There are 10 ways to put 5 balls in 2 boxes
A Combination formula C(n , r) = [tex]\frac{n!}{r! (n -r)!}[/tex] is used when
We wish to find the total number of ways of distributing objects that are not distinguishable Given that, a total set of objects is nDistributed in r other objectsGiven that, the total balls are 5:
n=5
We have wished to distribute them in 2 boxes:
r=2
Since the objects are indistinguishable, we can be used the combinations formula:
C(n , r) = [tex]\frac{5!}{2! 3!} = 10[/tex]
Hence, there are 10 ways to put 5 balls in 2 boxes.
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Evaluate
-10/3 · -7/10 = ??
Answer: -10x/3-7/10
Step-by-step explanation:
Answer:7/3 in exact form.
Step-by-step explanation:
If you need it in mixed form or decimal form. Decimal form:2.3
Mixed number form:2 1/3
Line v has an equation of y= – 2x+5. Perpendicular to line v is line w, which passes through the point (6, – 5). What is the equation of line w?
2y = x -8 is the equation of line w.
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given, Line v has an equation of y= – 2x+5.
also given Perpendicular to line v is line w
Slope of the perpendicular line w = -1/(Slope of the line v)
From Slope intercept form
y = mx + c
where m is the slope
Slope of the perpendicular line w = -1/ (-2)
The slope of the perpendicular line w = 1/2
Thus, the equation of a line:
y = 1/2x + c
Since, w passes through the point (6, – 5).
Thus,
-5 = 1/2 * 6 + c
c = -8
So, the equation of line y = 1/2x -8
Therefore, the Equation of line w is 2y = x -8.
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A metalworker has a metal alloy that is 20% copper and another alloy that is 70% copper. How many kilograms of each alloy should the metalworker combine to create 90 kg of a 60% copper alloy?
If a metalworker has a metal alloy that is 20% copper . The number of kilograms of each alloy should the metalworker combine to create 90 kg of a 60% copper alloy is: 18kg (20% copper), 72kg (70% copper).
How to find the number of kilograms?Let the amount of 20% copper be x kg. Since, total of 90 kg is needed, amount of 70% copper is 90-x kg .
So,
0.20x +0.70(90-x) = 0.60(90)
0.20x + 63 - 0.70x = 54
Combine like terms
0.50x =9
Divide both side by 0.50
x = 9/0.50
x = 18kg (20% copper)
Hence,
90-x
90 - 18 =72kg (70% copper)
Therefore the number of kilograms of each alloy is: 18kg (20% copper), 72kg (70% copper).
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HELP PLEASE!! The price of the once high-flying tech stock fell by 22% the week before last and by another 15% (from its new, lower price) last week. If the price of the stock is now $132.60 what was it originally (before both price declines)
The original price of the tech stock would be = $358.38
How to calculate the original price of the tech?The decrease in price of the stock tech in first week = 22%
The decrease in the second week = 15%
The total decrease = 22+15 = 37%
If 37% of the price after its decrease = $132.60 then it's 100% would = X
That is 37% = $132.60
100% = X
Make X the subject of formula;
X = 100 × $132.60/ 37
= 13260/37
= $358.38
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Please help!!!
What is the slope if the graph???
Answer:
-4/-5 the line is negative
Step-by-step explanation:
What is the range of the function shown in the graph below?
Therefore ,as a result the domain and range for the given function problem are Domain: (-∞, ∞) and Range: (0,∞).
Describe function.The function will only return one or no results for any input. If there are multiple outputs for a specific input, the phrase does not specify the function. Anything that is a function must only have one output value for the y variable for each value of x.
Here,
Given : f(x)= 2ˣ+1
The curve of an exponential function often achieves a horizontal equilibrium state at y=0 or the x-axis if a number has not been added. If it has, the curvature is altered.
Since it does not applied to the full function, this function's multiplication on the exponent has no impact on the asymptote.
Its y-axis values remain in the range of 0 and. This is the range, or the set, of y values.
However, the spectrum of exponentials might vary depending on the unit vector. The graph flips inside out and the spectrum reaches - if the result is negative. Additionally, this is inadequate.
The function is moved to the left sans modifying the range when the exponent is added to 1.
In exponential functions, the x values are frequently unaffected but all are taken into consideration. Even while it varies, the domain remains constant. The range of it is 0 to ∞ .
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How do you translate a log function?
A log function can be translated by using a combination of operations such as addition, subtraction, multiplication and division to shift the function up or down, left or right on the graph.
For example, multiplying the log function by a constant (e.g. 3) will shift the graph up 3 units, while dividing the log function by a constant (e.g. 2) will shift the graph down two units. Another example would be adding a constant (e.g. 4) to the log function will shift the graph to the right 4 units, while subtracting a constant (e.g. 5) will shift the graph to the left 5 units on the graph.
Log functions can be translated by using a combination of operations such as addition, subtraction, multiplication and division to shift the graph up, down, left or right. Multiplying a log function by a constant will shift the graph up, while dividing the log function by a constant will shift the graph down. Adding a constant to the log function will shift the graph to the right, while subtracting a constant will shift the graph to the left.
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Graph the linear inequality y>−x−3
Answer:
see attached
Step-by-step explanation:
www desmos com/calculator
mark brainliest
What is the volume of a kiddie pool? Select the better estimate.
1,015 milliliters
Or
1,015 liters
I HAVE A DOUBT WITH THIS PROVING QUESTION
hope it helps you
thank you
A cubic polynomial with rational coefficients has the roots 2+ sqrt 7 and 3/8. Find one additional root
A cubic polynomial with rational coefficients has the roots 2 + √7 and 3/8, so the one additional root is: 2 - √7
What is polynomials?When exponents, constants, and variables are joined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable).
According to the conjugate root theorem, irrational roots of P(x) = 0 with the formula (a + √b) occur in conjugate pairs if P(x) is a polynomials with rational coefficients. This means that (a - √b) is likewise a root if (a + √b) is an irrational root and (a and b) are rational.
In this case, a cubic polynomial with rational coefficients has the roots 2 + √7 and 3/8, so the one additional root is: 2 - √7
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Luke started a weight-loss program. The first week, he lost x pounds. The second week, he lost pounds less than times the pounds he lost the first week. The third week, he lost 1 pound more than of the pounds he lost the first week.
Liam started a weight-loss program when Luke did. The first week, he lost 1 pound less than times the pounds Luke lost the first week. The second week, he lost 4 pounds less than times the pounds Luke lost the first week. The third week, he lost pound more than times the pounds Luke lost the first week.
Assuming they both lost the same number of pounds over the three weeks, complete the following sentences.
The total weight lost by Luke and Liam each is 6 pounds
What is simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression. Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form. Simplification usually involves making the expression simple and easy to use later.
Luke's weight loss journey;
Weight luke lost in the first week; x pounds
The weight he lost in the second week is 3/2 pounds less than 3/2 times the pounds he lost in the first week. Thus;
Weight luke lost in the second week = ³/₂x - ³/₂ pounds
In the third week, he lost 1 pound more than 3/4 of the pound he lost in the first week. Thus;
Weight luke lost in the third week = (³/₄x) + 1 pounds
Total weight lost by luke in 3 weeks = x + ³/₂x - ³/₂ + ³/₄x + 1
=¹³/₄x - ¹/₂
Liam's weight loss journey;
First week he lost 1 pound less than 3/2 times the pounds luke lost in the first week
Weight Liam lost in the first week; ³/₂x - 1 pounds
The weight he lost in the second week is 4 pounds less than 5/2 times the pounds luke lost in the first week. Hence:
Weight Liam lost in the second week = ⁵/₂x - 4 pounds
In the third week, he lost 1/2 pound more than 5/4 of the pound luke lost in the first week. Hence:
Weight Liam lost in the third week = (⁵/₄x) + ¹/₂ pounds
Total weight lost by Liam in 3 weeks = ³/₂x - 1 + ⁵/₂x - 4 + ⁵/₄x + ¹/₂
⇒ ²¹/₄x - ⁹/₂ pounds
uke and Liam lost the same weight over 3 weeks. Hence:
¹³/₄x - ¹/₂ = ²¹/₄x - ⁹/₂
⇒ ²¹/₄x - ¹³/₄x = ⁹/₂ - ¹/₂
⇒ 2x = 4
x = 4/2
x = 2
The expression for Luke's weight loss over the 3 weeks =
¹³/₄x - ¹/₂ pounds
The expression for Liam's weight loss over the 3 weeks =
²¹/₄x - ⁹/₂ pounds
The number of pounds Luke lost in the first week =
x = 2 pounds
The number of pounds Luke and Liam each lost over the three weeks = 6 pounds
Therefore, the total weight according to expression lost by Luke and Liam each will be 6 pounds
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The function can be expressed in the form
The function N(T(t)) will be N(T(t)) = 550t² - 30t - 54.5. Then the number of bacteria approximately will be 1.129 × 10⁹.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The functions are given below.
N(T) = 22T² - 72T + 4
T(t) = 5t + 1.5
Then the function N(T(t)) will be given as,
N(T(t)) = 22(5t + 1.5)² - 72(5t + 1.5) + 4
N(T(t)) = 550t² + 330t + 49.50 - 360t - 108 + 4
N(T(t)) = 550t² - 30t - 54.5
At t = 1433, then we have
N(T(t)) = 550(1433)² - 30(1433) - 54.5
N(T(t)) = 1.129 × 10⁹ - 42,990 - 54.5
N(T(t)) ≈ 1.129 × 10⁹
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The missing question is attached below.
Dan and Glenn are swimming buddies who love to challenge themselves while diving. The amount of time Dan can
hold his breath underwater, D, is 111 seconds with a standard deviation of 12. 5 seconds. The amount of time Glenn
can hold his breath underwater, G, is 105 seconds with a standard deviation of 10. 9 seconds. Assume that D and G
are independent random variables and X=D-G.
What is the probability that on any given dive Dan holds his breath for less time than Glenn?
O 0. 108
O 0. 359
O 0. 397
O 0. 641
ark this and return
Save and Exit
Next
Submit
The probability that Dan holds his breath for less time than Glenn on any given dive is 0.359.
The probability that on any given dive Dan holds his breath for less time than Glenn would be equal to the probability that X (D-G) is less than zero. Since X is the difference between two independent random variables (D and G), the mean of X is equal to the difference between the means of D and G and the standard deviation of X is equal to the square root of the sum of the variances of D and G. Therefore, the mean of X is 6 seconds and the standard deviation of X is approximately 13.3 seconds.
To calculate the probability that X is less than zero, we can use the standard normal distribution and calculate the cumulative probability of X being less than zero. Using a standard normal table or a calculator with a standard normal distribution function, we can find that P(X < 0) = P(Z < (0 - 6) / 13.3) = P(Z < -0.45) = 0.3589, or approximately 0.359.
Therefore, the probability that Dan holds his breath for less time than Glenn on any given dive is 0.359.
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Mr. Evans, the English teacher, requires his students to randomly select their next 2 out of 5 books to read. A student could select a book with 800, 700, 600, 500, or 400 pages. List all possible samples of selecting 2 of the 5 books, and then calculate the average number of pages for each sample of 2 books. Use that information to choose the dotplot that shows the complete sampling distribution. distribution 1 distribution 2 distribution 3 distribution 4
Answer:Distribution 2
Step-by-step explanation:
yes
What is the solution of the compound inequality
The compound inequality's solution set is represented by the symbol x. (2 , 6).
The compound inequality's answer is what?The intersection of the answers to each individual inequality is the answer to a compound inequality, which is a pair of inequalities connected by the word and. Alternatively put, both claims have to be accurate simultaneously.
The inequality is expressed as follows: 8x - 9 39 and 3.5x - 10 > -3.
Take one: 3.5x - 10 > -3
Then multiplying by 10 on each sides
⇒ 3.5x - 10 + 10 > -3 + 10
⇒ 3.5x > 7
the two sides are now divided by 3.5.
⇒ x > 2
Now, 8x - 9 < 39
On all sides, add 9.
⇒ 8x - 9 + 9 < 39 + 9
⇒ 8x < 48
then multiply both sides by 8 now.
⇒ x < 6
The compound inequality presented has the following solution set: x (2 , 6).
The complete question is,
In which case does the compound inequality's solution set exist? A, B, C, D for 3.5x-10>-3 and 8x-939.
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You paint four walls each wall is a rectangle with a length of 22 feet and a height of 12 feet 1 gallon of paint covers about 330 ft.² how many gallons of paint do you need in order to cover the walls 
The number of gallons to cover 4 walls will be 1.28 gallons
How to calculate the number of gallons?The walls are four in number. Each wall is rectangular in shape. The length of each wall is 14 feet and the height is 8 feet. A gallon of paint will cover an area of 350 square feet. For each wall, the area can be computed since the height and the length is known.
Area of each wall(rectangle) = Length × height
length = 14 feet
height = 8 feet
Area of each wall(rectangle) = 14 × 8
Area of each wall = 112 square feet
The total square feet is 112 × 4 walls
The total square feet of the 4 walls = 448 square feet
Since, 1 gallon will cover 350 square feet, the number of gallons will be:
= 448/350
= 1.28 gallons
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Write an expression so that when you divide 1/4 by a number, the quotient will be greater than 1/4
Answer:1/4 divided by 1/4
Step-by-step explanation:
Match the correct type of growth to it's definition.
Patterns where the output is addition or subtraction the same value is Linear
Patterns where the output is multiplying or dividing the same value is Exponential.
what is Linear EquationA linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
Given:
We know In a linear relationship the y-values have equal differences.
Then, we can say that linear relation support addition and subtraction.
Thus, Patterns where the output is addition or subtraction the same value is Linear
Now, In an exponential relationship, the y-values have equal ratios.
Then, we can say that exponential relation support multiplying or dividing.
Thus, Patterns where the output is multiplying or dividing the same value is Exponential.
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Which supermarket has a better buy?
Store A: 12 cans of cola for $9
OR
Store B: 18 cans of cola for $12.96
What is the formula for km per hour?
The formula for km per hour is used to calculate the speed of an object in kilometers per hour. It is calculated by dividing the distance in kilometers by the time in hours .Km per hour (km/h) = distance (km) / time (h) For example, if an object travels 30 kilometers in 2 hours, the speed of the object is 15 km/h.
Km per hour (km/h) is a unit of speed which measures the distance an object travels in one hour. The formula for km per hour is used to calculate the speed of an object in kilometers per hour. It is calculated by dividing the distance in kilometers by the time in hours. For example, if an object travels 30 kilometers in 2 hours, the speed of the object is 15 km/h. The formula for km per hour is an important tool to measure the speed of vehicles, and is commonly used in navigation and transport systems. It is also useful in determining the rate at which work is being done, or the rate at which someone needs to travel to reach a certain destination. The formula for km per hour is also beneficial in determining the average speed of an object, which is the total distance traveled divided by the total time taken to travel that distance. This can be used to measure the efficiency of a vehicle or any other form of transportation. In conclusion, the formula for km per hour is an invaluable tool for measuring speed and efficiency.
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A man walks into a bar and asks for a glass of water.The bartender pulls out a shotgun and points it at him.The man says, thank you and leaves.Why?
Answer:The man had hiccups. The barman recognized this from his speech and drew the gun in order to give him a shock. It worked and cured the hiccups so the man no longer needed the water.
Step-by-step explanation:
the mean annual salary for environmental compliance specialists is about $66,000. a random sample of 35 specialists is selected from this population. what is the probability that the mean salary of the sample is less than $60,000? assume s
The probability that the mean salary of the sample is less than $60,000 is approximately 0.3576.
To calculate the probability that the mean salary of a random sample of 35 specialists is less than $60,000, we can use the central limit theorem which states that the mean of a large enough sample size from a population with a finite mean and finite standard deviation will be approximately normally distributed.
Given that the mean annual salary for environmental compliance specialists is $66,000 and we are taking a random sample of 35 specialists, we can assume that the sample mean will be approximately normally distributed with a mean of $66,000 and a standard deviation of [tex]$\frac{66,000}{\sqrt{35}}$[/tex]
To find the probability that the mean salary of the sample is less than $60,000, we need to standardize the value of $60,000 by subtracting the population mean and dividing by the standard deviation of the sample mean:
[tex]$z = \frac{60,000 - 66,000}{\frac{66,000}{\sqrt{35}}} = -0.537$\\[/tex]
Using a standard normal table or calculator, we can find the probability that a standard normal variable is less than -0.537. This probability is approximately 0.3576 or 35.76%.
So, the probability that the mean salary of a random sample of 35 specialists is less than $60,000 is approximately 35.76%.
It's important to note that this is an approximation and actual probability would be determined through experimental measurements.
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find the number of routers in the path at each of the two hours. did the paths change during any of the hours?
A test using traceroute command is performed to a destination site. The number of routers in this test is 8. The second test is performed after two hours and the paths does not change. In general case, the paths might change if there are network problems and it needs to do re-routing.
Traceroute is a command like ping command used for isolating problems in the network. Unlike ping command, traceroute does not need to know the IP address of the destination site.
The TTL (Time to Live) field in the IP packet header is used by Traceroute. TTL is typically used to prevent packets from being sent indefinitely when there is a routing loop. When a router forwards an IP packet, the TTL is reduced by one. When the TTL reaches zero, the IP packet is dropped.
This is an example for the result of traceroute command:
C:\Users\ayuner>tracert [31.13.64.35]
Tracing route to [31.13.64.35]
over a maximum of 30 hops:
1 9 ms 8 ms 8 ms D5644061.static.ziggozakelijk.nl [215.99.12.17]
2 9 ms 14 ms 8 ms tb-rc0001-cr101-ae40-0.core.as9143.net [213.51.158.66]
3 10 ms 12 ms 11 ms asd-tr0042-cr101-ae5-0.core.as9143.net [213.51.158.18]
4 14 ms 12 ms 12 ms br02.ams1.tfbnw.net [80.249.209.164]
5 12 ms 12 ms 13 ms po131.asw01.ams3.tfbnw.net [157.240.35.46]
6 12 ms 12 ms 13 ms po232.psw01c.amt2.tfbnw.net [157.240.35.175]
7 13 ms 12 ms 12 ms msw1ad.01.amt2.tfbnw.net [173.252.64.255]
8 12 ms 11 ms 13 ms edge-star-mini-shv-01-amt2 [31.13.64.35]
Trace complete.
In this test, the number of routers in the path is 8A test was conducted again after two hours, the number of routes is still 8.Your question is incomplete. Most likely it was:
Perform a Traceroute between source and destination on the same continent at three different hours of the day. Find the number of routers in the path at each of the two hours. Did the paths change during any of the hours?
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For what value of K system has non zero solution?
The required value of k will the system of linear equations has infinite number of solutions is 6.
What is Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Given:
3x + 5y = 0.
2: kx + 10y = 0.
Both equations are expressed as: Whereas a1 & a2 are the coefficients of x, b1 & b2 are the coefficients of y, and c1 & c2 are the constants
The solution indicates that:
a1 = 3 a2 = k b1 = 5 b2 = 10 c1 = 0 c2 = 0
Only when the equation is satisfied by a nontrivial solution, or with values other than x = 0 and y = 0,
will the equation have a nonzero solution. If the above numbers are entered into the equation for the given system of equations, there will be a non-zero solution.
[tex]\frac{a_{1}}{a_{2}} =\frac{b_{1}}{b_{2}}[/tex]
9/k = 5/10
5k = 30
k = 6
Thus, required value of k is 6.
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Complete Question:
The value of k for which the system of equations 3x + 5y = 0 and kx + 10y = 0 has a non - zero solution, is
The scores of a recent test taken by 95 students had an approximately
normal distribution with a mean of 85 and a standard deviation of 14.
Determine the number of students who scored more than 85.
According to the scores of a recent test taken by 95, the number of students who scored more than 85 is determined using z-score, which is 48 students.
What is a z-score?
Simply said, a z-score, also known as a standard score, informs you of how far a data point is from the mean. Technically speaking, however, it's a measurement of how many standard deviations a raw score is from or above the population mean.
The number of observations is, n = 95.
The mean value is, μ = 85.
The observed value is, x = 85.
The standard deviation value is, σ = 14
The formula for z-score is -
Z = (x - μ)/σ
Where, Z = standard score
x = observed value
μ = mean of the sample
σ = standard deviation of the sample
Substitute the values in the formula -
Z = (x - μ)/σ
Z = (85 - 85)/14
Z = 0/14
Z = 0
Now, from Cumulative normal distribution table the value for -
Z(0.0) = 0.5000
To find the number of students who scored more than 85 -
= (1 - Z-score) × n
= (1 - 0.5000) × 95
= 0.5000 × 95
= 47.5 ≈ 48
Therefore, 48 students got score higher than 85.
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ASAP PLS
you use bottles of 100% vegetable juice and 40% vegetable juice to make an energy drink for a fitness class. how many gallons of each type of juice should you mix to make 6 gallons of 60% vegetable juice
Answer:
2 gallons 100% vegetable juice
4 gallons 40% vegetable juice
Step-by-step explanation:
x = gallons of 100% vegetable juice
y = gallons of 40% vegetable juice
1x + .4(6 - x) = 6(.6)
1x + 2.4 - .4x = 3.6
.6x + 2.4 = 3.6
.6x = 1.2
x = 2
y = 6 - x
y = 6 - 2
y = 4
2 gallons 100% vegetable juice
4 gallons 40% vegetable juice
Nonlinear systems of equations
Solution of the non linear equations are (-5, √11) , (-5,-√11) and (6,0)
What is Non linear system of equation ?When two or more equations are being solved concurrently, at least one of them must be a system of nonlinear equations. Be aware that just one of your equations—not all of them—can be linear in a nonlinear system.
Any function whose graph is NOT a line is said to be nonlinear. It has the equation f(x) = ax + b. With the exception of the form f(x) = ax + b, its equation can take any form. Any two points on the curve have the same slope. Every pair of points on the graph do not have the same slope.
A function is nonlinear if its graph does not like a line.A function is nonlinear if its equation does not have the form f(x) = ax + b.It is possible for the goal function, z = ax + by, to be linear or nonlinear.Nonlinear functions include rational functions, polynomial functions, exponential functions, logarithmic functions, etc.The non linear equations are :
(i) y² = 6 - x
(ii) x² + y² = 36
From , (i) putting y² = 6 - x in equation (ii) we get
x² + 6 - x = 36
⇒ x² - x - 30 = 0
⇒x² +5x - 6x -30 =0
⇒x(x+5) -6(x+5) = 0
⇒(x+5)(x-6) = 0
so, x = -5 and x = 6
when x = -5
y² = 6 - x is
y² = 6 + 5 = 11
⇒ y = ±√11
and when x = 6
y² = 6 - x is
y² = 6-6
y = 0
Solution of the non lineae equations are (-5, √11) , (-5,-√11) and (6,0).
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Which statement best describes the function represented by the graph?
A) The function is decreasing on the interval (-∝,0) and increasing on the interval (0,∝). B) The function is decreasing on the interval (∝,∝)
C) The function is increasing on the interval (∝, ∝).
D) The function is increasing on the interval (∝,0) and decreasing on the interval (0, ∝).
A statement which best describes the function represented by the graph include the following: B) The function is decreasing on the interval (-∞, ∞).
What is a decreasing function?For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value (domain or x-value) is increased, then, the function is generally referred to as a decreasing function.
On the other hand (conversely), if the output value (range or y-value) is increasing when the input value (domain or x-value) is increased, then, the function is generally referred to as an increasing function.
By critically observing the graph above, we can reasonably infer and logically deduce that this function is decreasing over the interval -∞ < x < ∞, from left to right.
In conclusion, the output values (range or y-values) of this function are decreasing from left to right i.e as we move towards the right.
Read more on function here: https://brainly.com/question/3990145
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A large university accepts 50% of the students who apply. Of the students the university accepts, 40% actually enroll. If 30,000 students apply, how many actually enroll?
Answer:
6000 students
Step-by-step explanation:
We know
30,000 students apply
The university accepts 50% of the students who apply.
50% of 30,000 students = 15,000 students
So, the University accepts 15,000 students
40% actually enroll
40% = 0.4
15,000 times 0.4 = 6000 students
So, 6000 students actually enroll.