Clare has some blocks. Jasmine
has 6 blocks. Together, they
have 14 blocks. How many
blocks does Clare have?
blocks

a) To re-express the given differential equation as a first-order differential equation using matrix and vector notation, we can rewrite it in the form:

\(x' = Ax\)

where x is a vector and A is a square matrix.

b) To determine the stability of the system obtained in part (a), we need to analyze the eigenvalues of matrix A.

If all eigenvalues have negative real parts, the system is stable.

If at least one eigenvalue has a zero real part, the system is neutrally stable.

If at least one eigenvalue has a positive real part, the system is unstable.

c) To compute the eigenvalues and eigenvectors of matrix A, we solve the characteristic equation

\(det(A - \lambda I) = 0\),

where λ is the eigenvalue and I is the identity matrix.

By solving this equation, we obtain the eigenvalues.

Substituting each eigenvalue into the equation

\((A - \lambda I)v = 0\),

where v is the eigenvector, we can solve for the eigenvectors.

d) Once we have computed the eigenvalues and eigenvectors of matrix A, we can construct the diagonalization relationship as follows:

\(A = PDP^{(-1)}\)

where P is a matrix whose columns are the eigenvectors of A, and D is a diagonal matrix whose diagonal elements are the eigenvalues of A.

To show that this relationship is valid, we can compute \(PDP^{(-1)}\) and verify that it equals A.

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Answer:

x= 3

    2

Step-by-step explanation:

Answer:

Now that you have x² - 8x + 16 = 9 + 16, apply the square root property to the equation.

✔ (x – 4)² = 25

Step-by-step explanation:

Refer to the attachment

After answering the presented questiοn, we can cοnclude that The fοrmula tο find the area and perimeter οf a twο-dimensiοnal shape depends οn the type οf shape

An equatiοn in mathematics is a statement that states the equality οf twο expressiοns. An equatiοn is made up οf twο sides that are separated by an algebraic equatiοn (=). Fοr example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpοse οf equatiοn sοlving is tο determine the value οr values οf the variable(s) that will allοw the equatiοn tο be true.

The fοrmula tο find the area and perimeter οf a twο-dimensiοnal shape depends οn the type οf shape. Here are sοme cοmmοn fοrmulas:

1. Rectangle:

• Area: A = length x width

• Perimeter: P = 2(length + width)

2. Square:

• Area: A = side x side (οr A = side²)

• Perimeter: P = 4 x side

3. Circle:

• Area: A = π x radius²

• Circumference (perimeter): C = 2π x radius (οr C = π x diameter)

4. Triangle:

• Area: A = (base x height) / 2

• Perimeter: P = side1 + side2 + side3

5. Trapezοid:

• Area: A = ((base1 + base2) x height) / 2

• Perimeter: P = side1 + side2 + side3 + side4

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\(~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$8.75\\ P=\textit{original amount deposited}\dotfill & \$1000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &\frac{1}{4} \end{cases} \\\\\\ 8.75 = (1000)(\frac{r}{100})(\frac{1}{4})\implies 8.75=\cfrac{10r}{4} \\\\\\ 8.75=\cfrac{5r}{2}\implies 17.5=5r\implies \cfrac{17.5}{5}=r\implies \stackrel{\%}{3.5}=r\)

The only true f(x) is

when x=5 and y = -1

B is the correct option

Note that the vertical line is the y-axis while x - axis is the horizontal line

Answer:

956= 9/56

125= 1/25

Step-by-step explanation:

Answer:

x is 70°

hopefully this will help u

Using the substitution method equation form is x is 3 and y is1

Form of Point: (3 , 1 )

Equation Form: x = 3 and y =1

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Answer:

ok what is it

Step-by-step explanation:

Answer:

ok...ask the questions

Step-by-step explanation:

The solution for x, y, and z is x = 2, y = 2, and z = 2.

To solve the equation (35)"4(23)"5(25)"7 = 2"x3"y*5"z, let's break it down step by step:

Simplify the expressions within the parentheses using the power of operator ("^").

\((35)"4 = 15^4\\(23)"5 = 6^5\\(2\times5)"7 = 10^7\)

Apply the power rule of exponents, which states that \((a^b)^c = a^{(b\times c).\)

\(15^4 \times 6^5 \times 10^7 = (15610)^{(4+5+7)\)

Simplify the expression within the parentheses.

\((15610)^{16 }= 900^{16\)

Express both sides of the equation in terms of prime factors.

\(900 = 2^2 \times 3^2 \times 5^2\)

quate the powers of the prime factors on both sides of the equation.

\(2^2 \times 3^2 \times 5^2 = 2"x \times 3"y \times 5"z\)

From this, we can conclude that x = 2, y = 2, and z = 2.

Therefore, the solution for x, y, and z is x = 2, y = 2, and z = 2.

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Answer:

y=-6x-60

Step-by-step explanation:

You want to find the equation for a line that passes through the point (-9,-6) and has a slope of -6.

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

To start, you know what m is; it's just the slope, which you said was -6. So you can right away fill in the equation for a line somewhat to read:

y=-6x+b.

Now, what about b, the y-intercept?

To find b, think about what your (x,y) point means:

(-9,-6). When x of the line is -9, y of the line must be -6.

Because you said the line passes through this point, right?

Now, look at our line's equation so far: . b is what we want, the -6 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the the point (-9,-6).

So, why not plug in for x the number -9 and for y the number -6? This will allow us to solve for b for the particular line that passes through the point you gave!.

(-9,-6). y=mx+b or -6=-6 × -9+b, or solving for b: b=-6-(-6)(-9). b=-60.

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:

Three

Step-by-step explanation:

Assuming the grade score from 70 to 100 is A; for grade score from 60 to 69 is B and grade score from 50 to 59 is C. Well it is certain there are three peaks in the distribution of scores

Part A: Grocery Store: unit price = $1.65 (Tomatoes)

Farmer's Market: unit price  = $1.75

Part B: Grocery Store offers a better deal because the unit price is less.

Unit price is defined as the price for one of something. For example, if 10 oranges cost $50, the unit price will be $50/10 = $5 i.e.  $5 for one orange.

PART A:

Let's choose tomatoes

Grocery Store

8 tomatoes for $13.20

Unit price = $13.20/8 = $1.65

10 tomatoes for $17.50

Unit price = $17.50/10 = $1.75

Part B:

The location that offers a better deal is Grocery Store. This is because the unit price is less.

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Answer:

Problem 3: 51°

Problem 5: 5 feet

Step-by-step explanation:

Image 1:

We are asked to find the missing angle. First off, we know that the full semi-circle equals 180 degrees. knowing this, subtract the second angle from 180 to get the smaller angle.

180 - 129 = 51

The unkown angle is 51 degrees.

Image 2:

We are asked to find the missing side. Apply the numbers of the known sides to the Pythagorean Theorem.

a² + b² = c²

a² + 12² = 13²

a² + 144 = 169

a² = 25

a = 5

The missing side is 5 feet.

Answer:

C (20,5)

Step-by-step explanation:

The committees should contain 5 persons each

The number of people are 20

Apply combination concept

where

²⁰₅C =  20! /[ {20-5}!*5! ]

=20! / 15!*5!

=15504  ------The number of 5 person committees that could be formed from a group of 20 people.

Step-by-step explanation:

31 + 6x + x + 16 = 180

7x + 47 = 180

7x = 180 - 47

x = 133/7

x = 19

The ordered pair solutions for the system of equations are (-1, 0) and (2, 3).

To find the ordered pair solutions for the system of equations, we need to solve the equations simultaneously by setting them equal to each other:

y = x^2 + 1 ........(1)

y = x + 1 ........(2)

Since both equations are set equal to y, we can set them equal to each other:

x^2 + 1 = x + 1

Rearranging the equation, we get:

x^2 - x = 0

Factoring out x, we have:

x(x - 1) = 0

This equation is satisfied when either x = 0 or x - 1 = 0.

For x = 0, substituting back into equation (2), we find:

y = 0 + 1

y = 1

Therefore, one solution is (0, 1).

For x - 1 = 0, we have x = 1. Substituting this back into equation (2), we find:

y = 1 + 1

y =2

Therefore, another solution is (1, 2).

Hence, the ordered pair solutions for the system of equations are (-1, 0) and (2, 3).

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Answer:

369

Step-by-step explanation:

One nickel = 0.05

0.05x=18.45

x=369

Answer:

That is true but still remember that playing the knight at the start can be very useful.

Answer:

600

Step-by-step explanation:

Answer:

The value increases

Step-by-step explanation:

the smaller the divisor, the larger the quotient.

Answer:

you have the highest chance of getting peanuts

Answer:

Given:

Area of the sector (A) = 104π/9 square inches

Central angle (θ) = 65 degrees

The formula for the area of a sector of a circle is:

A = (θ/360) * π * r^2

We can rearrange this formula to solve for the radius (r):

r^2 = (A * 360) / (θ * π)

Plugging in the given values:

r^2 = (104π/9 * 360) / (65 * π)

r^2 = (104 * 40) / 9

r^2 = 4160 / 9

r^2 ≈ 462.22

Taking the square root of both sides:

r ≈ √462.22

r ≈ 21.49

Therefore, the radius of the circle is approximately 21.49 inches.

Answer: 8 inches

Step-by-step explanation:

Answer:

5 > \(\sqrt{18\)

Step-by-step explanation:

The square root of 18 is approximately 4.24.

5 is greater than 4.24, so we can use the inequality sign >.

The base case in a recursive solution to the problem of finding the factorial of a number is n = 0 .

Given :

the base case in a recursive solution to the problem of finding the factorial of a number. recall that the factorial of a non-negative whole number is defined as n! .

Base case :

The base case is the condition to stop the recursion. The recursive case is the part where the function calls on itself .

we know that ,

def func ( n ) :

     if   n == 0 :

return 1

Here the base case is clearly n = 0

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When 'x' is 5, the Algebraic  expression 3x - 4 evaluates to 11.

To find the algebraic expression for "4 less than the product of 3 and some number," let's break it down step by step.

First, let's define the unknown number as 'x.' Since the problem states "the product of 3 and some number," we can express this as 3 * x or simply 3x.

Next, we want to subtract 4 from this product. The phrase "4 less than" indicates subtraction, so we subtract 4 from 3x. This can be represented as 3x - 4.

In summary, the algebraic expression for "4 less than the product of 3 and some number" is 3x - 4, where 'x' represents the unknown number.

To calculate the value of this expression for a specific value of 'x,' you substitute that value into the expression and simplify. For example, if 'x' is 5, you would substitute 5 into the expression:

3(5) - 4

This simplifies to:

15 - 4 = 11

So, when 'x' is 5, the expression 3x - 4 evaluates to 11.

In general, the algebraic expression allows us to represent a mathematical relationship between quantities using symbols and operations. By substituting specific values into the expression, we can calculate the corresponding results.

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Note the complete question:

Algebraic expression for 4 less than the product of 3 and some number

What is the algebraic expression for "4 less than the product of 3 and some number?

Please help me understand the meaning of how to calculate.

Answer:

m<wzx = 71

Step-by-step explanation:

Assuming these are interior angles of a triangle.

The sum of all three interior angles of a triangle is always 180 degrees, therefore:

m<xyz + m<wxz + m<wzx = 180

Substitute our values:

58 + 51 + m<wzx = 180

m<wzx = 180 - 58 - 51

m<wzx = 71