Find two positive numbers whose product is 36 and whose sum is a minimum.
To find two positive numbers whose product is 36 and whose sum is a minimum, set up an equation using the arithmetic mean and geometric mean inequality. Solve for the two numbers.
Explanation:To find two positive numbers whose product is 36 and whose sum is a minimum, we can use the concept of the arithmetic mean and geometric mean inequality. Let the two numbers be x and y. Since the product of the numbers is 36, we have xy = 36. Using the arithmetic mean and geometric mean inequality, we know that the minimum value of the sum of two positive numbers is attained when the two numbers are equal. Therefore, x = y. Substituting this into the equation xy = 36, we have x^2 = 36. Taking the square root of both sides, we get x = √36 = 6. So, the two positive numbers are x = 6 and y = 6.
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The two positive numbers whose product is 36 and whose sum is a minimum are 6 and 6.
Explanation:To find two positive numbers whose product is 36 and whose sum is a minimum, we can use the concept of the Arithmetic Mean-Geometric Mean Inequality.
Let x and y be the two numbers.
According to the inequality, the minimum sum occurs when the numbers are equal.
So, we have x = y = √36 = 6.
Therefore, the two positive numbers whose product is 36 and whose sum is a minimum are 6 and 6.
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What is the slope of the line whose equation is 12=4x−6y ? Enter your answer in the box.
Answer:
Slope of the line 12=4x−6y is [tex]\frac{2}{3}[/tex] .
Step-by-step explanation:
The slope line form is denoted by
y = mx + c
Where m is the slope and c is the y- intercept .
As given
The equation of the line is given by .
12=4x−6y
It is also written as
6y = 4x - 12
[tex]y = \frac{4x}{6} -\frac{12}{6}[/tex]
Simplify the above
[tex]y = \frac{2x}{3} -2[/tex]
(Compare with y = mx + c )
Thus
[tex]m = \frac{2}{3}[/tex]
Therefore the slope of the line 12=4x−6y is [tex]\frac{2}{3}[/tex] .
Which of the following is a solution to the inequality y > –2x + 6? a.(4, 4) b.(0, 0) c.(1, 1) d.(2, 2)
The correct answer is a.(4, 4) because when you substitute x = 4 and y = 4 into the inequality y > -2x + 6, the inequality holds true, indicating that (4, 4) is a solution.
To determine which of the given points is a solution to the inequality y >
-2x + 6, we substitute the x and y values of each point into the inequality and check if the inequality holds true.
Therefore, the correct answer is a.(4, 4), since it is the only point that satisfies the inequality y > -2x + 6.
Find the value of x and the value of y.
PleAse help and show how you got it if you don’t mind
Find the value of x and y
x+4y=21, 4x-16=y
Choose all the numbers that are perfect squares.
64
24
12
49
144
84
4
It takes to sell A three hours to produce two cells.If you start with cell A,how many cells will you have in 24 hours
In 24 hours, you will have 48 cells if you start with cell A and keep making cells at the same rate.
If it takes three hours to produce two cells, we can calculate the production rate as follows:
Production rate of A = 2 cells / 3 hours
Now, we want to find out how many cells will be produced in 24 hours:
Number of cells produced in 24 hours = Production rate of A × Number of hours
Number of cells produced in 24 hours = (2 cells / 3 hours) × 24 hours
Number of cells produced in 24 hours = 2 cells/hour × 24 hours
Number of cells produced in 24 hours = 48 cells
Therefore, if you start with cell A and continue producing at the same rate, you will have 48 cells in 24 hours.
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What is the value of f(−1) when f(x)=2x+2 ?
Enter your answer in the box.
f(−1)=
Can someone check this for me? Thanks.
(b) Suppose it is also known that AD ≅ CD. Which postulate or theorem can be used to prove that ΔABD ≅ ΔCBD?
I'm guessing it's the SAS congruence postulate but I'm not very good at this so I'm not sure.
Which ordered pairs in the form (x, y)(x, y) are solutions to the equation
7x−5y=287x−5y=28 ?
Select each correct answer.
(4, 10)(4, 10)
(−1, −7)(−1, −7)
(7, 9)(7, 9)
(−6, −14)
help me solve this???
3p - 1 = 5(p - 1) - 2(7 - 2p)
The table below shows the average yearly balance in a savings account where interest is compounded annually. no money is deposited or withdrawn after the initial amount is deposited. which type of function best models the given data?
a. linear function with a negative rate of change
b. linear function with a positive rate of change
c. exponential decay function
d. exponential growth function
The given data represents the average yearly balance in a savings account where interest is compounded annually. The function that best models the data is an exponential growth function.
Explanation:The given data represents the average yearly balance in a savings account where interest is compounded annually. Since the balance is increasing over time, the function that best models the data is an exponential growth function. Option d, exponential growth function, is the correct answer.
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When u.s. students took the timss, 53 percent of them: a. overestimated their math skills. b. were realistic about their math skills?
The sum of the squares of two consecutive odd integers is 1570. find the integers
Final answer:
Two consecutive odd integers whose squares sum to 1570 are found by setting up a quadratic equation. Solving this equation gives us 27 and 29 as the required integers.
Explanation:
The question requires us to find two consecutive odd integers whose squares add up to 1570. Let's consider the smaller integer to be n, which means the next consecutive odd integer would be n + 2 (since there is always a difference of 2 between consecutive odd numbers). Our equation based on the given information will be:
[tex]n^2 + (n + 2)^2[/tex] = 1570
To solve for n, we will expand the equation and simplify:
[tex]n^2 + n^2 + 4n + 4[/tex] = 1570[tex]2n^2 + 4n + 4[/tex] = 1570[tex]2n^2 + 4n - 1566[/tex] = 0Divide the entire equation by 2: n2 + 2n - 783 = 0Solving the quadratic equation, we find that n = 27 and n = -29.
As we are looking for positive integers, we take n = 27. Therefore, the two consecutive odd integers are 27 and 29.
which set of ordered pairs in the form of x y does NOT represent a function of x?
A. {(1, 1.5), (2, 1.5), (3, 1.5), (4, 1.5)}
B. {(0, 1.5), (3, 2.5), (1, 3.3), (1, 4.5)}
C. {(1, 1.5), (-1, 1.5), (2, 2.5), (-2, 2.5)}
D. {(1, 1.5), (-1, -1.5), (2, 2.5), (-2, 2.5)}
A function is a relationship that maps elements from one set (the inputs) into elements of another set (the outputs). Such that each input can be mapped into only one output.
The correct option is B: {(0, 1.5), (3, 2.5), (1, 3.3), (1, 4.5)}
Using the general definition, to find which set of ordered pairs does not represent a function, we need to see in which set we have the same input (the first element of the ordered pair) assigned to two different outputs (the second element of the ordered pair).
Here the one that does not represent a function is option B:
{(0, 1.5), (3, 2.5), (1, 3.3), (1, 4.5)}
Because we have the input x = 1 assigned to two different outputs, y = 3.3 and y = 4.5
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During the first quarter of the year, 351,875 people downloaded an app for their smartphones. During the second quarter of the year, 101,949 fewer people downloaded the app than during the first quarter. How many downloads occurred during the two quarters of the year?
a. Round each number to the nearest hundred thousand to estimate how many downloads occurred during the first two quarters ofthe year.
What does the triangle exterior angle theorem make sense based on the triangle sum theorem??
Write the equation of the line perpendicular to the given line and passing through the given point: y=3x−2 through (3,4)
Answer:
all work is shown and pictured
Answer:
y= -1/3x+5
Step-by-step explanation:
write "all horses drink water" as a conditional statement
An isometry preserves distance.
True
False
HELP!
Solve −2(2x + 5) − 3 = −3(x − 1). (1 point)
−10
−16
16
−13
Solve 4(x + 1) = 4x + 4. (1 point)
1
All real numbers
0
No solution
Answer:
all numbers are real
Step-by-step explanation:
Imagine a 10 kg block moving with a velocity of 20 m/s to the left. Calculate the kinetic energy of this block
A die is rolled twice. what is the probability of showing a 3 on both rolls?
If only one number in a fraction is negative,does that mean the whole fraction is negative
Which answer is the solution set to the given inequality |x+7| < 17
What is the measure of each interior angle of a regular 10 sided polygon?
Find all real and imaginary zeros for a polynomial function
A polynomial function is an algebraic expression with one or more terms. The real zeros can be found by setting the function equal to zero and solving for x. The imaginary zeros can be found using the complex conjugate theorem.
Explanation:A polynomial function is an algebraic expression that consists of one or more terms. The real zeros of a polynomial function are the values of x that make the function equal to zero. To find the real zeros, set the polynomial function equal to zero and solve for x using methods such as factoring, synthetic division, or the quadratic formula.
The imaginary zeros of a polynomial function are the values of x that make the function equal to a complex number. These can be found by using the complex conjugate theorem. If a + bi is a zero, then a - bi is also a zero, where a and b are real numbers and i is the imaginary unit, sqrt(-1).
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How many solutions does the equation have?
2x + 3 = 4x + 2
A. no solutions
B. 1 solution
C. many solutions
Solution for 5y-4=9y+8 equation