3s + a = 38 and 3s + 2a =52

Answer: Circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle and π is a constant.

We know that the diameter is twice the radius (d = 2r).

So when we increase the circumference of the circle from 12π cm to 18π cm, we are increasing the radius from r to r'.

To find the increase in diameter, we can use the formula for the diameter, and subtract the original diameter from the new diameter.

d' = 2r' and d = 2r

d' - d = 2r' - 2r

We know that the relationship between circumference and radius is C = 2πr.

So we can write:

12π = 2πr and 18π = 2πr'

r = 6/π and r' = 9/π

then

d' - d = 2r' - 2r = 2(9/π) - 2(6/π) = 18/π - 12/π = 6/π

Therefore, the diameter must increase by 6/π cm in order to increase the circumference of the circle from 12π cm to 18π cm.

Step-by-step explanation:

Answer:

The answer is 3x-11

Step-by-step explanation:

x+x+x-11 = 3x-11. I'm assuming the answer is an algebraic equation.

The missing number of all the ratios are given  below.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

The ratios are given.

1. 1:2=4:N

2: 3:8=N:16

3.15:20=30:N

4.N:25=2:5

5.10:N=40:80

p:q can be written as p/q.

To find the missing number:

1. 1:2=4:N

1/2 = 4/N

So, N = 8

2: 3:8=N:16

So, N = 6

3.15:20=30:N

So, N = 40

4.N:25=2:5

So, N = 10

5.10:N=40:80

N = 20

Therefore, all the missing numbers are given above.

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El número de este problema es 72, y la suma de sus cifras da 9.

En este problema tenemos un numero de dos cifras, que podemos escribir como:

a*10 + b

Donde a y b son numeros enteros entre 0 y 9, y son las cifras de nuestro número.

Sabemos que si a este número le aumentamos 3 veces la cifra de decenas, resulta en 93, entonces podemos escribir:

a*10 + b + 3*a = 93

a*13 + b = 93

Ok, ahora simplemente devemos reemplazar los valores de b por numeros enteros y resolver la ecuación para a, asi hasta que el resultado de a tambien de un numero entero.

si b = 5

a*13 + 5 = 93

a*13 = 93 - 5

a*13 = 88

a = 88/13 = 6.7

No es una solucion.

si b = 2

a*13 + 2= 93

a*13 = 93 - 2

a*13 = 91

a = 91/13

a = 7

Esta es la solución.

Las cifras son a = 7 y b = 2, y su suma da:

7 + 2 = 9

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The coordinates of the remaining vertices exists (2√(13),1) and (-2, 4√(13)).

A group of values that exhibit precise positioning The first number on a graph represents the distance along, while the second number represents the distance up or down.

To find the coordinates of the remaining vertices of square ABCD, we can use the information given about diagonal AC and the properties of a square. Since a square has equal side lengths and right angles, we know that the distance between opposite vertices on a diagonal must be equal to the side length of the square.

Given the coordinates of vertex A and C, we can use the distance formula to find the length of AC :

Let the equation be Distance [tex]$d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$[/tex] substitute the values in the above equation, we get

[tex]$\mathrm{AC}=\sqrt{\left((2-(-2))^2+(4-1)^2\right)}$$[/tex]

simplifying the equation, we get

[tex]$A C=\sqrt{ }(4+9)=\sqrt{ }(13)$$[/tex]

We can utilize the knowledge of the square's side length to determine the locations of the remaining vertices. Vertex B is known to have the same y-coordinate as vertex A, while vertex C is two units to the left in terms of the x-coordinate. Therefore, the coordinates of vertex B exists (-2 + 2√(13), 1).

Similar to vertex A, vertex D is known to have an identical x-coordinate, but its y-coordinate is four units below vertex C. Therefore, the coordinates of vertex D exists (-2, 4√(13))

Therefore, the coordinates of the remaining vertices exists (2√(13),1) and (-2, 4√(13)) respectively.

The complete question is:

Square ABCD has a diagonal AC with vertices A(-2, 1) and C(2, 4). Find the coordinates of the remaining vertices. Express your answers as decimals, if necessary.

The coordinates are and D.

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The largest snack Sasha can make while still using the correct ratio of ingredients is 555g.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that after school Sasha likes to make snacks by mixing raisins and nuts in a ratio of 3:5 when she checked the cupboard today there were only 60g of raisins and 75g of nuts left.

The largest snack Sasha can make while still using the correct ratio of ingredients is calculated as,

E = ( 60 x 3 + 75 x 5 )

E = 180 + 375

E = 555 g

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The solution of the given differential initial value problem is

y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).

Given is the initial value problem -

y''' + 10y'' + 25y' = 0

We can write the -

[tex]$25 \frac{d}{d x} y{\left(x \right)} + 10 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 0$[/tex]

The given differential equation can be solved and written as -

y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6)

Therefore, the solution of the given differential initial value problem is

y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).

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Answer:

f(-4) = -36

Step-by-step explanation:

Step-by-step explanation:

A function assigns the value of each element of one set to the other specific element of another set. The value of the function when the value of x is -4 is 92.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

Given that F(x)=3x²-10x+4, therefore, the value of the function can be calculated by substituting the value of x as -4.

Therefore, the value of the function when the value of x is -4  can be calculated as shown below,

F(x) = 3x² - 10x + 4

F(-4) = 3(-4)² - 10(-4) + 4

= 3(16)  + 40 + 4

= 48 + 40 + 4

= 92

Hence, the value of the function when the value of x is -4 is 92.

Answer:

30

Step-by-step explanation: 30-60-90 theorem

Answer:

biquadratic polynomial

Step-by-step explanation:

The given polynomial is
[tex]-10x^4 - 7\\\\[/tex]

The degree of this polynomial (the highest power) is 4

Such a polynomial is called a quartic polynomial. If all the terms have even degree, which in this case is true since there is only one term and its degree is 4 it is called a biquadratic polynomial

If polynomial has degree 1 ex 4x + 3 it is called a linear polynomial

If it has degree 2 --> quadratic

If it has degree 3 --> cubic

i do not know the answer either

Answer:

below

Step-by-step explanation:

The INdependent variable is 'r'

  'C'  DEPENDS on the value of 'r'...it is the dependent variable

Answer: To find the coordinates of the remaining vertices of square ABCD, we can use the information we have been given about the diagonal AC and its vertices. The diagonal AC has been given as having the vertices A(-4, -1) and C(2, 5). Since a square has right angles, we know that the other two vertices of the square must form a right angle with the diagonal AC.

To find the coordinates of vertex B, we know that it must have the same y-coordinate as vertex A, but a different x-coordinate. Since the x-coordinate of vertex A is -4, we can deduce that the x-coordinate of vertex B must be the same as the x-coordinate of vertex C, which is 2. Therefore, the coordinates of vertex B are (2, -1).

To find the coordinates of vertex D, we know that it must have the same x-coordinate as vertex A, but a different y-coordinate. Since the y-coordinate of vertex A is -1, we can deduce that the y-coordinate of vertex D must be the same as the y-coordinate of vertex C, which is 5. Therefore, the coordinates of vertex D are (-4, 5).

In summary, the coordinates of the remaining vertices of square ABCD are B(2, -1) and D(-4, 5)

Step-by-step explanation:

Gradient-based optimization: This method is commonly used for more complex models, such as deep neural networks. The goal is to find the set of model parameters that minimizes a loss function.

Generally, There are a variety of ways to estimate mathematical models, depending on the type of model and the available data. Some common methods include:

Least squares: This method is commonly used for linear regression models, where the goal is to find the line of best fit through a set of data points. The least squares method finds the line that minimizes the sum of the squared differences between the predicted values and the actual values.

Maximum likelihood: This method is commonly used for probabilistic models, such as those used in statistics and machine learning. The goal is to find the set of model parameters that maximizes the likelihood of the observed data.

Bayesian inference: This method is similar to maximum likelihood, but it also incorporates prior knowledge or beliefs about the model parameters into the estimation process. This can be done by specifying a prior distribution over the parameters, which is then updated based on the observed data to give a posterior distribution.

These are just a few examples, and there are many other methods available depending on the type of model and the data available.

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Answer:

5,3,3-1 the box are illustrate the the number of the triangle

Answer:

b) The bond Sandy purchased has a face value of $2500 and a coupon rate of 7%. The coupon rate is the interest rate paid on the bond, which is typically paid semiannually. To find how much interest Sandy will receive semiannually, we can use the formula:

Interest = Face value x Coupon rate / 2

Interest = $2500 x 7% / 2 = $87.50

So Sandy will receive $87.50 in interest semiannually from the bond.

c) The fund Sandy invested in is expected to grow by 3.5% per year. To find how long it will take for the fund to be worth $10,000, we can use the formula:

Future value = Present value x (1 + Interest rate)^Years

We can solve for Years by dividing both sides of the equation by the present value and taking the natural logarithm of both sides:

Years = ln(Future value/Present value) / ln(1 + Interest rate)

Years = ln(10000/5000) / ln(1.035)

Years = 7.19

Therefore, the fund will take about 7.19 years to be worth $10,000.

d) Sandy's gross annual income is $51,350. She is paid biweekly, and 5% of her paycheck is deducted for her 403(b). Her employer matches her deduction, up to 4%. To find how much is deposited into Sandy's 403(b) each payday, we can use the following formula:

Contribution = (Gross pay x Contribution rate) + (Employer match x Employee contribution)

Gross pay = $51,350/26 (for bi-weekly paycheck) = $1977.50

Contribution = ($1977.50 x 5%) + ($1977.50 x 5% x 4%) = $98.87

So, $98.87 is deposited into Sandy's 403(b) each payday.

Answer: What is the question ?

Step-by-step explanation:

Answer: 2 7/8 hours per week

hectors rate is greater

Step-by-step explanation:

The rule for the exponential function is y=42(1/2)^x

A exponential decay is a function that, as the name implies, decays exponentially. So it decays fast at the beginning and slower as the value of the variable increases.

Here,

general form of exponential function is y=a(b)^x

a= y-intercept ,  b = multiplier

The initial y value 42 is multiplied by 1/2, we get next y value 21 as given in the graph, So, b = 1/2

y=a(1/2)^x

consider (x,y)=( 0,42)

=> x=0 and y=42

So 42=a(1/2)^0

=> 42=a

Thus, the rule for the function is y=42(1/2)^x

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Answer:

k=

v

2

4v

2

−4v−9

Step-by-step explanation:

Evaluate

(k−4)×v

2

+4v+9=0

Simplify

kv

2

−4v

2

+4v+9=0

Rewrite the expression

v

2

k−4v

2

+4v+9=0

Move the expression to the right side

v

2

k=0−(−4v

2

+4v+9)

Subtract the terms

v

2

k=4v

2

−4v−9

Multiply both sides

v

2

k×

v

2

1

​

=(4v

2

−4v−9)×

v

2

1

​

Simplify

v

2

k×

v

2

1

​

=

v

2

4v

2

−4v−9

​

Solution

k=

v

2

4v

2

−4v−9

​

Answer: 3

Step-by-step explanation:

The vertical distance between the sinusoidal axis and the maximum or minimum value of the function.

Trust

The expression which shows how many grams of raisins are in the bowl will be

(0.01x) * 150 + (0.01y) * 250

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

The expression which shows how many grams of raisins are in the bowl will be:

= (x% × 150) + (y% × 250)

= (0.01x) * 150 + (0.01y) * 250

This equation represents the total grams of raisins in the bowl by multiplying the weight of the Oreana's bag by the percentage of raisins in it, and adding that to the product of the weight of Brandon's bag and the percentage of raisins in it. The "0.01" is used to convert the percentages from x and y to decimal form.

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The profit for Mr Christopher is #1000.

Profit is the money that is earned in trade or business after paying the costs of producing and selling goods and services.

Given that, Mr. Christopher contributed #500 to a business, Miss Uche contributed #300 while Mrs. Amaka contributed #200, they share a profit #2000,

Let the ratio of their contribution = 5x : 3x : 2x

Therefore,

5x + 3x + 2x = 2000

10x = 2000

x = 200

Their profit share =

Mr. Christopher = 200 x 5 = 1000,

Miss Uche = 200 x 2 = 200

and

Mrs. Amaka = 200 x 3 = 600

Hence, the profit share of Mr. Christopher is #1000,

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Answer:

3x

Step-by-step explanation:

To answer this question, we have to understand what a product is. A product is the result of multiplication. For example, the product of 5 and 5 is 25 because 5 × 5 = 25.

We can apply this concept to the given expression.

"the product of 3 and a number"

means:

3 × "a number"

And since the problem specifies that "a number" is represented by the variable x, we can replace it with that.

3 × x

This looks a bit confusing with the x-like multiplication sign, so we can remove that and make 3 a coefficient of x.

3x

Answer:

3*x

Step-by-step explanation:

We can break down the problem piece by piece. We have "the product". The product of what? The product of 3 and a number. The problem tells us to replace a number with x. So it is 3*x.

The sum of the two matrices will be [tex]A+B = \left[\begin{array}{ccc}-1&-13&7\\5&-14&0\\7&1&4\end{array}\right][/tex]. The correct option is A.

A matrix, which is used to represent a mathematical object or an attribute of one, is a rectangular array or table containing numbers, symbols, or expressions that are organized in rows and columns.

The given matrices are:-

[tex]A = \left[\begin{array}{ccc}7&-6&2\\6&-5&-7\\2&-8&8\end{array}\right][/tex]

[tex]B = \left[\begin{array}{ccc}-8&-7&5\\-1&-9&7\\-5&9&-4\end{array}\right][/tex]

The sum of the matrix will be:-

[tex]A+B = \left[\begin{array}{ccc}(7-8)&(-6-7)&(2+5)\\(6-1)&(-5-9)&(-7+7)\\(2+5)&(-8+9)&(8-4)\end{array}\right][/tex]

[tex]A+B = \left[\begin{array}{ccc}-1&-13&7\\5&-14&0\\7&1&4\end{array}\right][/tex].

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The given expression is equivalent to (3y/x)(1 + 2x²y).

Given is that Luis, María and Ricky presented an essay about their respective ages. Ricky is 3 years older than Luis. Luis's age is 23 years and the sum of the ages of the three is 77 years.

Assume the age of Maria is {x} years old. So, we can write that -

Ricky's age = 23 + 3 = 26

And -

x + 26 + 23 = 77

x + 49 = 77

x = 77 - 49

x = 28

Therefore, the age of Maria is 28 years old.

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{Question in english -

Luis, María and Ricky presented an essay about their respective ages. Ricky is 3 years older than Luis. If Luis's age is 23 years and the sum of the ages of the three is 77 years, how old is Maria?}

Answer: The value of x is 0 and y is -5 using the elimination method.

Step-by-step explanation: To use the elimination method, we will remove one variable and find the value of the other one. Rewriting the equation -

-2y + 5x = 10 : equation 1

-3y + 4x = 15 : equation 2

Multiplying equation 1 with 4 and equation 2 with 5

-8y + 20x = 40 : equation 3

-15y + 20x = 75 : equation 4

Subtracting equation 3 from equation 4 to eliminate variable y

-7y = 35

y = - 35/7

y = -5

Keep the value of y in Equation 1 to find the value of x

-2(-5) + 5x = 10

10 + 5x = 10

5x = 10 - 10 5x = 0

x = 0

So, the value of x is 0 and y is -5.

Answer:5=y

Step-by-step explanation:

10 − 5x=−2y

15 − 4x =−3y

• (10 − 5x=−2y)4

         (40 - 20x=−8y)

          15 − 4x =−3y

         (15 − 4x =−3y)5

         (75 - 20x=−15y)

• (75 - 20x=−15y)

• (40 - 20x=−8y)

•  35 =-7y

• 35/7=y

• 5=y

The speed of the boat against the current is (13+x)mph and with the current is (13-x) mph.

If boat goes along the stream flow (downstream), then the speed of boat will be increased as stream will help boat go faster. In contrast, the upstream flow of boat will be slower than its speed in normal flow due to stream resistance.

Speed of boat with the current = Speed of boat + Speed of current

Speed of boat against the current = Speed of boat - Speed of current

Given that the speed of a boat in still water is 13 mph. Also, the speed of the water current is x mph. Therefore, the speeds in the given cases can be written as,

a.) The of speed going against a current with a rate of x mph can be written as,

Speed of boat with against the water current

= Speed of Boat - Speed of water current

= 13 mph - x mph

= (13-x) mph

b.) The of speed going with a current with a rate of x mph can be written as,

Speed of boat with the water current

= Speed of Boat + Speed of water current

= 13 mph + x mph

= (13+x) mph

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Answer:

The appropriate notation to represent the inequality x < 4 is O (-∞, 4)

Step-by-step explanation:

This notation states that x can be any value less than 4.

The other options are:

(-∞0, 4]: This notation states that x can be any value between negative infinity and 4, including 4.

[-∞, 4]: This notation states that x can be any value between negative infinity and 4, including negative infinity and 4.

(-00, 4): This notation is not a valid notation.

(4,00): This notation states that x can be any value greater than 4.

Answer:

To verify that [n+3]! / n! = (n+1), we can use the definition of factorial:

[n+3]! = (n+3) * (n+2) * (n+1) * n!

And we can cancel out n! from both sides of the equation:

(n+3) * (n+2) * (n+1) = n+1

Which is true, and thus [n+3]! / n! = (n+1) holds true.

Another way to verify this is by simplifying the RHS and LHS

(n+1) = (n+1)

And the LHS,

(n+3)! = (n+3)(n+2)(n+1)n! = (n+1)(n+2)(n+3)n! = (n+1)(n+2)(n+3)!/n!

which is also equal to (n+1)

So, [n+3]! / n! = (n+1) is true.

Answer:

12% increase

Step-by-step explanation:

First, find the difference between 18.48 and 16.50:

18.48 - 16.50 = 1.98

Now, what percent of 16.50 is 1.98?:

1.98 / 16.50 = 0.12

0.12 * 100% =   ==> 100% = 1. Anything multiplied by 1 is itself ( 1 * 3 = 3 )

0.12 * 100% = 12%

Hence, $16.50 to $18.48 is an increase of $1.98 or 12%.

Answer:

12% increase

Step-by-step explanation:

(V2−V1)|V1|×100

=(18.48−16.5)|16.5|×100

=1.9816.5×100

=0.12×100

=12%change

=12%increase