Diagonalize the following matrix. The real eigenvalues are given to the right of the matrix. -2 1 1 - 4 3 4 ; 2 = -1,4 -2 2 1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. For P=___ D= 0 4 0 0 0 4 -1 0 0 O B. For Pa = ___ D = 0 -1 0 0 04 OC. O The matrix cannot be diagonalized.

Answer:

[tex]x=\sqrt{153}[/tex]

Step-by-step explanation:

[tex](\overline{BC})^2 = (\overline{AB})^2 + (\overline{AC})^2\\\\(13)^2=(x)^2+(4)^2\\\\169 = x^2+16\\\\169-16=x^2\\\\153=x^2\\\\\sqrt{x^2} = \sqrt{153}\\\\x=\sqrt{153}[/tex]

The table representing the given absolute function should be completed as follows;

x          f(x)

6          8

-1          6

4          4

9         14

Based on the information provided, we have the following absolute function:

f(x) = |-2x + 4|

When x = 6, the value of the absolute function is given by;

f(6) = |-2(6) + 4|

f(6) = |-12 + 4|

f(6) = |-8|

f(6) = 8

When x = -1, the value of the absolute function is given by;

f(-1) = |-2(-1) + 4|

f(-1) = |2 + 4|

f(-1) = |6|

f(-1) = -6.

When the value of the absolute function y = 4 is given by;

4 = |-2x + 4|

±4 = -2x + 4

2x = 4 ± 4

2x = 8

x = 4 or 0.

When the value of the absolute function y = 14 is given by;

14 = |-2x + 4|

±14 = -2x + 4

2x = 4 ± 14

2x = 18

x = 9 or 5.

Learn more about function here: https://brainly.com/question/17136585

#SPJ1

Answer:

The probability that the two biscuits were not the same type is 58.4%.

How much is the probability that the two biscuits were not the same type?

The probability that they are different is the opposite of the probability that they are the same.

The probability that they are the same is:

⇒ P(plain, plain) = (12/20) (11/19) = 132 / 380

⇒ P(chocolate, chocolate) = (5/20) (4/19) = 20 / 380

⇒ P(currant, currant) = (3/20) (2/19) = 6 / 380

⇒ P(same) = 132/380 + 20/380 + 6/380

⇒ P(same) = 158/380

⇒ P(same) = 79/190

Therefore, the probability that they are different is:

⇒ P(different) = 1 − 79/190

⇒ P(different) = 111/190

⇒ P(different) ≈ 58.4%

What does probability mean?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

Answer:

y = -3x + 12.96

y = [tex]\frac{-4}{3}[/tex] x + 11.31

Step-by-step explanation:

6x + 2y = 25.92  Subtract 6x from both sides

2y = -6x + 25.92  Divide all the way through by 2

y = -3x + 12.96

4x + 3y = 33.93  Subtract 4x from both sides

3y = -4x + 33.93  Divide all the way through by 3

y = [tex]\frac{-4}{3}[/tex] x + 11.31

Null hypothesis (H0): There’s no effect in the population. Alternative hypothesis (Ha or H1): There’s an effect in the population.

The null and alternative hypotheses are two opposing ideas that researchers use a statistical test to analyze evidence for and against: The null hypothesis (H0) states that there is no influence in the population. Alternative hypothesis (Ha or H1): There is a population effect.

Identify the null and alternative hypotheses.

As well as the sample size, specify.

Choose a suitable statistical test.

Gather information (note that the previous steps should be done prior to collecting data)

Based on the sample data, compute the test statistic.

Examine the null hypothesis, usually indicated by H0.

Always write the alternative hypothesis, which is usually marked by Ha or H1, with less than, greater than, or not equals symbols, i.e., (,>,or).

To learn more about alternative hypotheses to refer:

https://brainly.com/question/28331914

#SPJ4

Her painting rate in window frames per hour will be;

⇒ 1.6 frames per hour

Her painting rate in hours per window frame will be;

⇒ 0.25 hours per window frame

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Joyce painted 8 window frames in 5 hours while earning money for college.

Here, Joyce painted 8 window frames in 5 hours while earning money for college.

Hence, Her painting rate in window frames per hour is,

⇒ 8/5

⇒ 1.6 frames per hour

And, Her painting rate in hours per window frame is,

⇒ 5/8

⇒ 0.25 hours per window frame

Thus, Her painting rate in window frames per hour = 1.6 frames per hour

Her painting rate in hours per window frame = 0.25 hours per window frame

Learn more about the divide visit:

https://brainly.com/question/28119824

#SPJ1

Interval Notation is a way of expressing a subset of real numbers by the numbers that bound them. We can use this notation to represent inequalities. We know an interval expressed as 1 < x < 5 denotes a set of numbers lying between 1 and 5.

Interval notation is a method to represent an interval on a number line. In other words, it is a way of writing subsets of the real number line. An interval comprises the numbers lying between two specific given numbers. For example, the set of numbers x satisfying 0 ≤ x ≤ 5 is an interval that contains 0, 5, and all numbers between 0 and 5.

Interval Notation is a way of expressing a subset of real numbers by the numbers that bound them. We can use this notation to represent inequalities. We know an interval expressed as 1 < x < 5 denotes a set of numbers lying between 1 and 5.

To learn more about interval notation:

https://brainly.com/question/29531272

#SPJ4

The beads in each bucket will weigh 1 pound

A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole.

From the graph, we have weights of 0, 1/2, 1 1/2 and 2 pounds.

In order for Clare to distributes all of the beads equally among the buckets, she need to add up weight of the beads and divide by 5.

weight in each bucket = (0 + 1/2 + 1 1/2 + 2)/5 = 5/5 = 1 pound

Thus, each bucket weighs 1 pound

Learn more about fractions on:

brainly.com/question/11562149

#SPJ1

The required phrase to translate the expression x + 7 is, A number increases by 7 or an Addition of number and 7.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Given expression x + 7,
The expression can be translated as a number increase by 7 or the Addition of the number and 7.

Thus. the required phrase to translate the expression x + 7 is, A number increases by 7 or an Addition of number and 7.

Learn more about models here:
https://brainly.com/question/22591166
#SPJ1

Answer: 12 units

Step-by-step explanation:

∴ Area of Square = side length × side length

⇒144 = lengt²

⇒length = √144

⇒length = 12 units ANSWER

hope that helps...

FG is an abbreviation for "Femtogram," which is a unit of mass equal to one quadrillionth of a gram (10^-15 g).

An exclamation is an emphatic expression of emotion or emphasis. It is often used to express strong feelings such as surprise, joy, excitement, anger, or disbelief. Exclamations are also used to emphasize a point or give an opinion. Exclamations are most commonly used in spoken language, particularly in informal conversations. They can also be used in written language, but they should be used sparingly. Exclamations are often followed by an exclamation point, although they can also be followed by a question mark or an ellipsis. Exclamations can be used to add emphasis or emotion to a statement, making it more powerful and memorable.

Learn more about unit here

https://brainly.com/question/19866321

#SPJ4

Answer:Mathematics2 minutes ago

+5 pts

J31) what are the undefined values for sinx cosx / 1 - sin²x , where 0 ≤ x < 2pi ? how?

Step-by-step explanation:

Earth's rotation and revolution are both very slow motions, so slow that we don't feel them. The rate of Earth's rotation is about 1,000 miles per hour, and the speed of its revolution is about 67,000 miles per hour, but both of those speeds are so slow that we don't feel any movement or acceleration.

Earth's rotation and revolution are both very slow motions, so slow that we don't feel them. The rate of Earth's rotation is about 1,000 miles per hour and its revolution is about 67,000 miles per hour, but both of these speeds are too slow to be felt.Earth's rotation and revolution are both very slow motions, so slow that we don't feel them. The speed of Earth's rotation is about 1,000 miles per hour, and the speed of its revolution is about 67,000 miles per hour, but both of those speeds are so slow that we don't feel any movement or acceleration.

Learn more about rate here

https://brainly.com/question/13481529

#SPJ4

The ^ operator in logical mathematics means the OR operation . Therefore , the statement ∧ and ∠means that a or the negation of a is joined by the or operation .

These are known as logical operations as they are based upon logic.The meaning of the term logic is reasoning which means to resonate. The reasoning may be a legal opinion or mathematical confirmation.

We apply logic on expression to check whether they are true of false . Some of the mathematical logics are a negation, conjunction, and disjunction logical operations. The symbols used for them in mathematical logic is, ‘~’ for negation ‘^’ for conjunction and ‘ v ‘ for disjunction.

To learn more about logical operations

brainly.com/question/13092292

#SPJ4

Answer: In order to calculate the value of 3h(2) + 4g(1), we would need to know the specific functions h(x) and g(x) that you are referring to. Without more information, it is not possible to determine the value of the expression.

Typically, piecewise functions are defined by several different expressions, each defined over a different interval of the input variable x. To evaluate a piecewise function at a specific value of x, we must first determine which interval that value of x falls into, and then use the corresponding expression for that interval to find the output value.

Are you able to provide the piecewise functions, or are you just using them as an example?

Also, in case if you want to describe the functions in words, please let me know.

Step-by-step explanation:

Answer:

No, I will not simplify -164

Step-by-step explanation:

You can not Simplify -164

so the answer will be you can not simplify it

Answer:

x = 11

Step-by-step explanation:

The two angles are consecutive interior angles so they add up to 180

13x -26 + 5x + 8 = 180

13x + 5x -26 + 8 = 180

18x - 18 = 180
18x = 180 + 18

18x = 198

x = 11

Answer:

9, after being converted to a mixed number

Step-by-step explanation:

Just divide 27 by 3, it’ll equal 9

yw :)

hope i helped, reach out if it’s wrong (it’s not lol)

Have a great day :3

Answer: 9

Step-by-step explanation:

since fraction means we divide the numerator by denominator, we divide 27 by 3

⇒27/3

⇒27 ÷ 3

⇒9 answer

hope that helps ...

Answer:

b

Step-by-step explanation:

I think number B is the answer. because the square becomes root when it crosses the = . So, the answer is B

Answer:

  b.  ±√60

Step-by-step explanation:

You want to know the solution to x² = 60.

In general, the process of solving for a variable's value requires you to "undo" what is done to the variable. This generally means you use inverse operations. The inverse of the squaring operation is the square root operation.

Taking the square root of both sides, we get ...

  √(x²) = √60

  |x| = √60 . . . . . . simplify the left side

  x = ±√60 . . . . . . . write the equivalent without the absolute value bars

__

Additional comment

As with any operation performed on an equation, it must be done to both sides of the equal sign.

You will get a ±(radical) result whenever you take an even-index root: square root, fourth root, sixth root, and so on. Odd-index roots will have the same sign as the value under the radical.

  √64 = ±8

  ∛64 = 4; ∛-64 = -4

The required solution are as follows,
(A) Kyra's equation of line, passes through 15 pts.
(B) Liam's equation of line, passes through 20 pts.
(C) the equation of line passes through 30 pts is y = 4/3x + 5.

A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.

here,
Drawing the graph on the graph and evaluating which line pass through which points,

(A)

Kyra's equation of a line is y = 1/2 x
And from the graph, it is seen that the line passes through 15pts

Similarly,
(B) passes through 20 pts

(C)

from the graph, it is seen that equation y = 4/3x + 5 passes through 30 points.

Learn more about lines here:

brainly.com/question/2696693

#SPJ1

Victoria has 37 dimes and 28 quarters in total.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.

Given is that Victoria has a total of 65 dimes and quarters worth $10.70.

We can write the system of equations as -

x + y = 65

(1/10)x + (1/4)y = 10.70

Refer to the graph attached. On solving the equation graphically, we get-

x = 37, y = 28

Therefore, Victoria has 37 dimes and 28 quarters in total.

To solve more questions on equations & expressions visit the link below -

brainly.com/question/17421223

#SPJ1

Answer: No rectangle can make this shape

Step-by-step explanation:

The function g(x) = 1. 8x2 greater than the average rate is k(x) = 2x^2

How to calculate average rate?

The average rate is a measure of how quickly a quantity changes over a specific period of time. It can be calculated by dividing the change in the quantity by the change in time. The formula for calculating the average rate is:

Average rate = (final value - initial value) / (final time - initial time)

Given a function y, the average rate of change S of y = f(x)  in an interval (Xs, Xf)  will be given by the following equation:

In this problem, we have that:

Interval (1,5), so

Then

S = f(5) - f(1)/4

All options are compared to g(x).

g(5) = 1.8*(5)^2 = 45

g(1) = 1.8*(1)^2 = 1.8

An average rate of change greater than 10.8.

D.=k(x) = 2x^2

k(5) = 2*(5)^2 = 50

k(1) = 2*(1)^2 = 2

Greater than 10.8, this is the answer.

Hence, The function g(x) = 1. 8x2 greater than the average rate is k(x) = 2x^2

To learn more about average rate, Visit

https://brainly.com/question/24313700

#SPJ4

Answer:

g (x) = −7 x 2 + 26 x + 8

Step-by-step explanation:

The measures of three angles are 40.5°, 43.5° and 95.8°.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

Given that, an interior designer plans to use triangular tiles that are 8 cm×9 cm×13 cm for a backsplash.

Using cosine rule, we get

9²= 8²+ 13²- 2(8)(13) cos θ (angle opposite 9 cm side.)

81=64+169-208 cos θ

81-233=-208 cos θ

-208 cos θ=-152

cos θ=-152/(-208)

cos θ=0.7307

θ=43.7°

Using sine rule,

The formula for sine rule is sinA/a=sinB/b=sinC/c

sinA/8 =sin43°/9=sinC/13

sinA/8 =0.7307/9

sinA/8=0.0811

sinA=0.6495

A=40.5°

So, ∠A+∠B+∠C=180°

40.5°+43.7°+∠C=180°

∠C=95.8°

Therefore, the measures of three angles are 40.5°, 43.5° and 95.8°.

Learn more about the sine rule here:

https://brainly.com/question/22288720.

#SPJ1

No, 1 gram is not equal to 1 mole. The numerical values of mole and gram are different for an object.

What is 1 gram?

Avogadro number of atoms makes up one mole. It is possible to convert a mole into grams if you know the mole quantity.

Mole: The International System of Units uses the mole (symbol: mol) as the unit of material quantity. How many elementary entities of a particular substance are present in an object or sample is determined by the quantity of that material. It is specified that the mole contains exactly 6.02214076×10²³ elementary entities.

The relation between  gram  and mole is

1 gram = Mole × atomic weight.

To learn more about mole and gram, click on the below link:

https://brainly.com/question/29061471

#SPJ4

The 8-year-old car could be worth approximately $3000.

The graphs that show the association between two variables in a data collection are called scatter plots. It displays data points either on a Cartesian system or a two-dimensional plane.

The X-axis is used to represent the independent variable or characteristic, while the Y-axis is used to plot the dependent variable. These diagrams or graphs are frequently used to describe these plots.

In the graph attached below, we can see that when the age of the car is 8 years, the resale value of the car is between points 40 and 20.

Thus, The 8-year-old car could be worth approximately $3000.

(Refer to the image attached for the complete question and graph)

To know more about scatter plot visit: brainly.com/question/29231735

#SPJ4

It will cost $10.00 to waterproof a canvas truck cover that is 15' x 24'.

To find this, we need to first convert the dimensions of the canvas truck cover from feet to yards, since the cost is given per square yard. 15' x 24' = 180 sq ft. 1 sq yard is equal to 9 sq ft, so 180 sq ft/9 sq ft/yard = 20 sq yard. Then we multiply the square yards by the cost per square yard to find the total cost:

It's important to note that the measurements of the canvas truck cover are given in feet and the cost is given per square yard. It's important to convert it to square yards to match the unit of measurement and calculate the cost.

Learn more about Dimensions here:

https://brainly.com/question/27404871

#SPJ4

The ratios on the double line are 3:7, 6:14, 12:28 and 15:35.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given that, Lin makes her favorite juice blend by mixing cranberry juice with apple juice in the ratio shown on the double number line.

From the given double line, the ratio is 9:21.

Completed double line has the following ratios

3:7, 6:14, 12:28, 15:35

Therefore, the ratios on the double line are 3:7, 6:14, 12:28 and 15:35.

To learn more about the ratio visit:

brainly.com/question/13419413.

#SPJ1

Answer:

a) 3

b) 16 Celsius

Answer:

A. -4°C

B. 16°C

Step-by-step explanation:

A. (-7°C)-(-3°C)= -4°C

Therefore Paris is -4°C colder than Malé.

B. 23+(-7°C)=16°C

Therefore the temperature in Rome is 16°C

Hope it helps you

PLS RATE AS BRAINLIEST ANSWER