the largest possible value of the greatest common divisor of 2m and 3n is 3.
To find the largest possible value of the greatest common divisor (GCD) of 2m and 3n, we can examine the given equation and determine the relationship between m and n.
The equation given is m = 24n + 51.
We can rewrite this equation as m = 3(8n) + 3(17).
Now, let's consider 2m and 3n:
2m = 2(3(8n) + 3(17))
= 6(8n) + 6(17)
= 48n + 102
3n = 3n
The GCD of 2m and 3n will be maximized when the common factors between 48n + 102 and 3n are maximized.
We can observe that both 48n and 102 are divisible by 3.
48n = 3 * (16n)
102 = 3 * 34
So, the greatest common divisor (GCD) of 2m and 3n will be maximized when it is equal to 3.
Therefore, the largest possible value of the greatest common divisor of 2m and 3n is 3.
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Complete question is below
Let m and n be positive integers such that m = 24n + 51. What is the largest possible value of the greatest common divisor of 2m and 3n?
What is the total change in the cat's weight for
oll 3 months?
Answer:the answer is -0.5 pound(s)
Step-by-step explanation:
Negative values means the cat's weight decreased from the previous month.
Positive values means the cat's weight increased from the previous month.
We want how much change in the last 3 months cat had gone though. We simply add up the changes.
-0.7 + 0.5 - 0.3 = -0.5
This means the cat's total weight change in all three months is decrease of 0.5 pounds.
Graph y = -1/3x + 5
khan academy
Graph the line using the slope and y-intercept, or two points.
Slope:
−1/3
y-intercept:
(0, 5)
x y
0 5
15 0
Hong made 162 for 9 hours of work. At the same rate, how much would he make for 13
hours of work?
Since Hong made 162 dollars for 9 hours of work, we can set up the proportion:
162 dollars / 9 hours = x dollars / 13 hours
where x is the amount of money Hong would make for 13 hours of work.
To solve for x, we can cross-multiply and simplify:
162 dollars × 13 hours = 9 hours × x dollars
2106 = 9x
x = 234
Therefore, at the same rate, Hong would make 234 dollars for 13 hours of work.
true or false: when two variables are highly correlated, a change in the value of one will cause a change in the value of another.
The given statement "a change in the value of one variable will result in a change in the value of the other when the two variables are highly linked" is FALSE.
What are variables?Any feature, characteristic, or circumstance that can exist in various amounts or types is considered a variable.
Independent, dependent, and controlled variables are typically present in an experiment.
The variable that is altered by the scientist is the independent variable.
A false correlation between two variables indicates that their correlation coefficient is almost zero.
When two variables have a strong correlation, altering the value of one will not affect the other.
Therefore, the given statement "a change in the value of one variable will result in a change in the value of the other when the two variables are highly linked" is FALSE.
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Triangle XYZ is similar to triangle JKL.
triangle XYZ with side XY labeled 8.7, side YZ labeled 7.8, and side ZX labeled 8.2 and triangle JKL with side JK labeled 12.18
Determine the length of side LJ.
11.48
11.59
12.80
12.92
The correct answer among the choices provided is A. 11.48.
How to solveGiven that side XY of triangle XYZ corresponds to side JK of triangle JKL, we can set up the following proportion:
XY/JK = YZ/LJ
Substituting the given values:
8.7 / 12.18 = 7.8 / LJ
We solve this for LJ:
LJ = (7.8 * 12.18) / 8.7
Calculating that gives us:
LJ ≈ 11.48
So, the correct answer among the choices provided is A. 11.48.
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Leo earned $2.40 for delivering a small parcel and earned more for delivering a big parcel. he delivered 3 times as many small parcels as big parcels and earned a total of $170.80. he earned $45.20 less for delivering all big parcels than all small parcels. how many big parcels did leo deliver?
Leo delivered 62.80 big parcels.
Let's denote the amount Leo earned for delivering a big parcel as "B" and the amount he earned for delivering a small parcel as "S". We'll set up a system of equations based on the given information.
From the problem statement, we have the following information:
1) Leo earned $2.40 for delivering a small parcel: S = 2.40
2) Leo earned more for delivering a big parcel: B > 2.40
3) He delivered 3 times as many small parcels as big parcels: S = 3B
4) Leo earned a total of $170.80: B + S = 170.80
5) Leo earned $45.20 less for delivering all big parcels than all small parcels: S - B = 45.20
Now, let's solve the system of equations:
From equation (3), we can substitute S in terms of B:
3B = 2.40
From equation (5), we can substitute S in terms of B:
S = B + 45.20
Substituting these values for S in equation (4), we get:
B + (B + 45.20) = 170.80
Simplifying the equation:
2B + 45.20 = 170.80
2B = 170.80 - 45.20
2B = 125.60
B = 125.60 / 2
B = 62.80
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PLS HELP FIRST CORRECT ANSWER GETS BRAINLEIST
Answer:
The area of one face is 25 units squared. The cube has 6 faces. The surface area is 150 units squared.
Step-by-step explanation:
Answer:
A) the area of one face is 20
B) the cube has 6 faces
C) the total surface area is 120
Step-by-step explanation:
for A you would need to multiply 5 by 4 which is 20
for B if you have common sense you would know that every cube has 6 faces
for C you just multiply the area of on face (20) by 6 which is 120
The function S(n)= 10(1-0.8ⁿ) / 0.2 represents the sum of the first n terms of an infinite geometric series.
a. What is the domain of the function?
The domain of the function is all real numbers.
The domain of the function S(n) = 10(1-0.8ⁿ) / 0.2 is all real numbers.
To find the domain of a function, we need to consider any restrictions on the values of the variable. In this case, there are no restrictions on the value of n. Therefore, the domain of the function is all real numbers.
In other words, we can plug in any real number for n and get a valid output for the function.
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The volume of a cone is 36piin to the power of 3. What is the volume of a cylinder with the same base and height as the cone?
Answer:
108πin³
Step-by-step explanation:
The volume of a cone = ⅓ of the volume of a cylinder
Thus, volume of cylinder = 2πr²h
Where, r = radius, h = height of cylinder.
Volume of cone = ⅓×πr²h
So therefore, the volume of a cone given = ⅓ of the volume of a cylinder with the same height and and base of the cone
Thus,
If Volume of cone = 36πin³ , volume of cylinder would be 3 × 36πin³
Volume of cylinder = 108πin³
PLEASE HELP THIS IS SUPER URGENT
Answer:
13344yhgf567yf4edbui
Answer:
Choice: E
Step-by-step explanation:
Trust me
Let f (x) = x e^(8x)Find a formula for the nth derivative of f, where n is any positive integer. Use x and n in your answer if needed.f ^((n))(x) =
The nth derivative of f(x) = xe^(8x) can be written as f^((n))(x) = x^(n)e^(8x) * (8^n + nP(n-1)). Here, P(n-1) stands for the (n-1)th derivative of the exponential function, e^(8x). This formula makes use of the product rule for derivatives and the chain rule. The product rule states that the derivative of the product of two functions is the product of the derivatives of the individual functions.
The chain rule explains how the derivative of a function composed of other functions (e.g. f(x) = xe^(8x)) can be calculated. To use the chain rule, the derivatives of the individual functions are multiplied together. In this case, the first function is x and its nth derivative is nx^(n-1). The second function is e^(8x) and its (n-1)th derivative is 8^(n-1)e^(8x). The product of these two derivatives is x^(n)e^(8x) * (8^n + nP(n-1)).
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A circular patio has a diameter of 12 feet. Holly is stringing lights around the edge of the patio.
Approximately how many feet of stringed lights does Holly need?
Use 3.14 for π.
Enter your answer as a decimal in the box.
feet
Answer:
37.68
Step-by-step explanation:
ayo
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Answer:
The answer is 37.68
Step-by-step explanation:
I took the test! :)
Find the value of r so the line that passes through the pair of points has the given slope.
(12, 10), (−2, r), m=−4
As per the slope intercept form, the value of r is 66.
Slope intercept form:
In order to find the slope intercept form, we have to use the formula,
y = mx + c
where
(x, y) refers the point
m refers the slope
c refers the y-intercept.
Given,
Here we have the pair of points (12, 10), (−2, r) and the value of slope which is m = -4.
Now, we need to find the value of r.
We know that the general form of the slope intercept form is
y = mx + c
First we have to use the slope and the point (12, 10), to find the intercept of the line,
So, we have to apply the value on the formula, then we get,
10 = -4(12) + c
10 = -48 + c
c = 58
So, the slope intercept form equation is
y = -4x + 58
In order to find the value of r, we have to apply the point (-2,r) on the equation, then we get,
r = -4(-2) + 58
r = 8 + 58
r = 66
Therefore, the value of r is 66.
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Combine like terms to create an equivalent expression. 1.3 b 7.8 − 3.2 b
The equivalent expression is -1.9b + 7.8.
What is an equivalent phrase?There is a concept known as an analogous expression, which is an expression that has the same value as another expression but has a different appearance.
Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.
Combine similar phrases now:
The definition of like words is the terms that have the same variable raised to the same power. Only the numerical coefficients can change in algebra.
When we combine the term b's coefficient, we get
1.3b + 7.8–3.2b
= (1.3−3.2)⋅b + 7.8
By condensing the equation, we obtain
= (- 1.9) +b + 7.8
= −1.9b + 7.8
There is a condensed equivalent formula of -1.9b + 7.8.
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please guys someone help i need the answer
Step-by-step explanation:
2x + y + x+ 2y = 180
3x + 3y = 180
3y +20+2x+y=180
4y + 2x = 160
3x + 3y = 180
2x + 4y = 160
elimination
6x + 6y= 360
6x + 12y = 480
= 6y = 120
y= 20
substitute
3x + 3y = 180
3x + 3(20)= 180
3x + 60 = 180
3x = 120
x= 40
x+2y
40+2(20)=80
<4=<8= 80°
<7=180-<8=<180-80= 100°
angle 7 = 100°
angle 8 = 80°
During the holiday, students went swimming in a local rectangular pool. The pool measures 20 feet by 35 feet. It is surrounded by a patio that is uniform width. Find the width of the patio if the total area of the pool and patio is 1350 sqr feet. Write a quadratic equation to solve the problem.
Answer:
The width of the patio is 3/2 feet.
Step-by-step explanation:
following equation to solve for w:
(20+2w) * (35+2w) = 1350
Expanding the equation, we get:
700 + 140w + 70w^2 = 1350
Subtracting 700 from both sides, we get:
140w + 70w^2 = 650
Dividing both sides by 10, we get:
14w + 7w^2 = 65
We can now solve for w using the quadratic formula:
w = (-b +/- sqrt(b^2-4ac)) / 2a
where a = 7, b = 14, and c = -65. Substituting these values into the formula, we get:
w = (-14 +/- sqrt(14^2-47(-65))) / 2*7
w = (-14 +/- sqrt(196+1820)) / 14
w = (-14 +/- sqrt(2016)) / 14
w = (-14 +/- 44) / 14
To find the width of the patio, we need to find the area of the pool and the area of the patio. Let's call the width of the patio "w". The area of the pool is 20 * 35 = <<20*35=700>>700 square feet. The area of the patio is (20+2w) * (35+2w) = 1350 sqr feet. We can set up the following equation to solve for w:
(20+2w) * (35+2w) = 1350
Expanding the equation, we get:
700 + 140w + 70w^2 = 1350
Subtracting 700 from both sides, we get:
140w + 70w^2 = 650
Dividing both sides by 10, we get:
14w + 7w^2 = 65
We can now solve for w using the quadratic formula:
w = (-b +/- sqrt(b^2-4ac)) / 2a
where a = 7, b = 14, and c = -65. Substituting these values into the formula, we get:
w = (-14 +/- sqrt(14^2-47(-65))) / 2*7
w = (-14 +/- sqrt(196+1820)) / 14
w = (-14 +/- sqrt(2016)) / 14
w = (-14 +/- 44) / 14
This means that the width of the patio is either 3/2 or -5/2 feet. Since the width cannot be negative, the width of the patio must be 3/2 feet.
The quadratic equation we can use to solve this problem is:
w^2 + 14w - 65 = 0
A term is a constant, a variable, or a ___ of numbers and variables.
A term is a constant, a variable, or a number-variable product.
What exactly is a variable?In algebra, a symbol (usually a letter) used to indicate an unknown numerical value in an equation or algebraic statement. A variable is a quantity that is changeable rather than fixed. In mathematics, a variable is an alphabet or phrase that represents an unknown amount, unknown value, or unknown number. Variables are very useful in algebraic expressions or algebra. As an example, the variables x and 9 are constants in the linear equation x+9=4.
A term can be a number, a constant, a variable, or the product of a number and a variable in this context.
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PLEASE HELP ME THIS IS MOST OF MY GRADE. I PUT 100 POINTS. SERIOUS ANSWERS ONLY. I WILL GIVE BRAINLIEST
Answer:
Step-by-step explanation:
hehe good luck loser T^T
Answer:
1. Cheese burger, French fries (regular), Ice cream (regular), any of the beverages.
2. Fried Chicken, Macaroni soup, Mango pie, any of the beverages.
3. Cheese burger, French fries (regular), Ice cream (regular), any of the beverages, because, there are going to be 40 guests and that are a lot of people to feed so I would rather spend more money than on some random people who come to my 2 year old son.
4. PhP 222.2 repeated
Step-by-step explanation:
Help
Algebra 2 please help answer 17
The natural logarithm function is ln(p) = ln(100) - 0.35t
How to determine the natural logarithm functionFrom the question, we have the following parameters that can be used in our computation:
The table of values
The function can be represented as
p = ae^kt
Using the points on the table, we have
ae^(k * 0) = 100
So, we have
a = 100
This gives
p = 100e^kt
Using another point, we have
70.5y = 100e^(k * 1)
70.5y = 100e^k
So, we have
e^k = 0.705
Take the natural logarithm of both sides
k = ln(0.705)
k = -0.35
The function becomes
p = 100e^(-0.35t)
Take the natural logarithm of both sides
ln(p) = ln(100) - 0.35t
Hence, the function is ln(p) = ln(100) - 0.35t
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Find the distance between each pair of points, to the nearest tenth. (-5,-5),(1,3)
The distance between the points (-5, -5) and (1, 3) is 10 units.
To find the distance between the points (-5, -5) and (1, 3), we can use the distance formula.
The distance formula is:
\(d = \sqrt{((x_2 - x_1)^2+ (y_2 - y_1)^2)}\)
Let's substitute the values into the formula:
\(d = \sqrt{((1 - (-5))^2 + (3 - (-5))^2)}\\d = \sqrt{((1 + 5)^2 + (3 + 5)^2}\\d = \sqrt{(6^2 + 8^2)}\\d = \sqrt{(36 + 64)}\\d = \sqrt{100}\\d = 10\)
Therefore, the distance between the points (-5, -5) and (1, 3) is 10 units.
Explanation:
The distance formula is derived from the Pythagorean theorem.
It calculates the length of the hypotenuse of a right triangle formed by the coordinates of two points.
In this case, we have a right triangle with legs of length 6 and 8.
Using the Pythagorean theorem, we find that the hypotenuse (the distance between the two points) is 10 units.
Remember to round your answer to the nearest tenth, so the final answer is 10 units.
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What is the quotient of the equation 51.6 ÷ 12 = ________? Use an area model to help you solve. 3.9 4.1 4.3 4.6
Answer:
The correct answer is 4.3
7. The ratio of width to length of the United States flag is 10:19.
If the width of the flag at Emersen's school is 4 feet, what is its length in feet?
What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?
The factor of the polynomial f(x) graphed on the coordinate plane is
(x - 1).
What is factor of the polynomial?
A polynomial with coefficients in a certain field or in integers is expressed as the product of irreducible factors with coefficients in the same domain in mathematics and computer algebra, which is known as polynomial factorization.
A polynomial can be factored by expressing it as the product of two or more components; this is somewhat the opposite of multiplying.
From the given graph we can see that, graph crosses x - axis at points
x = 1 and x = 8.
That means x = 1, 8 are the zero of the polynomial.
Since, if x = a is a zero of the polynomial, then (x - a) is the factor of the polynomial.
As x = 1, 8 are zero of the polynomial so (x - 1) and (x - 8) are the factors of the polynomial.
Hence, from the given options (x - 1) is factor of the polynomial.
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A proportional relationship between the number of pounds of lettuce (x) and the price in dollars (y) is graphed, and the ordered pair (5, 3) is on the graphed line. Part A: What is the price of 1 pound of lettuce? Show your work. (8 points) Part B: What does the ordered pair (10, 6) on the graph represent? Explain in words.
Answer:
A) $0.6
The point (5,3) means that you get 5 pounds of lettuce for 3 dollars, which means that one pound of lettuce would cost 3/5 dollars.
B) It tells us that 10 pounds of lettuce costs $6.
The x value of the point on the this graph tells us the number of pounds of lettuce and the y value of the point tells us the cost of those pounds of lettuce.
Step-by-step explanation: BABABOOEY
Find the value of x.
Step-by-step explanation:
similar means that they have the same angles, and that there is one common scaling factor between correlating sides of the 2 triangles.
so,
38/60 = (x + 10)/36
x + 10 = 38×36/60 = 38×3/5 = 114/5
x = 114/5 - 10 = 114/5 - 50/5 = 64/5 = 12.8
What is the slope intercept form of through: (-4,-5) slope: 5/4
Answer:
y = 5/4 x
Step-by-step explanation:
We already know the slope, so now we need to find the y-intercept. To do that, you need to simply plug the coordinates into the equation which is
y = 5/4 x + b
-5 = 5/4 (-4) + b
-5 = -5 + b
0 = b
y = 5/4 x + 0 or simply just y = 5/4 x.
Refer to pictures above
Answer:
6.9
Step-by-step explanation:
Cos ∆ = Adjacent/Hypotenuse
therefore x=12Cos55°
=6.88
=6.9 to the nearest tenth
Line JK passes through points J(–3, 11) and K(1, –3). What is the equation of line JK in standard form?
7x + 2y = –1
7x + 2y = 1
14x + 4y = –1
14x + 4y = 1
Answer:
b
Step-by-step explanation:
edge2020
The equation of the line is 7x+2y = 1
What is an equation of a line?The equation of a line is linear in the variables x and y which represents the relation between the coordinates of every point (x, y) on the line. i.e., the equation of line is satisfied by all points on it.
Given that a line is passing through two points J(-3, 11) and K(1, -3). we need to find the equation of line JK,
So, we know that the equation of a line passing from two points (x₁, y₁) and (x₂, y₂) is =
y-y₁ = y₂-y₁/x₂-x₁ (x-x₁)
Here, (x₁, y₁) and (x₂, y₂) = J(-3, 11) and K(1, -3)
Therefore, the equation of the line =
y-11 = -3-11 / 1+3 (x+3)
y-11 = -7/2(x+3)
Multiply by 2,
2y-22 = -7(x+3)
2y-22 = -7x-21
7x+2y = 1
Hence the equation of the line is 7x+2y = 1
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Stock Market At the beginning of the day the stock market goes up 40 1/2 points and stays at this level for most of the day. At the end of the day the stock market goes down 100 1/4 points from the high at the beginning of the day. What is the total change in the stock market from the beginning of the day to the end of the day? . The total change in the stock market is points. (Type an integer, proper fraction, or mixed number.)
Answer:
hm
Step-by-step explanation:
Answer:
it would be 20
Step-by-step explanation:
o what I did was: 100 1/4 - 60 1/2: 100 - 60 = 40 and then I subtracted 1-1 which is 0 then 4-2 which is 2, and got 40/2 or just simplify which will be equal to 20 .
Solve:
6a=2(8a-[6a+(4a-5)])+4
1: 3/5
2: -7/5
3: 7/5
4: -3/5
Please show me how?
Answer: \(\frac{7}{5}\)
Step-by-step explanation:
\(6a=2(8a-(6a+4a-5))+4\)
\(6a=2(8a-(10a-5))+4\)
\(6a=2(8a-10a+5)+4\)
\(6a=2(-2a+5)+4\)
\(6a=-4a+10+4\)
\(6a=-4a+14\)
\(6a+4a=14\)
\(10a=14\)
\(a=\frac{7}{5}\)
please give me a brainliest answer