to Poisson distribution with Exponential distribution for service time and the system has two servers. Queuing system M/D/3 indicates that the customers arrive according to Poisson distribution while the service time is constant with 3 servers.
More comprehensive Kendall notation consists up to 6 letters: a/b/c/d/e/ff
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There are 43,560 square feet in an acre. There are 3.28 feet in a meter. How many square meters would there be in 20 acres?
If there are 43,560 square feet in an acre and 3.28 feet in a meter, the there would be approximately 80,937.68 square meters in 20 acres.
First, let's calculate the total number of square feet in 20 acres:
20 acres × 43,560 square feet/acre = 871,200 square feet
Now we can convert this to square meters using the conversion factor given:
Substitute the value of conversion factor in the equation
= 871,200 square feet × (1 square meter / 3.28 feet)^2
Multiply the numbers
= 80,937.68 square meters (rounded to two decimal places)
Therefore, there would be approximately 80,937.68 square meters in 20 acres.
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P1 = (__ + P2)/(1 + R)
This is the formula for calculating the present value of a future payment, where P1 is the present value, P2 is the future payment, and R is the interest rate.
To use the formula, you need to know the value of P2, the future payment, and the interest rate, R. Then, you can solve for P1, the present value of that payment. The formula works by discounting the future payment to account for the time value of money, which means that money today is worth more than the same amount of money in the future.
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2. What is the product of the following expression?
2x(x2 + x-5)
A. 2x3 + x-5
B. 2x3 + 2x – 10
C. 2x3 + 2x2 – 5x
D. 2x3 + 2x2 – 10x
(Please help)
Hi, this is the real Coco Quinn and I would love it if u answer my question, you will be marked brainiest and you get 30 points!!!
The box plots show the lengths of the songs on two digital music players in minutes.
Which statement is best supported by the information in the box plots?
A- The interquartile range of the data for Music Player X is greater than the interquartile range of the data for Music Player Y.
B- The interquartile range of the data for Music Player X is equal to the interquartile range of the data for Music Player Y.
C- The median length of the songs on Music Player X is less than the median length of the songs on Music Player Y.
D- The median length of the songs on Music Player X is equal to the median length of the songs on Music Player Y.
Answer:
HI ther COCO QUINN i don't know you and never heard of you before in my life so the answer I got is D
Step-by-step explanation:
Answer:
Answer is D
Step-by-step explanation:
What is the probability that I will choose a cat owner and a bird owner. Please help. Thanks
Answer:
The probability is 1/36.
Step-by-step explanation:
2/3 are dog owners
1/6 are cat owners
1/6 are bird owners
If you choose two owners, there is a 1/6 chance that you will choose a cat owner and a 1/6 chance you will choose a bird owner. Each of these are independent, so you simply multiply 1/6 by 1/6.
1/6 * 1/6= 1/36
In a survey, 250 people were asked if they smoke…..
Answer:
90%
Step-by-step explanation:
22%
If the mean height is 180cm and the standard deviation is 4. What percentage of the population would lie between 176cm and 184cm?
A.50%
B.68%
C.95%
D.34%
Standard Deviation: Is a measure of how spread out values are in a data set compared to the mean. It is calculated by finding the square root of the variance, which is the average of the squared differences from the mean.
Mean: The average value of a set of numbers. It is calculated by summing up all the numbers in the set and dividing the result by the total number of numbers in the set.
Distribution Curve: is a bell shaped curve that displays the mean with a line down the center of the curve and standards deviations within standard deviations.
See attached file for model of curve, from: https://commons.wikimedia.org/wiki/File:Standard_deviation_diagram.svg
Given the mean and standard deviation we can use a general rule to determine the population between the given lengths.
Generally in a normal distribution:
68% of the data falls between -1σ and +1σ95% of the data falls between -2σ and +2σ99.75 of the data falls between -3σ and +3σ176 cm is 1 standard deviation less than the mean and 184 cm is 1 standard deviation greater than the mean. Using the general rules above, 68% of data falls between -1σ and +1σ. Therefore, the answer to this question would be B. 68%
Corey walked three blocks east and then six blocks north. All the blocks were the same length. What is the value of the slope of the line from where Corey began walking to where he finished?
A= -3
B= -2
C= 2
D= 3
Write the equation of a parabola that has a complex root at 4+5i and goes through the point (2,87)
Answer:
John is verey not smart
Step-by-step explanation:
Because he has fat
If the radius of a coin is 1cm than calculate its area
Answer:
3.14 square cm
Step-by-step explanation:
Since, a coin is circular in shape, hence its area would be equal to the area of a circle.
\(\therefore are \: of \: coin = \pi {r}^{2} \\ = 3.14 \times {1}^{2} \\ = 3.14 \times 1 \\ = 3.14 \: {cm}^{2} \\ \)
Graph the line that represents a proportional relationship between ddd and ttt with the property that an increase of 555 units in ttt corresponds to an increase of 222 units in ddd. What is the unit rate of change of ddd with respect to ttt
a) The unit rate of change of d with respect to t is equal to 1.6
b) the graph of the line in the attached figure.
Given: A proportionate relationship between d and t with the characteristic that a rise in t of 5 units causes a rise in d of 8 units.
To locate: A rise of 5 units in t causes a rise of 8 units in d, according to the line's unit rate of change with respect to t.
=> Slope = Δd/Δt = 8/5 = 1.6
the proportional relationship between d and t
=> d ∝ t
=> d = 1.6t
t d=1.6t
0 0
1 1.6
2 3.2
3 4.8
Plot the points and draw a line passing through points.
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The clearinghouse and research center on servant leadership is now called a. The Center for Applied Ethics b. The Service and Leadership Center c. The Greenleaf Center for Servant Leadership d. The Center for Service and Ethical Behaviors
The clearinghouse and research middle on servant management is now called c. The Greenleaf Center for Servant Leadership.
The middle turned into named after Robert K. Greenleaf, who first brought the idea of servant leadership in his essay "The Servant as Leader" published in 1970. The Greenleaf Center for Servant Leadership serves as a worldwide useful resource for promoting the knowledge and exercise of servant leadership.
It conducts studies, provides educational applications, and gives a platform for individuals and businesses to study and interact with servant management ideas. The middle's recognition is on nurturing moral and compassionate management that prioritizes the nicely-being and growth of individuals and the groups they serve. Through its initiatives, the Greenleaf Center pursuits to inspire and empower leaders to create a superb and impactful exchange by embracing the servant management philosophy.
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The clearinghouse and research center on servant leadership is called The Greenleaf Center for Servant Leadership.
The clearinghouse and research center on servant leadership is called The Greenleaf Center for Servant Leadership. It is a nonprofit organization that was founded in 1964 by Robert K. Greenleaf. The center is dedicated to promoting the principles of servant leadership, which emphasizes serving others and putting their needs first.
The Greenleaf Center conducts research, provides resources and training, and serves as a hub for individuals and organizations interested in servant leadership.
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Find the slope of the line that passes through
Answer:
Slope = 5/2
Step-by-step explanation:
Slope = (y2-y1)/(x2-x1)
In this case the two points are (6,7) and (4,2)
Using the formula we find that the slope is:
slope = (2-7)/(4-6)
slope = -5/-2
The negatives cancel out and therefore the final answer or slope is 5/2.
A rectangular storage container without a lid is to have a volume of 10 m3. the length of its base is twice the width. material for the base costs $15 per square meter. material for the sides costs $9 per square meter. let w denote the width of the base. Find a function in the variable w giving the cost C in dollars) of constructing the box.
The function in variable w giving the cost C (in dollars) of constructing the box is C(w) = 30w² + 270/w. The result is obtained by using the formula of volume and area of the box.
How to determine the function?We have a rectangular storage container without a lid.
Volume, V = 10 m³Length, l = 2wWidth, w = wBase costs $15/m²Sides costs $9/m²The formula of volume of the box is
V = l × w × h
Where
l = lengthw = widthh = heightSo, the height is
10 = 2w × w × h
10 = 2w² × h
h = 10/2w²
h = 5/w²
To find the total cost, calculate the area of base and sides of the box!
See the picture in the attachment!
The base area is
A₁ = 2w × w = 2w² m²
The sides area is
A₂ = 2(2wh + wh)
A₂ = 2(3wh)
A₂ = 6wh
A₂ = 6w(5/w²)
A₂ = 30/w m²
The total cost is
C = $15(2w²) + $9(30/w)
C = $30w² + $270/w
The function of the total cost is
C(w) = 30w² + 270/w
Hence, the function of constructing the box is C(w) = 30w² + 270/w.
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Define natural numbers, whole numbers, integers and rational numbers with examples. Properties of Rational numbers : Closure and commutativityof whole numbers , Integers and Rational numbers. Associativity : Whole numbers, Integers and Rational numbers Distributivity of multiplication over addition for rational numbers
Natural Numbers: Natural numbers are the counting numbers starting from 1 and extending infinitely. They are denoted by the symbol "N." Examples of natural numbers include 1, 2, 3, 4, 5, and so on.
Whole Numbers: Whole numbers are the set of natural numbers along with zero. They are denoted by the symbol "W." Examples of whole numbers include 0, 1, 2, 3, 4, and so on.
Integers: Integers are the set of whole numbers along with their negative counterparts. They are denoted by the symbol "Z." Examples of integers include ..., -3, -2, -1, 0, 1, 2, 3, ... The ellipsis represents that integers extend infinitely in both the positive and negative directions.
Rational Numbers: Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. They are denoted by the symbol "Q." Examples of rational numbers include 1/2, 3/4, -5/7, 2, and -3.25.
Properties of Rational Numbers:
1. Closure: The sum, difference, product, or quotient of any two rational numbers is always a rational number. For example, if we add two rational numbers 1/3 and 2/5, the result is 11/15, which is also a rational number.
2. Commutativity: The order of addition and multiplication does not affect the result for rational numbers. For example, if we add 1/2 and 3/4, the result is the same as adding 3/4 and 1/2. Similarly, multiplication of rational numbers follows the same rule.
3. Associativity: The associative property holds for addition and multiplication of rational numbers. For example, if we add three rational numbers (1/2 + 3/4) + 2/3, it is equal to 1/2 + (3/4 + 2/3).
4. Distributivity: Multiplication is distributive over addition for rational numbers. For example, if we multiply (1/2) by the sum of (3/4 + 2/3), it is equal to (1/2 * 3/4) + (1/2 * 2/3).
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
Sam has ⅙ of a book left to read. He wants to finish the book by reading the same amount every day for 4 days. How much of the book will Sam need to read each day?
4 (1/16) = 4/16 = 1/4
(1/4) / 4 = 1/16 each day
Answer:
\(\frac{5}{24}\) of the book each day
\(83\frac{1}{3}\) % of the book each day
Step-by-step explanation:
1 - ⅙
⅚
⅚ ÷ 4
\(\frac{5}{24}\)
If x = 9 when y = 36 and x is directly
proportional to y, what is x when y= 6?
Answer:
\(x = 1.5\)
\(Explaination :\\\frac{36}{9} = 4\\\frac{6}{4} =1.5\\Answer = 1.5\)
Answer:
x = 1.5
Step-by-step explanation:
\(\frac{9}{36} :\frac{x}{6}\)
Cross multiply.
36 · x = 9 · 6
Simplify.
36x = 54
Divide each side by 36.
36x ÷ 36 = 54 ÷ 36
Simplify.
x = 1.5
At which points are the equations y = x- + 3x + 2 and y = 2x + 3 approximately equal?
Select all the correct locations on the graph. At which points are the equations y = x2 + 3x + 2 and y = 2x + 3 approximately equal? 2.
Answer:
The equations are approximately equals at the points (0.618,4.236)(0.618,4.236) and (-1.618,-0.236)(−1.618,−0.236)
when you calculate the slope, if there is a zero on the top of the fraction, then the line is
If there is a zero on the top of the fraction when calculating the slope, then the line is horizontal.
If the numerator (y2 - y1) is zero, it means that the y-coordinates of the two points on the line are the same. This indicates that the line is horizontal, because no matter how far apart the two points are horizontally (i.e., the difference between their x-coordinates), the vertical distance (y2 - y1) between them is zero.
In this case, the denominator (x2 - x1) will be non-zero, because the two points will have different x-coordinates, but since the numerator is zero, the overall fraction will be zero.
So, a zero on the top of the fraction indicates that the line has zero or undefined slope, which happens only for a horizontal or vertical line, respectively. Therefore, if there is a zero on the top of the fraction when calculating the slope, then the line is horizontal.
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The number of machine parts produced at a manufacturing plant is based on the number of parts made in a given day
and the number of hours worked. Let P = 14x + 100 give the number of parts that are produced since the start of the
shift and H = x be the number of hours that are to be worked that particular day. Create the equation that would give
the number of parts produced per hour.
Answer:
The equation that would give the number of parts produced per hour, \(P_H\) is given as follows;
\(P_H\) = P/H - 100/H
Step-by-step explanation:
The given parameters are;
The number of parts produced is given by the equation, P = 14·x + 100, where x represents the number of hours worked on a particular day
The number of hours worked = H
Therefore, we have;
P = 14·H + 100
At H = 0, P₀ = 100
At H = 1, P = 114
At H = 2, P = 128
Therefore, the rate of change of the number of parts produced with the number of hours spent = The number of parts produced per hour, ΔP/ΔH = \(P_H\), is given as follows;
ΔP/ΔH = \(P_H\) = (P - P₀)/(H - 0) = P/H - P₀/H = (128 - 100)/(2 - 0) = 14
∴ The number of parts produced per hour, \(P_H\) = P/H - 100/H.