Mathematics College

Which of the following is a subspace of R^3? (A) All vectors of the form(0, a, a^2), (B) All vectors of the form(a+2, a, 0), (C) All vectors of the form (a, b, 2), (D) All vectors of the form(a, b, a-2b)

Answers

Answer 1

All vectors of the form(a, b, a - 2b) is a subspace of R³. So, the correct option is option(D).

Subspace:

If W is a set of one or more vectors from a vector space V, then W is a subspace of V if and only if

If u and v are vectors in W, then u + v in W. ku is in W if k is any scalar and u is any vector in W.

Now, check the options and find out the option which satisfy the subspace conditions.

A) All the vectors are of form (0, a,a²)

let (0,1,1) = u and v=(0,2,4) and both are belongs to { 0, a,a² : a∈R }, (0,0,0)∈ {0, a,a² : a∈R }.

u + v = (0,1,1) + (0,2,4) = (0,3, 5) not belongs to

{ 0, a,a² : a∈R }. So, this is not correct option.

B) Here, (0,0,0) does not belongs to

{0, a, a+2 : a∈R } because if a= 0 then a+2 =/ 0 .

So, it is also not subspace.

C) All vectors of the form (a, b, 2)

The third tuple is 2 which never be equal to zero. Hence, (0,0,0) does not belongs to (a, b, 2) and it is not form subspace.

D) All vectors of the form (a, b, a - 2b)

When a = 0 , b = 0 => (0,0,0) ∈(a, b, a - 2b)

let u = ( a1, b1 , a1- 2b1) and v = ( a₂, b₂ , a₂ - 2b₂)

and α∈R

u + v = ( a₁, b₁ , a₁- 2b₁ ) + ( a₂, b₂ , a₂ - 2b₂)

= ( a₁ +a₂ , b₁+b₂ , a₁+a₂ -2(b₁ - b₂)) €(a, b, a - 2b)

αu = α(a₁ , b₁ , a₁- 2b₁)

=( αa₁ , αb₁ , α(a₁ - 2b₁))∈(a, b, a - 2b)

both the conditions are satisfied, so it is Subspace of R³.

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Related Questions

Two elephants are being delivered to the zoo. One elephant weighs 23,453 pounds, and the other elephant weighs 19,916 pounds. How many pounds do the elephants weigh together?

Answers

The required weight of the two elephants together is 43369 pounds.

How to add two similar quantity?

Addition is an approach to consolidating things and considering them all together.Addition in math is a course of consolidating at least two numbers. Addends are the numbers added, and the outcome or the last response we get after the interaction is known as the total.

According to question:

We have,

One elephant weighs 23,453 pounds, and the other elephant weighs 19,916 pounds.

To find total weight of two elephant together,we have to add them.

23,453 pounds + 19,916 pounds

43369 pounds

Thus, required weight of two elephant is 43369 pounds.

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(×+13)²=(×+12)²+(×-5)²
Give it to me please :(

Answers

To solve the problem, we will use the law of signs, to solve the problem

Law of signs:- × - = +- × + = -+ × - = -+ × + = +

With the law of signs, we solve, but first we must know the following.

¿What are the equations?

We know that the equations are those mathematical expressions that are called in members and separated, by their equal sign, which these carry their known data and unknown or unknown data, these are related through their mathematical operations.

Solving problem: x² + 26x + 169 = x² + 24x + 144 + x² - 10x + 25x² + 26x + 169 = 2x² + 14x + 169x² + 26x - 2x² - 14x = 0-x² + 12x = 012x - x² = 0x (12 - x) = 0x = 0.12

So, the result of this equation is x = 0.12

¡Hope this helped!

Answer:

x = 0, x = 12

Step-by-step explanation:

Given equation:

[tex](x+13)^2=(x+12)^2+(x-5)^2[/tex]

Expand:

[tex]\implies (x+13)(x+13)=(x+12)(x+12)+(x-5)(x-5)[/tex]

[tex]\implies x^2+26x+169=x^2+24x+144+x^2-10x+25[/tex]

Collect and combine like terms on the right side of the equation:

[tex]\implies x^2+26x+169=x^2+x^2+24x-10x+144+25[/tex]

[tex]\implies x^2+26x+169=2x^2+14x+169[/tex]

Subtract 169 from both sides:

[tex]\implies x^2+26x=2x^2+14x[/tex]

Subtract x² from both sides:

[tex]\implies 26x=x^2+14x[/tex]

Subtract 26x from both sides:

[tex]\implies 0=x^2-12x[/tex]

[tex]\implies x^2-12x=0[/tex]

Factor out the common term x:

[tex]\implies x(x-12)=0[/tex]

Apply the zero-product property:

[tex]\implies x=0[/tex]

[tex]\implies x-12=0 \implies x=12[/tex]

Solution:

x = 0, x = 12

URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!

Answers

The answer would be A.

Answer: a is a rational number

Step-by-step explanation

Rational numbers are written in p/q form.

-3x-4y=-1, 3x-y=-4 solve by elimination

Answers

Answer: x=-1 and y=1

Hope it’s correct

y = 1, and x = -1

if you need to show your work:

if you combine the two equations together (eliminating x), it goes like this

-3x - 4y = -1

3x - y = -4

-5y = -5

y = 1

this means:

-3x - 4 = -1

-3x = 3

x= -1

and

3x - 1 = -4

3x = -3

x = -1

Determine a series of transformation that would map Figure S onto Figure T.

Answers

Answer:

reflection then rotation

Answer:

100.72

Step-by-step explanation:

[tex]Given,[/tex]

event requires each runner to jump 10 hurdles that are spaced 8.5 meters apart.

If there are 13.72 meters from the starting line to the first hurdle and 10.5 meters from the last hurdle to the finish line,

To Find: how long is the race

Solution:

runner to jump 10 hurdles that are spaced 8.5 meters apart.

Distance between 10 hurdles

=(10-1)* 8.5

=9*8.5

=76.5

If there are 13.72 meters from the starting line to the first hurdle and 10.5 meters from the last hurdle to the finish line,

Hence length of race = 13.72+76.5+10.5

=100.72

Mark me Brainliest pls

Answer:

100.72 meters

Step-by-step explanation:

To find the total length of the race, we need to sum:

The distance from the starting line to the first hurdle.The distances between the hurdles.The distance from the last hurdle to the finish line.

The distance from the starting line to the first hurdle is 13.72 meters.

The distance between each of the 10 hurdles is 8.5 meters.

There are 9 spaces between hurdles 1 and 10, so the distance between the hurdles is 9 × 8.5 = 76.5 meters.

The distance from the last hurdle to the finish line is 10.5 meters.

To find the total length of the race, add these distances together:

[tex]\begin{aligned}\textsf{Total length of the race} &=\sf 13.72\; meters + 76.5\; meters + 10.5 \;meters\\\\&=\sf 100.72\; meters\end{aligned}[/tex]

Therefore, the race is 100.72 meters long.

Emily loves to go the spa she and her friends go twice a month each visit she gets a 90 minute massage for $125 and a deluxe manicure and pedicure for $65. How much does she spent at the spa each month?

Answers

Answer: $380

Step-by-step explanation:

First, we will find the price per visit using addition.

$125 + $65 = $190

Next, we notice it says "twice a month" in the question. We will multiply the value above by two to find the price per month.

$190 * 2 = $380

Answer:

twice a month of 125 + 65

2($125 + $65)

= 2($190)

= $380

Step-by-step explanation:

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(Multiplying Linear Expressions MC)

Simplify −5g(3g + 4).
A: −15g + 4
B: −15g − 20g
C: −15g2 + 4
D: −15g2 − 20g

Answers

The multiplication of the linear expression - 5g(3g + 4) is given by -15g² - 20g.

The correct answer option is option D

How to multiply linear expression?

Multiplication: This is the process of computing the sum of a number with itself a specified number of times, or any other analogous binary operation that combines other mathematical objects.

- 5g(3g + 4)

open parenthesis

= -5g × 3g - 5g × 4

= -15g² - 20g

In conclusion, the linear expression - 5g(3g + 4) when simplified equals -15g² - 20g

Answers

The measure of an angle X is 11° and 3X+2°=35° , 4X-9° =35° .

What is meant by an angle?

In Euclidean geometry, an angle is a figure made up of two rays that have a shared vertex, also known as a common terminus, and are referred to as the angle's sides. The angles of two rays are situated in the plane containing the rays. An angle is also created when two planes intersect at an angle. These are referred to as dihedral angles. Another technique to define two curves is to specify the angle generated by rays that are tangent to the intersection of two curves. Angle is another word for how long a rotation or angle is.

∠QPA = ∠UPA

3X+2 =4X- 9

4X-3X= 9 + 2

X= 11

The measure of X is 11

3X+2°=3(11)+2°

=35°

(4X-9)°=(4(11)-9)°

=35°

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1. Mr. C has a square soccer field. The length of the soccer field is 18 feet.
What is the area of the soccer field:,
What is the perimeter of the soccer field

Answers

Answer:

Area = 324ft²

Perimeter = 72ft

Step-by-step explanation:

Area of a square = length²

Area of a square = (18ft)² = 324ft²

Perimeter of a square = 4*length

Perimeter of a square = 4ft*18 = 72ft

If a₁ = 6 and an
an-1 + 3 then find the value of a4.

Answers

Answer:

a₄ = 15

Step-by-step explanation:

using the recursive relation [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 3 and a₁ = 6 , then

a₂ = a₁ + 3 = 6 + 3 = 9

a₃ = a₂ + 13= 9 + 3 = 12

a₄ = a₃ + 3 = 12 + 3 = 15

work out and simplify where possible 9/10 - 7/10

Answers

Answer:

1/5

Step-by-step explanation:

(9-7)/10

2/10

(2:2) / (10:2)

1/5

in a survey, 32 people were asked how much they spent on their child's last birthday gift. the results were roughly bell-shaped with a mean of $48 and standard deviation of $7. construct a confidence interval at a 80% confidence level. give your answers to one decimal place.

Answers

The required 80% confidence interval is (46.15, 49.85).

What is a confidence interval?

In frequentist statistics, a confidence interval is a range of estimates for an unknown quantity.

The most common confidence level is 95%, but when calculating confidence intervals, other levels, such as 90% or 99%, are also occasionally employed.

So, we know that:

n = 32

χ' = 48

s = 8

Create an 80% confidence interval using the equation below:

[tex]\left(\bar{X} \pm t_{\frac{\alpha}{2}} \times \frac{s}{\sqrt{n}}\right)[/tex]

To determine the critical value t for n-1 degrees of freedom and 1 -cl level of significance, use the formula below:

[tex]t_{0.2, d f=31}=\pm 1.309[/tex]

Create the confidence interval now:

[tex]\begin{aligned}& \left(48 \pm 1.309 \times \frac{8}{\sqrt{32}}\right) \\& (48 \pm 1.85) \\& (46.15,49.85)\end{aligned}[/tex]

Therefore, the required 80% confidence interval is (46.15, 49.85).

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A company has found that the demand for its product varies inversely as the price of the product. When the price x is 4.75 dollars, the
demand y is 500 units.
Find a mathematical model that gives the demand y in terms of the price x in dollars.

Answers

With the help of algebra mathematical model equation for demand of company's product is given by the equation d = 1800 / p.

What is algebra?

The area of mathematics known as algebra deals with the representation of problems as mathematical expressions. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division.

Let demand for company's product d vary inversely with its price p, which means

d ∝ ( 1/p ) or d = k * ( 1/ p) = k / p ----- 1

As when p = 4.5, d = 400

Putting these in (1), we get 400 = k/ 4.5

Hence #k=400 x 4.5=1800 and our model equation is

d = 1800/p

Hence mathematical model equation for demand of company's product is given by the equation d = 1800 / p.

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Find (f - g)(x), if f(x) = 2x2 + 2 and g(x) = 6x2 + 6.

Answers

To find (f - g)(x), you can subtract g(x) from f(x):

(f - g)(x) = f(x) - g(x)

= (2x2 + 2) - (6x2 + 6)

= -4x2 + (-4)

= -4(x2 - 1)

Therefore, the result of (f - g)(x) is -4(x2 - 1).

Fill in the blanks 30 = 27 __ ___x 9 = 54 81 / ___ = 9 2 = ___ / 5 8 x ___ = 32 72 / ___ = 8 7* __ = 49

Answers

Step-by-step explanation:

this is a college level question, and you need help with that ? elementary school students have to be able to answer this.

30 = 27 + 3

6 × 9 = 54

81 / 9 = 9

2 = 10 / 5

8 × 4 = 32

72 / 9 = 8

7 × 7 = 49

I’ll give BRAINLIEST if correct need asap question is in the photo attached

Answers

Graph the line using the slope and y-intercept, or two points.

Slope:

y-intercept: (0,3)

x y

0 3

1 4

Let a,b,c,d be real numbers such that 1/a+Ï + 1/b+Ï + 1/c+Ï = 2/Ï
where Ï is non real cube root of unity choose the correct answer. abc+bcd+acd+abd is equal to

Answers

First, we can rewrite the given equation as:

1/a+Ï + 1/b+Ï + 1/c+Ï = (1/Ï)(1/a + 1/b + 1/c)

where Ï is the non real cube root of unity.

We can then multiply both sides of the equation by Ï to get:

1/a + 1/b + 1/c = 2(1/a + 1/b + 1/c)

This simplifies to:

1/a + 1/b + 1/c = 0

Since a, b, and c are all real numbers, we know that 1/a, 1/b, and 1/c are also real numbers. Therefore, the sum of these three real numbers must also be a real number. The only way that 1/a + 1/b + 1/c can equal 0 is if all three of these terms are equal to 0.

Thus, we can conclude that a = b = c = 0.

Since a, b, and c are all equal to 0, we know that abc + bcd + acd + abd must also equal 0. Therefore, the answer is 0.

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work out and simplify where possible 7/8 - 1/4

Answers

Answer:

5/8

Step-by-step explanation:

1/4=2/8

7/8-2/8=5/8

5/8 cannot be simplified

Answer:

5/8

Step-by-step explanation:

(7-2)/8

5/8

graph the line y=3/2x

Answers

The equation of the line passes the origin. And the inclination of the line with the x-axis is 3/2. And the graph is given below.

What is a linear equation?

An association between various factors brings about a straight model when a diagram is shown. The variable will have a level of one.

The straight condition is given as,

y = mx + c

Where m is the incline of the line and c is the y-block of the line.

The equation of the line is given below.

y = (3/2)x

The y-intercept is zero. Then the condition of the line passes the beginning. Furthermore, the tendency of the line with the x-pivot is 3/2.

The graph of the line is drawn below.

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A shoe store uses a 60% markup for all of the shoes it sells. What would be the selling price of a pair of shoes that has a wholesale cost of $55?

Answers

Answer:The selling price of shoes after a markup of 60% of the price will be equal to $81.60

Step-by-step explanation:

i don't think this is right

11/3 of x is 55 find x

Answers

Answer:

16.5

Step-by-step explanation:

11/3 =3 and 1/3 so 55/3 and 1/3 = 16.5 or 16 and 1/2

11/3 x = 55

11 x = 55x3

11 x = 165

x=165/11

X=15

what is the translation rule

Answers

Answer:

A translation is a type of transformation that moves each point in a figure the same distance in the same direction

Step-by-step explanation:

Translations are often referred to as slides. You can describe a translation using words like "moved up 3 and over 5 to the left" or with notation.

A bag contains 3 gold marbles, 7 silver marbles, and
28 black marbles. Someone offers to play this game:
You randomly select one marble from the bag. If it
is gold, you win $3. If it is silver, you win $2. If it is
black, you lose $1.
What is your expected value if you play this game?

Answers

To calculate the expected value of playing this game, we need to multiply the value of each possible outcome by its probability of occurring and then add these values together. In this case, there are 3 gold marbles, 7 silver marbles, and 28 black marbles in the bag, for a total of 38 marbles. So, the probability of selecting a gold marble is 3/38, the probability of selecting a silver marble is 7/38, and the probability of selecting a black marble is 28/38. The value of winning $3 if a gold marble is selected is $3 * (3/38) = $0.21. The value of winning $2 if a silver marble is selected is $2 * (7/38) = $0.37. And the value of losing $1 if a black marble is selected is -$1 * (28/38) = -$0.74. Adding these values together, we get $0.21 + $0.37 - $0.74 = -$0.16. Therefore, the expected value of playing this game is approximately -$0.16.

7. Sketch a model to represent the equation
2x + 2 = 12. Then, solve the equation.

Answers

x = 5 will be the correct answer and Model is provided in attachment don't look at the beauty of my figure.

The solution of the equation 2x + 2 = 12 is x = 5. And the model and the graph are given.

What is an equation?

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given:

Equation 2x + 2 = 12

The model for the equation is given in the attached image.

And the graph is also given in the attached image.

To solve for x:

2x + 2 = 12

Simplifying,

2x = 12 -2

2x = 10

Divide by 2,

2x / 2 = 10 / 2

x = 5.

Therefore, the solution of the equation is x = 5

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