Angela used (1)/(5) of her beads to make some bracelets. She gave 78 beads to Santiago and had (1)/(2) of the beads left. How many beads did Angela have left?

The two linearly independent solutions are y₁(x) = 1 - (x²/3) + (x⁴/81) - (x⁶/2187) + … and y₂(x) = x - (x³/9) + (x⁵/405) - (x⁷/21870) + ...

We can use the power series method to find the two solutions of the given differential equation:

Let y = ∑anxn be a power series solution. Then, we have:

y' = ∑nanxn-1

y'' = ∑nan(n-1)xn-2

Substituting these into the differential equation and equating coefficients of like powers of x, we get:

3x∑nan(n-1)xn-1 + ∑anxn = 0

Simplifying, we obtain:

∑[3nan(n-1) + an-1]xn = 0

Since x ≠ 0, the coefficients of like powers of x must be zero. This gives us the recurrence relation:

an = -an-1/(3n(n-1)), n ≥ 1

Using this recurrence relation and the initial condition y(0) = 1, we can find the power series solution:

y₁(x) = 1 - (x²/3) + (x⁴/81) - (x⁶/2187) + ...

To find a second linearly independent solution, we can use the method of reduction of order. Let y₂(x) = v(x)y₁(x). Then, we have:

y₂' = v'y₁ + vy₁'

y₂'' = v''y₁ + 2v'y₁' + vy₁''

Substituting these into the differential equation and simplifying, we get:

v''y1x + (2v'y1' + vy1'')x + 3vy1 = 0

Since y₁(x) is a solution, we have:

y₁'' + (1/3x)y₁ = 0

Multiplying by y1 and integrating, we obtain:

(y₁')² + y₁²/3 = C

where C is a constant of integration. Using the initial condition y₂(0) = 0, we can find the second solution:

y₂(x) = x - (x³/9) + (x⁵/405) - (x⁷/21870) + ...

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The value of the constant of variation for the direct variation is k = -1/2.

Variation depicts the relationship between two variables and how it changes. Often, a ratio is used to illustrate this connection. When we remark that a variation is continuous, we are referring to how consistently the ratio changes. Hence, whenever you read the phrase "constant of variation," just keep in mind that it refers to the stability of the relationship between the variables.

The direct variation is given by the following relations:

y = kx

Now, using the table substitute the value of y = f(x) and x:

y = kx

-2 = k(4)

k = -2/4

k = -1/2

Hence, the value of the constant of variation for the direct variation is k = -1/2.

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Therefore , the solution of the given problem of proportionality comes out to be connection is not proportional as a result.

When a relationship consistently has the same number, it is considered to be proportional. For instance, the average amount of apples created by each tree determines how many trees there are in an area and how many apples are harvested. Mathematicians refer to a linear relationship between two numbers or factors as being proportional. The other amount doubles if the original amount does.

Here,

When there is a constant multiple between two variables in a relationship, that relationship is called a proportional relationship.

The expense of the 10 apples, which cost $4 plus a $0.20 surcharge, is not directly related to the quantity because the surcharge is a set price regardless of the quantity of apples.

The quantity being measured is growing by a fixed proportion (in this instance, 100%) every time period, so the bacteria doubling every day is an exponential relationship rather than a proportional one.

Last but not least, because the price per book varies, the $9 cost of 4 volumes is also not proportional. We would anticipate spending $18 if we were to purchase 8 books, which is not twice as much as 4 books. The connection is not proportional as a result.

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The value of the account at the end of the specified time period is option B.$6749.81. It can be calculated using the formula for compound interest, which is:

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

Where A is the final amount, P is the principal, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

Plugging in the given values, we get:

A = 6000(1 + 0.04/4)^(4*3)

A = 6000(1.01)^12

A = 6749.18

Therefore, the correct answer is B. $6749.18 using the compound interest formula.

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Answer:

X: 45° Y:16°

Step-by-step explanation:

by help of teacher

(5g^(2)+6g-10)-(2g^(2)+2g+9) = 3g^(2) + 4g - 19

To subtract the two polynomials, we will use the vertical form. This means that we will line up the like terms and subtract them.

Step 1: Line up the like terms in the vertical form.

5g^(2) + 6g - 10

- (2g^(2) + 2g + 9)

Step 2: Distribute the negative sign to each term in the second polynomial.

5g^(2) + 6g - 10

- 2g^(2) - 2g - 9

Step 3: Subtract the like terms.

5g^(2) - 2g^(2) = 3g^(2)

6g - 2g = 4g

-10 - 9 = -19

Step 4: Write the final answer.

3g^(2) + 4g - 19

Therefore, the answer is 3g^(2) + 4g - 19.

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Answer:

5,6 and 7.

Step-by-step explanation:

I am not sure what the three step method is, but here is how I solved it.

Consecutive integers means integers in a row.  For example, 5,6 7 are consecutive integers or -4,-3,-2 are consecutive integers.

Integers are all the whole numbers (0,1,2,3...) and their opposites (..., -3, -2, -1)  1/2 or -.23 are not integers.

Let x = the first number

Let x + 1 = the second number

Let x + 2 = the third number

x + (x + 1) + (x + 2) = 18  I do not need the parentheses, but I want you to see that  the first number, plus the second number, plus the third number equals 18.

x + x + 1 + x + 2  = 18  Combine like terms

3x + 3 = 18  Subtract 3 from both sides of the equation

3x + 3 - 3 = 18 - 3

3x = 15  Divide both sides by 3

[tex]\frac{3x}{3}[/tex] = [tex]\frac{15}{3}[/tex]

x = 5

The first number is 5.  The second number is 6 and the last number is 7.

Check:

5 + 6 + 7 = 18

18 =18 Checks.

Helping in the name of Jesus.

The equation of the tangent line of y = sqrt(3x) passing through (3, 3) is y = (1/2)x + 3/2.

To use Descartes' method of slopes, we need to find the derivative of the function first.

Taking the derivative of y = sqrt(3x) gives:

y' = (1/2) * (3x)^(-1/2) * 3 = (3/2√(3x))

Now we can find the slope of the tangent line at (3, 3) by plugging in x = 3 into the derivative:

y' = (3/2√(3*3)) = 3/6 = 1/2

So the slope of the tangent line is 1/2.

Next, we use the point-slope form of a linear equation to find the equation of the tangent line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the point (3, 3).

Plugging in the values, we get:

y - 3 = (1/2)(x - 3)

Simplifying, we get:

y = (1/2)x + 3/2

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Answer:

Step-by-step explanation:

30x453.6=13608 grams

A rectangular prism actually has three pairs of bases. Each pair of bases is a set of two opposite and parallel faces on the rectangular prism.

The first pair of bases is the two opposite and parallel rectangles on the top and bottom of the prism. The second pair of bases is the two opposite and parallel rectangles on the front and back of the prism. The third pair of bases is the two opposite and parallel rectangles on the left and right sides of the prism.

Each pair of bases is congruent, meaning they have the same shape and size. This is because a rectangular prism is a type of polyhedron with six rectangular faces, and each pair of opposite faces is parallel and congruent to each other.
In conclusion, a rectangular prism has three pairs of bases, each consisting of two opposite and parallel rectangular faces.
I hope this helps! Let me know if you have any further questions.

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The correct answer is b. 81°F.

On a certain day, the temperature of the pool rose at a constant rate from 76°F at 10 A.M. to 91°F at 1 P.M. To find the temperature at 11 A.M., we need to find the rate of change in temperature and then use it to calculate the temperature at 11 A.M.

The rate of change in temperature can be found by dividing the difference in temperature by the difference in time:

Rate of change = (91°F - 76°F) / (1 P.M. - 10 A.M.) = 15°F / 3 hours = 5°F per hour

Now, we can use this rate of change to find the temperature at 11 A.M.:

Temperature at 11 A.M. = 76°F + (5°F per hour)(1 hour) = 81°F

Therefore, the correct answer is b. 81°F.

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Answer:

218.88

Step-by-step explanation:

 x = 4/3 and y = 2/3

To solve this system of linear equations using a matrix equation, we first need to construct a matrix by writing the coefficients of the variables and the constants from the equation in a rectangular array.

The matrix for the given equations will be:

Now, we can solve the system by multiplying the inverse of the matrix of coefficients with the matrix of constants. To find the inverse of the matrix, we can use the following equation:

where |A| is the determinant of the matrix, and adj(A) is the adjoint of the matrix.

We can use this equation to find the inverse of the matrix, which is:

We can then multiply this inverse by the matrix of constants to get the solution for the system:

Therefore, the solution for the system is x = 4/3 and y = 2/3.

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The change is negative, Rachel needs to provide an additional $1.25 to pay for the sweater.

What is the basic arithmetic operations?

The four basic arithmetic operations are Addition, subtraction, multiplication, and division.

To calculate Rachel's change, we first need to determine the sale price of the sweater after the discount and then subtract it from the $10 bill.

Let's say the original price of the sweater was $30, and it was discounted by 50% to $15. Rachel's coupon gives her an additional 25% off the sale price, so she can get the sweater for 75% of the sale price.

To calculate the final price Rachel will pay, we can multiply the sale price by 0.75:

Final price = $15 * 0.75 = $11.25

Rachel pays with a $10 bill, so her change will be:

Change = $10 - $11.25 = -$1.25

Hence, the change is negative, Rachel needs to provide an additional $1.25 to pay for the sweater.

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Step-by-step explanation:

addition and subtraction:

y + z - z = y

b. multiplication and division:

When y ≠ 0:

yz / y = z

When z ≠ 0:

y / z * z = y

The value of the model expression when simplified is (d)

From the question, we have the following representation that can be used in our computation:

Using the above as a guide, we have the following:

The given expression is

3 * Black triangle + 2 * White triangle + 2 * Black square + 1 * White square

This gives

-3x + 2x - 2 + 1

Evaluate the like terms

-x - 1

This means

1 Black triangle and 1 Black square

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The area of the shaded region is 90 cm².

The space filled by the surface of an object or any flat shape can be thought of as the area in terms of geometry. The quantity of unit squares that cover an object's surface when it is closed is known as the area of the object. Inches, millimeters, square feet, and other square measurements are used to determine the area.

The area of shaded region = area of given square - area of all given triangles

Now, Area of given square = side × side

                                             = 12 × 12

                                             = 144 cm²

Similarly, Area of all triangles

             = 4 × (area of small triangle) + 4 × (area of big triangle)

             = 4 × ( 1/2 × 3× 3) + 4 × ( 1/2 × 3 × 6)

             = 18 + 36

             = 54 cm²

∴ The area of shaded region = 144 - 54

                                                = 90 cm²

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Yes

Yes, \( W \) is a subset of \( R^{2} \) since it consists of vectors of the form
\[ \mathbf{x}=\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right] \]. Therefore, for Exercises \( 1-8 \), the answer is yes.

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Statement C is true: Either quarterback could have completed more passes

What are basic attributes of a good conclusion?

Rephrase the thesis statement first, then explain what you mean and back it with information from the prompt to show what you mean. Describe how the evidence supports your claims in further detail.

We cannot determine which quarterback completed more passes based solely on their completion percentages.

For example, if Drew Brees attempted 100 passes and completed 73.5% of them, he would have completed 73.5 passes. If Patrick Mahomes attempted 200 passes and completed 68.8% of them, he would have completed 137.6 passes, which is more than Drew Brees.

On the other hand, if Drew Brees attempted 200 passes and completed 73.5% of them, he would have completed 147 passes, which is more than Patrick Mahomes' 137.6 completed passes in the above example.

Therefore, statement C is true: either quarterback could have completed more passes, depending on the number of passes attempted.

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Given:

What is the interest earned when $46,230 is invested for 9 years at 7.8% p.a?

To find:

The interest

Solution:

Answer: 20 gallons of red paint and 30 gallons blue paint

Step-by-step explanation:

The minimum of P is 16 and the maximum of P is 24.

Calculating the value of P for these points, we get:


P(2,6) = 4*2 + 2*6 = 20


P(0,8) = 4*0 + 2*8 = 16


P(4,2) = 4*4 + 2*2 = 24


P(3,3) = 4*3 + 2*3 = 18


Therefore, the minimum of P is 16 and the maximum of P is 24.

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The cost of 5 pounds of bananas in 1939 would have been $2.709.

According to the US Bureau of Labor Statistics, the cost of 1 pound of bananas is $0.63/lb. In 1939, the cost of bananas was 14% lower. Therefore, to find the cost of bananas in 1939, we need to calculate 14% of $0.63/lb and then subtract it from $0.63/lb.

Calculate 14% of $0.63/lb
0.14 * $0.63/lb = $0.0882/lb

Subtract $0.0882/lb from $0.63/lb to get the cost of bananas in 1939
$0.63/lb - $0.0882/lb = $0.5418/lb

Multiply the cost of bananas in 1939 by the number of pounds Pam buys
$0.5418/lb * 5 lb = $2.709

Therefore, the cost of 5 pounds of bananas in 1939 would have been $2.709.

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Answer:

[tex]\large\boxed{\textsf{Option B. Right Scalene Triangle.}}[/tex]

Step-by-step explanation:

[tex]\textsf{For this problem, we are asked which triangle has no equal sides and a right angle.}[/tex]

[tex]\textsf{Let's review the types of triangles, according to the options.}[/tex]

[tex]\large\underline{\textsf{What is an Isosceles Triangle?}}[/tex]

[tex]\textsf{An Isoceles Triangle is a triangle that has \underline{2 congruent sides}.}[/tex]

[tex]\textsf{Option A is incorrect.}[/tex]

[tex]\large\underline{\textsf{What is a Right Scalene Triangle?}}[/tex]

[tex]\textsf{An Isoceles Triangle is a triangle that has \underline{no congruent sides} and has \underline{1 right angle}.}[/tex]

[tex]\boxed{\textsf{Option B is correct.}}[/tex]

[tex]\large\underline{\textsf{What is a Right Isosceles Triangle?}}[/tex]

[tex]\textsf{A Right Isoceles Triangle is a triangle that has \underline{2 congruent sides}. and 1 right angle}[/tex]

[tex]\textsf{Option C is incorrect.}[/tex]

[tex]\large\underline{\textsf{What is a Right Triangle?}}[/tex]

[tex]\textsf{A Right Triangle is a triangle that has \underline{1 right angle}.}[/tex]

[tex]\textsf{We're not sure how many equal sides this triangle has as it can be none, or 2.}[/tex]

[tex]\textsf{Option D is incorrect.}[/tex]

Answer:

There are different methods to express a two logarithm into a single logarithm, depending on the specific form of the logarithms involved. Here are some examples:

Logarithms with the same base:

If you have two logarithms with the same base, you can use the following logarithmic identity:

log_a(x) + log_a(y) = log_a(xy)

Using this identity, you can express a sum or difference of logarithms with the same base as a single logarithm:

Example 1: log_2(3) + log_2(5) = log_2(3*5) = log_2(15)

Example 2: log_5(7) - log_5(2) = log_5(7/2)

Logarithms with different bases:

If you have two logarithms with different bases, you can use the following change of base formula to express them with a common base:

log_a(x) = log_b(x) / log_b(a)

Using this formula, you can rewrite a logarithm with a base a as a logarithm with a base b:

Example 1: log_2(7) = log_10(7) / log_10(2)

Example 2: log_5(2) = log_2(2) / log_2(5)

Once you have expressed both logarithms with the same base, you can apply the logarithmic identity from method 1 to simplify them into a single logarithm.

2x2 - 9xy - 1 is the expression for how much money the buddies still need to gather to reach their objective.

A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations. This mathematical procedure makes it possible to multiply, divide, add, or subtract quantities.

The total of what they have already raised towards the overall fundraising target.

The total contribution goal is given as: 7x² - 4xy + 8

The amount Martin has already collected is: 5xy + 16

The amount Tyreese has already collected is: x²

The amount Braydon has already collected is: 4x² - 7

Adding the amounts already collected:

= (5xy + 16) + x² + (4x² - 7)

= 5xy + x² + 4x² + 16 - 7

= 5xy + 5x² + 9

By deducting the total of the contributions from the overall contribution target:

= (7x² - 4xy + 8) - (5xy + 5x² + 9)

= 2x² - 9xy - 1

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Answer: A

Step-by-step explanation: i wish other people would just put the letter, but here ya go c:

Step-by-step explanation:

for % questions always find 100% and/or 1%. everything else can be calculated based on these.

100% = $115

1% = 100%/100 = 115/100 = $1.15

how many % are $21 ?

as many as times 1.15 (1%) fits into 21 :

21/1.15 = 18.26086957...% ≈ 18.26%

The temperature on mountaintop was -10° and the temperature on the ground was 10°. The solution has been obtained by using the linear equation.

What is a linear equation?

One is the degree of the linear equation. It is obvious that there are no variables in linear equations with exponents greater than 1. The graph's equation results in a straight line.

We are given that the temperature on the mountaintop was 20° lower than temperature on the ground.

Let the temperature on the ground be 'x'.

So, temperature on the mountaintop = x - 20

Also, the temperature on a mountaintop and the temperature on the ground had opposite values.

So,

x = - (x - 20)

On solving this, we get

⇒x = -x + 20

⇒2x = 20

⇒x = 10°

So, x - 20 = 10 - 20 = -10°

Hence, the temperature on mountaintop was -10° and the temperature on the ground was 10°.

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The solution to this equation 9ˣ - 1 = 2 is 1/2.

The correct option is A.

What is an equation?

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given:

An equation:

9ˣ - 1 = 2

Simplifying,

9ˣ  = 3

3²ˣ = 3

Comparing, we get,

2x = 1

x = 1/2

Therefore, the solution is x = 1/2.

The answer are LCD (least common denominator) of the set of fractions (7)/(20) and (9)/(40) is 40.

Here is a step-by-step explanation on how to find the LCD:

1. Find the multiples of each denominator.

- Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200...

- Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400...

2. Compare the multiples of each denominator and find the smallest number that appears in both lists.

- The smallest number that appears in both lists is 40.

3. The smallest number that appears in both lists is the LCD.

- Therefore, the LCD of the set of fractions (7)/(20) and (9)/(40) is 40.

So the answer to the question "Find the LCD (least common denominator) of the set of fractions. Do not combine the fractions; only find the LCD. (7)/(20) and (9)/(40)" is 40.

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