Express2a powered −5 with a positive exponent.

Answer:

О  B. Standard deviation.

Step-by-step explanation:

Standard deviation measures the dispersion of a data distribution (variability in scores).

...

The general solution in both vector and scalar form is as follows:

Vector form:

\(\[\mathbf{x} = c_1\mathbf{v}_1e^{\lambda_1t} + c_2\mathbf{v}_2e^{\lambda_2t}\]\)

Scalar form:

\(\[\begin{aligned}x &= c_1v_{11}e^{\lambda_1t} + c_2v_{21}e^{\lambda_2t} \\y &= c_1v_{12}e^{\lambda_1t} + c_2v_{22}e^{\lambda_2t}\end{aligned}\]\)

What are eigenvalues?

Eigenvalues are a concept in linear algebra that are used to analyze the properties of linear transformations or matrices. In simple terms, eigenvalues represent the scaling factors by which a vector is stretched or compressed when it is transformed by a linear transformation or multiplied by a matrix.

To find the general solution for the given system of differential equations:

\(\[\begin{aligned}x' &= -6x + 5y \\y' &= -5x - 4y\end{aligned}\]\)

We can rewrite the system in matrix form as follows:

\(\[\mathbf{x'} = \begin{bmatrix} -6 & 5 \\ -5 & -4 \end{bmatrix} \mathbf{x}\]\)

where \($\mathbf{x} = \begin{bmatrix} x \\ y \end{bmatrix}$.\)

To find the general solution, we need to find the eigenvalues and eigenvectors of the coefficient matrix\($\begin{bmatrix} -6 & 5 \\ -5 & -4 \end{bmatrix}$.\)

The characteristic equation is given by:

\(\[\det(\mathbf{A} - \lambda \mathbf{I}) = 0\]\)

where \($\mathbf{A}$\) is the coefficient matrix,\($\lambda$\)is the eigenvalue, and \($\mathbf{I}$\)is the identity matrix.

Substituting the values, we have:

\(\[\begin{aligned}\det \begin{pmatrix} -6-\lambda & 5 \\ -5 & -4-\lambda \end{pmatrix} &= 0 \\(-6-\lambda)(-4-\lambda) - (5)(-5) &= 0 \\\lambda^2 + 10\lambda + 6 &= 0\end{aligned}\]\)

Solving this quadratic equation, we find the eigenvalues \(\lambda_1$ and $\lambda_2$.\left \{ {{y=2} \atop {x=2}} \right.\)

Once we have the eigenvalues, we can find the corresponding eigenvectors\($\mathbf{v}_1$ and $\mathbf{v}_2$\) by solving the equation:

\(\[(\mathbf{A}-\lambda\mathbf{I})\mathbf{v} = 0\]\)

Substituting the eigenvalues, we solve for the eigenvectors.

Let's denote the eigenvalues as \(\lambda_1$ and $\lambda_2$,\) and the corresponding eigenvectors as \(\mathbf{v}_1$ and $\mathbf{v}_2$.\)

Once we have the eigenvalues and eigenvectors, we can express the general solution in both vector and scalar form as follows:

Vector form:

\(\[\mathbf{x} = c_1\mathbf{v}_1e^{\lambda_1t} + c_2\mathbf{v}_2e^{\lambda_2t}\]\)

Scalar form:

\(\[\begin{aligned}x &= c_1v_{11}e^{\lambda_1t} + c_2v_{21}e^{\lambda_2t} \\y &= c_1v_{12}e^{\lambda_1t} + c_2v_{22}e^{\lambda_2t}\end{aligned}\]\)

wherec_1 andc_2 are arbitrary constants\(, $v_{ij}$\) that represent the \(i$-th\)component of the jth eigenvector and \($e^{\lambda_it}$\) represent the exponential term with the eigenvalue.

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The dimensions of the rectangle are 7 feet by 9 feet.

Let's use algebra to solve this problem.

Let x be the width of the rectangle in feet. Then, according to the problem, the length of the rectangle is 2 feet longer than the width, or x + 2 feet.

The area of a rectangle is given by the formula\(A = length x width.\) So, we can write:

A = (x + 2) x x

Simplifying this expression, we get:

A = x^2 + 2x

We know from the problem that the area of the rectangle is 63 square feet. So, we can substitute this value for A and solve for x:

63 = x^2 + 2x

Rewriting this equation in standard form:

x^2 + 2x - 63 = 0

Now, we can use the quadratic formula to solve for x:

x = (-2 ± sqrt(2^2 - 4(1)(-63))) / (2(1))

x = (-2 ± sqrt(4 + 252)) / 2

x = (-2 ± sqrt(256)) / 2

x = (-2 ± 16) / 2

x = -9 or x = 7

Since the width of the rectangle cannot be negative, we reject the solution x = -9. Therefore, the width of the rectangle is 7 feet.

The length of the rectangle is 2 feet longer than the width, or x + 2 = 7 + 2 = 9 feet.

So, the dimensions of the rectangle are 7 feet by 9 feet.

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Answer:

64,339 = π(r^2)(20)

r^2 = 1,023.987

r = 32 ft

The new term-to-term rule is to subtract 13 and then divide it by 6.

What is a sequence?

A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. It has members, just like a set does. The length of the sequence is determined by the number of items.

Given term-to-term rule multiply by 6 and then add 13.

Assume the three terms of the sequence are

a₁, a₂, a₃.

a₂ =( a₁ × 6)+ 13

a₂ = 6a₁ + 13....(i)

Again,

a₃ =( a₂ × 6)+ 13

a₃ = 6a₂ + 13 .....(ii)

If the sequence reverse, then the terms are a₃, a₂, a₁

calculating the value of a₂ in term of a₃:

a₃ = 6a₂ + 13

a₃ - 13 = 6a₂

a₂ = (a₃ - 13)/6

calculating the value of  a₁  in term of a₂:

a₂ = 6a₁ + 13

a₂ - 13 = 6a₁

a₁ = (a₂ - 13)/6

The general rule is \(T_n = \frac{T_{n-1}-13}{6}\).

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Answer:

10:24

Step-by-step explanation:

if school starts at 7:15 and you stay in the first 4 periods for 47 minutes each, that totals 3 hours, 8 minutes

7:16 + 3 hrs, 8 min = 10:24

However, we need to substitute a with s since that is the value we have calculated. Therefore, we get \(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

Let's consider that s be the length of a side of the regular pentagon.

The perimeter of the regular pentagon will be 5s. Therefore, we have the equation:5s = 140s = 28 cm

Also,

we have the formula for the area of a regular pentagon as:

\($A=\frac{1}{4}(5 +\sqrt{5})a^{2}$,\)

where a is the length of a side of the pentagon.

In order to represent the area of a regular pentagon whose perimeter is 140 cm, we need to substitute a with s, which we have already calculated.

Therefore, we have:\(A(s) = $\frac{1}{{4}(5 +\sqrt{5})s^{2}}$\)

Now, we have successfully used function notation (with the appropriate functions above) to represent the area of a regular pentagon whose perimeter is 140 cm.

The area of a regular pentagon can be represented using function notation (with the appropriate functions above). The first step is to calculate the length of a side of the regular pentagon by dividing the perimeter by 5, since there are 5 sides in a pentagon.

In this case, we are given that the perimeter is 140 cm, so we get 5s = 140, which simplifies to s = 28 cm. We can now use the formula for the area of a regular pentagon, which is\(A = (1/4)(5 + sqrt(5))a^2\), where a is the length of a side of the pentagon.

However, we need to substitute a with s since that is the value we have calculated. Therefore, we get\(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

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To combine like terms in the expression 2.5x + (-5x) - 2.5, we need to add or subtract the coefficients of the terms with the same variable.

In this case, we have two terms with the variable "x": 2.5x and -5x. The coefficients of these terms are 2.5 and -5, respectively.

Combining the like terms, we get:

2.5x + (-5x) - 2.5

Since (-5x) is equivalent to subtracting 5x, we can rewrite the expression as:

2.5x - 5x - 2.5

To simplify this further, we can subtract the coefficients:

(2.5 - 5)x - 2.5

Simplifying the coefficients, we have:

(-2.5)x - 2.5

Finally, we can write the expression as:

-2.5x - 2.5

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Answer:

A) perimeter

B) (surface) area

C) perimeter

The domain and range are the set of x and values of the function are in the table.

the function as a table,

Input (x) | Output (y)

-3         |        -4

-1          |         2

0         |         0

-3         |         5

2         |         4

What is the domain and range?

The domain and range are fundamental concepts in mathematics that are used to describe the input and output values of a function or relation.

The domain of a function refers to the set of all possible input values, or x-values, for which the function is defined.

The range of a function refers to the set of all possible output values, or y-values.

To find the domain and range of functions and represent them in different formats.

To find the domain and range of a function:

The domain refers to the set of all possible input values (x-values) for the function.

The range refers to the set of all possible output values (y-values) for the function.

To represent the function as a table, you would list the input-output pairs. For example:

Input (x) | Output (y)

-3         |        -4

-1          |         2

0         |         0

-3         |         5

2         |         4

To represent the function as a mapping, you would indicate the correspondence between the input and output values.

For example:

-3     ->   -4

-1     ->     2

0     ->     0

-3    ->     5

2     ->     4

To represent the function as a graph, The x-values would be on the horizontal axis, and the y-values would be on the vertical axis.

The points (-3, -4), (-1, 2), (0, 0), (-3, 5), and (2, 4) would be plotted accordingly.

Hence, The domain and range are the set of x and values of the function are in the table.

the function as a table,

Input (x) | Output (y)

-3         |        -4

-1          |         2

0         |         0

-3         |         5

2         |         4

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Answer:

1500

Step-by-step explanation:

\(\frac{1350}{0.9}=1500\)

Answer:

Option D.

Step-by-step explanation:

We have the function:

f(x) = -a*(x + b)^(1/2)

Where:

a > 0

b > 0

Now, as a is positive and we have the coefficient "-a", we will have that the function is always negative.

Why? because (x + b)^(1/2) is always positive.

then: -a*(x + b)^(1/2) is always negative.

We also should see that the domain is not the set of all real numbers, because if:

x + b < 0, then we have the square root of a negative number, and we know that this is a complex number.

The only option that meets these two conditions is option D.

Answer

C

Step-by-step explanation:

Got it mf wrong

Answer:

Step-by-step explanation:

To find out how much of the 100 foot roll of fencing Martin will need to enclose the garden, you need to calculate the perimeter of the rectangular garden.

The perimeter is the total distance around the garden. To find the perimeter, you add up the lengths of all four sides of the rectangle.

The formula for the perimeter of a rectangle is: P = 2L + 2W

Where P is the perimeter, L is the length, and W is the width.

In this case:

P = 2 x 10 feet + 2 x 100 feet = 20 feet + 200 feet = 220 feet

Martin will need 220 feet of fencing to enclose his rectangular garden.

Answer: The last one

Step-by-step explanation: there is two zeros and every input (x) can only have one output.

Answer:

The last one

Step-by-step explanation:

zero and every input (x) can only have one out put

Answer:

The length of the rectangle is 17 yards and the width of the rectangle is 14 yards.

Explanation:

To find the perimeter of the rectangle, you had to add twice the length of the rectangle to twice the width of the rectangle since the shape of a rectangle is made up of two legs (each representing the rectangle's length) and two legs (each representing the rectangle's width.

The perimeter can be mathematically seen as p = 2l+2w, where p is the amount corresponding to the perimeter of the rectangle, l is the amount representing the length of the rectangle, and w is the quantity reflecting the width of the rectangle. This equation can be modified using the equation l = w+3, since it is given that the length is 3 yards longer than the width.

Therefore, the p = 2l+2w equation can be modified to solve for w using the given conditions and the equation defining l.

p = 2l+2w  

p = 2(w+3)+2w               [Substituting l = w+3]

p = 2w+6+2w

p = 4w+6

p-6 = 4w+6-6

p-6 = 4w

(p-6)/4 = 4w/4

w = (p-6)/4

w = (62-6)/4                  

w = 56/4

w = 14

Now the length of the rectangle can be determined using the equation l = w+3.

l = 14+3 = 17

Hope this helps Also Plz mark brainliest:)

Answer:

its c)

Step-by-step explanation:

just looked it up

Hence the given statement  that there exists an s such that for any r > s there exists an m 2 n such that for all n m we have x n < r is proved.

What is non-decreasing sequence?

Non-decreasing sequences are a generalization of binary covering arrays, which has made research on non-decreasing sequences important in both math and computer science.

Proof:

For n 2 N, let s = sup x n.

Then, there exists a m 2 N such that x m r for any r > s.

Given that x n is a non-decreasing sequence, we get x n r for any n > m.

As a result, there is a m 2 N such that for any n > m, x n r for any r > s.

Hence proved.

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Answer:

b=5

Step-by-step explanation:

-b - 19 = -3b – 9

Add 3b to each side

-b+3b - 19 = -3b+3b – 9

2b -19 = -9

Add 19 to each side

2b-19+19 = -9+19

2b = 10

Divide by 2

2b/2 =10/2

b=5

This research suggests a strong correlation between the number of hours spent watching television and the level of aggression shown at school.

This correlation implies a relationship between the two variables, however, further research is needed to determine the exact cause and effect relationship between television viewing and aggression.

It can be concluded that there is a link between the number of hours spent watching television and levels of aggression exhibited in school.

However, it is impossible to determine from this correlation whether watching television directly causes increased levels of aggression in school, or if there is some other factor that is influencing both variables.

Further research is needed to determine the exact cause and effect relationship between television viewing and aggression.

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The appropriate methods for analyzing the variables Birth Rate and Death Rate at the same time would be scatterplot, two-way table, and stacked bar chart.

Scatterplot: A scatterplot can be used to visually display the relationship between two quantitative variables, such as Birth Rate and Death Rate. Each point on the scatterplot represents a pair of values for the two variables, making it easy to identify patterns or trends in the data.

Two-way table: A two-way table can be used to display the distribution of two categorical variables, such as Birth Rate and Death Rate, and how they relate to each other. It can help identify the joint frequency or relative frequency of different categories.

Stacked bar chart: A stacked bar chart can be used to show how two categorical variables, such as Birth Rate and Death Rate, are related to each other. Each bar represents the total frequency for each category, and the bars are divided into sections representing the subcategories of the other variable. This makes it easy to compare the distribution of the two variables across each category.

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Answer: option 3

Step-by-step explanation:

Answer:step 3

Step-by-step explanation:

Answer:

Step 3.

Step-by-step explanation:

She subtracted the 5 from 10.2b even though 5 did not have the variable b.

1. The X axis is the line going left and right

2. The Y axis is the line going up and down

3. The origin is the point where the X and Y axis meet; (0,0); by the 0

4. The points will be written as A, B, C. This is going from left to right. So the first box on the coordinate plane furthest to the left with be labeled with A. Then the second box furthest from the left; the middle box; will be labeled with B. Then the last box will be labeled C

5. (4,6)

6. (2,9)

7. (0,4)

8. When Allie identified the point, she mixed the X and Y coordinates. To identify a point you first want to find the point following the X axis. Then do the same with the Y axis. After doing this you should have 2 numbers, in which are 3 and 7. Now when writing the coordinates, the X axis ALWAYS comes first. So it should look like (7,3)

The length of the segment  BZ is approximately 2.78

The above value is obtained by using the following process:

The given parameters of the triangle are;

The angle bisectors of the triangle = BY and CZ

The point at which BY and CZ meet = The point I

The length of CY = 4

The length of AY = 6

The length of AB = 8

The unknown parameter;

The length of the segment BZ

Method:

Apply the angle bisector theorem

According to the angle bisector theorem we have;

AY/CY = AB/BC

BZ/AZ = BC/AC

From AY/CY = AB/BC,  we get;

6/4 = 8/BC

6 × BC = 8 × 4 = 32

BC = 32/6 = 16/3 =  5.33

BC = 5.33

From BZ/AZ = BC/AC, we have;

AC = CY + AY

∴ AC = 4 + 6 = 10

AZ = AB - BZ

∴ AZ = 8 - BZ

Therefore;

BZ/8 - BZ = 5.33/10

10 × BZ =  ×(8 - BZ) = (16/3) × 8 -  (16/3)·BZ

10·BZ + (16/3)·BZ = (16/3) × 8

(46/3)·BZ = 128/3

BZ = 128/46 = 64/23

Length of the line BZ = 64/23 = 2 ≈ 2.78

Therefore, the length of the segment  BZ is approximately 2.78.

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Answer:

(7,-3)

Step-by-step explanation:

x = 7

-2x - 9y = 13

* Substituition is the easieat way to solve such a function.

- Firstly, put "7" instead of "x" in the equation.

- multiply "7" by "-2"

- Solve for "y"

* -2x-9y = 13

* -2×7-9y = 13

* -14-9y = 13

* -9y = 27

* -9y/-9 = 27/-9

* y = -3

# Since x = 7, the output/"y" will be -3

(7,-3)

The Markup percentage based on cost if the wholesaler paid $780 for the guitar is 79%

Given,

The cost price of the guitar = $780

The selling price of the guitar = $1396.20

We have to find the markup percent based on the cost;

Markup percentage;

The gross profit of a unit, which is its sales price less its cost to produce or acquire for resale, is divided by the unit's cost to determine the markup %.

Markup percent = (Selling price - cost price) / cost price x 100

= (1396.20 - 780) / 780 x 100

= 616.20 / 780 x 100

= 0.79 x 100

= 79%

That is,

The Markup percentage based on cost if the wholesaler paid $780 for the guitar is 79%

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Answer:

f(- 3) = 27 and g(6) = - 15

Step-by-step explanation:

Substitute x = - 3 into f(x) and x = 6 into g(x) , that is

f(- 3) = - 2(- 3)² - 3(- 3) = - 2(9) + 9 = 18 + 9 = 27

g(6) = - 2(6) - 3 = - 12 - 3 = - 15

The statement "a line segment is a part of a line that is bounded by two distinct end points and contains every point on the line between its endpoints." is True because a line segment is defined as a part of a line that is bounded by two distinct end points and contains all the points on the line between those endpoints.

A line segment is a part of a line that has two endpoints and connects them. It is the shortest distance between two points and has a definite length, but no width or height. A line segment can be part of a straight line or a curved line.

A line segment is a section of a line that is defined by two distinct end points and includes every point on the line between them. It is the basic building block of geometry and can be used to measure distances, angles, and shapes.

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Answer:

This doesn't make sense because there is no C variable, but I will solve for f if that helps.

Step-by-step explanation:

\(f=1.80+32\)

       \(-32\)   \(-32\)          

\(f=-30.2\)      

Answer:

Line 1 = Negative

Line 2 = Zero

Line 3 = Positive

Line 4 = Undefined

Step-by-step explanation:

Line 1's gradient is negative since it's sloping down.

Line 2's gradient stays at 0 since it does not go upwards or downwards.

Line 3's gradient is positive since it's tilting upwards.

Line 4's gradient is undefined since the line shoots up on the same point on the x-axis so the gradient cannot be determined by a single rational number.