Exercise 2.4.28 LetAbe ann×nmatrix and letIbe then×nidentity matrix. a. IfA2=0, verify that(I−A)−1=I+A. b. IfA3=0, verify that(I−A)−1=I+A+A2.

Hence, the shape is rectangular prism with the dimensions 10mm, 8mm, and 8mm has a surface area of 448mm2.

We must first calculate the surface area of each face of a rectangular prism with 10mm, 8mm, and 8mm measurements before adding them all up.

The top and bottom faces, which are both rectangles with measurements of 10 mm by 8 mm, are first measured for area:

Area of the top and bottom faces is equal to 2 (10 x 8 mm) or 160 mm2.

The area of the front and back faces, which are both rectangles measuring 10 mm by 8 mm, is then determined: Area of the front and back faces is equal to 128mm2 (8mm x 8mm).

The area of the two side faces, which are both rectangles with dimensions of 10 mm by 8 mm, is then determined: Area of the side sides is equal to 2 (10mm x 8mm) = 160mm2.

We add up the areas of all the faces to determine the overall surface area:

Whole surface area equals the sum of the areas of the top and bottom faces, the front and back faces, and the side faces.

Surface area total = 160 mm2 + 128 mm2 + 160 mm2

448 mm2 is the total surface area.

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Answer: B : 5cm, 12cm and 13cm

Step-by-step explanation:

it says the amount of centimeters on each side on the ruler. its the small numbers

Answer:

42 minutes are not spent on instructions

Step-by-step explanation:

First, we must find out how many minutes is in [tex]\frac{7}{8}[/tex] hour

[tex]60*\frac{7}{8}=\frac{60*7}{8} =\frac{420}{8} =52.5[/tex]

In [tex]\frac{7}{8}[/tex] hour, there is about 52 [tex]\frac{1}{2}[/tex] minutes

Then we must add up the fractions that are NOT the instructions

[tex]\frac{1}{2} +\frac{3}{10} =\frac{5}{10} +\frac{3}{10} =\frac{8}{10} =\frac{4}{5}[/tex]

[tex]\frac{4}{5}[/tex] of the total time (52 [tex]\frac{1}{2}[/tex] minutes) is not spent on instructions

Then we must multiply the fraction of time spent on other things ([tex]\frac{4}{5}[/tex]) by total time (52 [tex]\frac{1}{2}[/tex] minutes) in order to find out how many minutes weren't spent on instructions.

[tex]\frac{4}{5}*52 \frac{1}{2} =\frac{4}{5}* \frac{105}{2}=\frac{420}{10} =42[/tex]

42 minutes are not spent on instructions

Answer: The representations of these functions are alike in that they both describe the movement of the falling object. They are different in that one function measures the distance the object has traveled from its starting point, while the other measures its distance from the ground.

Step-by-step explanation:

We will see that the measure of angle z is 70°

First we can get the angle in the right vertex in the triangle in the right side.

We know that the right angle and the 40° one are vertical angles, then the right angle also measures 40°

Also remember that the sum of the interior angles of any triangle is 180°, then:

105° + 40° +x = 180°

x = 180° - 40° - 105° = 35°

Then the right angle of the second triangle (the one that is below the line) also measures 35°

The bottom angle measures:

y + 85 = 180

y = 180 - 85 = 95

And if the last angle is k:

k + 95 + 35 = |80

k = 180 - 35 - 95 = 50

Then the right angle of the last triangle is also 50°, then we can write:

z + 60 + 50 = 180

z = 180 - 50 - 60 = 70°

That is the measure.

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23) The equation for the hyperbola is (y-2)^2/9 - (x-1)^2/16 = 1.

24) The equation for the circle is (x+1)² + (y-3)² = 17.

23. The equation for a hyperbola with center (h,k) and vertices (h,k+a) and (h,k-a) is:

(y-k)²/a²- (x-h)²/b² = 1

In this case, the center is (1,2), so h = 1 and k = 2. The vertices are (1,5) and (1,-1), so a = 3. To find b, we can use the fact that c^2 = a^2 + b^2, where c is the distance from the center to the foci. The foci are (1,7) and (1,-3), so c = 5. Therefore:

5² = 3² + b²

b² = 25 - 9

b² = 16

b = 4

So the equation for the hyperbola is:

(y-2)^2/3^2 - (x-1)^2/4^2 = 1

(y-2)^2/9 - (x-1)^2/16 = 1

24. The equation for a circle with center (h,k) and radius r is:

(x-h)² + (y-k)² = r²

In this case, the center is (-1,3), so h = -1 and k = 3. To find the radius, we can use the distance formula with the center and the point (3,2):

r = sqrt((3-(-1))² + (2-3)²

r = sqrt(4² + (-1)²)

r = sqrt(16 + 1)

r = sqrt(17)

So the equation for the circle is:

(x-(-1))² + (y-3)² = (sqrt(17))²

(x+1)² + (y-3)² = 17

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The slope of the line in simplest form is 1/3.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = rise/run

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-2 + 5)/(9 - 0)

Slope, m = 3/9

Slope, m = 1/3

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The volume of the cone in terms of π is [tex]90.312\ inches^{3}[/tex].

A cone is a three-dimensional body with a flat base that is connected to a pointed top.

The formula for the volume of a cone is :

[tex]Volume,V = \frac{\pi r^{2}H }{3}[/tex]

It is given that height, H = 15 inches.

The formula for the circumference of the base is = [tex]2\pi r[/tex]

So, we can say that :

[tex]2\pi r=8.5\pi[/tex]

[tex]r=\frac{8.5}{2} =2.25[/tex] inches

Therefore, the volume of the cone is, V:

[tex]=\pi \times 4.25^{2} \times 15\\ =90.312\ \text{inches}^{3}[/tex]

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Answer: $170

Step-by-step explanation:

6x + 18(6) = 1128.

6x + 108 = 1128

6x = 1020

x = 170

The price of one ticket is 170

Yes, the production manager should be concerned about production rate variations. Based on the data provided, the standard deviation of the daily production rate of fiberglass boats from Dhaka Glass is 4.6 boats, which is higher than the threshold of 3 boats a day set by the production manager. This indicates that there are significant variations in the production rate of fiberglass boats, which should be a cause for concern.

To further explain, the standard deviation measures the spread of a set of data. In this case, the data provided shows that the daily production rate of fiberglass boats can vary from 17 to 32 boats a day. The large standard deviation of 4.6 boats suggests that the daily production rate can vary significantly from the average, and this can lead to instability in production.

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Answer:

The answer is 13.

Step-by-step explanation:

First, we must find the hypotenuse for right angle:

[tex]c^{2} = a^{2} + b^{2}\\ \\\\c^{2} = 12^{2} + 5^{2} \\c^{2} 144 + 25 \\c^{2} = 169 \\c^{2} =\sqrt{169}\\c^{2} = 13[/tex]

c = 3.

a) A is linearly dependent for any value of c because the vectors are not linearly independent.

This means that one of the vectors can be written as a linear combination of the others.

For example, the vector (1,2,c) can be written as (2,2,0) + (-1,0,c-0) = (1,2,c).

This means that the set of vectors is linearly dependent.

b) For c = 0, Vector (A) is the set of all linear combinations of the vectors (2,2,0), (1,2,0), (0,0,0), and (1,0,0).

This means that Vect (A) is the set of all points in the xy-plane, or the set of all vectors in R^2.c).

To find all the values of c for which (4,1,3) is in Vect (A),

we need to solve the equation (4,1,3) = a(2,2,0) + b(1,2,c) + d(0,0,c) + e(1,0,0) for the scalars a, b, d, and e.

This gives us the system of equations:4 = 2a + b + e1 = 2a + 2b3 = bc + dc.

Solving this system of equations gives us the values of a, b, d, and e in terms of c.

We can then use these values to find the values of c for which (4,1,3) is in Vect (A).

After solving the system of equations, we find that c = 3 and a = 1, b = -1, d = 0, and e = 2.

Therefore, the value of c for which (4,1,3) is in Vect (A) is c = 3.

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The area of the triangle with the given vertices is 4.47.

To find the area of the triangle with the given vertices, we can use the formula:
Area = (1/2) * |(B-A) x (C-A)|
Where "x" represents the cross product of two vectors.
First, we need to find the vectors B-A and C-A:
B-A = (1-5, 1-(-1), 0-(-2)) = (-4, 2, 2)
C-A = (3-5, 2-(-1), -1-(-2)) = (-2, 3, 1)
Next, we need to find the cross product of these two vectors:
(B-A) x (C-A) = (2*1 - 2*3, 2*(-2) - (-4)*1, (-4)*3 - 2*(-2)) = (-4, 0, -8)
Finally, we can find the area of the triangle by plugging in the values into the formula:
Area = (1/2) * |(-4, 0, -8)|
Area = (1/2) * √((-4)^2 + 0^2 + (-8)^2)
Area = (1/2) * √(80)
Area = (1/2) * 8.94
Area = 4.47
Therefore, the area of the triangle with the given vertices is 4.47.

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The distance between the points (-9, 4) and (3, 12) is approximately 14.42 units.

what exactly is distance?

Distance is the amount of space between two objects or locations. It is a measure of how far apart two things are from each other, typically expressed in units such as meters, kilometers, miles, feet, or yards. Distance can be measured in a straight line, known as the "Euclidean distance," or it can be measured along a path or route, known as the "distance traveled." Distance is a fundamental concept in many areas of science and mathematics, including physics, geography, and geometry

The formula for calculating the distance between two points is d = ((x2 - x1)2 + (y2 - y1)2).

Let's use this formula to find the distance between the two points (-9, 4) and (3, 12):

d = √((3 - (-9))² + (12 - 4)²)

= √(12² + 8²)

= √(144 + 64)

= √208

≈ 14.42

So the distance between the points (-9, 4) and (3, 12) is approximately 14.42 units.

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The distance between the hunter and the bird is 5.39

We know that the distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula below.

distance = √( (x₂ - x₁)² + (y₂ - y₁)²)

The hunter is at (0, 0) and shoots at (2, 5), so we can plug those values ​​into the formula for the distance:

distance = √( (2 - 9)² + (5 - 0)²)

distance = √( (2 )² + (5 )²)

distance = √( 4 + 25) = 5.39

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The volume of the right square pyramid is 320 in³.

Volume is a measure of the amount of space that an object takes up. It is usually measured in cubic units, such as cubic centimeters, cubic meters, or cubic feet. Volume is an important concept in mathematics, physics, and engineering, as it can be used to calculate the size and mass of an object. It can also be used to calculate the amount of liquid or gas that can fit into a container.

The volume of a right square pyramid can be calculated using the formula V = (1/3)lhs.

Therefore, the volume of the right square pyramid with the given dimensions is:

V = (1/3) x 10 in x 6 in x 16 in

V = 320 in³

Therefore, the volume of the right square pyramid is 320 in³.

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The volume of the pyramid is 320in cubic units

volume is a measure of space occupied by an object,

the formula for the volume of a pyramid is equal to one third of the product of the height and the base area of the pyramid

The pyramid that has a square base is known as Square pyramid.

square pyramid has 4 faces and 1 square base.

The volume of the square pyramid is given by the formula

V=(1/3)*(base area of a square)*(height of the square pyramid)cubic units

V=(1/3)AH cubic units

The volume of the pyramid is V= (base length*base width*height)/3

V=(1/3)l*s*h

V=(1/3)10*16*6

V=320 in

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Answer:

To determine the location of point H, we need to first find the length of the three sides of the fenced area using the given points E, F, and G.

The length of EF is:

sqrt[(3-1)^2 + (5-5)^2] = 2 units

The length of FG is:

sqrt[(6-3)^2 + (1-5)^2] = sqrt(25) = 5 units

The length of EG is:

sqrt[(6-1)^2 + (1-5)^2] = sqrt(20) = 2sqrt(5) units

The total length of the three sides is:

2 + 5 + 2sqrt(5) = 7 + 2sqrt(5) units

Since Landon has 16 units of fencing, he needs to find a point H such that the length of the fourth side of the fenced area (EH) is:

16 - (7 + 2sqrt(5)) = 9 - 2sqrt(5) units

Let's assume that point H has coordinates (x, y). Then, we can use the distance formula to find the length of EH:

sqrt[(x-1)^2 + (y-5)^2] = 9 - 2sqrt(5)

Squaring both sides and simplifying, we get:

(x-1)^2 + (y-5)^2 = 81 - 36sqrt(5) + 20

(x-1)^2 + (y-5)^2 = 101 - 36sqrt(5)

Now, we can plug in the coordinates of each of the answer choices and see which one satisfies this equation:

For (0, 1):

(0-1)^2 + (1-5)^2 = 16, which is not equal to 101 - 36sqrt(5)

For (0, -2):

(0-1)^2 + (-2-5)^2 = 65, which is not equal to 101 - 36sqrt(5)

For (1, 1):

(1-1)^2 + (1-5)^2 = 16, which is not equal to 101 - 36sqrt(5)

For (1, -2):

(1-1)^2 + (-2-5)^2 = 65, which is equal to 101 - 36sqrt(5)

Therefore, the answer is (1, -2), and Landon can place point H at coordinates (1, -2) to fence in the dog park without having to buy more fencing.

Answer:

To express the value 0.0000547 in scientific notation, we need to move the decimal point to the right until there is only one non-zero digit to the left of the decimal point.

0.0000547 = 5.47 × 10^(-5)

The exponent -5 indicates that we moved the decimal point 5 places to the right.

The correct slope and y-intercept for the linear equation y=2x+7 are 2 and 7, respectively.

The y-intercept of a graph is the point where the graph crosses the y-axis. It is written as (0, b), where b is the y-intercept. The y-intercept is the value of y when x is equal to zero. It can be used to determine the equation of a line when two points on the line are known.

The slope of a linear equation is the coefficient of the x variable, which is 2 in this case. The y-intercept is the constant term, which is 7 in this case.

So, the slope is 2 and the y-intercept is 7.

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Answer:

Step-by-step explanation:23.80*34=809.20

a) (TRUE)

If b is a linear combination of the columns of the matrix A, then the linear system Ax = b has a unique solution.

b) (FALSE)

If {u, v, w} is linearly independent, then {u+w, v + w} is linearly independent.

c) (FALSE)

If V = span{V1, V2, V3} and dim(V) = 2, then {V2, V3} is a basis of V.

a) If b is a linear combination of the columns of matrix A, then the linear system Ax = b has a unique solution. This is (always) true because if b is a linear combination of the columns of matrix A, then it can be written as Ax.

Therefore, if A is invertible, then x = A^(-1)b is a unique solution to Ax = b.

b) If {u, v, w} is linearly independent, then {u+w, v+w} is linearly independent. This is (possibly) false because {u+w, v+w} is linearly dependent if u = -v = w.

Therefore, {u+w, v+w} is not linearly independent.

c) If V = span{V1, V2, V3} and dim(V) = 2, then {V2, V3} is a basis of V.

This is (possibly) false because {V2, V3} is a basis for V if and only if V2 and V3 are linearly independent and span(V).

However, dim(V) = 2 implies that V is a 2-dimensional subspace of R^3, so {V1, V2, V3} cannot be linearly independent.

Therefore, {V2, V3} is not necessarily a basis for V.

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With an APR of 6.75% over a 20-year period, the annual payment for the loan will be $81,371.52.

To find the annual payment for the loan, we need to first find the total cost of the land and the amount of the loan.

Total cost of the land = 245 acres x $4,700/acre = $1,151,500

Down payment = 25% of total cost = 0.25 x $1,151,500 = $287,875

Loan amount = Total cost - Down payment = $1,151,500 - $287,875 = $863,625

Next, we need to use the loan amount, APR, and loan term to find the annual payment. We can use the following formula:

Annual payment = (Loan amount x APR) / (1 - (1 + APR)^(-Loan term))

Plugging in the values we have:

Annual payment = ($863,625 x 0.0675) / (1 - (1 + 0.0675)^(-20))

Annual payment = $58,294.69 / (1 - 0.2837)

Annual payment = $58,294.69 / 0.7163

Annual payment = $81,371.52

Therefore, the annual payment for the loan is $81,371.52.

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Answer:

8 - w

Step-by-step explanation:

In my opinion, an expression for eight minus w would be 8 - w. Thanks.

Hope it helps.

This is the final factored form of the original expression. = (4x^(2)-x-265)/((4(x-9)(x+6)))

To find the factored form of (x^(2)-64)/(x^(2)-3x-54)-(x^(2)-81)/(4x^(2)-12x-216), we will first factor each of the expressions in the numerator and denominator.

The factored form of x^(2)-64 is (x+8)(x-8).

The factored form of x^(2)-3x-54 is (x-9)(x+6).

The factored form of x^(2)-81 is (x+9)(x-9).

The factored form of 4x^(2)-12x-216 is (2x-18)(2x+12).

Now, we can substitute the factored forms back into the original expression:

((x+8)(x-8))/((x-9)(x+6))-((x+9)(x-9))/((2x-18)(2x+12))

Next, we will simplify the expression by canceling out common factors:

((x+8)(x-8))/((x-9)(x+6))-((x+9)(x-9))/(2(x-9)(2x+12))

= ((x+8)(x-8))/((x-9)(x+6))-(1/2)((x+9)/(2x+12))

= ((x+8)(x-8))/((x-9)(x+6))-(1/2)((x+9)/(2(x+6)))

= ((x+8)(x-8))/((x-9)(x+6))-(1/4)((x+9)/(x+6))

Now, we will find a common denominator and combine the two fractions:

= ((4(x+8)(x-8))-(x+9))/((4(x-9)(x+6)))

= ((4x^(2)-256)-(x+9))/((4(x-9)(x+6)))

= (4x^(2)-x-265)/((4(x-9)(x+6)))

This is the final factored form of the original expression.

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Answer:

12:44

12:16

12:08

12:32

12:28

Correct answer:

12:16

Step-by-step explanation:

Explanation:

The path traveled by the tip of the minute hand over the course of one hour is a circle of radius r=6. The circumference of that circle is

C=2πr=2π⋅6=12π.

The tip has traveled 10 inches since noon, so the fraction of the circle traveled is 1012π,

and the number of minutes that have expired since noon is 1012π⋅60≈16.

Therefore, to the nearest minute, the time is 12:16.

Answer:

Bears: 12

Tigers: 5

Step-by-step explanation:

9:15

the common factor of 9 and 15 is 3. so we divide both sides by 3.

3:5

12:20

We can use LCM to find a common denominator for these fractions. The LCM of 70, 2, and 5 is 70 x 2 x 5 = 700. The result of the expression is approximately 29.3885.

To solve this problem using LCM, we first need to convert all the mixed numbers to improper fractions:

Three and three seventieths = (3 x 70 + 3) / 70 = 213 / 70

Six and a half = (6 x 2 + 1) / 2 = 13 / 2

Nine and three fifths = (9 x 5 + 3) / 5 = 48 / 5

Now we can use LCM to find a common denominator for these fractions. The LCM of 70, 2, and 5 is 70 x 2 x 5 = 700.

We can then convert each fraction to an equivalent fraction with denominator 700:

213/70 = 3.042857... ≈ 3.043

13/2 = 455/70 = 6.5

48/5 = 192/20 = 96/10 = 480/50

Now we can substitute these equivalent fractions into the original expression and simplify:

3.043 × 6.5 + 480/50 = 19.7885... + 9.6 = 29.3885.

LCM stands for the "Least Common Multiple" and is a mathematical concept used to find the smallest multiple that two or more numbers have in common. In other words, it is the smallest positive integer that is divisible by all the given numbers.

To find the LCM of two or more numbers, we can start by finding their prime factorization. Then, we can take the highest power of each prime factor that appears in any of the factorizations and multiply them together to get the LCM. Taking the highest power of each prime factor (2^3 x 3^1), we get 24, which is the smallest multiple that both 6 and 8 have in common.

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Answer:

Below

Step-by-step explanation:

f(-5) = 85 * .95^(-5)   = 109.9 mg remaining after -5 hours   this does not fit the context of the problem  

 ( domain ( values of 'x')  should be   0 ---> infinity)

f(24) = 85 * .95^24 = 24.8 mg remaining after 24 hours   this does fit the context of the problem

Answer:

5.66666666667

Step-by-step explanation:

5.66666666667  Because you do 22-5 divided by 3 I believe.