use this triangle for problems 4 and 5
1. What is the length of AB
2. What is the area of this triangle​

A is invertible and its inverse is B = (-1/3)(A^3 + 2A - In). To show that A is invertible, we need to find a matrix B such that AB = BA = In, where In is the identity matrix of size

n × n.

First, let's rearrange the given equation:
A – 2A^2 -A^4 + 3In = 0
A^4 + 2A^2 - A + 3In = 0
Next, let's factor out A from the left side of the equation:
A(A^3 + 2A - In) = -3In

Now, let's multiply both sides of the equation by -1/3:
(-1/3)A(A^3 + 2A - In) = In

finally, let's set B = (-1/3)(A^3 + 2A - In):
AB = (-1/3)A(A^3 + 2A - In) = In
Therefore, the inverse of A is B = (-1/3)(A^3 + 2A - In).

To check our answer, we can multiply A and B to see if we get the identity matrix:
AB = A[(-1/3)(A^3 + 2A - In)] = (-1/3)(A^4 + 2A^2 - A) = (-1/3)(0) = In
You can read more about matrix at https://brainly.com/question/1279486

#SPJ11

To add or subtract the given expressions, we need to combine like terms. Like terms are terms that have the same variable and exponent.

Step 1: Combine like terms for a^(2):
6.9a^(2) + 0 = 6.9a^(2)
Step 2: Combine like terms for b^(2):
-2.3b^(2) + (-2.5b^(2)) = -4.8b^(2)
Step 3: Combine like terms for ab:
2ab + 0 = 2ab
Step 4: Combine like terms for a:
0 + 3.1a = 3.1a
Step 5: Combine like terms for b:
0 + b = b
Step 6: Put all the combined terms together:
6.9a^(2) + (-4.8b^(2)) + 2ab + 3.1a + b
Step 7: Simplify the expression:
6.9a^(2) - 4.8b^(2) + 2ab + 3.1a + b

So the final answer is 6.9a^(2) - 4.8b^(2) + 2ab + 3.1a + b.

To know more about expressions refer here:

https://brainly.com/question/14083225

#SPJ11

Answer:

Step-by-step explanation:

The solution of inequality is n < - 9

The equation that can be used to determine Greg's score is 15 - 8 = x. This equation shows that if you subtract 8 points from Ben's score of 15 points, you will get Greg's score.

Step-by-step explanation:

In conclusion, the equation 15 - 8 = x can be used to determine Greg's score.

For more information about equation, visit:

https://brainly.com/question/22688504

#SPJ11

The six primary sources of greenhouse gas emissions in the United States are:

2. The seven types of greenhouse gases of climate change are:

3. The four types of Machine learning are:

Learn more about greenhouse

brainly.com/question/13706708

#SPJ11

Answer: 50 chocolate cones

Step-by-step explanation: if 5 is 125 vanilla then 125/5= 25 so every 1=25 and that means 2*25= 50

Answer:

50. There were 50 chocolate cones sold.

Step-by-step explanation:

so we do it like this: see the attachment for the work i did to solve

*Baige=Vanilla*

*brown=chocolate*

when you cross multiply you get 50

Convert the expression as follows:

To Show:-

Answer:-

The ratio given to us is ,

[tex]\implies (y + 2) : ( y + 7) = k : 1 \\[/tex]

In fraction form we can write it as ,

[tex]\implies \dfrac{y+2}{y+7}=\dfrac{k}{1} \\[/tex]

Now solve for y , by cross multiplying,

[tex]\implies 1( y + 2 ) = k( y + 7) \\[/tex]

Simplify the brackets,

[tex]\implies y + 2 = ky + 7k \\[/tex]

Subtract ky on both sides ,

[tex]\implies y - ky + 2 = 7k \\[/tex]

Subtract 2 on both sides,

[tex]\implies y - ky = 7k - 2 \\[/tex]

Take out y as common from LHS ,

[tex]\implies y ( 1 - k ) = 7k - 2 \\[/tex]

Divide both the sides by (1-k) ,

[tex]\implies \underline{\underline{ \green{y =\dfrac{7k-2}{1-k}}}} \\[/tex]

Hence Proved !

and we are done!

The use of gears enables the exchange of torque for angular velocity (i.e., if the gears are of unequal size, the larger gear will experience higher torque but lower angular velocity than the smaller gear).

Any organized assembly of resources and procedures united and regulated by interaction or interdependence to accomplish a set of specific functions.

here, we have,

Two gears or pulleys must rotate at the same angular velocity if they are attached to the same axle.

Since the angle doesn't change the unit in any way, the work unit is also in ft-lbs. The rotating equivalent of a formula you might remember from physics is "Work = Force * Distance."

Energy is preserved in a gear train if friction-related heat losses are disregarded.

A gear ratio is the comparison of the number of rotations made by the driving gear system and the driven gear.

Learn more about system here-

brainly.com/question/27162243

#SPJ1

The values of h and k are h=7 and k=46. The equation in the form (x+h)^(2)=k is (x+7)^(2)=46.

To solve the equation x^(2)+14x+3=0 by completing the square method, we need to follow these steps:

1. Rearrange the equation so that the constant term is on the right side: x^(2)+14x=-3

2. Find the value of h by taking half of the coefficient of the x term: h=14/2=7

3. Add the square of h to both sides of the equation: x^(2)+14x+7^(2)=-3+7^(2)

4. Simplify the right side of the equation: x^(2)+14x+49=46

5. Write the left side of the equation in the form (x+h)^(2): (x+7)^(2)=46

Therefore, the values of h and k are h=7 and k=46. The equation in the form (x+h)^(2)=k is (x+7)^(2)=46.

To know more about equations refer here:

https://brainly.com/question/2228446#

#SPJ11

Answer: -4

Basically, just plug in m and n as the values you were given:

The resulting amount should be zero, indicating that all the money was spent. The unknown quantity in this context is the number of players 'p', which we can solve for by rearranging the equation.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

The amount raised by the lacrosse team is $2080.50.

They rented a bus for $970.50.

For each player, they budgeted $74 for meals.

Let's represent the number of players as 'p'.

The equation that represents the context is:

2080.50 - 970.50 - 74p = 0

Or we can represent it in the tape diagram as follows:

             _______

            |       |

            | $2080.50|

            |_______|

             _______

            |       |

            | -$970.50|

            |_______|

             _______

            |       |

            | -$74p  |

            |_______|

             _______

            |       |

            |   $0   |

            |_______|

This tape diagram shows that the total amount raised by the team was reduced by the cost of the bus rental and the cost of meals for each player.

Therefore, The resulting amount should be zero, indicating that all the money was spent. The unknown quantity in this context is the number of players 'p', which we can solve for by rearranging the equation

To learn more about Algebraic expression from given link.

brainly.com/question/28884894

#SPJ1

In order to outline the yard and the garden allotment with bricks and Using Pythagorean theorem, Mariah will need to buy about 69.4  yards³ of brick.

what is pythagoras theorem ?

According to the Pythagorean Theorem, the square of the length of the hypotenuse in a right triangle equals the total of the squares of the lengths of the other two sides. The hypotenuse is the side that faces the right angle. In mathematics, it can be expressed as:

c² = a² + b²

where the lengths of the other two sides (the legs) of the right - angled triangle are a and b, and c is the length of the hypotenuse. Pythagoras, an ancient Greek mathematician, is attributed with discovering and proving this theorem, so it bears his name. Geometry, algebra, and other fields of mathematics and science all make extensive use of the Pythagorean Theorem.

given

The Pythagorean formula can be used to determine side C.

C² = A² + B²

C²= 30² + 50²

C² = 900 + 2500

C² = 3400

C ≈ 58.3

As a result, the triangle-shaped yard's circumference is:

30 + 50 + 58.3 ≈ 138.3 feet

We require information regarding the measurements of the rectangular garden plot. Let's assume it is 20 feet long and 15 feet wide.

Thus, the vegetable plot's perimeter is as follows:

2(20 + 15) = 70 feet

The perimeters must now be converted from feet to yards (since we are calculating square yards).

circumference of a triangular yard: 46.1 yards x 138.3 feet

Garden plot boundaries measured as 70 feet by 23.3 yards.

In order to calculate the overall number of bricks required, we add the two perimeters:

46.1 plus 23.3 equals 69.4 square yards.

In order to outline the yard and the garden allotment with bricks, Mariah will need to buy about 69.4  yards³ of brick.

To know more about Pythagorean theorem visit:

https://brainly.com/question/14930619

#SPJ1

The solution to the equation [tex]82-u=266[/tex] is [tex]u=-184[/tex].

To solve for u in the equation [tex]82-u=266[/tex], we can use the additive property of equality. The additive property of equality states that if you add the same value to both sides of an equation, the equation will still be true.

Step 1: We can start by isolating the variable u on one side of the equation. To do this, we can add u to both sides of the equation:

[tex]82-u+u=266+u[/tex]

Step 2: Simplify the equation by canceling out the u terms on the left side of the equation:

[tex]82=266+u[/tex]

Step 3: Next, we can use the additive property of equality again to isolate the variable u on one side of the equation. To do this, we can subtract 266 from both sides of the equation:

[tex]82-266=266+u-266[/tex]

Step 4: Simplify the equation by canceling out the 266 terms on the right side of the equation:

[tex]-184=u[/tex]

Step 5: The final step is to write the solution in the form of u=____. We can do this by simply switching the sides of the equation:

[tex]u=-184[/tex]

Therefore, the solution to the equation [tex]82-u=266[/tex] is [tex]u=-184[/tex].

See more about equations at: https://brainly.com/question/22688504

#SPJ11

The velocity of the bird is approximately 40.04 km/hour.

What is velocity ?

Velocity is a measure of the rate at which an object changes its position in a particular direction. It is a vector quantity, which means that it has both a magnitude (speed) and a direction.

To find the velocity of the bird, we can use the formula:

velocity = distance/time

Given that the bird flies 961 km in 24 hours, we can substitute these values into the formula:\

velocity = 961 km / 24 hours

Simplifying this expression, we get:

velocity = 40.04 km/hour (rounded to two decimal places)

Therefore, the velocity of the bird is approximately 40.04 km/hour.

To know more about velocity visit :

https://brainly.com/question/80295

#SPJ1

The chemist must use 12 ml of the 11% acid solution and 42 ml of the 20% acid solution to make a solution of quantity 54 ml of 18% concentration acid solution.

It is already given that the chemist wishes to make a solution of 54 milliliters of 18 percent concentration using two different solutions of concentration 11% and 20% each.

Now let us consider that the quantity of acid to be present in the final solution is (18/100)×54 = 9.72 ml

If we consider that x ml of 11% solution and y ml of 20% solution are added, then following relations can be obtained:

Total volume of x and y in the final solution = x + y = 54 ...(1)

Considering the concentration of acid and its volume, the following equation is formed:

0.11x + 0.2y = 9.72 ...(2)

Solving the equations (1) and (2) for the value of x and y, we get:

x = 54 - y

∴ 0.11(54 - y) + 0.2y = 9.72

⇒ 5.94 - 0.11y + 0.2y = 9.72

⇒ 0.09y = 3.78

⇒ y = 42 ml

Putting the value of y in equation (1), we get

x = 54 - y

x = 54 - 42 = 12 ml

Learn more about concentration at:

brainly.com/question/29437746

#SPJ4

The size (n) of the given arithmetic series is 4.

To determine the size (n) of the given arithmetic series, we need to use the formula for the sum of an arithmetic series, which is S_n = (n/2)(a_1 + a_n), where S_n is the sum of the series, n is the number of terms, a_1 is the first term, and a_n is the last term.

In this case, we are given that S_n = 968, a_1 = 38, and the common difference is 10 (since each term is 10 more than the previous one). We need to find the value of n.

Rearranging the formula to solve for n, we get:

n = (2S_n)/(a_1 + a_n)

Substituting in the given values, we get:

n = (2(968))/(38 + a_n)

Since we don't know the value of a_n, we can use the formula for the nth term of an arithmetic series, which is a_n = a_1 + (n-1)d, where d is the common difference. Substituting in the given values, we get:

a_n = 38 + (n-1)(10)

Simplifying, we get:

a_n = 10n + 28

Now we can substitute this value of a_n back into the equation for n:

n = (2(968))/(38 + 10n + 28)

Simplifying, we get:

n = (1936)/(66 + 10n)

Multiplying both sides by (66 + 10n), we get:

n(66 + 10n) = 1936

Expanding, we get:

10n^2 + 66n - 1936 = 0

Using the quadratic formula, we get:

n = (-66 ± √(66^2 - 4(10)(-1936)))/(2(10))

Simplifying, we get:

n = (-66 ± √(19396))/(20)

n = (-66 ± 139.27)/(20)

n = 3.66 or n = -10.26

Since n must be a positive integer, the only valid solution is n = 4.

To know more about arithmetic series click on below link:

https://brainly.com/question/16415816#

#SPJ11

As a result, approximately 22,500 spectators at the Super Bowl will likely not be donning club jerseys. The correct response is (C) 22,500 people.

A mathematical concept known as proportionality describes the relationship between two quantities that change in a way that keeps their ratio constant. This means that if the size of one quantity increases or decreases by a certain amount, the size of the other quantity will do the same, maintaining their relative size. In other words, we can state that A is directly proportional to B if we have two quantities, A and B, and their ratio is constant. Frequently, this is expressed as: A ∝ B or A = k * B where k is a ratio constant.

given

The number of spectators who won't be sporting team jerseys at the Super Bowl can be estimated using proportions:

If 150 out of the first 500 individuals to enter through the main gate were not donning team uniforms, then the percentage of those without team uniforms is:

150/500 = 0.3

This indicates that 30% of those who entered through the main gate did not have team jerseys on.

We can determine the approximate number of spectators who won't be donning team jerseys as follows, assuming that this proportion is representative of the entire 75,000 people in attendance:

0.3 * 75,000 = 22,500

As a result, approximately 22,500 spectators at the Super Bowl will likely not be donning club jerseys. The correct response is (C) 22,500 people.

To know more about proportionality visit:

https://brainly.com/question/29126727

#SPJ1

The value of 8#(8#8) is (A) 1/2

An operation \# for positive real numbers is defined by the equation a#b=ab/a+b. The value of 8#(8#8) is (A) 1/2. To solve, use the equation given:

8#(8#8) = (8*8)/(8+8)

= 64/16

= 1/2

Hope this helps!

Learn more about Equation

brainly.com/question/29657988

#SPJ11

The equation of the polynomial is f(x) = (1/36)(x - 3)2(x + 4)2(x + 1)3.

The equation of the polynomial can be found using the given information about the degree, zeroes, and y-intercept. The general form of a polynomial is:

f(x) = a(x - x1)n1(x - x2)n2...(x - xk)nk

Where x1, x2, ..., xk are the zeroes of the polynomial, n1, n2, ..., nk are the multiplicities of the zeroes, and a is the leading coefficient.

Using the given information, we can plug in the values for the zeroes and their multiplicities:

f(x) = a(x - 3)2(x + 4)2(x + 1)3

The degree of the polynomial is 7, which is the sum of the multiplicities of the zeroes. So, the equation is correct in terms of the degree.

Now, we need to find the value of a using the y-intercept. The y-intercept is the point where the graph of the polynomial crosses the y-axis, which means that x = 0. So, we can plug in x = 0 and the given y-intercept (0,4) into the equation and solve for a:

4 = a(0 - 3)2(0 + 4)2(0 + 1)3

4 = a(9)(16)(1)

4 = 144a

a = 4/144

a = 1/36

Now, we can plug in the value of a back into the equation to get the final answer:

f(x) = (1/36)(x - 3)2(x + 4)2(x + 1)3

Therefore, the equation of the polynomial is f(x) = (1/36)(x - 3)2(x + 4)2(x + 1)3.

Learn about Polynomial

brainly.com/question/11536910

#SPJ11

Using a graphing calculator or algebraic methods, we can find that x ≈ 71.6. Therefore, the model projects the civilian labor force to be 152 million in the year 1950 + 71.6 = 2021.6, or approximately in the year 2022.

According to the given model, the size of the civilian labor force (in millions) for selected years from 1950 and projected to 2050 can be modeled by y = - 0.0001 x^3 + 0.0058 x^2 + 1.43x + 56.7, where x is the number of years after 1950.

To find the projected civilian labor force in 2013, we need to plug in the value of x as 2013-1950 = 63 into the given model:

y = - 0.0001 (63)^3 + 0.0058 (63)^2 + 1.43(63) + 56.7
y = - 0.0001 (250047) + 0.0058 (3969) + 90.09 + 56.7
y = - 25.0047 + 23.0002 + 90.09 + 56.7
y = 144.7855

Therefore, the model projects the civilian labor force to be approximately 144.7855 million in 2013.

To find the year when the model projects the civilian labor force to be 152 million, we need to set y = 152 and solve for x:

152 = - 0.0001 x^3 + 0.0058 x^2 + 1.43x + 56.7
0 = - 0.0001 x^3 + 0.0058 x^2 + 1.43x - 95.3

Learn more about algebraic

brainly.com/question/24875240

#SPJ11

We can use the properties of logarithms to evaluate each expression. The properties of logarithms include:

1) loga (xy) = loga (x) + loga (y)

2) loga (x/z) = loga (x) - loga (z)

3) loga (x^p) = p loga (x)

4) loga (square root x) = (1/2) loga (x)

Using these properties, we can evaluate each expression as follows:

(a) loga (xy) = loga (x) + loga (y) = 3.1 + 5.8 = 8.9

(b) loga (x/z) = loga (x) - loga (z) = 3.1 - 1.1 = 2

(c) loga (y^7) = 7 loga (y) = 7 * 5.8 = 40.6

(d) loga (square root y) = (1/2) loga (y) = (1/2) * 5.8 = 2.9

Therefore, the answers are:

(a) loga (xy) = 8.9

(b) loga (x/z) = 2

(c) loga (y^7) = 40.6

(d) loga (square root y) = 2.9

Know more about properties of logarithms here:

https://brainly.com/question/30226560

#SPJ11

The value of x for the given pentagon will be 125 degrees.

In Mathematics, a polygon can be defined as a two-dimensional geometric figure that consists of straight line segments and a finite number of sides. Additionally, some examples of a polygon include the following:

• Triangle

• Quadrilateral

• Pentagon

• Hexagon

• Heptagon

• Octagon

• Nonagon

Given the values exterior angles of the pentagon such that, 70°, 60°, 65°, 40°, x°.

To calculate the value of x.

Since the Sum of all exterior angles of a pentagon is 360°,

Thus,

70 + 60 + 65 + 40 +x = 360

x + 235 = 360

x = 360 - 235

x = 125°

Therefore, the value of x for the given pentagon will be 125 degrees.

Read more on regular polygon here:

brainly.com/question/20911145

#SPJ1

The value of CB and DB are 3.25 and 5.2

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

CA = √ 4²+3²

CA = √ 16+9

CA = √ 25

CA = 5

represent DB by x

5/3+x = 4/5

25 = 4(3+x)

3+x = 25/4

3+x = 6.25

x = 6.25 - 3

x = 3.25

represent CB by y

y² = 3.25² + 4²

y²= 10.56+16

y² = 26.56

y = √ 26.56

y = 5.2

learn more about similar triangles from

https://brainly.com/question/14285697

#SPJ1

The first step would be to multiply both sides by 5 when solving the equation (3(x+4))/(5)=6.

This will allow us to eliminate the denominator on the left side of the equation and simplify the equation.After multiplying both sides by 5, the equation becomes: 3(x+4) = 30

Next, we can distribute the 3 on the left side of the equation: 3x + 12 = 30

Then, we can subtract 12 from both sides of the equation: 3x = 18

Finally, we can divide both sides by 3 to solve for x: x = 6

Therefore, the solution to the equation is x=6.

To know more about equation click on below link :

https://brainly.com/question/29538993#

#SPJ11

The probability that the selected marble is red is 0

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

Number of marbles = 10

Blue = 3

Yellow = 7

Using the above as a guide, we have the following:

P(Red) = Number of red/Number of marbles

Substitute the known values in the above equation, so, we have the following representation

P(Red) = 0/10

Evaluate

P(Red) = 0

Hence, the probability is 0

Read more about probability at

https://brainly.com/question/251701

#SPJ1

The desired solution is to the nearest quarter of a unit, the approximate solution is x=2.25.

A quarter is a fraction that represents one-fourth of a whole number or quantity. It can be written as a ratio, a decimal, or a percentage. A quarter is one of the simplest fractions, and it can be used to divide an object or number into four equal parts. It is also used to calculate percentages and proportions.

A table of values is a great way to approximate a solution to an equation. To approximate a solution to the equation f(x)=g(x) to the nearest quarter of a unit, the table of values must contain the x-values and the corresponding f(x) and g(x) values.

For example, if the equation was f(x)=2x+3 and g(x)=x+2, the table of values would look like this:

x f(x) g(x)

0 3 2

1 5 3

2 7 4

3 9 5

4 11 6

To find the approximate solution to f(x)=g(x), the table must be examined for the first x-value where the f(x) and g(x) values are equal. In this case, the x-value is 2 and the corresponding f(x) and g(x) values are both 7. Since the desired solution is to the nearest quarter of a unit, the approximate solution is x=2.25.

This method of using a table of values to approximate a solution to an equation is very simple and quick. It is a great way to get a rough answer to an equation without having to solve it. It is also a useful tool for double-checking the exact solution to an equation.

For more questions related to fraction

https://brainly.com/question/78672

#SPJ9

Answer:

19-21 inches.

Step-by-step explanation:

The average term infant's length at birth is between 19-21 inches. As would be expected, taller parents tend to produce longer neonates. At the end of their first month, most infants have increased their length by approximately 1 inch.

The mean number of days to fix defects is 3.2 days.

The random variable in this case is the number of days it takes to fix defects in a pair of eyeglasses. Therefore, the correct answer is:
rv X = the number of days to fix defects

The corresponding histogram for this frequency table would be right-skewed. This is because there is a higher probability of it taking fewer days to fix the defects, with the probability decreasing as the number of days increases.

To find the mean number of days to fix defects, we need to multiply each number of days by its corresponding probability and then sum the results. The formula for this is:

mean = ∑(x * P(x))

Where x is the number of days and P(x) is the probability of it taking that number of days.

Using the data from the table, we can calculate the mean as follows:

mean = (1 * 0.1) + (2 * 0.2) + (3 * 0.3) + (4 * 0.25) + (5 * 0.1) + (6 * 0.05)

mean = 0.1 + 0.4 + 0.9 + 1 + 0.5 + 0.3

mean = 3.2

To learn more about Mean :

https://brainly.com/question/1136789

#SPJ11

Zachary will need to earn a score of 23 on his sixth quiz to have a mean score of 22 for all six quizzes.

To find out what score Zachary needs to earn on his sixth quiz to have a mean score of 22,

We need to use the formula for the mean (or average) of a set of numbers:

Mean = (sum of all the scores) / (number of tests)

Zachary's mean score for the first five quizzes is 22.

Using the above as a guide, we have the following:

(20 + 25 + 22 + 18 + 24 + x) / 6 = 22

Evaluate the like terms

(109 + x) / 6 = 22

So, we have

109 + x = 132

Evaluate the like terms

x = 23

Hence, the score must be 23

Read more about mean at

https://brainly.com/question/14532771

#SPJ1