\(3a-2b=8\\2a-2b=4\)
solve the following simultaneous equations using elimination method

volume of pyramid = 1/3(5.2)h cm3

Prism is a three dimensional figure. A prism is a 3-dimensional shape with two identical shapes (bases) facing each other.

we know that,

The volume of the pyramid is equal to

volume = (1/3) × base area × height

we have height = h cm

area of base = 5.2 cm^2

substitute in the formula

                       v = 1/3 × 5.2 × h

                        volume = 1.73h cm^3

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Answer:

A)20% because we added water not alcohol

Answer:

h = 22.5

Step-by-step explanation:

Volume Cylinder = πr²h

Radius = diameter/2

radius = 3

Solve:

-Chetan K

Answer:

y = 2x +20

Step-by-step explanation:

Times at gym = x

You get a waterbottle every x times = 2x.

The equation represents total in a month so the flat fee is not included.

If a=4, b= 7, and B= 75°, the area of triangle ABC is approximately 13.476 square units.

To find the area of triangle ABC given the values of a, b, and B, we can use the formula:

Area = (1/2) * a * b * sin(B)

where a and b are the lengths of two sides of the triangle and B is the angle between them, measured in degrees.

Substituting the given values, we get:

Area = (1/2) * 4 * 7 * sin(75°)

Using a calculator to evaluate the sine of 75°, we get:

Area = (1/2) * 4 * 7 * 0.96593

Area ≈ 13.476 square units

The formula for the area of a triangle involves using the length of two sides and the angle between them.

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In section 20 of the south half of the map, find the contour line that intersects the encircled area. The distance between that contour line and the ground surface represents the required well depth to access the water table.



To locate the point in question, refer to section 20 on the south half of the map where it is encircled. Next, examine the water table contours provided in Exercise 14A. Identify the contour line that intersects with the encircled area. This contour line represents the depth of the water table at that point.

To determine the depth a well would need to be drilled to access the water table, measure the vertical distance from the ground surface to the identified contour line. This measurement corresponds to the required depth for drilling the well.

Therefore, In section 20 of the south half of the map, find the contour line that intersects the encircled area. The distance between that contour line and the ground surface represents the required well depth to access the water table.

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Answer:

−12

Step-by-step explanation:

To solve this expression, we need to use the order of operations. The order of operations is a set of rules that dictate the sequence in which operations should be performed in a mathematical expression. The order of operations is often abbreviated using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

-2x+9y=41.... equation 1

-2x-5y=1 ....equation 2

________________

14y=43

y=43/14

y=43/14 in equation 1

-2x+9(43/14)=41

-2x+387/14=41

-2x=41-387/14

-2x=187/14

x=187/-28

x=187/28 , y=43/14

if you want to check your answer

-2(187/28)+9(43/14)=41

Answer:-3

Step-by-step explanation: -7 -4

Answer:

Step-by-step explanation:

chicken

Answer:

B. Carlos ate 13 pounds of cereals in two months

The extreme values of f(x, y) = xy occur at the points (2, 1) and (-2, -1) on the ellipse \(3x^{2} +2y^{2} =1\).

To find the extreme values of f(x, y) = xy on the ellipse \(3x^{2} +2y^{2} =1\), we can use the method of Lagrange multipliers.

Define the function g(x, y) = \(3x^{2} +2y^{2} -1\). We need to find points (x, y) where the gradient of f is proportional to the gradient of g:

∇f = λ∇g

The gradient of f is ∇f = (y, x), and the gradient of g is ∇g = (6x, 4y). Therefore, we have the following system of equations:

y = 6λx
x = 4λy

Substitute the second equation into the first:

y = 6λ(4λy)
y = \(24λ^{2y}\)

If y ≠ 0, then 1 = \(24λ^{2}\), and λ = ±1/2. Plugging this value into the second equation gives x = ±2. Thus, we have two potential extreme points: (2, 1) and (-2, -1).

Now consider the case when y = 0. The constraint equation becomes \(3x^{2} =1\), and x = ±1/√3. However, these points correspond to f(x, y) = 0, which is not an extreme value.

Therefore, the extreme values of f(x, y) = xy occur at the points (2, 1) and (-2, -1) on the ellipse \(3x^{2} +2y^{2} =1\).

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Answer:

6 miles

Step-by-step explanation:

The distance formula is expressed as;

D = √(x2-x1)²+(y2-y1)²

D = √(2-4)²+(8-2)²

D = √(-2)²+(6)²

D = √4 + 36

AD = √40

AD = 6.32

Hence the approximate distance between the library  and the mall is 6 miles

The probability of choosing a ball numbered 25 in a lottery game that contains 24 balls numbered 1 through 24 is 0.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event will not occur and 1 indicating that the event will definitely occur.

Since a lottery game contains 24 balls numbered 1 through 24, it does not contain the ball numbered 25. So it can not be chosen at all.

probability = 0

Therefore, the probability of choosing a ball numbered 25 is 0.

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The minimum radius of convergence R of power series solutions about the ordinary point x = 0 is 4.123 and that about the ordinary point x = 1 is 4 units.

What is radius of convergence?

In mathematics, the radius of convergence of a power series is  stated as the radius of the largest disk at the center of the series in that the series converges. Radius of convergence is either a non-negative real number or infinity.

The given differential equation is

(x² -2x+17) y" +xy' -4y =0

We have to find the minimum radius of convergence R of power series solutions about the ordinary point x = 0 and x = 1.

The minimum radius of convergence can be defined as the distance between the ordinary point and the singularity of the differential equation.

Singularity point is the root of the polynomial attached with the second derivative. So, the singularity points can be calculated as,

(x² -2x+17)=0 Comparing this with ax²+bx+c=0 we get,

x=\(\frac{-b+\sqrt{b^{2} -4ac } }{2a}\)  and x= \(\frac{-b-\sqrt{b^{2} -4ac } }{2a}\)

x= \(\frac{2+\sqrt{4 -68 } }{2}\)    and x= \(\frac{2-\sqrt{4 -68 } }{2}\)

x= (2±8i)/2

x= 1±4i

So, the singularity points are x₁= 1+4i  and x₂ = 1-4i

Now, the ordinary points can be written as  z₁= 0+0i and z₂ = 1+0i

The minimum radius of convergence can be calculated as,

r₁ = | z₁ - x₁ |

   = | 0+0i-1-4i |

   = | -1-4i |

   = √17

   = 4.123

r₂ =  | z₂ - x₂ |

   = | 1+0i-1+4i |

   = | 4i |

   = √16

   = 4

Hence, the minimum radius of convergence R of power series solutions about the ordinary point x = 0 is 4.123 and that about the ordinary point x = 1 is 4 units.

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Answer:

Triangle area = 20.91 cm^2

Step-by-step explanation:

area = 1/2(b*h)

area = 1/2(8.2*5.1)

area = 1/2(41.82)

area = 20.91 cm^2

The percentage of water in the milk cup and the percentage of milk in the water cup are same.

What is milk?

A white liquid meal called milk is generated by mammals' mammary glands. Before they can digest solid food, it is the main source of nutrition for young mammals. Milk immunity is influenced by immune components and immune-modulating elements.

Given:

There are a cup of milk and a cup of water.

Take one teaspoon of milk, put into the water cup; mix well.

Take one teaspoon of the mixture in the water cup and put into the milk cup then mix well.

Suppose the percentage of water cup are 'p' and the percentage of milk cup are 'q'.

When we add one teaspoon of milk and put into water cup then the percentage of water cup are 'p + 1'.

And the percentage of milk cup are 'q - 1'.

Again one teaspoon of mixture in the water cup put into the milk cup.

So, the percentage of milk cup are, q - 1 + 1 = q.

And the percentage of water cup are p + 1 - 1 = p.

The percentage will be same for both milk cup and water cup.

Hence, the percentage of water in the milk cup and the percentage of milk in the water cup are same.

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Answer:

y=27 and x=9

Step-by-step explanation:

the ratio is 4 to 3

In analyzing the performance of implementing the given methods over Singly Linked List and Doubly Linked List data structures, we consider the Big-O notation, which provides insight into the time complexity of these operations as the size of the list increases.

Add to Start of List:

Singly Linked List: O(1)

Doubly Linked List: O(1)

Both Singly Linked List and Doubly Linked List offer constant time complexity, O(1), for adding an element to the start of the list.

This is because the operation only involves updating the head pointer (for the Singly Linked List) or the head and previous pointers (for the Doubly Linked List). It does not require traversing the entire list, regardless of its size.

Add to End of List:

Singly Linked List: O(n)

Doubly Linked List: O(1)

Adding an element to the end of a Singly Linked List has a time complexity of O(n), where n is the number of elements in the list. This is because we need to traverse the entire list to reach the end before adding the new element.

In contrast, a Doubly Linked List offers a constant time complexity of O(1) for adding an element to the end.

This is possible because the list maintains a reference to both the tail and the previous node, allowing efficient insertion.

Add at Given Index:

Singly Linked List: O(n)

Doubly Linked List: O(n)

Adding an element at a given index in both Singly Linked List and Doubly Linked List has a time complexity of O(n), where n is the number of elements in the list.

This is because, in both cases, we need to traverse the list to the desired index, which takes linear time.

Additionally, for a Doubly Linked List, we need to update the previous and next pointers of the surrounding nodes to accommodate the new element.

In summary, Singly Linked List has a constant time complexity of O(1) for adding to the start and a linear time complexity of O(n) for adding to the end or at a given index.

On the other hand, Doubly Linked List offers constant time complexity of O(1) for adding to both the start and the end, but still requires linear time complexity of O(n) for adding at a given index due to the need for traversal.

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Answer:

I think the answer is a.i^7

0.5 bateria in the dish at 11 am

The solutions of the equation  x² + 2x + 10 = - 3x + 4 are  x=-2 and x=-3

The given equation is x² + 2x + 10 = - 3x + 4.

Take all the terms to the left side

x² + 2x + 10+3x-4=0

Combine the like terms

x²+5x+6=0

x²+2x+3x+6=0

Take out the factors

x(x+2)+3(x+2)=0

(x+3)(x+2)=0

x=-2 and x=-3

Hence, x=-2 and x=-3 are the solutions of the equation  x² + 2x + 10 = - 3x + 4.

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Based on typical expectations for the relationship between trunk circumference and tree height, the slope is most likely to be closer to 1.

The slope of the regression model represents the change in the dependent variable (height of the pine tree) for every one-unit increase in the independent variable (circumference of the trunk).

In this scenario, the slope is most likely to be closer to 1. This is because we expect a reasonably linear relationship between the circumference of the trunk and the height of the pine tree. Generally, as the trunk's circumference increases, we anticipate a proportional increase in the height of the tree.

If the slope were closer to 0, it would suggest little to no relationship between the circumference of the trunk and the height of the tree. However, in reality, there is usually a positive correlation between these variables.

If the slope were closer to 0.1 or 100, it would indicate a more extreme relationship where a small change in trunk circumference results in a significantly larger or smaller change in tree height. While this is possible in some cases, it is less likely to be the norm.

Therefore, based on typical expectations for the relationship between trunk circumference and tree height, the slope is most likely to be closer to 1.

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Therefore, the general solution of the given second-order differential equation is: y = c1 e^(0t) + c2 e^(-1/2 t).

To find the general solution of the given second-order differential equation 2y'' + y' = 0, we can assume that the solution is of the form y = e^(rt), where r is a constant to be determined.

First, we find the first and second derivatives of y with respect to t:

y' = re^(rt)

y'' = r^2 e^(rt)

Substituting these expressions into the differential equation, we get:

2r^2 e^(rt) + r e^(rt) = 0

Factoring out e^(rt), we get:

e^(rt) (2r^2 + r) = 0

This equation will be satisfied if either e^(rt) = 0 or 2r^2 + r = 0.

Since e^(rt) is never zero, we must have:

2r^2 + r = 0

Factoring out r, we get:

r(2r + 1) = 0

So, either r = 0 or r = -1/2.

Therefore, the general solution of the given second-order differential equation is:

y = c1 e^(0t) + c2 e^(-1/2 t)

Simplifying this expression, we get:

y = c1 + c2 e^(-1/2 t)

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\(3 \times \frac{5}{11} \)

turns into

\( \frac{3}{1} \times \frac{5}{11} = \frac{15}{11} = 1 \frac{4}{11} \)

\(12 \times \frac{3}{4} = \frac{12}{1} \times \frac{3}{4} = \frac{36}{4} = 9\)

Because 36 goes into 4 nine times.

The correct value of approximately 19 payments are required to settle the loan.

To determine the number of payments required to settle the loan, we need to calculate the loan balance and divide it by the payment amount.

First, let's calculate the loan balance. The down payment made by General Computers Inc. is 30% of $61,000, which is $18,300. This means the loan amount is the remaining balance:

Loan amount = Purchase price - Down payment

= $61,000 - $18,300

= $42,700

Next, let's calculate the interest rate per period. The given interest rate is 3.50% compounded semi-annually. Since the payments are made quarterly, we need to adjust the interest rate accordingly. The semi-annual interest rate is:

Semi-annual interest rate = Annual interest rate / Number of compounding periods per year

= 3.50% / 2

= 0.035 / 2

= 0.0175

Now, let's calculate the loan balance after each payment. We'll use the formula for the future value of an ordinary annuity to calculate the loan balance at the end of each quarter:

Loan balance after each payment = Loan amount * (1 + Semi-annual interest rate)^(-Number of payments)

In this case, the loan amount is $42,700 and the payment amount is $2,250.53.

Let's calculate the number of payments required to settle the loan by iteratively subtracting the payment amount from the loan balance until the loan balance becomes zero:

Loan balance after payment 1 = $42,700 * \((1 + 0.0175)^(-1)\)

Loan balance after payment 2 = (Loan balance after payment 1 - Payment amount) * \((1 + 0.0175)^(-1)\)

Loan balance after payment 3 = (Loan balance after payment 2 - Payment amount) *\((1 + 0.0175)^(-1)\)

...Loan balance after payment n = (Loan balance after payment n-1 - Payment amount) *\((1 + 0.0175)^(-1)\)

We continue this calculation until the loan balance becomes zero.

Using this iterative calculation, we find that it takes approximately 19 payments to settle the loan.

Therefore, approximately 19 payments are required to settle the loan.

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Answer:

12 cups of orange juice and 18 cups of cranberry juice

Step-by-step explanation:

First, let's determine the number of cups used in the recipe.

2 cups of orange juice + 3 cups of cranberry juice = 5 cups

Now, if every person only has 0.5 cups of juice, how many people can drink 5 cups of juice?

5 / 0.5 = 10

If one batch is enough for 10 people, how many batches will we need for 60 people?

60 / 10 = 6

So, we will need to make the recipe 6 times in order to make enough punch for everyone.

Lastly, let's mutliply the recipe by 6.

6 * (2 cups of orange juice + 3 cups of cranberry juice)

12 cups of orange juice + 18 cups of cranberry juice

So, Bethany will need 12 cups of orange juice and 18 cups of cranberry juice to make enough punch for 60 people to have 0.5 cups of punch.

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18 cups of cranberry juice and 12 cups of orange juice to make enough punch for 60 people.

To determine how many cups of orange juice and cranberry juice Bethany needs to combine, we can use the given ratio of the two juices, which is 2 cups of orange juice for every 3 cups of cranberry juice. Let's assume that x cups of cranberry juice are needed. Then, we can find the amount of orange juice needed by multiplying x by the ratio of orange juice to cranberry juice, which is 2/3. Thus, the amount of orange juice needed is (2/3)x.

To find the total amount of punch needed, we can multiply the serving size (0.5 cups) by the number of people (60), which gives us 30 cups.

To find the total amount of cranberry juice needed, we can set up the equation:

x + (2/3)x = 30

Simplifying this equation, we get:

(5/3)x = 30

Dividing both sides by 5/3, we get:

x = 18

Therefore, Bethany needs 18 cups of cranberry juice and (2/3) * 18 = 12 cups of orange juice to make enough punch for 60 people.

Answer:

4^15/ b^21

Step-by-step explanation:

( b^7 / 4^5) ^ -3

b^7 ^ -3  / 4^5^-3

We know that x^y^z = x^ (y*z)

b^ (7*-3) / 4^(5*-3)

b ^ -21 / 4 ^ -15

We know that a^ -b = 1/ a^b

We do not like to leave negative exponents

1 * b^21  * 4  ^15

4^15/ b^21

Answer:

D.  - 5 ≤ x < 1

Step-by-step explanation:

The numerator cannot be the square root of a neg. no.

So, x + 5 ≥ 0 or x ≥ -5

The denominator cannot be a neg. no. or 0.

So, 1 - x > 0

      1 > x   or  x < 1

So, altogether  - 5 ≤ x < 1

Therefore, D is the correct answer.

Answer:

The biologist did not use proper labeling on the pieces of paper.

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