16. Suppose that 7₁, 72 are linear dependent in a vector space V. Show that V₁ + V2, V₂ - V₁ are also linearly dependent.

Answer:

1. 1=18°, 2=90°

2. 1=85°

3. 1=97°

4. 2=83°

5. 3=49°

6. 1=94°

7. 4=45°

8. 3=65°

9. 2=79°

10. 5=73°

11. 6=147°

12. 1=26°

13. 2=32°

Step-by-step explanation:

1. all angles of a triangle equal 180. 2 is 90 degrees because you can look across to find the symbol. Then you subtract 180 by 72 and 90 to get 18.

2. do the same thing as last time, 180 minus 40 and 55.

3. In order to figure this out, you need to have the angle 2. One you have 83, angles like this, together will add up to 360 if you put 2 of them together. 83×2=166. 360-166=194. 194/2=97.

4. To figure this out, you find the angle across from it because those are always the same. Follow the same process to subtract 39 and 58 from 180 to get 83.

5.Now that you have the angle 2 you can figure this one out as well, again, follow the process of subtracting the two opposite angles from 180 to get 49.

(This is taking really long to explain so if you have questions just ask.)

Lily would need 40.64 centimeters of copper wire for her experiment.

Given data ,

We may use the conversion factor that 1 inch is equivalent to 2.54 centimeters to convert 16 inches to centimeters .

From the unit conversion ,

1 inch = 2.54 inches

Consequently, 16 inches is equivalent to :

40.64 centimeters are equal to 16 inches at 2.54 centimeters per inch.

Hence , Lily would thus want 40.64 centimeters of copper wire for her experiment.

To learn more about unit conversion click :

https://brainly.com/question/19420601

#SPJ1

Answer:

Step-by-step explanation:

I don't see a graph from which to choose.  Are the brackets in "[x+1]" supposed to be parentheses, or are they absolute value signs?

The graph of functions

(F(x) = (x+1), and

(F(x) = |x+1| are both attached.

Answer:

82.083333333333%

Step-by-step explanation:

If (x, y, z) and (x, y, z) are two distinct solutions, there must be an infinite number of solutions along the line passing through them. If 25 planes meet at two points, they meet at a common point i.e., the plane is concurrent.

If (x, y, z) and (x, y, z) are two solutions to a system of linear equations, then the line passing through these two points is also a solution. This is because the line passing through two points can be parameterized by the equation (x, y, z) = t(x1, y1, z1) + (1 - t)(x2, y2, z2) for some value of t between 0 and 1, where (x1, y1, z1) and (x2, y2, z2) are the two given solutions.

If 25 planes meet at two points, then those two points must lie on all 25 planes. Therefore, the planes must be concurrent (i.e., they meet at a common point). By the Fundamental Theorem of Linear Algebra, the number of equations in a system of linear equations must be greater than or equal to the number of unknowns for there to be a unique solution.

In this case, since there are only two points of intersection among the 25 planes, the system of equations cannot have a unique solution and must either have no solutions or an infinite number of solutions.

To know more about Linear equations:

https://brainly.com/question/11897796

#SPJ4

Answer: 10

Step-by-step explanation:

Your answer would be 10 popcorn orders.

The number of popcorn orders must be 10 in order for the total cost at Theater P and Theater Q to be the same. The correct option is B.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that theater, P charges an admission fee of $10.00 and $4.55 per small popcorn order. Theater Q charges an admission fee of $8.00 and $4.75 per small popcorn order.

The number of orders will be calculated by assuming the number of popcorn orders to be x.

Theater P charges :- 10 + 4.55x

Theater Q charges :- 8 + 4.75x  

Equate both equations.

10 + 4.55x  = 8 + 4.75x  

10 - 8 = 4.75x - 4.55x

2 = 0.2x

x = 2 / 0.2

x = 10

Therefore, the number of popcorn orders must be 10 in order for the total cost at Theater P and Theater Q to be the same. The correct option is B.

To know more about expression follow

https://brainly.com/question/723406

#SPJ2

The probability is 0.96 that a randomly selected camper does not like to have a cookout, based on the given information and the complement rule of probability.

To determine the probability that a randomly selected camper does not like to have a cookout, we need to find the complement of the event C (the event that the camper likes to have a cookout).

Looking at the Venn diagram, we see that the probability of event C is 0.04 (represented by the intersection of circles C and A). Therefore, the probability of the complement of event C (not liking to have a cookout) is equal to 1 minus the probability of event C.

1 - 0.04 = 0.96

Hence, the probability that a randomly selected camper does not like to have a cookout is 0.96.

For more such questions on  probability

https://brainly.com/question/24756209

#SPJ8

Statement (c) is correct for a simple graph. Every trail is a path, and every path is a trail.

In graph theory, a simple graph is an undirected graph with no loops or multiple edges between the same pair of vertices. A path in a graph is a sequence of vertices where each consecutive pair is connected by an edge. A trail in a graph is a path that allows for repeated vertices and edges.

Statement (a) is not correct because not every path is a trail. A path does not allow for repeated vertices or edges, whereas a trail does.

Statement (b) is not correct because not every trail is necessarily a path. A trail may contain repeated vertices or edges, but a path does not.

Statement (d) is not correct because paths and trails do have a relation. A trail is a more general concept that encompasses paths by allowing for repetition of vertices and edges.

Therefore, statement (c) is the correct statement. In a simple graph, every trail is a path, and every path is a trail.

Learn more about vertices here : https://brainly.com/question/29154919

#SPJ11

The probability that 9% or less of the people sampled are left-handed is 0.377.

Using the terms proportion, probability, and considering the constraint of 200 words, I'll provide you with an answer to your question.
The proportion of left-handed people worldwide is believed to be 10%. In a random sample of 128 Americans, you want to find the probability that 9% or less of them are left-handed.
To calculate this probability, we can use the normal approximation to the binomial distribution. First, we find the mean (μ) and standard deviation (σ) for a binomial distribution:
μ = n * p = 128 * 0.1 = 12.8
σ = √(n * p * (1-p)) = √(128 * 0.1 * 0.9) ≈ 3.24
Next, we convert the desired proportion of 9% to the number of people, which is 0.09 * 128 ≈ 11.52. Now, we'll find the z-score:
z = (x - μ) / σ = (11.52 - 12.8) / 3.24 ≈ -0.396
Finally, we use the standard normal distribution table or a calculator to find the probability associated with this z-score. The probability of having 9% or less left-handed people in the sample is approximately 0.346 or 34.6% when rounded to 3 decimal places.

Learn more about probability here:

https://brainly.com/question/2520617

#SPJ11

Answer:

12 square feet

Step-by-step explanation:

2*6=12

Answer:

G : C : A = 1 : 12 : 4

Step-by-step explanation:

Alex - A

George - G

Carl - C

A = G+12

C = 3A

A + G + C = 68

G : C : A = ?

A = G+12, --->  G = A - 12

C = 3A

A + G + C = 68 ---> A + A - 12 + 3A = 68  ---> 5A = 80 ---> A = 16

G = A - 12, G = 16 - 12 = 4, G = 4

C = 3A = 3*16 = 48, C = 48

G : C : A = 4 : 48 : 16 = 1 : 12 : 4

Answer:

Step-by-step explanation:

we do first the multiplication 3*6=18

-2+18=16

16/5 is your answer or 3.2

Answer:

75% of people own a dog.

Step-by-step explanation:

We apply the percentage formula in this problem

Total People * X/100 = Groups of people

Fill in the values

24 * X/100 = 18

We now Simplify the equation.

After simplifying you should get X=75, meaning 75% of people own a dog.

Answer:

Parallel lines never intersect, but they must be in the same plane. The definition does not require the undefined term point, but it does require plane. Because they intersect, perpendicular lines must be coplanar; consequently, plane is not required in the definition.

Step-by-step explanation:

Answer:

We can rewrite the given expressions as:

(3x² - y² - 2yz - z²) and (y² - z² - 2zx - x²)

To find the H.C.F., we can use the Euclidean algorithm. We start by dividing the first expression by the second expression:

(3x² - y² - 2yz - z²) ÷ (y² - z² - 2zx - x²)

Using long division or synthetic division, we get:

(3x² - y² - 2yz - z²) = (3x + y + z)(x - y + z) + 2y(x - z)

Therefore, the remainder is 2y(x - z). We can now divide the second expression by this remainder:

(y² - z² - 2zx - x²) ÷ 2y(x - z)

Using long division or synthetic division, we get:

(y² - z² - 2zx - x²) = -x(x - y + z) + z(x - y + z)

Therefore, the remainder is z(x - y + z).

Since the second remainder is not zero, we need to continue with the algorithm. Now we divide the remainder 2y(x - z) by the remainder z(x - y + z):

2y(x - z) ÷ z(x - y + z)

Using long division or synthetic division, we get:

2y(x - z) = 2y(x - y + z) - 2y²

Therefore, the remainder is -2y². Now we divide the previous remainder z(x - y + z) by this new remainder:

z(x - y + z) ÷ (-2y²)

Using long division or synthetic division, we get:

z(x - y + z) = -1(-2y²) + z²

Therefore, the H.C.F. of the original expressions is the absolute value of the last remainder, which is |-2y²| = 2y².

Therefore, the H.C.F. of (3x² - y² - 2yz - z²) and (y² - z² - 2zx - x²) is 2y².

The triangle DEF's section EF measures 24 units in length.

As per the data given in the above question are as bellow,

The provided details are as follow,

Procedure: Calculating the length that results from distorting a triangle by a scale factor

The triangle mentioned in the previous sentence is summarised in the diagram below. Using a trigonometric relationship, we discover that the following formula best describes the length of the section EF:

\($\sin a^{\circ}=\frac{E F}{D E}$\)

If we know that DE=30 and \($\sin a^{\circ}=\frac{4}{5}$\), then the length of the segment EF is:

\(E F=D E \cdot \sin a^{\circ} \\& E F=30 \cdot\left(\frac{4}{5}\right) \\\)

EF=24

Sine (sin), cosine (cos), and tangent (tan), which are defined in terms of the ratios of the sides of a right triangle, are the fundamental trigonometric functions.

For such more question on triangle

https://brainly.com/question/17335144

#SPJ4

Note: The correct question would be as bellow,

A triangle was dilated by a scale factor of 6. If sin a° = four fifths and segment DE measures 30 units, how long is segment EF?triangle DEF in which angle F is a right angle, angle D measures a degrees, and angle E measures b degrees

15.5 units

24 units

30 units

37.5 units

\(y = {x}^{3} + {x}^{2} + 1 \\ y = {x}^{5} + 1 \\ y - 1 = {x}^{5} \)

The linearized form of the function \(\(x^{2}+\sin(x)\)\) for x near 1.1 radians is \(\(f(x)\approx1.31002+2.45360(x-1.1)\)\)

The function \(\(x^{2}+\sin(x)\)\) needs to be linearized for x near 1.1 radians.

To linearize the given function, follow the steps below:

Step 1: Find the first derivative of the given function which is

\(\(f(x)=x^{2}+\sin(x) \) \(\frac{d}{dx}f(x)=2x+\cos(x)\)\)

Step 2: Compute the value of the function at

\(\(x=1.1\)\(f(1.1)=(1.1)^{2}+\sin(1.1) \)\(f(1.1)\approx1.31002\)\)

Step 3: Compute the value of the first derivative at

\(\(x=1.1\)\(\frac{d}{dx}f(x)=2x+\cos(x)\)\(\frac{d}{dx}f(1.1)=2(1.1)+\cos(1.1) \)\(\frac{d}{dx}f(1.1)\approx 2.45360\)\)

Step 4: Substitute the values obtained in Steps 2 and 3 into the linearization formula,

\(\(f(x)\approx f(a)+f'(a)(x-a) \)where \(a=1.1\) and \(x\) is near \(1.1\).\)

Substituting the values,

\(\(f(1.1)\approx 1.31002\) and \(\frac{d}{dx}f(1.1)\approx 2.45360\)\)

we get,

\(\(f(x)\approx1.31002+2.45360(x-1.1)\)\)

This is the linearized form of the function \(\(x^{2}+\sin(x)\)\) for x near 1.1 radians.

Learn more about function visit:

brainly.com/question/30721594

#SPJ11

The congruent corresponding parts are PQ & TS, QR & SR and PR & TR

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

PQR is congruent TSR

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

When two points are combined, we have the congruent corresponding parts to be:

Read more about similar shapes at

https://brainly.com/question/14285697

#SPJ1

Answer:

a) 14

b) 514

Step-by-step explanation:

use number line for b

514 is 14 away from 500

485 is 15 away from 500

so 514 is closer to 500

A. Using only two of the cards the smallest two-digit number that can be made is 14.

B. Using only three cards the three-digit number closest to 500 that can be made is 514.

For mathematicians, inductive and deductive reasoning are two essential types of reasoning. These two methods of thinking were the origin of the formal theorems and proofs that we use today. These two methods of reasoning are still actively used by mathematicians today to find new theorems and proofs. Whether you realize it or not, when you create assumptions about how the universe operates, you may be employing both inductive and deductive reasoning.

Four number cards are given they are 4, 5, 1, and 8.

A. Now, Using only two of the cards the smallest two-digit number that can be made is 14.

As the smallest number among them is 1 and the next smallest number is 4.

B. Using only three cards the three-digit number closest to 500 that can be made is 485 or 514 and it should be 514 as the difference between 500 and 514 is less.

learn more about mathematical reasoning here :

https://brainly.com/question/11679298

#SPJ2

Answer:

1) A, 2) A, 3) B, 4) D, 5) A, 6) proportion, 7) 4 : 3, 8) a) The simplest ratio of 14 : 42 is 1 : 3, b) The simplest ratio of 56 : 80 is 7 : 10, 9) a) The series 4, 6, 8, 12 is in proportion, since each element after the first one is equal to the sum of the previous element and 2 units, b) The series 15, 45, 5, 25 is not in proportion, since it is an alternating series, 10) 4 cans of juice cost 140, 11) a) 3 : 2, b) 3 : 1, 12) The ratio of 15 centimeters to 2 meters is 3 : 40.

Step-by-step explanation:

1) The ratio is determined by following operation:

\(x = \frac{300}{100}\)

\(x = \frac{3}{1}\)

3 : 1 is the ratio of 300 to 100. (Answer: A)

2) The weight of 1 book is found by the total weight of books divided by the total amount of books, that is:

\(x = \frac{80\,kg}{20}\)

\(x = 4\,kg\)

The weight of 1 book is 4 kilograms. (Answer: A)

3) The equivalent ratio of 3 : 2 is found by multiplicating both numerator and denominator by a given positive number:  

\(x = \frac{3\times 2}{2\times 2}\)

\(x = \frac{9}{4}\)

An equivalent ratio of 3 : 2 is 6 : 4. (Answer: B)

4) The middle terms of ratio correspond with the denominator of the ratio on the left and the numerator of the ratio on the right. Hence, the middle terms of 3 : 15 = 21 : 105 are 15 and 21. (Answer: D)

5) 8 : 4 is not proportional to 8 : 16, since both numerators and denominators are not multiplied by the same number. That is:

\(x = \frac{8\times 1}{4\times 4}\)

\(x = \frac{8}{16}\)

8 : 4 :: 8 : 16 is not proportional. (Answer: A)

6) If two ratios are equal, then they are in proportion. That is:

\(a \,:\,b \,::c\,:\,d\), where \(r = \frac{c}{a} = \frac{d}{b}\), \(\forall\,r > 0\).

If two ratios are equal, then they are in proportion. (Answer: proportion)

7) The ratio of 20 boys to 15 girls is derived of 20 divided by 15 until a denominator of the least integer is found by simplifying the fraction:

\(\frac{20}{15} = \frac{4}{3}\)

The ratio of 20 boys to 15 girls is 4 : 3. (Answer: 4 : 3)

8) Express the following ratios in the simplest form:

a) \(\frac{14}{42} = \frac{7}{21} = \frac{1}{3}\).

The simplest ratio of 14 : 42 is 1 : 3.

b) \(\frac{56}{80} = \frac{28}{40} = \frac{14}{20} = \frac{7}{10}\)

The simplest ratio of 56 : 80 is 7 : 10.

9) When a series is in proportion, it must be in increasing or decreasing order at constant rate.

a) The series 4, 6, 8, 12 is in proportion, since each element after the first one is equal to the sum of the previous element and 2 units.

b) The series 15, 45, 5, 25 is not in proportion, since it is an alternating series.

10) We determine the cost of 4 cans of juice by simple rule of three:

\(x = \frac{4\,cans}{6\,cans}\times 210\)

\(x = 140\)

4 cans of juice cost 140.

11) a) The ratio of her earning to her expenditure is:

\(x = \frac{150000}{150000-50000}\)

\(x = \frac{3}{2}\)

The earning to expenditure ratio is 3 : 2.

b) The ratio of her earning to her savings is:

\(x = \frac{150000}{50000}\)

\(x = 3\)

The earning to savings ratio is 3 : 1.

12) 1 meter equals 100 centimeters. Then, the given ratio is:

\(x = \frac{15\,cm}{200\,cm}\)

\(x = \frac{3}{40}\)

The ratio of 15 centimeters to 2 meters is 3 : 40.

The probability to get a 3 or 4 in the third toss and 6 in the fourth toss is 1/18.

The sample space for a six-sided die is

{1, 2, 3, 4, 5, 6}

Hence the total number of possibilities = 6

The rolling of a die is IID that is Independently and Identically distributed.

Hence,

the result of one toss will not affect the result of the successive tosses.

Probability

= n(E)/n

= no of favorable outcomes for any event /total no. of outcomes

Here,

n = 6

Let A be the event of getting a 3 or 4 in the third toss

Let B be the event of getting 6 on the fourth toss

E(A) = {3,4}

n(A) = 2

Hence,

P(A) = 2/6

= 1/3

B = {6}

n(B) = 1

P(B) = 1/6

Since these are IID,

P(A and B) = P(A) X (B) [Property of independent events]

Hence P(A∩B) = 1/3 X 1/6

= 1/18

To learn more about probability visit

https://brainly.com/question/17142351

#SPJ4

Answer:

D) 6 yds

Step-by-step explanation:

Rearrange pythagoras theory:

a² + b² = c² → c² - b² = a², c is the longest side (hypotenuse)

10² - 8² = x²

100 - 64 = 36

x² = 36

x = √36 = 6

Hope this helps!

Answer:

  112

Step-by-step explanation:

It appears that the relation is f(a, b) = a(a+b).

  f(3, 4) = 3(3+4) = 21

  f(2, 5) = 2(2+5) = 14

  f(7, 7) = 7(7+7) = 98

  f(8, 6) = 8(8+6) = 112

__

The symbol "+" has apparently been repurposed from its usual meaning in math. It is being used as an infix operator with two arguments. We have shown the relation above as a function f with two arguments (a, b). In our definition ...

  f(a, b) = a(a+b)

the symbol "+" has its usual meaning.

_____

Additional comment

This sort of question requires a little bit of "out of the box" thinking. It helps immensely if you're familiar with your addition and multiplication facts. Then you are in a position to recognize how the outputs may be related to the inputs.

The definition of percent helps you write fraction and decimal equivalents by understanding that "per cent" means "per hundred".

For example, if you are asked to write the fraction and decimal equivalent of 25%, you would divide 25 by 100 to get the fractional equivalent of ¼, and divide 25 by 100 to get the decimal equivalent of 0.25.

The decimal equivalent of a fraction or percentage is the numerical value expressed in decimal form. For example, the decimal equivalent of 1/2 is 0.5 and the decimal equivalent of 25% is 0.25. Decimal equivalents are useful for calculations and can be used to convert fractions and percentages into decimal form.

Learn more about decimal equivalent :

https://brainly.com/question/28513467

#SPJ74

(a) To find three integral values of x such that there are no real-valued eigenvalues for the 2x2 matrix A, we can consider values of x that make the determinant of A negative. Since A is a 2x2 matrix, its determinant can be expressed as ad - bc, where a, b, c, and d are the elements of the matrix.

For A = [4], we have a = 2, b = 3, c = 3, and d = 2. We can select integral values of x that make the determinant negative. For example, if we choose x = -1, then the determinant of A becomes 2*2 - 3*(-1) = 7, which is positive. Therefore, x = -1 is not a suitable value. We can continue this process to find three integral values of x for which the determinant is negative and thus ensure there are no real-valued eigenvalues.

(b) To calculate one eigenvalue and the corresponding eigenvector of the matrix B = [[-x, 0, x], [-6, -2, 0], [19, 5, -4]], we need to substitute the smallest positive integral value of x determined in part (a). Let's assume x = 1. We can find the eigenvalues λ by solving the characteristic equation |B - λI| = 0, where I is the identity matrix. Solving this equation for B = [[-1, 0, 1], [-6, -2, 0], [19, 5, -4]], we find the eigenvalues λ = -2 and -3.

For λ = -2, we substitute this value back into the equation (B - λI)v = 0 and solve for the corresponding eigenvector v. We obtain the system of equations:

-3v1 + 0v2 + v3 = 0

-6v1 - 0v2 + 0v3 = 0

19v1 + 5v2 - 2v3 = 0

Solving this system, we find v1 = 5/7, v2 = 1, and v3 = 0. Therefore, the eigenvector corresponding to the eigenvalue λ = -2 is v = [5/7, 1, 0].

(c) To calculate the determinant of matrix B, we substitute the smallest positive integral value of x determined in part (a) into matrix B and find its determinant. Assuming x = 1, we have B = [[-1, 0, 1], [-6, -2, 0], [19, 5, -4]]. Evaluating the determinant, we have det[B] = (-1)*(-2)*(-4) + 0*(-6)*19 + 1*(-2)*5 = 8. Therefore, the determinant of B is 8.

(d) The command in MATLAB for solving the equation -1i + 5j - 2 = -21 - 3j = 3 would involve defining the system of equations and using the solve function. Assuming the equation is -1*i + 5*j - 2 = -21 - 3*j + 3, the MATLAB commands would be as follows:

syms i j

eq1 = -1*i + 5*j - 2 == -21 - 3*j + 3;

sol = solve(eq1, [i, j]);

The solution sol will provide the values of i and j.

Learn more about matrix : brainly.com/question/28180105

#SPJ11

To find the percentage, we can use the following formula:

Percentage = (Part / Whole) * 100

So, $131,701.32 is approximately 16.67% of $790,207.91.

In this case, the part is $131,701.32 and the whole is $790,207.91.

Percentage = ($131,701.32 / $790,207.91) * 100

Calculating the value:

Percentage ≈ 0.1667 * 100

Percentage ≈ 16.67%

Therefore, $131,701.32 is approximately 16.67% of $790,207.91.

Alternatively, we can calculate the percentage by dividing the part by the whole and multiplying by 100:

Percentage = ($131,701.32 / $790,207.91) * 100 ≈ 0.1667 * 100 ≈ 16.67%

So, $131,701.32 is approximately 16.67% of $790,207.91.

If you have any further questions, feel free to ask!

Learn more about Percentage here

https://brainly.com/question/24877689

#SPJ11

The value of f'(4) is -E/4.

The derivative is a fundamental concept in calculus that measures the rate at which a function changes. Geometrically, the derivative represents the slope of a function at a particular point. The derivative of a function f(x) at a point x = a is denoted by f'(a).

To find f'(4), we need to take the derivative of f(t) with respect to t and then evaluate it at t=4.

f(t) = 2V1 - VE

Taking the derivative of f(t) with respect to t,

f'(t) = 0 - E d/dt(t)^(1/2)

f'(t) = - E / (2 sqrt(t))

Now we can substitute t=4 to get:

f'(4) = - E / (2 sqrt(4))

f'(4) = - E / 4

To know more about derivatives, here

https://brainly.com/question/30365299

#SPJ4