Let A be a 5-by-5 matrix whose determinant is -2. Use properties of determinants to evaluate the following:

det(2A) =

det(A^2) =

det(A^-1) =

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

Algebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.

Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.

For example, d + d = 2d

This is an example of an algebraic expressionns.

Given the algebraic expressions,

\(\frac{1}{2}x + 4 \\ x + 6 - \frac{1}{2}x - 2\)

Substituting 2 for x in the first expression gives:

(1/2 × 2) + 4

1 + 4

5

Substituting 2 for x in the second expression gives:

2 + 6 - (1/2 ×2) - 2

8 - 1 - 2

8 - 3

5

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

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Answer:

Step-by-step explanation:

This equation represents the relationship between the exponential functions y = e^x and y = (10^(x-1)). These two functions are equal to each other for all values of x. This can be shown by taking the natural logarithm of both sides of the equation, which gives us:

ln(e^x) = x-1

In this equation, ln(e^x) is equal to x, since the natural logarithm of an exponential expression with a base of e is the exponent. Therefore, we can simplify the equation by taking the natural logarithm of both sides:

ln(10^(x-1)) = x-1

e^(x-1) = 10^x

The two functions e^x and 10^(x-1) are the same function with different bases, so they follow the same pattern. The fact that these two functions are equal to each other for all values of x can also be shown by graphing the two functions and seeing that they overlap perfectly.

Answer:

Abdul's tank can hold 27 gallons of gas.

Step-by-step explanation:

Given that Abdul's gas tank is 1/3 full, and after he buys 12 gallons of gas, it is 7/9 full, to determine how many gallons can Abdul's tank hold the following calculation must be performed:

1/3 = 0.3333

7/9 = 0.7777

0.777 - 0.333 = 0.444

0.444 = 12

1 = X

12 / 0.444 = X

27 = X

Therefore, Abdul's tank can hold 27 gallons of gas.

Answer:

6

Step-by-step explanation:

42 x 36 and (40 + 2) X (30 + 6) are the same thing, they are just written differently. Hope This helps!

Answer:

The Second Site

Step-by-step explanation:

The domain is determined by the set of x values covered by the graph, and the range is determined by the set of y values covered by the graph.

In the given question we have to find the domain and range of a dot graph.

A function's domain and range are really the collection of all possible outputs and inputs respectively. The range includes all of the function's output values, while the domain contains all possible input data from the set of real numbers.

If the graph of a function is known or available, it is fairly simple to determine its domain and range. The domain is determined by the set of x values covered by the graph, and the range is determined by the set of y values covered by the graph.

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Answer:

y = -13

Step-by-step explanation:

a) Subtract y from both sides.

2y + 6 − y = y − 7 − y

y + 6 = −7

b) Subtract 6 from both sides.

y + 6 − 6 = −7 − 6

y = -13

Answer:

a) The value of q is 0.2.

b) E(X) = 1.85.

Step-by-step explanation:

Question a:

The sum of all the probabilities must be 1. So

\(0.3 + x + 0.1 + 0.15 + 0.25 = 1\)

\(x + 0.8 = 1\)

\(x = 0.2\)

The value of q is 0.2.

Question b:

Multiplication of each value of x by its probability. So

\(E(X) = 0*0.3 + 1*0.2 + 2*0.1 + 3*0.15 + 4*0.25 = 1.85\)

So the answer is E(X) = 1.85.

Let's denote the amount Jolene invested at 3 percent interest as 'x' dollars. Since she put twice as much in the lower-yielding account, the amount she invested at 9 percent interest would be '2x' dollars.

To calculate the interest earned from each account, we'll use the formula: Interest = Principal × Rate × Time.

For the 3 percent interest account:

Interest_3_percent = x × 0.03

For the 9 percent interest account:

Interest_9_percent = 2x × 0.09

We know that the total annual interest is $3120, so we can set up the equation:

Interest_3_percent + Interest_9_percent = 3120

Substituting the above equations, we have:

x × 0.03 + 2x × 0.09 = 3120

Simplifying the equation:

0.03x + 0.18x = 3120

0.21x = 3120

Dividing both sides of the equation by 0.21:

x = 3120 / 0.21

x = 14857.14

Therefore, Jolene invested approximately $14,857.14 at 3 percent interest and twice that amount, $29,714.29, at 9 percent interest.

Answer:

Step-by-step explanation:

X is the amount invested at 6%

Y is the amount invested at 9%

0.06X + 0.09Y = 4998

X = 2Y

0.06(2Y) + 0.09Y  = 4998

.12Y + 0.09Y = 4998

0.21Y = 4998

21Y = 499800

Y = 499800/21 = 23800

So X = 2*23800 = 47600

$47,600 is invested at 6% and $23800 is invested at 9%

For the given figure, we will find the area

The given figure can be divided into two shapes as shown in the following figure:

Shape (1) is a rectangle:

Length = 9 cm

Width = 6 cm

Area of shape (1) = 9 x 6 = 54 cm²

Shape (2) is a triangle:

Base = 6 cm

Height = 14 - 9 = 5 cm

Area of shape (2) = 1/2 x 6 x 5 = 15 cm²

So, the area of the given figure = 54 + 15 = 69 cm²

Answer: 8

Step-by-step explanation:

"Of" is the same as multiplication so,

2/5 × 20/1 = ?  

20/1 is the same as 20. (20÷1 = 20/1)

In fraction multiplication, we multiply the numerators and then we multiply the denominators and get ↓↓↓↓

Below is a fraction.↓↓↓

2 x 20            40

______    =  ____

5 x 1                 5

Since 40 divided by 5 equals 8 then,

40/5 = 8

Therefore :

2/5 of 20 is 8.

So:

Kara drew 8 of the 20 pictures in art class.

If you are satisfied with my answer, consider making it the brainliest!

Answer:

Step-by-step explanation:

8.008.009

Answer:

70

Step-by-step explanation:

The missing measures in triangle STU are given as follows:

ST = 9.

TU = 12.

m < S = 70º.

m < T = 46º.

m < R = 64º.

Similar triangles are triangles that share these two features presented as follows:

Congruent angle measures.

Proportional side lengths.

For the angle measures, we have that:

Equivalent sides have the same angle measures.

The missing angle measure is of:

m ∠ R = (180 - 70 + 46)

          = 64º.

By sum of the measures of the internal angles of a triangle is of 180º.

The proportional relationship for the side lengths of the triangle is given as follows:

6/14 = ST/21 = TU/28.

Then the length ST is given as follows:

14ST = 21 x 6

ST = 1.5 x 6

ST = 9.

The length TU is given as follows:

14TU = 28 x 6

TU = 2 x 6

TU = 12.

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The amount of solution A and B required are 60 and 90 ounces respectively.

Creating simultaneous equations for the problem:

Mass of solution A = a

Mass of solution B = b

a + b = 150 _____(1)

0.65a + 0.90b = 150×0.80

0.65a + 0.90b = 120 __(2)

From (1)

a = 150-b ____(3)

substitute (3) into (2)

0.65(150-b) + 0.90b = 120

97.5 - 0.65b + 0.90b = 120

0.25b = 120-97.5

0.25b = 22.5

b = 22.5/0.25

b = 90

a = 150 - b

a = 150 - 90

a = 60

Therefore , 60 ounces of solution A and 90 ounces of solution B is required.

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The area of the square is given as 100 square unit

You should be aware that the square has all its sides equal

The perpendicular from opposite vertices represent distance

The given vertices are

(2,2) and (10,8)

Using the formula for distance between two points

d=√(10-2)²+(8-2)²

d=√8²+6²

d = √64+36

d=√100

This implies that d=10

The area of a square is given as s²

Area = 10²

Atrea = 100 square units

In conclusion, the area of the square is 100 square units

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Translated question:

The vertices of a square ABCD are A(2,2) and B(10,8), Find the area of the square

Answer: I believe

M = 80

Step-by-step explanation:

100 - 20 = 80

Answer:

Step-by-step explanation:

Remark

Formula

cos(theta) = adjacent side / hypotenuse

Givens

Theta = 57 degrees

Hypotenuse = x

Side adjacent = 13

Solution

Step-by-step explanation:

I hope this answer is helpful ):

If the function g(x) is defined for all real-numbers, then the value of g(-5) is 7/2, g(-2) is -1 and g(-1) is 0.

A piecewise function is a function that is defined by different rules or formulas on different parts of its domain. The piecewise function "g(x)" is given as :

g(x) = {-(1/2)x + 1,    for x<-2

       = {-(x+1)²,        for -2≤x≤1

      =  {4                 for x>1

We have to find the value of g(-5) ,g (-2), and g(-1),

For x = -5, the number -5 is less than -2, so the first function "-(1/2)x + 1" will be used,

⇒ g(-5) = -(1/2)(-5) + 1 = 5/2 + 1 = 7/2,

For x = -2, the number -2 lies in the interval "-2≤x≤1", so second function

"-(x+1)²" will be used,

⇒ g(-2) = -(x+1)² = -(-2+1)² = -(-1)² = -1,

For x = -1, the number -1 lies inn the interval "-2≤x≤1", so second function "-(x+1)²" will be used,

⇒ g(-1) = -(x+1)² = -(-1+1)² = -(0)² = 0,

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Answer:

54

Step-by-step explanation:

Multiply:

37x37=72

Subtract:

180-72=108

Divide:

108/2=54

Answer:

143 degrees

Step-by-step explanation:

37(2) + 2x = 360
74 + 2x = 360
2x = 286

x = 143

Hope this helps :)

Using system of linear equations, the length and width of the rectangle are 9cm and 3cm respectively

The system of linear equations is the set of two or more linear equations involving the same variables. To find the length and width, we use both equations to solve for l and w

In this problem, the rectangle has a perimeter of 24 cm and the given area . Its length is three times more than its width.

2l + 2w = 24 ...eq(i)

l = 3w ...eq(ii)

Solving both equations; the length is 9cm and width is 3cm

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Complete Question : The rectangle shown has a perimeter of 24 cm and the given area. Its length is three times more than its width. Write and solve a system of equations to find the dimensions of the rectangle.

Answer:

1 \(\frac{11}{12}\)

Step-by-step explanation:

Answer:

The answer is b) x = 42

Answer:

The length of the first side of a triangle = 6 m

The length of the second side of a triangle = 6 m

The length of the third side of a triangle = 9 m

Step-by-step explanation:

The complete question is: Two sides of a triangle have the same length. The third side measures 3 m less than twice the common length. The perimeter of the triangle is 21 m. What are the lengths of the three​ sides?

We are given that two sides of a triangle have the same length. The third side measures 3 m less than twice the common length. The perimeter of the triangle is 21 m.

Let the common length of the two sides of a triangle be 'x m'.

So, the length of the first side of a triangle = x m

the length of the second side of a triangle = x m

the length of the third side of a triangle = (2x - 3) m

As we know that the perimeter of a triangle is given by;

The Perimeter of a triangle = Sum of all sides of a triangle

                   21 m = x + x + (2x - 3)

                   21 m = 2x + 2x - 3

                   21 m = 4x - 3

                   4x = 21 + 3

                   4x = 24 m

                    x = \(\frac{24}{4}\) = 6 m

Hence, the length of the first side of a triangle = x = 6 m

the length of the second side of a triangle = x = 6 m

the length of the third side of a triangle = (2x - 3) = 12 - 3 = 9 m

The ways a member can make a selection is 76904685

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

List =40

Choice = 8

The number of ways is calculated as

Ways = C(40, 8)

Apply the combination formula

So, we have the following representation

Ways = 40!/(32! * 8!)

Evaluate

Ways = 76904685

Hence, the number of ways is 76904685

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ANSWER: y = (1/2)x - 1.

To find the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1), we need to determine the slope of the tangent line and its y-intercept.

First, let's find the derivative of the function y = √(x - 3) using the power rule:

dy/dx = 1/(2√(x - 3))

Now, we can substitute x = 4 into the derivative to find the slope of the tangent line at that point:

m = dy/dx = 1/(2√(4 - 3)) = 1/2

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

Next, we can use the point-slope form of a line to find the equation of the tangent line. Given the point (4, 1) and the slope m = 1/2, the equation becomes:

y - y1 = m(x - x1)

Substituting the values (x1, y1) = (4, 1):

y - 1 = (1/2)(x - 4)

Simplifying the equation:

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

y = (1/2)x - 1

Therefore, the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1) is y = (1/2)x - 1.

Answer:

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

Step-by-step explanation:

Step 1: Find the derivative of the function

The derivative of a function gives the slope of the tangent line to the curve at any point. To find the derivative of the given function y = sqrt(x - 3), we can use the power rule of differentiation which states that:

d/dx (x^n) = nx^(n-1)

Applying this rule to our function, we get:

dy/dx = d/dx sqrt(x - 3)

To differentiate the square root function, we can use the chain rule of differentiation which states that:

d/dx f(g(x)) = f'(g(x)) * g'(x)

Applying this rule to our function, we have:

g(x) = x - 3

f(g) = sqrt(g)

So,

dy/dx = d/dx sqrt(x - 3) = f'(g(x)) * g'(x) = 1/(2*sqrt(g(x))) * 1

Substituting g(x) = x - 3, we get:

dy/dx = 1/(2*sqrt(x - 3))

So, the derivative of y with respect to x is 1/(2*sqrt(x - 3)).

Step 2: Evaluate the derivative at the given point

To find the slope of the tangent line at the point (4, 1), we need to substitute x = 4 into the derivative expression:

dy/dx = 1/(2*sqrt(4 - 3)) = 1/2

So, the slope of the tangent line at the point (4, 1) is 1/2.

Step 3: Use point-slope form to write the equation of the tangent line

Now that we know the slope of the tangent line at the point (4, 1), we can use point-slope form to write the equation of the tangent line. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is the point on the line and m is the slope of the line.

Substituting the values x1 = 4, y1 = 1, and m = 1/2, we get:

y - 1 = (1/2)*(x - 4)

Simplifying this equation, we get:

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

So, the equation of the tangent line to the curve y = sqrt(x - 3) at the point (4, 1) is y = (1/2)x - 1/2.

Hope this helps!

Answer:

9

Step-by-step explanation:

You don't need to pass through each edge once.

If we name the top vertex 1 and the bottom vertex 2 then here are the possible combinations:

A-1-B

A-B

A-2-B

A-1-B-A-2-B

A-2-B-A-1-B

A-B-1-A-2-B

A-B-2-A-1-B

A-1-B-2-A-B

A-2-B-1-A-B

Some people say 6 because they think you need to pass through all the edges. But the only restriction with travelling on the edges is you can't pass one twice. The point is read the wording and it becomes easy.

Hope this helps!

Answer:

1:3

Step-by-step explanation:

there are 25 raisins for every 75 peanuts.

You can set this up as a fraction and simplify

25/75 = 1/3

so there is 1 raisin for every 3 peanuts.

Dividend income and agricultural income are examples of tax exempt incomes.

In mathematics, the tax calculation is related to the selling price and income of taxpayers. It is a charge imposed by the government on the citizens for the collection of funds for public welfare and expenditure activities. There are two types of taxes: direct tax and indirect tax.

The right to have some or all of your income free from your country's taxes is known as a tax exemption. While certain individuals and organizations are completely exempt from paying taxes, the bulk of taxpayers are eligible for a number of exemptions that can be used to reduce their taxable income.

Income that is exempt from taxation is that which is unlikely to be taxed. Dividend income, agricultural income are a few examples.

Therefore, dividend income and agricultural income are examples of tax exempt incomes.

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