The function at its maximum value will be at point (9,2) and its value is 51 which can be derived keeping in mind the constraints that have been given.
What is Maximizing a function ?The maximum value of any kind of a function is the place where the said function reaches its highest point, or vertex, on a graph. If your kind of quadratic equation has something as a negative of a term, it will also have a maximum value.
There are a bit of three ways to find that maximum, depending on which form of a quadratic function you have got.
here, we have,
Herein we can find the closed region ABC from the three equations or constraints given
and can mark the points as
A = (2,2)
B = (5, 2)
C = (9, 2)
if we put up the values of the points, we get
at (9, 2) ,
z=5x+3y
=45+6
=51 that is the maximum value amongst the three.
Thus, the maximum point of the function can be calculated as (9,2)
How do you extract out the maximum or minimum value of a function?
We will at first set out the first derivative of the function to absolute zero and then solve for x to get the exact critical point.
If we then take the second derivative or f’’(x), there in we can find out whether this point will be a maximum or minimum. If the second derivative is seen as positive, it will be a minimum value
What is the maximum value of a function called?
The maximum or minimum value that is calculated over the entire function is called an “Absolute” or “Global” maximum or minimum of the function.
There is presence of only one global maximum (and only one global minimum) but there can be several that is more than one local maximum or minimum
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The table shows how much money Earl's grandmother gave him each birthday.
Age Birthday Money
5 15
8 24
10 30
18 ?
At this rate, how much money should Earl receive from his grandmother when he turns 18?
$38
$48
$54
$81
At this rate, Earl should receive $54 from his grandmother when he turns 18.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
The table shows how much money Earl's grandmother gave him each birthday.
Age Birthday Money
5 15
8 24
10 30
18 ?.
Here, we find the common ratio,
15/5 = 3,
24/8 = 3.
Hence, r = 3.
Now, the missing value,
= 18 x r
= 18 x 3
= 54.
Therefore, Earl will receive $54.
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A new spending tax of 25 percent is imposed on electrical goods. A shop decides to reduce all of its electrical goods in a sale. What percentage reduction is needed to restore all prices to their pre-tax values?
Consider what happens to the price of an item that costs £100 before the tax is imposed.
When a new spending tax of 25% is placed on electrical items, the price of a product that costs £100 before the tax is imposed is reduced to $25.
what is percentage ?In economics, a percentage is a percentage or ratio that is specified as a fraction of 100. Occasionally, this same acronyms "percentage points.," "%," and "pm" are also used. But it is broadly classified into the following by the percent sign, "%." The % sum has no dimensions. Rates are effectively fractions when the sum is 100. Use the percent sign (%) to indicate that a number seems to be a fraction by placing it next to it. So instance, you score a 75% if you properly answer 75 out from 100 respondents on a test (75/100). Divide the money by the total as well as multiply it by 100 to calculate percentages. The formula used to calculate the percentage is (value/total) x 100%.
given
All prices must be reduced by a certain amount in order to return to their pre-tax levels.
percentage = £100 / 100 * 25%
= 25
When a new spending tax of 25% is placed on electrical items, the price of a product that costs £100 before the tax is imposed is reduced to $25.
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As part of their employee benefits , all workers at Middletown Electronics receive a pension that is calculated by multiplying the number of years worked times 1.56% of the average of their three highest years’ salary. Maureen has worked for Middletown for 30 years and is retiring. Her highest salaries are $107,000, $107,800, and $108,198. Calculate Maureen’s pension.
Maureen's pension would be $50,035.20.
What is Percentage?
To compute a percentage, divide the value by the entire amount and multiply the result by 100. A percentage is a quantity or ratio that is stated as a fraction of one hundred. The percent sign, "%," is frequently used to represent it.
First, we need to calculate the average of Maureen's three highest salaries:
Average = (107,000 + 107,800 + 108,198) / 3
Average = 322,998 / 3
Average = 107,666
Next, we need to calculate 1.56% of this average:
Percentage = 1.56% * 107,666
Percentage = 1,667.84
Finally, we multiply this percentage by the number of years worked to find the pension:
Pension = 30 * 1,667.84
Pension = 50,035.20
So, Maureen's pension would be $50,035.20.
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Look at the image below:
Answer:
Last choice
Step-by-step explanation:
There are two ways to solve this problem.
1. Simplify both fractions
2. Cross multiply (If a/b = c/d, then ad = bc)
Now for the answer choices:
1. 5/7 is less than one while 7/5 is greater
2. 3/12 = 1/4, which is not equal to 3/4
3. 16/20 = 4/5, while 15/25 = 3/5
4. 6/9 = 2/3, and 10/15 also equals 2/3.
Answer:
6 / 9 and 10 / 15
Step-by-step explanation:
Hope this helps :)
How is the sum expressed in sigma notation?
22 + 27 + 32 + 37 + 42 + 47
Enter your answer by filling in the boxes.
the sum from i is equal to 1 to blank of open paren close paren$$
The sum of the arithmetic sequence is S = 207 and the summation notation is S = ∑i=1 to 6 ( 5n + 17 )
What is Arithmetic Progression?An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Given data ,
Let the arithmetic sequence be represented as A
Now , the value of A is
A = 22 + 27 + 32 + 37 + 42 + 47
The number of terms n = 6
So , the value of i ranges from 1 to 6
Now , the summation is represented as ∑i=1 to 6 ( 5n + 17)
when n = 1
S₁ = 5 ( 1 ) + 17 = 22
when n = 2
S₂ = 22 + 5 ( 2 ) + 17
S₂ = 22 + 27
when n = 3
S₃ = 22 + 27 + 5 ( 3 ) + 17
S₃ = 22 + 27 + 32
Hence , the sum of the arithmetic sequence is S = 207
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(x+6) divided by 3+5x divided by 3 Please help me answer this question. I am really having a really hard time.
The value of expression after divide is,
⇒ (3x + 18) / (3 + 5x)
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
We have to given that;
⇒ (x + 6) divided by 3+5x divided by 3.
Now, We can write as;
⇒ (x + 6) ÷ (3 + 5x) ÷ 3
⇒ (x + 6) ÷ (3+ 5x) / 3
⇒ (x + 6) × 3 / (3 + 5x)
⇒ 3 (x + 6) / (3 + 5x)
⇒ (3x + 18) / (3 + 5x)
Thus, The value of expression after divide is,
⇒ (3x + 18) / (3 + 5x)
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Including a 5% sales tax, an inn charges $126 per night. Find the inn's nightly cost before tax is added.
The cost of the inn's nightly before the tax is added will be $120.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Let 'x' be the cost before tax is added. Then the equation is given as,
5% = [(126 - x) / x] × 100
0.05x = 126 - x
1.05x = 126
x = 126 / 1.05
x = $120
The cost of the inn's nightly before the tax is added will be $120.
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A number cube is tossed 60 times.
Outcome Frequency
1 12
2 13
3 11
4 6
5 10
6 8
Determine the experimental probability of landing on a number less than 2.
35 over 60
25 over 60
13 over 60
12 over 60
Answer:
12 over 60
Step-by-step explanation:
The experimental probability of landing on a number less than 2 can be calculated by counting the number of times the outcome was 1, which is 12, and dividing it by the total number of trials, which is 60.
So, the experimental probability is 12/60 = 1/5 = 12 over 60.
Answer: 12 over 60
Step-by-step explanation:
Step 1: Count the number of times a number less than 2 was landed on.
Answer: 12
Step 2: Count the total number of times the number cube was tossed.
Answer: 60
Step 3: Divide the number of times a number less than 2 was landed on by the total number of times the number cube was tossed.
Answer: 12 over 60
Final Answer: 12 over 60
Which postulate or theorem would you use to prove MXQ = PXN?
A. AAS
B. SAS
C. ASA
D. SSS
E. HL
The postulate or theorem you would use to prove MXQ = PXN is (b) SAS
How to determine the congruence statementFrom the question, we have the following parameters that can be used in our computation:
The triangles
On the triangles, we can see that
Two corresponding sides have the same mark i.e. I and IIThe angle between the correspondng sides are equalThis means that two corresponding sides and one angle are equal
So, the triangles are congruent by SAS
The
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What is the sum of the infinite geometric series?
16 minus 12 plus 9 minus twenty-seven fourths plus continuing
four thirds
twenty-five fourths
forty-eight sevenths
sixty-four sevenths
The solution is Option D.
The sum of the infinite geometric progression is S = ( 64/7 )
What is Geometric Progression?A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.
The nth term of a GP is aₙ = arⁿ⁻¹
The general form of a GP is a, ar, ar2, ar3 and so on
Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
Given data ,
Let the sum of the geometric progression be represented as S
Now , the equation will be
S = 16 , -12 , 9 , -( 27/4 ) ...
The sum of the infinite GP is S = a / ( 1 - r ) , where r is the common ratio
Substituting the values in the equation , we get
a₁ = 16
a₂ = -12
So , the common ratio r = a₂ / a₁
The common ratio r = -3/4
Substituting the values in the equation , we get
The sum of the infinite GP is S = a / ( 1 - r )
The sum of the infinite GP is S = 16 / ( 1 - ( -3/4 ) )
The sum of the infinite GP is S = 16 / ( 1 + 3/4 )
The sum of the infinite GP is S = 16 / ( 7/4 )
The sum of the infinite GP is S = ( 16 x 4 ) / 7
The sum of the infinite GP is S = ( 64/7 )
Hence , the sum of GP is ( 64/7 )
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need help with surface area of a cone
Answer:
I have tried
Step-by-step explanation:
Formula= πrl + πr²
π × 4 × 10 + π + 4²
40π + 16π
56π
56 × 3.14
175.952
Hot dogs come in packs of 8. While buns come in packs of twelve. What is the least number of packs you should buy in order to have the same number of hot dogs and buns?
On solving the provided question, we can say that, by Least Common Multiple the amount to buy - 4 packs of buns and 5 packs of hot dogs.
What is least common multiple?The smallest positive integer that is divisible by both a and b is known as the least common multiple, also known as the least common multiple, or the least common multiple of two numbers a and b. Least Common Multiple is referred to as LCM. The least frequent multiple of two numbers is also the least frequent multiple of both. A number and an integer are combined to create a multiple of that number. For instance, 10 is a multiple of 5, as 10 can be divided by 5, 2, and 5, making it a multiple of 5. The smallest positive integer that can be divided by both 5 and 2 is 10, making it the lowest common multiple of these numbers.
Least Common Multiple (LCM) between 10 and 8 is = 40
Buns is = 10-20-30-40
Hot dogs is = 8-16-24-32-40
So, stock would be equal for both products.
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The length of a rectangle is 2 meters less than twice its width. If the
perimeter of the rectangle is 92 meters, find the measure of the length and width
of the rectangle.
In the rectangle, the measure of the length is 30 meter and width is 16 meter,
.
What is a rectangle?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. The length and breadth are the two dimensions that define a rectangle. The rectangle's longer side is its length, while its shorter side is its breadth.
Let the width of the rectangle is x meter, than the length of the rectangle is 2x-2.
Perimeter of rectangle = 2*(length + width)
⇒ 92 = 2*(2x-2 + x)
⇒ 92 = 2*(3x-2)
⇒ 92 = 6x - 4
add 4 in both side
⇒ 92 + 4 = 6x
⇒ 96 = 6x
divide oth side by 6
⇒ x = 96/6
⇒ x = 16
So the width of rectangle is 16 meter
The length of the rectangle = 2x-2
⇒ The length of the rectangle = 2*16-2
⇒ The length of the rectangle = 32-2
⇒ The length of the rectangle is 30
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What is the fifth term of the arithmetic sequence? 5, 2, –1, –4,...
The fifth term of this arithmetic sequence 5, 2, –1, –4,... ..... is equal to -7.
How to calculate an arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.Next, we would determine the common difference as follows.
Common difference, d = a₂ - a₁
Common difference, d = 2 - 5
Common difference, d = -3
Substituting the given parameters into the formula, the 5th term of this arithmetic sequence is given by;
a₅ = a₁ + (5 - 1)d
a₅ = 5 + (4)(-3)
a₅ = 5 - 12
a₅ = -7.
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Draw a number line for two thirds plus two thirds
The number line would be
|---------|---------|
0 1/3 2/3
What is a number line?
A number line is a visual representation of real numbers on a straight line. It is used to graphically illustrate the relative position and size of numbers, and to perform operations like addition, subtraction, and comparison. The number line starts at a certain minimum value, and each point on the line represents a specific real number. The numbers increase as one moves to the right on the line, and decrease as one moves to the left. A number line is often used in mathematics education to help students understand basic concepts of numbers and operations.
2/3 + 2/3 = 4/6 = 2/3
|---------|---------|
0 1/3 2/3
hence, the number line would be
|---------|---------|
0 1/3 2/3
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Complete question:
Draw a number line for 2/3 + 2/3 on the given number line.
Help, what is the answer?
Answer:
a) 8 b) x= 8
Step-by-step explanation:
the coordinate of x is 8 because its a straight line nad the equation is x =8
Solve the equation below and remember to show all your calculations :
Mansoor and Saif are racing. Mansoor can run 100 meters in 7.6 seconds. Saif can run 30 meters in 2.6
seconds. Who would win a 400m dash, and by how much time?
The person who would win the dash is Mansoor by 4.26 seconds.
Who would win the race?The first step is to determine the average speed of each of them. Average speed is the total distance travelled per time.
Average speed = total distance / total time
Average speed of Mansoor = 100 / 7.6 = 13.16 meters / second
Average speed of Saif = 30 / 2.6 = 11.54 meters / second
Mansoor is faster because he covers more meters in one second.
Time it would take to compete the dash = total distance / average speed
Time it would take Mansoor to complete the dash = 400 / 13.16 = 30.40 seconds
Time it would take Saif to complete the dash = 400 / 11.54 = 34.66 seconds
Difference = 34.66 - 30.40 = 4.26 seconds
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State if the triangles in each pair are similar. If so, state how you know they are similar
and complete the similarity statement.
BCD~____
A) similar; SAS similarity; ABML
C) similar; AA similarity; ABML
B) not similar
D) similar; SAS similarity; ABLM
Triangle BCD and triangle BML are similar by AA similarity. Therefore, option C is the correct answer.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
From the given figure, ML║CD.
Consider ΔBCD and ΔBML
Here, ∠M=∠C (Corresponding angles are equal)
∠L=∠D (Corresponding angles are equal)
By AA similarity, ΔBCD ~ ΔBML
Therefore, option C is the correct answer.
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The value of the digit 6 in 23,640 is ? Times ? Than the value of the 6 in 167,892
Answer:
It is 100 times less than the value of the number 167,892.
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Create your own quadratic function ,f(x), and then evaluate the function at f(x-3). Find the domain of your function.
Answer:
f(x)= (x-3)^2
domain: set= {x| xER}
interval= (-infinity, Infinity)
Step-by-step explanation:
hope this helps
True or False: 8/11 < 12/17 .
Answer:true
Step-by-step explanation:
Simplify
4c^2+6c-3c^2-2c-3
Answer:
c^2+4c-3
Step-by-step explanation:
(4c^2-3c^2)+(6c-2c)-3 = c^2+4c-3
read the question on the paper please WILL GIVE BRAINILEST
A square's possible coordinates will be 7, as it has a perimeter of 28 units and a surface area of 49 units.
What does math's perimeter mean?The perimeter is the space surrounding a shape's edge. Find the perimeter of various forms by multiplying their side lengths.
For instance, what is a perimeter?The circumference of an object is known as its perimeter. For instance, your home has a yard that is enclosed. The length of the fence is the perimeter. The length of your fence is 200 feet if the yard is 50 feet by 50 feet. How do you calculate perimeter?
The circumference of a shape is known as its perimeter.
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A ternary digit is either 0, 1, or 2. How many sequences of seven ternary digits are possible containing a single 1 and a single 2?
The number of sequences of seven ternary digits containing a single 1 and a single 2 is given as follows:
42.
What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
When elements repeat [tex]n_1, n_2, n_3, \cdots, n_n[/tex] times, the number of arrangements is given as follows:
[tex]A_{n}^{n_1, n_2, n_3, \cdots, n_n} = \frac{n!}{n_1!n_2!n_3! \cdots n_n!}[/tex]
In this problem, we have an arrangement of seven elements, in which:
The zero appears five times.The one appears once.The two appears once.Hence the number of sequences is given as follows:
N = 7!/(5! x 1! x 1!)
N = 7 x 6
N = 42.
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Whoever gets correct answer gets 100 points
Answer:
A. 0.25
Step-by-step explanation:
The coefficient of friction can be calculated as follows:
friction coefficient = force of friction / force of weight
The force of friction is equal to the force applied to the book bag, which is 5 pounds, and the force of weight is equal to the weight of the book bag, which is 20 pounds.
friction coefficient = 5 / 20
friction coefficient = 1/4 or 0.25
So the coefficient of friction between the floor and the book bag is 0.25.
Lynne needs to borrow $5250 for cosmetic surgery. She obtains a loan from her grandmother for 24 months at a simple interest rate of 5.3%. What is the loans future value?
I need the formula explained as well
The future value of the loan is $5807.65.
What do you mean by Interest?It is expressed as a percentage of the amount borrowed and is paid over a specific period of time. The interest rate represents the cost of borrowing money and is one of the key factors in determining the overall cost of a loan. Interest is usually calculated on a yearly basis and can be compounded, meaning that the interest earned on a loan is added to the original principal and the interest rate is then applied to the new, higher amount. This process continues over time, leading to the growth of the original loan amount. The purpose of charging interest is to compensate the lender for the risk they are taking in lending the money and for the opportunity cost of not being able to invest the money elsewhere.
The future value of a loan is equal to the present value plus the interest earned over a specified time period. The formula to calculate the future value of a loan with simple interest is:
FV = PV (1 + rt)
where:
PV is the present value of the loan, which is $5250
r is the interest rate as a decimal, which is 5.3% ÷ 100 = 0.053
t is the time period in years, which is 24 months ÷ 12 months/year = 2 years
Substituting the values into the formula, we get:
FV = $5250 (1 + 0.053 * 2)
FV = $5250 (1.106)
FV = $5807.65
So, the future value of the loan is $5807.65. This is the amount Lynne will have to repay to her grandmother after 24 months, including the interest earned.
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help please im a 4th grader and my homework due in 3 days 23948 plus 92374 please please
Answer: 116322
Step-by-step explanation:
23948+92374= 116322
19. Write a sequence of transformations that maps quadrilateral ABCD onto quadrilateral
A"B"C"D"in the picture below.
Answer:
Down 2 and a flip with (-1,3)(1,0)(2,3)and(1,4)
Step-by-step explanation:
hope this works
Sequence of transformations that maps quadrilateral ABCD onto quadrilateral A"B"C"D".
Reflection of ABCD over Y-axis.Shift of factor 2 downwards.What is transformation?Transformations are changes done in the shapes on a coordinate plane by rotation, reflection or translation or dilation.
The translation is moving a function in a specific direction, rotation is spinning the function about a point, reflection is the mirror image of the function, and dilation is the scaling of a function.
Given,
Quadrilateral ABCD and A"B"C"D" in the graph.
Transformation of quadrilateral ABCD to A"B"C"D"
By the graph, Steps of transformation are as follows
Reflection of ABCD over Y-axis.Shift of factor 2 downwards.Hence,
Reflection of ABCD over Y-axis.
Shift of factor 2 downwards.
are the steps to transform ABCD to A"B"C"D".
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Determine which of the triangles below are unique. Share your reasoning.
Triangle A: All angles measure 60 degrees
Triangle B: All sides have length 6 cm.
Triangle C: Two sides have length 6 cm, and the included angle measures 55 degrees
Triangle D: Base has a length of 6 cm, and the base angles are 50 degrees.
Step-by-step explanation:
Triangle A: Equilateral triangle, all angles are equal (60 degrees) and all sides are equal. Unique.
Triangle B: Isosceles triangle, two sides are equal (6 cm) and two angles are equal. Unique.
Triangle C: Not unique, as different triangles can have two sides of equal length and an included angle of 55 degrees.
Triangle D: Not unique, as different triangles can have a base of 6 cm and base angles of 50 degrees.
Answer:
Step-by-step explanation:
Triangle A and Triangle B
Step-by-step explanation:
I think this is the answer because Triangle A, has a unique that all sides have a measure of 60 degrees. And I also think that Triangle B is unique because It's an Equilateral triangle, which means that all sides have the same length.
So hence, I think the answer is A and B
Always keep more than 2 smiles! You have to share them with people who don't have one too, right??
Thanks!
:D
Solve the inequality 1/4b−1/5b>3/10b−1/2 and write the solution in interval notation.
Answer: To solve the inequality 1/4b−1/5b > 3/10b−1/2, we need to simplify both sides:
1/4b - 1/5b > 3/10b - 1/2
5/20b > 7/20b
Then we isolate b by subtracting 7/20b from both sides:
-2/20b > -7/20
Finally, we divide both sides by -2/20 to get:
b < 35/2
The solution in interval notation is (-∞, 35/2).
Step-by-step explanation: