How to do this question

There exist no subspaces S, T, and U of R³ such that SIT, SIU, and T∩U.

In order to answer the given question, we first need to understand the definition of subspaces of a vector space.A subspace of a vector space is a subset that meets three requirements:

i) It includes the zero element of the vector space.

ii) It is closed under addition (if u and v belong to the subspace, then u + v is also in the subspace).

iii) It is closed under scalar multiplication (if u is in the subspace and k is a scalar, then ku is also in the subspace).

there exist no subspaces S, T, and U of R³ such that SIT, SIU, and T∩U.

The reason is simple because if T∩U = Ø, then either SIT or SIU will be the trivial subspace {0}.

However, this contradicts the fact that both SIT and SIU have to contain a non-zero vector as they are subspaces that are generated by S, T, and U.

Therefore, it is proven that there exist no subspaces S, T, and U of R³ such that SIT, SIU, and T∩U.

Know more about vector space here,

https://brainly.com/question/30531953

#SPJ11

Answer:

x=4

Step-by-step explanation:

so there are two triangles in that shape and they are similar to each other because their angles are equal and the ratio of their sides it 1:2

so the ratio of the side 5x & 40 is 1:2

5x/40=1/2

10x=40

x=4

After considering the given data we conclude that value of monthly payments will achieve this is $25,000 over 17 years at a 7% annual interest rate under monthly compounding is $203.

To evaluate the monthly payments that will amortize a debt of $25,000 over 17 years at a 7% annual interest rate under monthly compounding, we could apply the following steps:
Alter the annual interest rate to a monthly interest rate by applying division of 12. The monthly interest rate is 7% / 12 = 0.5833%.
Alter the number of years to the number of months by multiplying by 12. The number of months is 17 × 12 = 204.
Apply the formula for the monthly payment on an amortized loan:
[tex]P = (r * PV) / (1 - (1 + r)^{(-n))}[/tex]
Here,
P = monthly payment,
r = monthly interest rate,
PV = present value of the loan (which is $25,000),
n = total number of payments (which is 204).
Placing in the values, we get:
[tex]P = (0.005833 * 25000) / (1 - (1 + 0.005833)^{(-204))} = $202.91[/tex]
Hence, the monthly payments that will amortize the debt of $25,000 over 17 years at a 7% annual interest rate under monthly compounding is $203 (rounded to the nearest dollar).
To learn more about interest rate
https://brainly.com/question/25720319
#SPJ4

Answer:

x = 7.875

Step-by-step explanation:

Let the number = x

When a number is multiplied by 5 before subtracting from 78 the result obtained is the same as three times the sum of the number and 5 find the number

Hence,

78 -(x × 5) = 3(x + 5)

Expand the brackets

78 - 5x = 3x + 15

Collect like terms

78 -15 = 3x + 5x

63 = 8x

x = 63/8

x = 7.875

Answer:

900

Step-by-step explanation:

Answer: 34.5

Step-by-step explanation:

(Base · Height) ÷ 2 → (2 · 4.5) ÷ 2 = 5.5

5.5 · 5 = 27.5

27.5 + 7 = 34.5

2- y= -5

3-  y= 2x

4- y= -4

5- y= 6x,,, 60

6-   -4,,,,,,,,,   36

Answer: x^2+5x-14

Step-by-step explanation:

2 and -7 are the roots of the polynomial then we have to write them as

 x=2 ,x=-7

To convert these as factors, we have to write them as

(  x-2) (x+7)

The product of those factors will give the polynomial. Because we have two factors, we will get a quadratic polynomial.

x^2+7x-2x-14

x^2+5x-14

Number of factors  =  Highest exponent of the polynomial

Answer:

y = x² + 5x - 14

Step-by-step explanation:

Given roots x = a, x = b, then the corresponding factors are

(x - a) and (x - b) and the polynomial is the product of the factors

y = (x - a)(x - b)

Here the roots are x = 2 and x = - 7, then the factors are

(x - 2) and (x - (- 7)) = (x + 7), so

y = (x - 2)(x + 7) ← expand using FOIL

y = x² + 5x - 14

Answer:

hope this helps you out question 4 and 3 are the same

Answer:

2. 95

3. 85

4. 95

Step-by-step explanation:

Mark me brainliest? :)

To determine whether set H is a subspace of R², we need to check if H satisfies the three requirements for a subspace: closure under addition, closure under scalar multiplication, and contains the zero vector.

To determine if set H is a subspace of R², we need to check if it satisfies the three properties of a subspace.

Closure under addition: For any two vectors u and v in H, their sum u + v should also be in H. If the lines forming the boundary of H extend infinitely, then any two vectors u and v in H can be added to form a vector that lies within H. Thus, H is closed under addition.

Closure under scalar multiplication: For any vector u in H and any scalar c, the scalar multiple cu should also be in H. Similarly to the closure under addition, if the lines forming the boundary of H extend infinitely, then any vector u in H can be multiplied by a scalar to obtain a vector that lies within H. Hence, H is closed under scalar multiplication.

Contains the zero vector: The zero vector (0, 0) is part of R² and is also part of H since it lies within the boundary of H.

Since H satisfies all three requirements, it is a subspace of R².

Learn more about zero vector here:

https://brainly.com/question/13595001

#SPJ11

The given confidence interval is 0.14 < p < 0.342, where p represents the proportion of students who take notes. To interpret this interval correctly, we can say:  We are 99% confident that the true proportion of students who take notes lies between 0.14 and 0.342.

In other words, based on the data from the random sample of size 83, we estimate that the proportion of students who take notes falls within this range with a 99% level of confidence. This means that if we were to take multiple random samples of the same size and calculate confidence intervals, approximately 99% of those intervals would contain the true proportion of students who take notes.

Furthermore, the interval does not include the value of 0.5, which represents no preference or a 50% proportion. Since both 0.14 and 0.342 are less than 0.5, we can infer that the data suggests that a substantial proportion of students take notes, but we cannot conclude with certainty whether the majority or minority take notes without further information.

It's important to note that the interpretation assumes the random sampling method was appropriate and the sample is representative of the population of interest.

For more such questions interval

https://brainly.com/question/30460486

#SPJ8

Answer:

fourth answer choice) 5

Step-by-step explanation:

2x + 9 = 4x - 1

9 = 2x - 1

10 = 2x

5 = x

x = 5

I would appreciate Brainliest, but no worries.

The value of x that would make ASUV = ATUN by HL is 4, the correct option is C.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that;

SUV congruent to TUV

Now,

To solve for x in the equation 2x+9=4x+1, we need to isolate x on one side of the equation.

First, we can simplify both sides by subtracting 2x from each side:

2x+9-2x=4x+1-2x

Simplifying this gives us:

9=2x+1

Next, we can subtract 1 from each side:

9-1=2x+1-1

Simplifying this gives us:

8=2x

Finally, we can divide both sides by 2:

8/2=2x/2

Simplifying this gives us:

4=x

Therefore, by the algebra the answer will be x=4.

More about the Algebra link is given below.

brainly.com/question/953809

#SPJ7

Answer:

10 years

Step-by-step explanation:

Simple interest formula:

AV=PV(1+it)

13200=8000(1+.065t)

1.65=1+.065x

.65=.065x

10=x

The absolute maximum value of the function on the interval [-3, 1] is approximately 28.97, and the absolute minimum value is approximately 3.84.

To find the absolute maximum and minimum values of the function f(x) = 31/3 - 3x2/3 on the interval [-3, 1], we need to evaluate the function at its critical points and endpoints.

First, let's find the critical points by taking the derivative of the function:

f'(x) = (2/3)(31/3)(-3x^(-1/3)) = -2(31/3)(1/x^(1/3)) = -62/x^(1/3)

To find the critical points, we set f'(x) equal to zero and solve for x:

-62/x^(1/3) = 0

This equation has no solutions since the numerator is always non-zero.

Next, we evaluate the function at the endpoints of the interval:

f(-3) = 31/3 - 3(-3)^(2/3) ≈ 3.84

f(1) = 31/3 - 3(1)^(2/3) ≈ 28.97

Finally, we compare the values of the function at the critical points and endpoints to determine the absolute maximum and minimum:

Absolute maximum: f(1) ≈ 28.97

Absolute minimum: f(-3) ≈ 3.84

Therefore, the absolute maximum value of the function on the interval [-3, 1] is approximately 28.97, and the absolute minimum value is approximately 3.84.

Learn more about "absolute maximum":

https://brainly.com/question/19921479

#SPJ11

Answer:

See attachment

Step-by-step explanation:

Given

[tex]Side\ 1 = 10cm[/tex]

[tex]Side\ 2 = 12cm[/tex]

[tex]\theta = 90^\circ[/tex]

Required [Missing from the question]

Draw the top of the cake

See attachment for reference.

From the attachment,

[tex]2cm = 1\ unit[/tex]

So:

[tex]Side\ 1 = 10cm[/tex]

[tex]Side\ 1 = 5 * 2cm[/tex]

Substitute [tex]2cm = 1\ unit[/tex]

[tex]Side\ 1 = 5 * 1unit[/tex]

[tex]Side\ 1 = 5\ units[/tex]

[tex]Side\ 2 = 12cm[/tex]

[tex]Side\ 2 = 6 * 2cm[/tex]

Substitute [tex]2cm = 1\ unit[/tex]

[tex]Side\ 2 = 6 * 1unit[/tex]

[tex]Side\ 2 = 6\ units[/tex]

This means that, the given side lengths will be represented by 5 units and 6 units on the grid, respectively.

See attachment for drawing

The number of ways seven books can be arranged on a shelf if there are no restrictions is 7! = 5040.Why? As there are no restrictions, any of the seven books can occupy any of the seven places on the shelf. Therefore, there are 7 ways to place the first book. After the first book has been placed, there are 6 ways to place the second book (as one place is now occupied).Then, after the first and second books have been placed, there are 5 ways to place the third book (since two places are now occupied). Similarly, there are 4 ways to place the fourth book after the first four have been placed. There are 3 ways to place the fifth book after the first five have been placed.

There are 2 ways to place the sixth book after the first six have been placed. There is only one way to place the last book after the first six have been placed.

So, using the Multiplication Principle, the number of ways 7 books can be arranged on a shelf is:7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040.

To know more about Multiplication Principle, click here:

https://brainly.com/question/17514196

#SPJ11

The justification for the proof based on the information will be:

lm = np (Given)

lp = mn (Given)

(1) lmn = lm * n

Justification: Associative property of multiplication

(2) lmn = np * n

Justification: Substitute lm = np

(3) lmn = n * np

Justification: Commutative property of multiplication

(4) lmn = npl

Justification: Substitute lp = mn

Therefore, lmn = npl.

The associative property of multiplication is one of the fundamental properties of arithmetic. It states that the grouping of factors does not affect the result of multiplication.

In other words, when you multiply three or more numbers, you can change the grouping of the factors without changing the product.

Learn more about multiplication on

https://brainly.com/question/28768606

#SPJ4

A continuous function the graph of y = f(x) and the x-axis on the interval [a, b] evaluating the definite integral of f(x) over that interval, the changes of f(x) if applicable.

The area between the graph of y = f(x) and the x-axis on the interval [a, b]  by evaluating the definite integral of f(x) over that interval.

The definite integral of f(x) from a to b represents the signed area between the graph of f(x) and the x-axis. The sign of the area depends on the behavior of f(x) above and below the x-axis.

If f(x) is non-negative (greater than or equal to 0) on the interval [a, b], then the area between the graph of f(x) and the x-axis will be positive or zero.

If f(x) is non-positive (less than or equal to 0) on the interval [a, b], then the area between the graph of f(x) and the x-axis will be negative or zero.

If f(x) changes sign on the interval [a, b] (i.e., it is positive in some regions and negative in others), then the area between the graph of f(x) and the x-axis will be the sum of the positive areas minus the sum of the negative areas.

To know more about function here

https://brainly.com/question/31062578

#SPJ4

Answer:A. 3 inches

Step-by-step explanation: :)

Answer:

b and c

Step-by-step explanation:

Answer:

x = 19.48 or 19 12/25

Step-by-step explanation:

cos 41° = 14.7/x

x = 19.48 or 19 12/25

Answer:

surface area = 544 cm²

Step-by-step explanation:

surface area = (16)(8 + 6 + 8 + 6) + (2)(8)(6) = 448 + 96 = 544 cm²

Answer:

Rhombuses

Step-by-step explanation:

It has four vertical lines, then draw a Venn Diagram, opposite to opposite.

Order from Venn Diagrams:

Quadrilaterals

Rectangles

Squares

Rhombuses.

Answer:

the sequence is geometric sequence with common ratio (-2).

Option : D is correct.

Step-by-step explanation:

In this question table is given as

n          1          2         3           4            5

f(n)     48       -96      192      -385       768

We have to find out if the sequence is arithmetic or geometric.

For Arithmetic sequence :

Difference should be common in each term of fees.

common difference  = f(2) - f(1)

= -96 -48 = -144

similarly  = f(3) - f (2) = 192 + 96 = 288

Here,  ≠  so the sequence is not an arithmetic sequence.

For Geometric sequence :

Ratio  should be common in each term of f(n)

Common ratio  =

Therefore, the sequence is geometric sequence with common ratio (-2).

Option : D is correct.

Answer: 1,145,375cm^3

Step-by-step explanation:

The dimensions of the largest area that can be enclosed is 1590 × 795= 1264050 yd² when no fencing is required along the river.

Given the owner of the Rancho Los Feliz has 3180 yd of fencing to enclose a rectangular piece of grazing land along the straight portion of a river and then subdivide it by means of a fence running parallel to the sides. No fencing is required along the river.

We need to find the dimensions of the largest area that can be enclosed.

Therefore, the length of the land is the perimeter of the rectangle minus the river front.

We have; 2x + 3y = 3180 yd

Also, we can rewrite this equation in terms of x;

2x = 3180 - 3yy = (3180 - 2x) / 3

Substituting y in terms of x in the area equation;

Area A = x y= x(3180 - 2x) / 3

Taking the derivative of the area equation to find the maximum value of A;

A' = 1060 - 2x / 3 When A' = 0, x = 1590 / 2 = 795 yd.

Substitute x = 795 into the equation for y;

2(795) + 3y = 3180y = (3180 - 1590) / 3 = 530 yd

Therefore, the dimensions of the largest area that can be enclosed are; Length = 1590 yd Width = 795 yd

Hence, the area is given by; Area = Length × Width= 1590 × 795= 1264050 yd².

To learn more about area of rectangle

https://brainly.com/question/22242374

#SPJ11

Answer: 234 - 40 = 2x

              194 = 2x

              97 = x

x being the amount Trey had before mowing lawns

Answer:

Simplified : 1:3

Step-by-step explanation:

7:21 is equal to 1:3

Also, for algebra tips. Algebra is literally practice. There aren't too many complicated equations or anything until you get into a higher math class so practicing problems is best.

Answer:

7:21 = 1:3

Tips for algebra...

just know the basics and related rules or theorams and practice as much as u can

good day mate