To find the numbers with the largest and smallest sums of their squares, we can use the fact that the sum of two numbers is constant. By rearranging the equation and finding the maximum or minimum of a quadratic function, we can determine the numbers that yield the desired sums of squares.
Explanation:To find the numbers, let's call them x and y. We know that the sum of two nonnegative numbers is 20, so we can write the equation x + y = 20. To find the numbers that yield the largest sum of their squares, we can use the fact that the sum of two numbers is constant. Let's rearrange the equation as y = 20 - x and substitute it into the equation for the sum of squares: x^2 + (20 - x)^2.
Expanding and simplifying the equation, we get f(x) = 2x^2 - 40x + 400. Since this is a quadratic function, we can find the maximum by finding the vertex. The x-coordinate of the vertex can be found using the formula -b/2a, where a = 2 and b = -40. Plugging in the values, we get x = 10. Substituting this value back into the equation for y, we find that y = 20 - 10 = 10. Therefore, the numbers that yield the largest sum of their squares are 10 and 10.
Similarly, to find the numbers that yield the smallest sum of their squares, we can find the minimum of the quadratic function. The x-coordinate of the minimum can also be found using -b/2a. Plugging in the values, we get x = 20/2 = 10. Substituting this value back into the equation for y, we find that y = 20 - 10 = 10. Therefore, the numbers that yield the smallest sum of their squares are also 10 and 10.
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4 tens 19 tens 22 ones
According to rule of mathematics, these given numbers will be presented according to their respective decimal places:
Step-by-step explanation:
4 tens can be represented as 40.
19 tens can be represented as 190.
22 ones are simply 22.
Which expression is equivalent to 4t + 3t?
Final answer:
The expression that is equivalent to 4t + 3t is 7t, as you combine the like terms by adding their coefficients.
Explanation:
The student has asked which expression is equivalent to 4t + 3t. This is a problem in basic algebra and involves combining like terms. To find the equivalent expression, we simply add the coefficients (numbers in front of the variable 't') together. Since both terms have the same variable 't', we combine 4 and 3 to get 7. Therefore, the equivalent expression to 4t + 3t is 7t.
How many ways can you make 17 as the product of two numbers in multiplication?
What step in the construction of copying a line segment ensures that the new line segment has the same length as the original line segment?
To copy a line segment and ensure it has the same length as the original, use a compass to measure and create a duplicate line segment.
Explanation:To copy a line segment and ensure that the new line segment has the same length as the original, we can use a compass. Here are the steps:
Place the compass needle on one endpoint of the original line segment.Open the compass to the length of the original line segment.Without changing the compass width, place the compass needle on the other endpoint of the original line segment and draw an arc.Use the compass to measure the same length on the arc and draw a line segment connecting the two marks.By using this method, we can create a duplicate line segment with the same length as the original.
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The U in the upper right corner stands for the
bigger set
universal set
infinite set
complement
Answer:
Universal set
Step-by-step explanation:
We need to find U in the upper right corner stands for what
Option 1 : bigger set
We cannot say this a bigger set without comparing it with another sets and since it is also containing another sets So, it is not said to be a bigger set.
Option 1 is wrong .
Option 2 : Universal Set
Definition of Universal Set : The set which contains all elements or all objects and of which all other sets are subsets.
Since we can see that SET M and SET N are contained in SET U
Thus U is a universal set.
Option 2 is correct .
Option 3: infinite set
we can see in the figure that it is finite set .
So, it is not infinite set.
Option 3 is wrong .
Option 4: complement
it is not a complement set (refer given figure )
Option 4 is wrong .
Is x – 3 a factor of the polynomial p(x) = 2x^4– 9x^3 + 15x^2 – 22x + 12, and for what reason?
A) Yes, because p(3) is equal to 0.
B) Yes, because p(–3) is equal to 0.
C) No, because p(3) is not equal to 0.
D) No, because p(–3) is not equal to 0.
Can someone smart help me here?
Solve the mathematical puzzle.
S is a three digit number.
Determine the digits of S from the clues.
All the digits are odd.
The last two digits add to make ten.
The first and last digits add to make eight.
The first two digits add to make twelve.
S is
What is 0.666 in a fraction?
Is 8.92 greater or less than 8.9
URGENT MATH HELP!
Which shows the conversion of 0.21 millimeters to inches?
There is 0.03937 inch in 1 millimeter.
A.
0.21 mm × 0.03937 in./mm = 0.0083 inches
B.
0.21 mm + 0.03937 in./mm = 0.24937 inches
C.
0.21 mm ÷ 0.03937 in./mm = 5.34 inches
D.
0.21 mm × 0.03937 in./mm = 8.3 × 10^-2 inches
Will Upvote! Need help!
Find the balance in the account.
$700 principal earning 5%, compounded monthly, after 9 years
A: $79,380.00
B: $1,085.93
C: $1,096.79
D: $16,088.19
Hey anyone cane u answer these two questions and explain and show your work how u got the answer please. Step by step. Thank you!
What is the inverse of the function f(x) = 2x – 10? h(x) = 2x – 5 h(x) = 2x + 5 h(x) = x – 5 h(x) = x + 5
The inverse of a function is gotten by swapping the x and y coordinates.
The inverse of function f(x) is[tex]h(x) = \frac x2 + 5[/tex]
Given
[tex]f(x) = 2x - 10[/tex]
Rewrite as:
[tex]y = 2x - 10[/tex]
Swap x and y
[tex]x = 2y - 10[/tex]
Solve for y
[tex]2y = x + 10[/tex]
Divide by 2
[tex]y = \frac x2 + 5[/tex]
So, we have:
[tex]h(x) = \frac x2 + 5[/tex]
Hence, the inverse function is[tex]h(x) = \frac x2 + 5[/tex]
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Twice a number is 36 less than -104. Find the number
The question 'twice a number is 36 less than -104' is an algebraic problem which can be solved by simplifying the equation '2x = -104 - 36' and dividing through by two. The solution to the equation is x = -70.
Explanation:The problem presented is a simple algebraic equation. The question is: Twice a number is 36 less than -104. This can be expressed with the equation 2x = -104 - 36.
To solve for x, we first simplify the right side of the equation: 2x = -140. Next, we isolate x by dividing both sides of the equation by 2: x = -140 / 2. So, the number x is -70.
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The population of a small town increased by 25% two years ago and then decreased by by 25% last year. The population is now 4500 persons. What was the population before the two changes?
The khan's car averages 22 miles per gallon of gas. predict how far they can travel on 5 gallons of gas.
Answer:
110 miles
Step-by-step explanation:
If EACH GALLON of gas gives 22 miles, 5 GALLONS will give 5 times that. So,
[tex]22*5=110[/tex]
So in 5 gallons, Khan's should get around 110 miles
A father and his daughter together weigh seven times the daughter's weight x. The father weighs 180 lbs. Which equation can be used to find the daughter's weight?
A. 180-7x = x
B. x -180 = 7x
C. 180 -x = 7x
D. 180 + x = 7x
...?
1)A discriminant of 0 indicates what type of roots?
A)Two Complex
B)One Rational Double
C)Two Rational
D)Two Irrational
2)The quadratic 2x2 + 6x + 3 has what type of roots?
A)Two Irrational
B)Two Complex
C)One Rational Double
D)Two Rational
3)The quadratic x2 + 20x + 100 has what type of roots?
Answer
A)Two Irrational
B)Two Rational
C)One Rational Double
D)Two Complex
4)What is the possible discriminant of the graph?(graph in the link)
A)0
B)–11
C)73
D)25
5)What is the possible discriminant of the graph?(Graph in the link)
A)0
B)17
C)25
D)–15
...?
Which of these statements about statistical models is true? I. Statistical models help better understand real-world systems. II. Statistical models represent the real world. III. Statistical models help predict future behavior.
Final answer:
Statistical models help understand real-world systems, represent simplified versions of reality, and aid in predicting future behavior. However, they are not perfect and contain uncertainties.
Explanation:
The question at hand is about statistical models and their characteristics. Statistical models do indeed serve several key functions, and among the statements listed, all are true to a certain extent:
Statistical models help better understand real-world systems by simplifying complex phenomena and making them more approachable for analysis.Statistical models represent the real world, but it is important to note that they are simplifications and may not capture all the nuances of real-world behavior.Statistical models help predict future behavior by using historical data and probabilistic methods to make informed guesses about what might happen under similar circumstances.However, it is crucial to remember that while statistical models are powerful tools for interpretation and prediction, they are not perfect representations of reality and come with inherent uncertainties and limitations.
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Which equation is related to 89 = x + 61?
A. x = 150
B. 61 = 89 + x
C. x = 28
D. x = 18
What is the simplified form of the following expression? (x10)(x2)
I'm pretty sure the answer would be x^12
The measured weights of 1,000 men in a certain village follow a normal distribution with a mean of 150 pounds and a standard deviation of 15 pounds. Which sentence most closely summarizes the data?
About 160 people weigh more than 165 pounds.
About 320 people weigh more than 165 pounds.
About 320 people weigh less than 165 pounds.
About 640 people weigh less than 165 pounds.
The correct summary of the data is that about 160 people weigh more than 165 pounds, based on the empirical rule for a normal distribution.
Explanation:To summarize the data of the measured weights of 1,000 men in a certain village, which follows a normal distribution with a mean of 150 pounds and a standard deviation of 15 pounds, we can use the empirical rule (68-95-99.7). According to this rule, approximately 68% of data values fall within one standard deviation of the mean, 95% fall within two standard deviations, and 99.7% fall within three standard deviations.
In this context, since 165 pounds is one standard deviation above the mean (150 + 15 = 165), it means approximately 16% of men (100% - 84%) will weigh more than 165 pounds, which translates to about 160 people (0.16 * 1000).
Therefore, the correct summarization is: About 160 people weigh more than 165 pounds.
Jon earns $180 per week plus $25 for each sale.write an inequality to represent how many sales he at least $500
A bakery uses 3/10 of a cup of flour in one batch of biscuits. the bakery used 3/5 of a cup of flour yesterday. how many batches of biscuits did the bakery make?
Answer:
Step-by-step explanation:
Which statement is modeled by the expression?
150/k
The Henderson family drove 150 miles each day of their vacation. If their vacation lasted for k days, then 150/k is the total number of miles they traveled on their vacation.
The cafeteria has a capacity of 150 seats. If k is the number of people in the cafeteria at lunch time, then 150/k is number of seats that were not used at lunch time.
A librarian had 150 books to be placed on shelves with an equal number of books on each shelf. If k is the number of shelves to be used, then 150/k is the number of books on each shelf.
Cory had 150 dollars in his savings account. He withdrew k dollars to buy a catcher's mitt. He then had 150/k dollars left in his savings account.
Hey
I hope you are having a great day
The answer would be A librarian had 150 books to be placed on shelves with an equal number of books on each shelf. If k is the number of shelves to be used, then 150/k is the number of books on each shelf.
Explanation: Lets see Option 1 is obviously out Option 2 does not make
sense When it comes to option 3 that makes the most sense Option 4 could be right but option 3 is the best and correct answer
So that's your answer
Hope This Helps :)
-Sprinkles
What is the sum of 1/4 and 1/5?
3x^2 + 5x =8
Solve with the quadratic formula. I messed up somewhere in my solving... Steps would be great~!
which two square roots are used to estimate the square root of 42
25, 36
36,49
46,64
or 25,64
Solve the system of equations by using substitution y=x 10 and x=8-2y
What is the greatest common factor of 34n and 8n^2?
The greatest common factor of 34n and 8n² is 2n, as both expressions share the variable n and the highest common numerical coefficient is 2.
The greatest common factor (GCF) of two algebraic expressions can be found by identifying the highest powers of common factors in the terms. For the expressions 34n and 8n², both terms have n as a common factor. Since we want the greatest common factor, we take the highest power of n that appears in both terms, which is n (not n² because n is the highest power in the least degree term, 34n). Next, we find the GCF of the numerical coefficients 34 and 8, which is 2. Therefore, the greatest common factor of 34n and 8n² is 2n.