TRUE/FALSE: there is a basis of rn consisting of eigenvectors of a, then a is diagonalizable. TRUE/FALSE: if a is diagonalizable, then a is invertible.

The positive infinity and negative infinity on a graph is explain below.

the idea of something limitless, interminable, without bound. The normal sign of infinity, ∞, was concocted by the English mathematician John Wallis in 1655. Three principal sorts of vastness might be recognized: the numerical, the physical, and the supernatural

Positive infinity is shown by rightmost point on the graph.Its symbol is +∞.

Negative infinity is shown by leftmost point on the graph.Its symbol is -∞.

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A system of linear equations is created when two or more linear equations are put together.

Systems involving two linear equations in two unknowns will be the main topic of discussion in this section. In a subsequent chapter of this book, we will solve larger systems of equations.

Below is an illustration of a system of two linear equations. A brace is used to demonstrate how the two equations are combined to form a system of equations.

x-2y=6

2x+y=7

A two-variable linear equation like 2x+y=7 has an endless number of solutions. It has a linear graph.

Always keep in mind that every point on the line represents a solution to the problem, and vice versa.

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From the given graph we can see that the line is downwards and linear. So the correct answer is Negative, linear and strong.

In the given question,

Clear-cut harvesting of wood from forest creates long periods of time when certain animals cannot use the forest as habitats.

Partial cut harvesting is increasingly used to lessen the effects of logging on the animals.

The following scatterplot shows the relationship between the density of red squirrels, and squirrels per plot, 2 to 4 years after partial cut harvesting, and the percent of trees that were harvested in each of 11 Forests.

We have to find which of the following is the best description of the relationship displayed in the scatterplot.

From the given graph we can see that the line is downwards and linear. So the correct answer is Negative, linear and strong.

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(4, 8, 1), (0, 11, 2), and (4, 10, 8) are the translated vertices right along the y-axis.

it is given that,

A(4, 5, 1)

B(0, 8, 2)

C(4, 7, 8)

Which are in x, y, and z, format.

here we need to translate three units to the right along the y-axis.

Right means addition and we have to choose only y- coordinates.

A(4, 5, 1) → A'(4, 5+3, 1)

B(0, 8, 2) → B'(0, 8+3 , 2)

C(4, 7, 8) → C'(4, 7+3, 8)

This gives us,

(4, 5, 1) → (4, 8, 1) → (x, y, z)

(0, 8, 2) → (0, 11, 2) → (x, y, z)

(4, 7, 8) → (4, 10, 8) → (x, y, z)

thus, these are our required vertices.

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The standard deviation of days Spongebob needs to be in the office hour is 3.29.

First, we must find all probability distribution. Keep in mind, total probability is always equal to 1. So,

∑P(X) = 1

∑P(X) = P(X=3) + P(X=6) + P(X=7) + P(X=12)

1 = 0.16 + 0.2 + P(X=7) + 0.36

1 = 0.72 + P(X=7)

P(X=7) = 1 - 0.72

P(X=7) = 0.28

Next, to find standard deviation (σ) we can use this formula,

σ = [tex]\sqrt{\sum X^2\times P(X) - (\sum X\times P(X))^2[/tex]

= [tex]\sqrt{(3^2\times 0.16+6^2\times 0.2+7^2\times 0.28 + 12^2\times 0.36)-(3\times 0.16+6\times 0.2+7\times 0.28+12\times 0.36)}[/tex]

= [tex]\sqrt{74.2-(7.96)^2}[/tex]

= [tex]\sqrt{10.8384}[/tex]

= 3.29

So, standard deviation X or SD(X) is 3.29

Thus, standard deviation is 3.29 days for Spongebob needs to be in the office hour.

Your question is incomplete, but most probably your full question was (image attached)

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The change in gravitational potential energy of the climber-Earth system,=4.49*10^5j.

According to our question-

Vertical height of climber, h = 540 m

Climbers need to find changes in the gravitational potential energy of the Earth system. We know that gravitational potential energy is generated when an object changes position. It is given as

Hence, The change in gravitational potential energy of the climber-Earth system,=4.49*10^5j.

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the overall grade of bobby is 70.4%

%, which is a relative figure used to denote hundredths of any amount. Since one percent (symbolized as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified.

The word percentage comes from the Latin adverb per centum, which means "by the hundred." In the 16th century, the Latin phrase made its way into English. Later, it was shortened to percent and ended with a period. Later, the period was eliminated, and the two parts were combined to create the current one-word form of percent.

We must figure out what proportion of the overall grade each grade corresponds to in order to answer this challenge. Therefore:

85 times 30%, or 85 times 30 per 100, equals 25.5%.

tests = 72*20% = 72*20/100 = 14.4%

exam = 61*50% = 61*50/100 = 30.5%

sum of all tests, assignments, and exams

total = 25.5 + 14.4 + 30.5 = 70.4

The total grade for Bobby is 70.4%.

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f(xn) = 1 /nq → 0 ,while f(x0) = 1/q != 0

Given ε > 0,

Let N ∈ N such that , N < ε, and let δ = min(δ1, . . . , δN ).

Then if |x − x0| < δ, it means that x is either irrational or of the rational form p/q for some q > N.

Therefore , if |x − x0| < δ, it means

|f(x) − f(x0)| = |f(x)| <  1/N < ε

Rational numbers : when p and q are integers and q is not equal to 0, the representation of a rational number is in the p/q form. The integer p can be either positive, negative, or even zero. Example: 2/3

Irrational numbers are defined as decimal numbers that are not represented in fractional form. The reason for this is that there are countless repeating and non-repeating phrases after the decimal point. Example:  1.414

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The dimensions of the garden with the largest area she can enclose is  24×14 square yards.

We know very well that the area (A) of the rectangle is given by =Length ×Breadth

The maximum of y=ax²+bx occurs at x = -b/2a

Let assume the  length and width of the garden be L and W respectively.

We have given some information like my friend is using same type of fencing  for three sides and different type of fencing on the remaining side.

Rate of cedar fencing is $17/yard

So, we can say that she has to pay for cedar fencing = 17W

Rate of cheaper metal fencing is $7/yard

Then she has to pay for metal fencing = 7W+7*2L = 7W+14L

Then according to given condition, total cost paid by my friend is $672.

It means sum of cost of cedar fencing and cost of cheaper metal fencing is $672.

=>17W+7W+14L = 672

=>24W+14L = 672

=>12W+7L = 336

=>7L = 336-12W

=>L = (336-12W)/7

Then the area of the rectangular garden is given by,

A = L×W

So, here  after comparison we got that a = -12/7 and b = 48

Then maximum of W occurs at,

W = -48/(2×(-12/7)) = (48×7)/(2×12) = 336/24 = 14

Then maximum width = 14 yards

then length (L) = (336-12×14)/7 = 168/7 = 24 yards

Hence, the dimensions are 24×17 square yards.

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The 3 representation of sets Semantic form, Roster form and Set builder form

There are varoius types of set notations used for the representation of sets depending upon the way in which the elements are listed. The three set notations used for representing sets are:

a) Semantic form.

The semantic notation describes a statement to show what are the elements of a set.

b) Roster form.

In here, the elements of the sets are enclosed in curly brackets separated by commas.

c) Set builder form.

It uses a vertical bar in its representation, with a text describing the character of the elements of the set.

Therefore, Semantic form, Roster form and Set builder form are the three ways to represent a set.

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Answer:

Time when Jessie starts doing her he: 4:30

Time talked to complete the hw : 40minutes

Time Jessie finishes the hw: 5:10

The area of the semicircle is [tex]157.1 \ \text{ft}^2[/tex].

What is the are of a cirlcle?

The area of a circle is given by the following expression:

[tex]A=\pi r^2[/tex]

Here, A is the area and r is the radius of the circle.

Lenght of the perimeter of a circle is given by the following formula:

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

Here, C is the perimeter and r is the radius of the circle.

Now, length of the arc of a semicircle is given by the following formula:

[tex]\frac{C}{2}=\pi r[/tex]

Now, substitute values.

[tex]10\pi=\pi r\\r=10 feet[/tex]

Now, area of a circle is given by the following expression:

[tex]A=\pi r^2[/tex]

Here A is the area of the circle.

Now, area of the semicirle is given by the following expression:

[tex]\frac{A}{2}=\frac{1}{2} \pi r^2\\[/tex]

Now, substitute value in the above expression.

[tex]\frac{A}{2}=\frac{1}{2} \pi (10\ \text{ft})^2\\=157.1 \ \text{ft}^2[/tex]

Hence, the area of the semicircle is [tex]157.1 \ \text{ft}^2[/tex].

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Fractions can be defined as the representation of a part of a whole. A fractions consists of the numerator and the denominator.

let f(x) = [tex]\frac{p}{q}[/tex]

then 'p' represents the numerator; while 'q' represents the denominator;

where p and q belong to integers for simple fractions, while when p and q belong to other sets they can from complex fractions.

To convert a fraction into an integer we need to multiply the fraction with the the denominator so that it cancels out leaving only the numerator behind.

For fractions present in equations to get rid of all the fractions we new to multiply the equation by the LCM of the denominator of all the fractions.

Where LCM is the least common multiple.

To give an example:

let y = [tex]\frac{3}{4}[/tex]X + [tex]\frac{9}{5}[/tex]

Then the LCM for 4 and 5 will be 20;

as factor of 4 are 1,2 and that of 5 are 1,5

then to eliminate the fractions from the equation

Multiplying both sides by 20

y x 20= [tex]\frac{3}{4}[/tex]X x 20 + [tex]\frac{9}{5}[/tex] x 20

20y= 3 x 5X + 9 x 4

20y = 15X + 36

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The systems of linear equations has an infinite number of solutions  are 3x + 6y = 22 & 6x +12y = 44.

What is a linear equation?

A linear equation is an equation in which each term has at max one degree. Linear equations in variables x and y can be written in the form

y = mx + c

Main body:

Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.

When both the lines(represented by both the equations) are coincident(lying over each other), then there will have an infinite solution since in that case, they will have infinite points in common.

In the given equation

3x + 6y = 22 & 6x +12y = 44.

we can see that the cofficient are proportional to each other

[tex]\frac{x_{1}}{x_{2} } =\frac{y_{1}}{y_{2} } = \frac{z_{1}}{z_{2} }[/tex]

= 1/2

Thus, the equation must be 3x + 6y = 22 & 6x +12y = 44.

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The two lines are given as follows:

Their intersection is:

(2.19, 7.76).

The two points in which the line y = 4x - 1 passes are:

(2.19, 7.76) and (3,11).

The format of the linear function is given by:

y = mx + b.

The linear function is defined taking a pair of points, and then:

For the first line, the two points are:

(1,3) and (2,7).

The slope is:

m = (7 - 3)/(2 - 1) = 4.

Hence:

y = 4x + b.

When x = 1, y = 3, hence the intercept b is obtained as follows:

3 = 4 + b

b = -1.

Then the first line is:

y = 4x - 1.

For the second line, the points are:

(2,7) and (6,2).

Hence the slope is of:

m = (2 - 7)/(6 - 2) = -5/4 = -1.25.

Then:

y = -1.25x + b.

When x = 2, y = 7, hence the intercept b is obtained as follows:

7 = -1.25(2) + b

b = 10.5.

Hence the second line is:

y = -1.25x + 10.5.

The x-coordinate of the intersection is given as follows:

4x - 1 = -1.25x + 10.5

5.25x = 11.5

x = 11.5/5.25

x = 2.19.

The y-coordinate of the intersection is:

y = -1.25(2.19) + 10.5 = 7.76.

Another point in which the line y = 4x - 1 passes is:

y = 4(3) - 1 = 11.

Hence point (3,11).

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The absolute maximum value of the given function f(x) = 2x is 8.

Given, a function f(x) = 2x

we have to find the absolute maximum value of the function f(x) = 2x in x,

0 ≤ x ≤ 4

So, as it is clear that the given function is a one-one function and therefore it is either increasing or decreasing function.

then, the given function f(x) = 2x will be maximum at the maximum value in the domain of the function i.e. 4.

So, the absolute maximum value be

f(4) = 2(4)

f(4) = 8

8 is the absolute maximum value of the given function f(x) = 2x.

Hence, the absolute maximum value of the given function f(x) = 2x is 8.

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Between the ages of 18 and 25, the average adult in the United States B. has held seven jobs.

Emerging adulthood has been proposed as a new life stage between adolescence and young adulthood, lasting approximately 18 to 25 years. The majority of people in America are educated.

People in America between the ages of 18 and 25 want to work for themselves. As a result, they will use their educational credentials to obtain employment. So they can earn money and live their lives as they please. They do not limit themselves to one job. They always want to do so many things. So they can make more money.

As a result, the average adult in the United States worked seven jobs between the ages of 18 and 25. Therefore, based on the information given, the correct option is B.

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The length of the other leg is 8.48 cm

What is Pyhtagorean Theorem?

The Pythagorean theorem states that the sum of the squares on the legs of a right triangle equals the square on the hypotenuse (the side opposite the right angle)

Solution:

Given that:

Length of One Leg = 17 cm

Length of Hypotenuse = 19 cm

To Find:

Length of the other leg

= We know that by pythagorean theorem

[tex]base^{2} + length^{2} = hypotenuse^{2}[/tex]

17*17 + x^2 = 19*19

289 + x^2 = 361

x^2 = 72

x = 8.48 cm

The length of the other leg is 8.48 cm

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Answer:

10

Step-by-step explanation:

2-digit numbers are numbers that have two digit which they start from 10-99 so in this question i chose 10 as an example.

The required three consecutive numbers are 35, 36, 37

Let the three consecutive numbers as per the questions are x , x+1 , x+2

Since, According to the question, the product of these three consecutive numbers are 46620

Therefore, we can write

x ( x+1 )( x+2 ) = 46620

x([tex]x^{2}[/tex] + 2x + x + 2 ) = 46620

[tex]x^{3}[/tex]+ [tex]2x^{2}[/tex] + [tex]x^{2}[/tex] + 2x = 46620

Now, [tex]x^{3}[/tex] + [tex]2x^{2}[/tex] + [tex]x^{2}[/tex] + 2x - 46620 = 0

      [tex]x^{3}[/tex] + [tex]3x^{2}[/tex] + 2x - 46620 = 0

After factorization, we get

    ( x- 35 )( [tex]x^{2}[/tex] + 38x + 1332 ) = 0

x - 35 = 0 Since ( [tex]x^{2}[/tex] + 38x + 1332 ) will always be a positive number

Therefore, x = 35

So, x + 1 = 35 + 1 = 36

x + 2 = 35 + 2 = 37

Therefore, the numbers are 35 , 36 , 37

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The probability that at least 9 customers ordered an item from the value menu is 0.927​.

What is the simple definition of probability?

A probability is a number that expresses the possibility or likelihood that a specific event will take place.

                           In addition to being expressed as percentages ranging from 0% to 100%, probabilities can also be expressed as proportions between 0 and and 1.

Subtract the preceding probability from 1 to get the likelihood of 9 to 14 people ordering out from value menu.

The likelihood is 1 x 0.073 = 0.927.

Therefore, the probability that at least 9 customers ordered an item from the value menu is 0.927.

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The value of angle x is x = 50.5°

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be ΔABC

where AB = 7 cm

AC = 11 cm

∠BAC = x°

Let the angle x = θ

Now , from the trigonometric relations , we know that

sin θ = opposite / hypotenuse

So ,

sin θ = BC / AC

Now ,

From Pythagoras Theorem ,

Hypotenuse² = Base² + Height²

AC² = AB² + BC²

So , substituting the values , we get

BC² = AC² - AB²

BC² = 11² - 7²

BC² = 121 - 49

BC² = 72

BC = √72

BC = 6√2

Therefore , the value of BC is 6√2

Now ,

sin θ = BC / AC

sin θ  = 6√2 / 11

So , the value of θ is

θ = sin⁻¹ ( 6√2 / 11 )

θ = 50.478°

Therefore , the value of θ = 50.5° and x = 50.5°

Hence , The value of angle x is x = 50.5°

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The solution x is x= 5+√35 and 5-√35

What in mathematics is a quadratic equation?

A quadratic equation, or second-order polynomial equation with a single variable, is x ax2 + bx + c = 0. a 0. Since it is a second-order polynomial equation, which is ensured by the algebraic fundamental theorem, it must have at least one solution. The solution could be straightforward or difficult.

x2-10x+25=35

There were two options found:

x =(10-√140)/2=5-√ 35 = -0.916

x =(10+√140)/2=5+√ 35 = 10.916

Rearrange:

Add what is to the right of the equal sign to both sides of the equation, then rewrite the equation as follows:

x^2-10*x+25-(35)=0

Step-by-step answer:

Step 1 :

Attempting factoring by dividing the middle term

Factoring x2 – 10 – 10

x2 is the initial term, and it has a coefficient of 1.

The coefficient of the middle term, which is -10x, is -10.

"The constant," the final word, is -10.

Step 1: Multiply the constant by the coefficient of the first term. 1 • -10 = -10

Step 2 is to identify two factors of -10 whose combined value is equal to the middle term's coefficient, which is -10.

-10 + 1 = -9\s-5 + 2 = -3\s-2 + 5 = 3\s-1 + 10 = 9

No two of these factors can be discovered!!

Trinomial cannot be factored, thus.

Equation following the first step:

Step 2: x2 - 10x - 10 = 0.

Finding the Vertex of a Parabola:

2.1 Locate the vertex of y = x2 – 10x – 10.

The Vertex is the highest or lowest point of a parabola. Our parabola widens, and as a result, it has a lowest point, also known as the absolute minimum. We are aware of this even before graphing "y," as the first term's coefficient, 1 is a positive number (greater than zero).

A vertical line of symmetry runs across the vertex of every parabola. The line of symmetry would, for instance, run through the middle of the two x-intercepts (roots or solutions) of the parabola as a result of this symmetry. If the parabola actually has two true solutions, that is.

Many real-world scenarios, such as the height of an object thrown into the air that has risen after some time, can be modeled using parabolas. We can learn information from the parabola's vertex, such as the highest height an object thrown upwards can travel. We need to be able to determine the vertex's coordinates for this purpose.

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Answer:

[tex]\huge\boxed{\sf x = 7}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{x+11}{2x-5} =2\\\\Multiply \ 2x-5 \ to \ both \ sides\\\\x+11=2(2x-5)\\\\Distribute\\\\x+11=4x-10\\\\Subtract \ x \ to \ both \ sides\\\\11 = 4x-x-10\\\\11=3x-10\\\\Add \ 10\ to \ both \ sides\\\\11+10=3x\\\\21=3x\\\\Divide \ 3 \ to \ both \ sides\\\\7 = x\\\\x = 7\\\\\rule[25]{25}{2}[/tex]

We have a series of 3 transformation.

i) rotation about A 90 degree.

ii) Shifting to right by 7 units

iii) shifting up by 6 units

Given that,

In the given picture we can see 2 triangles.

Triangles abc and def are offered.

We have to find how can triangle abc be transformed into triangle def in the simplest possible way.

We know that,

ABC is transformed into DEF.

We find from the pictures given that

There are three processes in the transformation of ABC into DEF, the first of which is the Triangle transformation. ABC is 90 degrees rotated around Vertex A.

Then we would get a right triangle with AC horizontal on top and AB vertically down with vertex A same as (-5,-4)

Next is a straightforward transformation that shifts A to D, or a vertex (-5,-4) to (2,2)

To accomplish this, an initial movement of 7 units to the right is made A as (2,-4)

Now next is vertically up by 6 units so that A becomes (2,2)

Therefore, We have a series of 3 transformation.

i) rotation about A 90 degree.

ii) Shifting to right by 7 units

iii) shifting up by 6 units

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Implicit or Doubtful memory of actual events that was stored encrypted, but was not retrieved for a long time until subsequent events suddenly brought it back to consciousness. The establishing, stabilizing like processes include in this memory.

Implicit Memory is a type of long-term memory and it is also known as unconscious memory or automatic memory. Implicit memory draws on past experiences to remember things without thinking. The power of tacit memory is made possible by past experiences, regardless of how long ago those experiences were.

Second stage of long-term memory formation.

Implicit memory, a subset of procedural memory, allows you to perform many everyday physical activities, such as walking and cycling, without having to think about it. Most of the implicit storage is procedural in nature.

For example:

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If Archer can paint a room in 4 hours, while Ollie can do it in 3 hours. If they work together then it will take 206 minutes to paint two rooms.

What is the relation between work and time?

Work Problems are word problems that involve different people or entities doing work but at different rates.

Work = Efficiency x Time

According to the given question:

Archer paints a room in = 4 hours

Work done by him in an hour =1/4

Ollie paints a room in = 3 hours

Work done by him in an hour = 1/3

So, work done by them in an hour W = (1/4 +1/3)= 7/12.

They both will complete the work in = 1/W

= 1/7/12

= 12/7 hours

≈ 103 minutes

Therefore it take 103 minutes to paint one room together.

To paint two rooms it will take 103 x 2 = 206 minutes together.

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Option C is correct, If two variables are correlated to each other It is usually shown on the vertical axis of a scatter diagram.

In statistics, correlation or dependence is any statistical dating, whether or not causal or no longer, among random variables or bivariate records. Even though in the broadest sense, “correlation” may additionally imply any sort of association, in statistics it normally refers back to the diploma to which a couple of variables are linearly related.  

Acquainted examples of based phenomena consist of the correlation between the peak of mother and father and their offspring, and the correlation between the rate of an excellent and the amount the clients are inclined to buy, as it’s far depicted within the so-referred to as call for the curve.

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Another way to express 11 + 77 is to using absolute values making it  equal to

The use of equality sign introduces a number or equation which is equal and hence can be used to replace another item

solving this expression gives 11 + 77 = 88

The equation can also be replace in equation terms using absolute values

where it can be written as

|-11 + -77|

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A relation where each input has precisely one output was described as a function. Each input is mapped to a single output value, in other words. Every input value is translated into a single distinct output value in a one-to-one function. Another way to phrase it is that no two input items produce the same output value.

The function f(x)=x +2 is depicted in the graph above. This graph does not map the same x-value to the same y-value everywhere, indicating that it is a one-to-one function.

Here are some additional one-to-one functions:

Because no 2 input values have the same cube root and thus do not produce the same outputs, X³+1 is a one-to-one function.

Because different inputs might result in the same outputs, X² is not a function. Consider the numbers -1 and 1. These two values both produce the value 1, indicating that this equation is not one-to-one.

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