If 96 as a product of its prime factors is 2x2x2x2x2x3, find the greatest common divisor of 72 and 96

Answer:

The answer would be 5.

Step-by-step explanation:

Tthe other terms have a number being multiplied by a variable.

The area, in square units, of the region where the two triangles overlap is found as 1 square units.

We can determine the equation for each line with in diagram using its coordinates.

We can determine the coordinates for each point. (1/4,3/4) is one of the intersections.

d² = 2² + 2² = 8

A₁ = (1/3d + 1/6d )/2 * 1/4d

A₁ = 1/4d * 1/4d

A₁ = 1/ 16 d²

Now,

A = 2A₁

A = 2.(1/16)d²

A = 1/8d²

A = 1/8 *8

A  = 1

Thus, the area, in square units, of the region where the two triangles overlap is found as 1 square units.

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Answer:

1 square unit

Step-by-step explanation:

Answer:

Matthew: $ 3.60

Jade: $3.90

Step-by-step explanation:

2x + 2x = 14.50

-> 4x = 14.50

-> $3.60

4x + 3x = 27

-> 7x = 27

-> $ 3.90

We can conclude that the expression that represents the perimeter, in centimeters, of our triangle is:

P = (12b + 2c + 17d) cm

We know that the sides of our triangle measure:

And we want to get the perimeter of our triangle, which is basically the sum of the lengths of the 3 sides, so the equation for the perimeter is:

P = (2b + 5c)cm + (10b + 7d) cm + (4d - 3c) cm

Now we need to simplify that expression, we will get:

P = (2b + 5c + 10b + 7d + 4d - 3c) cm

P = (2b + 10b + 5c - 3c + 7d + 10d) cm

P = (12b + 2c + 17d) cm

Then we can conclude that the expression that represents the perimeter, in centimeters, of our triangle is:

P = (12b + 2c + 17d) cm

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4 parts of the given square are not equal.

We have,

A square has all four sides equal.

Now,

The square is in four parts.

We see that,

Each part of the square is not equal.

Two parts on the edge are more like a triangle.

The middle two parts are more like a trapezium.

To say that 4 parts of the square are equal we need to have similar shapes for all the four parts of the given square.

Thus,

4 parts of the given square are not equal.

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Answer: I think

#3- A

#4- C

Answer:

The answer is 5/30

Step-by-step explanation:

The answer is 5/30 because when multiplying a fraction by a fraction you have to multiply the numerator by the numerator and the denominator by the denominator so if you multiply 5 by 1 you get 5 and when you multiply 6 by 5 you get 30 so the answer is 5/30

a) The standard form of the equation for this hyperbola is (x-1)²/4 - (y-1)²/21 = 1.

b) The standard form of the equation for this hyperbola is (y+6)²/4 - (x-1)²/3 = 1.

c) The standard form of the equation for this hyperbola is (x+3)²/5 - (y-2)²/6 = 1.

a. To find the standard form of the equation of a hyperbola with the given vertices and foci, we need to first determine the center of the hyperbola. The center of the hyperbola is the midpoint between the two vertices, which in this case is (1, 1).

In this case, a = 2. To find the value of b, we can use the equation b² = c² - a². Substituting the values we have found, we get b² = 21. The standard form of the equation of a hyperbola is

=>  (x-h)²/a² - (y-k)²/b² = 1,

where (h,k) is the center of the hyperbola.

Substituting the values we have found that h = 1 and the value of k as 1, we get the equation

=>  (x-1)²/4 - (y-1)²/21 = 1.

b. In this case, we can see that the vertices have the same x-coordinate but different y-coordinates, so the hyperbola is vertical. We can use the equation (y-k)²/a² - (x-h)²/b² = 1 for a vertical hyperbola.

We know that the center of the hyperbola is the midpoint between the vertices, which is (1, -6).

We can use the distance formula to find the value of a, which is the distance between the center and each vertex. In this case, a = 2.

To find the value of b, we can use the point given and the equation of the hyperbola. Substituting the values we have found, we get the equation

=> (y+6)²/4 - (x-1)²/3 = 1.

c. To find the standard form of the equation of a hyperbola with the given vertices and asymptotes, we need to determine the center of the hyperbola.

The center of the hyperbola is the midpoint between the vertices, which in this case is (-3, 2). We can use the equation (y-k)/(x-h) = ±a/b for the asymptotes.

Substituting the values we have found, we get the equations

=>  (y-2)/(x+3) = 6/5

and

=> (y-2)/(x+3) = -5/1.

We can solve for a and b by setting a/b equal to the slope of the asymptotes.

In this case, a/b = 6/5 or a/b = -5. We also know that a² - b² = c², where c is the distance between the center and each vertex. We can use the distance formula to find the value of c, which in this case is c = 3√5. Substituting the values we have found, we get two possible standard form equations for the hyperbola:

   • If a/b = 6/5, then a² = 36 and b² = 30.

The standard form of the equation for this hyperbola is

=> (x+3)²/36 - (y-2)²/30 = 1.

   • If a/b = -5, then a² = 5 and b² = 6.

The standard form of the equation for this hyperbola is

=> (x+3)²/5 - (y-2)²/6 = 1.

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Each description should be matched with the given angles as follows;

In Mathematics and Geometry, a quadrant is the area that is occupied by the values on the x-coordinate (x-axis) and y-coordinate (y-axis) of a cartesian coordinate.

Generally speaking, sin(θ) is greater than 0, cos(θ) is greater than 0 and tan(θ) is greater than 0 in the first quadrant.

In the second quadrant, sin(θ) is greater than 0, cos(θ) is less than 0 and tan(θ) is less than 0. In the third quadrant, tan(θ) is greater than 0, sin(θ) is less than 0, and cos(θ) is less than 0.

In the fourth quadrant, sin(θ) is less than 0, cos(θ) is greater than 0, and tan(θ) is less than 0.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The only graph that correctly expresses the exponential function f(x) = 2(2.5)ˣ + 3 is: Graph A

The exponential function is given as:

f(x) = 2(2.5)ˣ + 3

Now, we will start by plugging in 0 for x into the exponential function to get:

f(0) = 2(2.5)⁰ + 3

Now, any number raised to the power of zero becomes 1 and as such, we have:

f(0) = 2(1) + 3

f(0) = 5

Now, the only graphs that have the y-intercept at 5 are Graphs A and Graph D

When x = 1, we have:

f(1) = 2(2.5)¹ + 3

f(1) = 5 + 3

f(1) = 8

Only graph A has it correct.

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Answer:

Should be 36

Step-by-step explanation:

45/2.5 = 18

36/2= 18

Each bag of beans weighs 70kg and each bag of salt weighs 90kg.

To find the mass of each bag, let's assign variables:
Let's say the mass of each bag of beans is B kg, and the mass of each bag of salt is S kg.

According to the given information, we know that:
\(2B + 3S = 410kg\) - (equation 1)
\(3B + 2S = 390kg\) - (equation 2)

To solve this system of equations, we can use the method of substitution.
From equation 1, we can express B in terms of S:
\(B = (410kg - 3S)/2\) - (equation 3)

Now we can substitute equation 3 into equation 2:
\(3((410kg - 3S)/2) + 2S = 390kg\)

Simplifying this equation, we get:
\(615kg - 4.5S + 2S = 390kg\\615kg - 2.5S = 390kg\)
Subtracting 615kg from both sides, we have:
\(-2.5S = -225kg\)
Dividing both sides by -2.5, we find:
\(S = 90kg\)
Now, substituting this value of S into equation 3, we can solve for B:
\(B = (410kg - 3(90kg))/2\\B = (410kg - 270kg)/2\\B = 140kg/2\\B = 70kg\)
Therefore, each bag of beans weighs 70kg and each bag of salt weighs 90kg.

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Answer:

Step-by-step explanation:

y = 6x + 2     ⇒    6x - y = -2

y = 6x - 4      ⇒    6x - y = 4

a₁ = a₂ = 6  ,  b₁ = b₂ = -1 ,  c₁ = -2 , c₂ = 4

a₁ = a₂ = 6   and  b₁ = b₂ = -1  and  c₁ ≠ c₂  ⇒  NO SOLUTIONS

By simplifying the given expression and substituting x = 0, we found that the limit evaluates to 0. This means that as x approaches 0, the expression approaches 0. This result holds for any value of m ∈ R{0}.

To evaluate the limit lim(x→0) [1 - (1 + x^2)/(1 - cos(mx))], we can simplify the expression and then substitute the value of x = 0 into the simplified expression.

Let's simplify the expression step by step:

1 - (1 + x^2)/(1 - cos(mx))

= (1 - 1 - x^2)/(1 - cos(mx)) [Expanding the numerator]

= (-x^2)/(1 - cos(mx))

Now, let's substitute x = 0 into the simplified expression:

lim(x→0) (-x^2)/(1 - cos(mx))

= lim(x→0) (-0^2)/(1 - cos(m*0))

= lim(x→0) 0/(1 - cos(0))

= 0/1

= 0

Therefore, the limit lim(x→0) [1 - (1 + x^2)/(1 - cos(mx))] in terms of m, where m ∈ R{0}, is equal to 0.

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Answer:

A, C, F

Step-by-step explanation:

JK is proportional to PQ, so that would be 8/x. Then, JL is proportional to PR, which would be 10/5. So, the answer is: 8/x = 10/5

Then, C would also be correct as KL is proportional to QR, and JK is proportional to PQ.

Finally, F is correct as JK to KL is proportional to PQ to QR, as JK is proportional to PQ, and KL is proportional to QR.

Answer:

$360

Step-by-step explanation:

Calculation for what would be the total cost of next month's order

First step is to calculate how much they paid per the two cases of printer papers

Two cases of printer paper=$48 /2

Two cases of printer paper=$24 per case

Second step is to calculate the cost of each package of printer paper

Cost of each package of printer paper=$24/12 packages of paper

Cost of each package of printer paper=$2

Last step is to calculate the total cost of next month's order

Total cost=180 packages*$2

Total cost=$360

Therefore what would be the total cost of next month's order is $360

It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. The rate of the machine is 0.15 pound per second

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. Hence:

Rate of the machine = 3 pounds / 20 seconds = 0.15 pound per second

It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. The rate of the machine is 0.15 pound per second

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Answer:

9/16 pounds

Step-by-step explanation:

1 pound = 16 ounces

With this information, we have make a proportion to find the number of pounds 9 ounces is

Let p = the number of pounds

16/1 = 9/p

Multiply both sides by 1 to get

16 = 9/p

Multiply both sides by p

16p = 9

Divide both sides by 16

p = 9/16

This fraction is in its simplest form and can't be simplified any more.

Answer:

9/16 is the answer brainliests

Step-by-step explanation:

Answer:

1 / 1

Step-by-step explanation:

Your line has a 1 to 1 ratio of rise over run.

The integral method for calculating ksn was chosen for the main analysis due to its reduced vulnerability to uncertainty.

In our study, we opted to utilize the integral method for determining the ksn (a parameter) in our main analysis. The selection of this method was primarily based on its ability to mitigate the impact of uncertainty. The integral method offers several advantages over alternative approaches when dealing with uncertainty.

Firstly, it incorporates a broader range of data points by integrating over a continuous range of values, resulting in a more comprehensive assessment. This helps to minimize the influence of outliers or errors in individual data points, leading to a more robust estimation of ksn.

Additionally, the integral method accounts for the distribution of uncertainty across the entire range of values, providing a more representative characterization of the parameter. By considering these factors, we can enhance the reliability and accuracy of our analysis, making the integral method a suitable choice for our main analysis.

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Selecting KSN calculated using the integral method for your main analysis due to its lower susceptibility to uncertainty suggests that you have found this particular approach to be more reliable or robust when dealing with uncertain data compared to other methods.

The integral method in KSN refers to the incorporation of information from integrals or cumulative distribution functions (CDFs) in the estimation process, which can help in reducing the impact of uncertainty in the data.

By choosing KSN with the integral method, it implies that you believe this approach provides more accurate or stable results in the presence of uncertainty. This could be due to the specific properties of the integral method in KSN, such as its ability to incorporate information from distribution functions or handle non-stationary data.

It's important to note that the suitability of any method depends on the specific characteristics of your data, the nature of the problem, and the goals of your analysis. Different interpolation methods have their strengths and weaknesses, and it's crucial to evaluate them based on the specific requirements of your study.

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we selected ksn calculated using the integral method for our main analysis due to its lower susceptibility to uncertainty. What does it suggests?

Step-by-step explanation:

the answer will be zero 0

Answer:

A.380160 B. 240

Step-by-step explanation:

1 Square foot (sq ft) is equal to 144 square inches (sq in). To convert square feet to square inches, multiply the square foot value by 144.

Answer:

domain :- (-4, 1, 4,5)

Range:- (-3,0,0,2)

Step-by-step explanation:

Answer:

domain :- (-4, 1, 4,5)

Range:- (-3,0,0,2)

Hope this helps! :)

Answer:

x= 10/3

or

x= 3.334

Depending on simplified form asked.

Step-by-step explanation:

6x +8 =28

subtract 8 from both sides

6x = 20

divide by 6

x=20 /6

x= 10/3 or x =3.334

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Answer:

8

Step-by-step explanation:

Since the first decimal place is greater than 5, it rounds to 8, because 8 is the next whole number to 7.

If my answer is incorrect, pls correct me!

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-Chetan K

Rounding to the nearest whole number, she will have run a total distance of 13 kilometers after 16 days.

To find out how far she will have run in total after 16 days, we can use the formula for calculating compound interest:

A = P(1 + r/100)^n

Where:

A = Total distance run after n days

P = Initial distance (4.8 kilometers)

r = Rate of increase per day (6.9%)

n = Number of days (16)

Plugging in the given values, we can calculate the total distance:

A = 4.8(1 + 6.9/100)^16

Using a calculator or performing the calculations step by step, we get:

A ≈ 4.8(1.069)^16 ≈ 4.8(2.092473)^16 ≈ 4.8(2.628)

A ≈ 12.6144

Rounding to the nearest whole number, she will have run a total distance of 13 kilometers after 16 days.

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Answer:

11 is the mode

Step-by-step explanation: it appears the most

The distance between the zoo and library is 600 feet, as seen with the help of concept of applications of trigonometry.

Given: height of helicopter = 300√3 feet from the ground.

To find: Distance between zoo and library.

Finding:

(Refer to the image attached.)

Let the distance from the plane to the zoo and library be d1 and d2 respectively.

Then, with the help of concepts of applications of trigonometry,

\(tan(60) = \frac{300\sqrt{3}}{d1}\)

=> \(\sqrt{3}=\frac{300\sqrt{3}}{d1}\)

=> d1 = 300 feet

\(tan(30) = \frac{300\sqrt{3}}{d2}\)

=> \(\frac{1}{\sqrt{3}}=\frac{300\sqrt{3}}{d2}\)

=> d2 = 300 (3) = 900 feet

The distance between zoo and library = d2 - d1 = 900 - 300 = 600 feet.

Hence, the distance between the zoo and library is 600 feet, as seen with the help of concept of applications of trigonometry.

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