A rectangle is 15 cm wide and 18 cm long. If both dimensions are
decreased by the same amount, the area of the new rectangle formed is
116 cm less than the area of the original. Find the dimensions of the
new rectangle

Perimeter of quadrilateral ABCD = 27.49 units.

Given quadrilateral ABCD has the following vertices:

A(-5, 4)

B(0, 3)

C(4, -1)

D(4, -5)

Perimeter of quadrilateral ABCD = AB + BC + CD + DA

Find each side lengths using the distance formula, d = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

AB = √[(0−(−5))² + (3−4)²]

AB = √26 ≈ 5.10 units

BC = √[(0−4)² + (3−(−1))²]

BC = √32 ≈ 5.66 units

CD = √[(4−4)² + (−5−(−1))²]

CD = √16 = 4 units

DA = √[(4−(−5))² + (−5−4)²]

DA = √162 = 12.73 units

Perimeter of quadrilateral ABCD = 5.10 + 5.66 + 4 + 12.73

Perimeter of quadrilateral ABCD = 27.49 units.

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The solution of above equation is

[ 0 81/3 ]

To find the matrix A, we need to compute the inverse of C times D times C:

C^(-1) = [-2  1]

        [ 1  0]

CDC^(-1) = [1 2][-2 1][4 0] = [4 -4]

                                [0 1]

Now we need to diagonalize A^4. First, let's find the eigenvalues of A:

|A - lambda*I| = 0

|4-lambda   -4   |   |lambda  0  |

|0           1-lambda| * |-4      1-lambda| = 0

Expanding the determinant, we get:

(4 - lambda)(1 - lambda) - 4*0 = 0

=> lambda^2 - 5*lambda + 4 = 0

=> (lambda - 4)*(lambda - 1) = 0

Therefore, the eigenvalues of A are λ1 = 4 and λ2 = 1. Now, let's find the eigenvectors associated with each eigenvalue:

For λ1 = 4:

(A - 4*I)x = 0

[(4 - 4)   -4  ] [x1]   [0]

[  0    (1-4) ] [x2] = [0]

=> -4*x2 = 0

=> x2 = 0

Any value of x1 will satisfy the equation, so we can choose x1 = 1:

eigenvector v1 = [1 0]'

For λ2 = 1:

(A - I)x = 0

[(4 - 1)   -4  ] [x1]   [0]

[  0    (1-1) ] [x2] = [0]

=> 3*x1 - 4*x2 = 0

=> x1 = (4/3)*x2

We can choose x2 = 3:

eigenvector v2 = [4 3]'

Now we can construct the diagonal matrix Λ with the eigenvalues on the diagonal:

Λ = [4 0]

[0 1]

And the matrix P with the eigenvectors as columns:

P = [1 4]

[0 3]

To compute A^4, we use the formula A^4 = P*Λ^4*P^(-1):

P^(-1) = (1/(13 - 40)) [ 3 -4]

[ 0 1]

Λ^4 = [4^4 0 ]

[0 1^4]

P^(-1) = (1/3) [ 3 -4]

[ 0 1]

A^4 = PΛ^4P^(-1) = [1 4][256/3 0 ][ 3 -4] = [4096/3 - 16384/3]

[0 3][ 0 1] [ 0 1] [ 0 81/3 ]

Therefore, the answer is:

[4096/3 -16384/3]

[ 0 81/3 ]

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We know a or b != 0

but a-b==0 so both are the same unknown number

b/a must = 1

so

a/b is equivalent to b/a as a/b=1 as well.

So the last answer choice.

Answer:

C.) =

Step-by-step explanation:

the absolute value of 5 is 5, and the absolute value of -5 is 5, so they will be equal

Answer:

=

Step-by-step explanation:

The absolute value of a number is how far the number is from zero on a number line.

Both 5 and -5 are 5 units from zero on a number line, so

|5| = |-5| since |5| = 5 and |-5| = 5.

Answer:

Pythagorean Theorum

Step-by-step explanation:

a^2*b^2= c^2

The statement "The number of intervals tells you the size of the data set" is not true of histograms. Option A

The number of intervals, or bins, in a histogram is determined by the data and by the preferences of the person creating the graph. A larger number of intervals will result in a graph with more detail, but may also make it harder to see trends or patterns in the data.

The size of the data set is not determined by the number of intervals in a histogram, but by the number of data points that are being represented.

The other statements are true of histograms. An outlier can show as a gap in the data if it falls outside the range of the intervals being used.

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The sum of the expressions 8x - 2 and - 3x² - 7 is, - 3x² + 8x - 9.

A quantity or number that is combined with a variable is known as a coefficient. The variable is often multiplied by an integer, which is then printed next to it.

Terms that have the same variables raised to the same power are referred to as like terms. The only difference is in the numerical coefficients.

Given, Two expressions, 8x - 2 and - 3x² - 7.

Now, Sum implies adding.

Therefore, The sum of 8x - 2 and - 3x² - 7 is,

(8x - 2) + (- 3x² - 7).

= - 3x² + 8x - 2 - 7.

= - 3x² + 8x - 9.

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We have to find a conformal mapping which maps the region between |Z + 3| < √10 and |Z - 2| < √5 onto the interior of the first quadrant.

The steps are as follows:

Step 1: We consider a mapping w = f(z) which maps the upper half-plane onto the interior of the first quadrant.

Step 2: Now we consider another mapping W = g(z) which maps the region between |Z + 3| < √10 and |Z - 2| < √5 onto the upper half-plane.

Step 3: Let us consider W = g(z) = (z + 3 + √10) / (z - 2 + √5)

Let z = x + iy.

Substituting, we get w = (x + 3 + √10 + iy) / (x - 2 + √5 + iy)

Converting into polar form: We get w = (r * cos θ + 3 + √10 + i r * sin θ) / (r * cos θ - 2 + √5 + i r * sin θ)

On rationalizing, we get w = [r² * cos θ * (r cos θ - 2 + √5) + r * sin θ * (3 + √10)] / [(r cos θ - 2 + √5)² + (r sin θ)²] - i [r² * sin θ * (r cos θ - 2 + √5) - r * cos θ * (3 + √10)] / [(r cos θ - 2 + √5)² + (r sin θ)²]

By setting r = 1 in the above expression, we get w = [cos θ * (2√5 - 2) + sin θ * (3 + √10) / [(2√5 - 2)² + sin² θ]] - i [sin θ * (2√5 - 2) - cos θ * (3 + √10) / [(2√5 - 2)² + sin² θ]]

Step 4: Substituting w = u + iv in the expression above, we get u = [cos θ * (2√5 - 2) + sin θ * (3 + √10) / [(2√5 - 2)² + sin² θ]]v = [-sin θ * (2√5 - 2) + cos θ * (3 + √10) / [(2√5 - 2)² + sin² θ]]

By setting cos θ = 0 and sin θ = 1 in the expression above, we get u = (3 + √10) / (2√5 - 2)

= 1 + √2v

= (2√5 - 4) / (2√5 - 2)

= -1 + 1 / √5

Therefore, the conformal mapping which maps the region between |Z + 3| < √10 and |Z - 2| < √5 onto the interior of the first quadrant is w = f(z) = 1 + √2 - (1 - 1 / √5) i.

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The highest point on a bell-shaped curve represents the peak or maximum value of the distribution. This point is known as the mode of the distribution.

In a bell-shaped curve, also known as a normal distribution or Gaussian distribution, the data is symmetrically distributed around the mean. The curve is characterized by a central peak, and the highest point on this peak corresponds to the mode.

The mode represents the most frequently occurring value or the value that has the highest frequency in the dataset. It is the point of highest density in the distribution.

The bell-shaped curve is often used to model naturally occurring phenomena and is widely applied in statistics and probability theory. The mode provides information about the most common or typical value in the dataset and is useful for understanding the central tendency of the distribution.

While the mean and median also have significance in a normal distribution, the highest point on the bell-shaped curve specifically represents the mode, indicating the value with the highest occurrence in the dataset.

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Answer:

B

Step-by-step explanation:

If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs do not classify the relationship as a function.

Answer:

D is Function and A, B and C are Non-Function

Step-by-step explanation:

If we looked at A, B and C we will see that X has the same values.

Rules: Function should always have different X values.

The small jar is a better value, as the price per gram is lower than the large jar. It costs approximately 0.0037 GBP per gram compared to 0.0035 GBP per gram for the large jar.

To determine which jar is the best value, we need to calculate the unit price per gram of jam for each jar. For the large jar, the unit price is 0.35 pence per gram (154p/440g), while for the small jar, the unit price is 0.37 pence per gram (126p/340g). Thus, the large jar provides a better value for money in terms of the cost per gram of jam.

In conclusion, based on the unit price per gram of jam, the large jar is the better value option between the two sizes.

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The sample space for choosing one marble from the given marbles which are red, green, blue, yellow, and orange is s = {red, green, blue, yellow, orange}

Given color of the marbles which are present in the paper bag are,

The five color marbles are present in the paper bag so, the sample space also contains all five marbles without repeating any color again.

Sample space: sample space is nothing but listing all the outcomes of the event. In the above event, we have to list the all outcomes when choosing one marble from the paper bag which containing five different marbles.

So, the sample space S = {red, green, blue, yellow, orange}

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The pattern on the table is x increases:

The functions on the table of values are:

sin(x), cos(x) and sin²(x) + cos²(x)

To describe the pattern, we simply observe how the values of the function change, as x increases.

As x increases, on the table:

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Answer:

10/2

Step-by-step explanation:

first 10/2=5

you divide 10 into 2 until you get 5 of such groups

The standard deviation for the total portfolio returns can be calculated using the weighted average of the standard deviations of the index fund and the risk-free asset. The standard deviation for the total portfolio returns is 10.5%.


The standard deviation of a portfolio measures the variability or risk associated with the portfolio's returns. In this case, the portfolio is 70% invested in an index fund (with a standard deviation of returns of 15%) and 30% invested in a risk-free asset.

To calculate the standard deviation of the total portfolio returns, we use the weighted average formula:

Standard deviation of portfolio returns = √[(Weight of index fund * Standard deviation of index fund)^2 + (Weight of risk-free asset * Standard deviation of risk-free asset)^2 + 2 * (Weight of index fund * Weight of risk-free asset * 1Covariance  between index fund and risk-free asset)]

Since the risk-free asset has a standard deviation of zero (as it is risk-free), the second term in the formula becomes zero. Additionally, the covariance between the index fund and the risk-free asset is also zero because they are independent. Therefore, the formula simplifies to:

Standard deviation of portfolio returns = Weight of index fund * Standard deviation of index fund

Plugging in the values, we get:

Standard deviation of portfolio returns = 0.70 * 15% = 10.5%

Hence, the standard deviation for the total portfolio returns is 10.5%. This means that the total portfolio's returns are expected to have a variability or risk represented by this standard deviation.

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The number of weeks when Jim and Sally would have the same amount of money is 20 weeks.

The expression that can be used to represent the amount of money Jim would have in his account after x weeks is: $1,250 + 27.50x.

The expression that can be used to represent the amount of money Sally would have in his account after x weeks is: $1,400 + $20x.

In order to determine the number of weeks when they would have the same amount of money, the two expressions must be equal to each other.

$1,250 + 27.50x =  $1,400 + $20x

Combine similar terms

$1,400 - $1,250 = $27.50x - $20x

150 = $7.50x

x = 150 / 7.50 = 20 weeks

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Answer:

The correct options are;

Adding rational expressions

Subtracting rational expressions

Step-by-step explanation:

When adding or subtracting rational numbers, the denominators of the  fractions representing the numbers should be equal

Therefore, when adding two or more rational expressions together, the following steps are required;

1) Looking for the Lowest Common Denominator

2) Finding the product of the quotient obtained from dividing the LCD by the denominator of a fraction and the numerator of the fraction

3) Placing the sum (or differences) of the products obtained in the above step as the numerator, while the LCD remain denominator

4) Simplifying the numerator in the above step

5) The faction so obtained, is the sum or difference of two or more rational expressions.

Answer:

-35 centimeters of erosion

Step-by-step explanation:

Answer:

7 x 2.6

Step-by-step explanation:

the square root of 7 is exactly 2.645751311064591, so in this case I converted it to a smaller number, using tenths place.

solution:

7 x 2.6 = 18.2

Answer:

\( {7}^{ \frac{3}{2} } \)

Step-by-step explanation:

\( \sqrt{7} \: can \: also \: be \: written \: as \: {7}^{ \frac{1}{2} } \)

We can use this information to rewrite the original expression:

\(7 \times {7}^{ \frac{1}{2} } \)

7 can also be written as

\( {7}^{1} \)

Remember that when multiplying exponents, if they have the same base, we can add the exponents. Therefore:

\( {7}^{1} \times {7}^{ \frac{1}{2} } \\ {7}^{1 + \frac{1}{2} } \\ {7}^{1 \frac{1}{2} } \\ {7}^{ \frac{3}{2} } \)

θ^ is said to be (the most) efficient only if var(θ^) is the minimum within the group of all linear unbiased estimators for θθ. Therefore, the option d.

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We need a sample size of 32 to achieve a 90% confidence level with a maximal error of estimate E = 0.37 for the mean price per 100 pounds of watermelon.

To find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.37 for the mean price per 100 pounds of watermelon, we can use the formula:
n = (z^2 * σ^2) / E^2
Where:
n = sample size
z = z-score for the desired confidence level (in this case, 1.645 for 90% confidence)
σ = standard deviation of the population (unknown)
E = maximal error of estimate

Since the standard deviation of the population is unknown, we can use a conservative estimate and assume that it is 1 (this is often a reasonable assumption for pricing data). Plugging in the values:

n = (1.645^2 * 1^2) / 0.37^2
n = 31.23

We need a sample size of 31.23, but since we can't have a fractional sample size, we round up to the nearest whole number:
n = 32

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She cannot draw an array of 17 counters with three rows.

The given parameters are:

Counter = 17

Rows = 3

An array is represented as:

Array = Rows * Columns

Where Rows and Columns are integers greater than 0

So, we have

3 * Column = 17

Divide by 3

Column = 5.667

Recall that Rows and Columns are integers greater than 0

This means that she cannot draw an array of 17 counters with three rows.

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Answer:

Step-by-step explanation:

slope of line y=4x+12 is 4

slope of line perpendicular to y=4x+12 is -1/4

eq. of perpendicular line or perpendicular linear function is y=-1/4x+b  where b is the y-intercept.

The range of the function at domain {-2, -1, and 0} will be { 12 , 3 and 0}.

A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Given that:-

The range for the given domain: {-2, -1, and 0} and the function is y = 3x².

The range will be the value of y at each given value of the domain.

Domain: { -2, -1, 0 }

y  =  3x²

At x = -2  →  y = 3 ( -2)² = 12

At x = -1   →  y = 3 (-1)²   = 3

At x = 0   →  y = 3 (0)    = 0

Therefore range of the function at domain {-2, -1, and 0} will be { 12 , 3 and 0}.

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Answer:

Step-by-step explanation:

Hopefully this is right.

Area = (pi)r²

Which is pi times the the radius squared

The radius is 2, so 2² is 4, So we multiply 3.14, which is pi, by 4.

Multiply 3.14 by 4, and the answer is 12.56, the question says round to the nearest tenth, so the final answer will be 12.6

My math teacher back in 7th grade gave us this sentence to help us memorize the equations.

Cherry Pie Delicious (C=(pi)d), Apple Pie Are Too (A=(pi)r²)

Do the same with the other two questions, and the answer for question two will be 3.14, rounded to the nearest tenth will be 3.1

Question three do the same as well, and the answer will be 660.185, rounded will be 660.2

Hope this helps!

Answer:

16

Step-by-step explanation:

To solve the equation,

r to the root of four = -2,

We must find -2^4

This is 16( Note this is positive because the minus sign becomes plus due to multiplying it 4 times )

Hope this helps

An equation is formed of two equal expressions. The value of x is -28/9.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The given expression can be simplified as,

\(2 \frac17+\dfrac37(3x-5)=-4\\\\\dfrac{15}{7} + \dfrac{9x-15}{7} = -4\\\\ \dfrac{15+9x-15}{7} = -4\\\\9x = -28\\\\x = \dfrac{-28}{9}\)

Hence, the value of x is -28/9.

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                 y=10/3x+12

The x is after the fraction

Partial derivative with respect to\(X = dF/dX = 2XY - (X + Y)2-2 + Y2e-XZ\)

Partial derivative with respect to \(Y = dF/dY = X2 - 6Y + (X + Y)2-2XYe-XZ\)

The first partial derivatives of the function F(X,Y) = X2Y - 3Y2 + X/(X + Y)2 + XY2e-XZ can be found by taking the partial derivative with respect to each of the variables X and Y separately.
For the partial derivative with respect to X, we have:
Partial derivative with respect to X = dF/dX = 2XY - (X + Y)2-2 + Y2e-XZ
For the partial derivative with respect to Y, we have:
Partial derivative with respect to \(Y = dF/dY = X2 - 6Y + (X + Y)2-2XYe-XZ\)
This completes the calculation of the first partial derivatives of the function F(X,Y).
The first partial derivatives of the functions are given below:

\(F(x, y) = x^2y - 3y^2\)

The first partial derivative with respect to x,

Fx (x, y) = 2xy

The first partial derivative with respect to y,\(Fy (x, y) = x^2 - 6yW = xy^2 e^-xz\)

The first partial derivative with respect to x,

\(Wx (x, y, z) = y^2e^-xz - x^2y^2e^-xz\)

The first partial derivative with respect to y, Wy (x, y, z) = 2xye^-xz

The first partial derivative with respect to z, \(Wz (x, y, z) = -xy^2e^-xz\)

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Answer:

It's a composite number

Answer:

57 is a composite number

Step-by-step explanation:

its not prime

it is composire (it has two or more factors)

ilt IS posiltive number