PLEASE HELP WITH
PART C.

1. V₁ is closed under addition. 2. V₁ is closed under scalar multiplication. 3. V₁ = Span(v₁) satisfies all the properties of a subspace, and hence it is a subspace of V.

To show that V₁ = Span(v₁) is a subspace of V, we need to demonstrate that it satisfies the three properties of a subspace: closure under addition, closure under scalar multiplication, and containing the zero vector.

1. Closure under addition:

Let u and w be vectors in V₁. Since V₁ = Span(v₁), we can write u = c₁v₁ and w = c₂v₁, where c₁ and c₂ are scalars.

Now, consider the vector u + w:

u + w = c₁v₁ + c₂v₁ = (c₁ + c₂)v₁.

Since c₁ + c₂ is a scalar, u + w can be expressed as a scalar multiple of v₁, which means u + w is in V₁. Therefore, V₁ is closed under addition.

2. Closure under scalar multiplication:

Let u be a vector in V₁ and c be a scalar. Since V₁ = Span(v₁), we can write u = c₁v₁, where c₁ is a scalar.

Consider the vector cu:

cu = c(c₁v₁) = (cc₁)v₁.

Since cc₁ is a scalar, cu can be expressed as a scalar multiple of v₁, which means cu is in V₁. Therefore, V₁ is closed under scalar multiplication.

3. Contains the zero vector:

The zero vector, denoted by 0, can be expressed as 0 = 0v₁,

where 0 is a scalar.

Since 0v₁ is a scalar multiple of v₁, it belongs to V₁.

Therefore, V₁ contains the zero vector.

Therefore, V₁ = Span(v₁) satisfies all the properties of a subspace, and hence it is a subspace of V.

To show that a subspace W contains v₁ if and only if V₁ ⊂ W, we need to prove two implications:

1. If W contains v₁, then V₁ ⊂ W:

Assume W contains v₁. Let u be an arbitrary vector in V₁.

Since V₁ = Span(v₁), we can write u = c₁v₁, where c₁ is a scalar.

Since W contains v₁, it also contains any scalar multiple of v₁.

Therefore, u = c₁v₁ is in W.

Since u was arbitrary, this holds for all vectors in V₁, proving that V₁ ⊂ W.

2. If V₁ ⊂ W, then W contains v₁:

Assume V₁ ⊂ W. Since v₁ is an element of V₁ and V₁ ⊂ W, it follows that v₁ is also an element of W. Therefore, W contains v₁.

By proving both implications, we have shown that a subspace W contains v₁ if and only if V₁ ⊂ W.

This means that V₁ is the smallest subspace of V containing v₁.

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Answer:

f i think andrew upright here's here's etext ueber yourself greatly they'd

Answer: total $1332

Step-by-step explanation:

1200x11%=132

1200+132=1332

Answer:

$1,332

Step-by-step explanation:

Okay, so we basically have to calculate how much 11% of 1,200 is.

To do this we have to multiply 0.11 (because percentages are decimals) and 1,200:

0.11 x 1,200 = 132

So 11% of 1,200 is 132

But that's not the end of the problem, we have to find how much she has to pay ALL TOGETHER. So we add 132 and 1,200:

1,200 + 132 = 1,332

So Susan actually pays $1,332

hope this helps:)

Answer:

D. 1146.05

Step-by-step explanation:

Answer:

yea its d im preety sure it is

Answer:

what are you asking the total or what

Since x represents a length, we reject the negative solution. Therefore, the value of x is approximately 4.88 inches.

In math, an equation is a statement that shows the equality between two expressions. It consists of two sides, a left-hand side (LHS) and a right-hand side (RHS), that are separated by an equals sign (=). For example, the equation 3x + 5 = 14 is an algebraic equation that states that the sum of three times a number x and five is equal to fourteen. Equations can have different types of expressions, including numbers, variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and more. Solving an equation involves finding the value of the variable that makes the equation true.

Here,

To find the value of x, we need to first determine the dimensions of the entire ad.

Let A be the area of the entire ad, and let P be the area of the photo. We are given that P = (1/2)A. We are also given that the dimensions of the photo are 7 inches by 9 inches, so P = 7 * 9 = 63 square inches.

Substituting P = 63 and P = (1/2)A into the equation P = (1/2)A, we get:

63 = (1/2)A

Multiplying both sides by 2, we get:

126 = A

So the area of the entire ad is 126 square inches.

Next, we need to find the dimensions of the entire ad. Let the length be L and the width be W. We know that L * W = 126. We are also given that the length of the photo is 7 inches, so L = 2x + 7.

Substituting L = 2x + 7 into the equation L * W = 126, we get:

(2x + 7) * W = 126

Dividing both sides by 2x + 7, we get:

W = 126 / (2x + 7)

We know that the width of the photo is 9 inches, so:

W - 9 = x

Substituting the expression for W from above, we get:

126 / (2x + 7) - 9 = x

Multiplying both sides by 2x + 7, we get:

126 - 9(2x + 7) = x(2x + 7)

Simplifying, we get:

93 = 2x² + 7x

2x² + 7x - 93 = 0

Using the quadratic formula, we get:

x ≈ 4.88, x ≈ -9.58

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The inequality 5p + 3n ≤ 20 represents the purchase of Tony

Tony received a $20 gift card for school supplies. Paper is $5 per pack and notebooks are $3 each. Which inequality represents the number of packs of paper, p, and notebooks, n,

We can start by using the data provided in the question to address this problem.

A $20 gift card for school supplies was given to Tony.

A pack of paper costs $5, while a notepad costs $3.

Let n be the number of notebooks Tony may buy and p be the number of packs of paper he may buy.

The paper costs five pence in total.

The price of notebooks is n dollars in total.

Tony has a $20 gift certificate, so we can write:

5p + 3n ≤ 20

This disparity shows how many notebooks and paper packs Tony is allowed to buy.

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In both the Vendor Compliance at Geoffrey Ryans (A) and Operational Execution at Arrows Electronics cases, there are common problems and challenges. These include issues related to vendor management.

One of the key problems faced by both companies is vendor compliance. This refers to the ability of vendors to meet the requirements and standards set by the company. Both cases highlight instances where vendors fail to meet compliance standards, leading to disruptions in the supply chain and operational inefficiencies. This problem affects the overall performance and profitability of the companies.

Another challenge faced by both companies is operational execution. This encompasses various aspects of operations, including inventory management, order fulfillment, and delivery. In both cases, there are instances where operational execution falls short, leading to delays, errors, and customer dissatisfaction. This challenge requires the companies to streamline their processes, improve communication and coordination, and enhance overall operational efficiency.

Overall, the problems and challenges in both cases revolve around effective vendor management, supply chain optimization, and operational excellence. Addressing these issues is crucial for both companies to improve their performance, meet customer demands, and maintain a competitive edge in the market.

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Answer:

I believe the inequality would be: p+2x3<40

Step-by-step explanation:

Not exactly sure if it is correct but p (number of pencils Sarahi has) added too the 2 more she finds, and then x3 (when she triples her amount). This is less then (<) what Damaris has (which is 40) so it would be p+2x3<40.

Again not sure if its completely correct, but i hope it helps :,)

Answer:

\(172\frac{1}{2}\) gallons

Step-by-step explanation:

Considering she waters her plants with 25 1/2 gallons  i.e 51/2

and with the new system, she does it with 19 3/4 i.e 79/4

taking the difference:

\(\frac{51}{2} - \frac{70}{4}\) = \(\frac{23}{4}\) gallons per day

For 30 days:

30 x \(\frac{23}{4}\) = 172.5 or \(172\frac{1}{2}\) gallons

To prove that when a sphere is moved about its center, it is always possible to find a diameter of the sphere whose direction in the displaced position is the same as in the initial position using orthogonal properties, follow these steps:

1. Consider a sphere with center O and any diameter AB.
2. When the sphere is moved about its center, the center O remains fixed.
3. Rotate the sphere such that diameter AB is now in a new position A'B'.
4. Since the sphere has been rotated about its center, the orthogonal properties are preserved. This means that the planes that are perpendicular to the diameter at the center O remain unchanged.
5. The orthogonal planes to diameter AB intersect at the center O and form a fixed line in space.
6. Now, rotate the sphere again, such that diameter A'B' returns to its initial position as AB. This rotation is possible because the orthogonal planes and their intersection (the fixed line) are preserved.
7. Since diameter A'B' has returned to the initial position of AB, it proves that it is always possible to find a diameter of the sphere whose direction in the displaced position is the same as in the initial position.

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Answer:

330°

Step-by-step explanation:

angle subtended=11×360/12=11×30=330°

What is the question for this so I can answer it?

The solution of the expressions are,

⇒ x = 5

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 2x - 4 = 6

Now, We can simplify as;

⇒ 2x - 4 = 6

Add 4 both side,

⇒ 2x - 4 + 4 = 6 + 4

⇒ 2x = 10

Divide by 2;

⇒ x = 10 / 2

⇒ x = 5

Thus, The solution of the expressions are,

⇒ x = 5

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Answer:

A square has 4 sides of equal length, so if you have been given the length, this is also the breadth.

Therefore, the perimeter is 4 x side length.

For example, imagine a square with side length 3 cm.  As all four side lengths are equal, the perimeter would be 4 x 3 cm = 12 cm

AB thus has a 12 unit length as the triangle ABE is a right triangle with hypotenuse AE and legs AB and 5 in length.

A closed triangle is a two-dimensional geometric shape having three straight edges and three angles. The shorter of a triangle's two sides is known as the hypotenuse, while its long sides are known as the triangle's legs. The longest side's opposing angle is referred to as the greatest or "opposite" angle in triangles. Angles are given names based on where they are in relation to the sides. An essential component of geometry is the study of triangles, and there are numerous varieties with distinctive characteristics. An equilateral triangle, on the other hand, has three equal edges and 3 equal angles that are each 60 degrees in length. A right triangle, for instance, has one angle that is 90 degrees in length.

given

The Pythagorean theorem can be used to determine the length of AB.

We can see from the diagram that triangle ADE is a right triangle with hypotenuse AE and legs measuring 12 and 5 (DE - AE = AD = 13 - 8 = 5). Well, here we are:

\(AD^2 + DE^2 = AE^2\\AE^2 = 5^2 + 12^2\\AE^2 = 169\)

AE = 13

In a similar way, we can observe that triangle ABE is a right triangle with hypotenuse AE and legs AB and 5 in length. Well, here we are:

AB2 = 169 - 25 when AE2 = AB2 + BE2 132 = AB2 + 5

AB^2 = 144

AB = 12

AB thus has a 12 unit length as the triangle ABE is a right triangle with hypotenuse AE and legs AB and 5 in length.

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\(~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 4700\\ P=\textit{original amount deposited}\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &11 \end{cases} \\\\\\ 4700=Pe^{0.04\cdot 11} \implies 4700=Pe^{0.44}\implies \cfrac{4700}{e^{0.44}}=P\implies 3027\approx P\)

Answer:

672

Step-by-step explanation:

In math, volume is the amount of space in a certain 3D object. To find the volume, you multiply length times width times height. So 8 x 14 x 6 = 672

Step-by-step explanation:

so, let me retype this.

horizontal asymptote : y = 2

that means lim x going to ±infinity f(x) = 2.

vertical asymptotes :

x = 3

x = -4

that means the function must have these 2 points, where the expression leads to a division by 0 or something similar that would make the result undefined.

we got 4 functions :

A) y = x²/(x² + x - 12)

B) y = x²/(x² - x - 12)

C) y = 2x²/(x² + x - 12)

D) y = 2x²/(x² - x - 12)

so, for which ones we have y = 2 as limit when x goes against + or - infinity ?

that would be C and D.

A and B lead to x²/x² = 1 as limit for gigantic numbers.

C and D lead to 2x²/x² = 2 as limit.

remember, when x gets really, really big, the "±x - 12" part becomes irrelevant.

so, we look at C and D.

which one lead to a division by 0 at x = 3 and x = -4 ?

that would be C.

for x = 3

x² + x - 12 = 3² + 3 - 12 = 9 + 3 - 12 = 12 - 12 = 0

for x = -4

x² + x - 12 = (-4)² - 4 - 12 = 16 - 4 - 12 = 12 - 12 = 0

D with x² - x - 12 would have x = -3 and x = 4 as zeroes.

these are different asymptotes than requested.

so, C is the right answer.

Answer:

t = 41.6 (the 6 is repeating)

Step-by-step explanation:

2.5t + 350 = 3t + 225

Subtract 2.5t from both sides to get:

350 = 3t + 225

Now subtract 225 from both sides to get:

125 = 3t

Divide both sides by three.

t = 41.6 (the 6 is repeating)

Answer:

D. 75 m²

Step-by-step explanation:

l = 15m

b = 5m

area of rectangle = l × b = 15 × 5 = 75 m²

Answer:

-8, 8

Step-by-step explanation:

\( {x}^{2} - 47 = 17 \\ \\ {x}^{2} = 17 + 47 \\ \\ {x}^{2} = 64 \\ \\ x = \pm\sqrt{64} \\ \\ x = \pm \: 8 \\ \\ x = - 8, \: \: 8\)

The triangle that is similar to the triangle ΔABC is the triangle ΔJKL, the correct option is therefore;

B. ΔJKL, in which m∠J = 15° and m∠L = 45°

Triangles are similar if they have the same measure of two of their interior angles, and therefore, have the same shape, but they may have different size.

The specified known angles of the triangle indicates that the known angles are;

m∠A = 15°, m∠B = 120°

Therefore, the third angle of the triangle is; 180 - (15 + 120) = 45

The third angle of the is 45 degrees

Therefore, the triangle that is similar to the specified triangle has an angle interior angle of either; 15°, or 120°, or 45°

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Answer:

6 3/14 pancake order s

Step-by-step explanation:

The question above is calculated as:

2/3 cup of syrup = 1 pancake order

3 8/7 cups of syrup = x

Cross Multiply

2/3 × x = 3 8/7 × 1

x = 3 8/7 ÷ 2/3

x = 29/7 ÷ 2/3

x = 29/7 × 3/2

x = 87/14

x = 6 3/14 order

The maximum number of complete pancake orders that Anton can serve with the syrup he has is 6 3/14 pancake orders

Answer:

x=9

Step-by-step explanation:

alright so first we eliminate the -15 and to do that we add 15 on both sides:

-3x-15+15=12+15

-3x=27

Now we divide 3 on both sides to make the equation equal to x

\( \frac{-3x}{-3} = \frac{27}{-3} \)

x=9

And that's your answer, you're welcome :)

True. A vector in space can be described by specifying its magnitude and its direction angles. The magnitude of a vector represents its length or size, while the direction angles determine the orientation of the vector with respect to a reference axis system.

In three-dimensional space, a vector can be decomposed into its components along the x, y, and z axes. By using trigonometric functions, the direction angles of the vector can be determined. The direction angles are typically measured with respect to the positive x-axis, the positive y-axis, and the positive z-axis.

Once the magnitude and direction angles of a vector are known, the vector can be fully described. This description allows for precise calculations and analysis of vector quantities, such as displacement, velocity, and force, in various physical and mathematical contexts.

It's worth noting that there are alternative ways to describe vectors, such as using Cartesian coordinates or unit vectors. However, specifying the magnitude and direction angles provides a convenient and comprehensive representation of a vector in space.

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Answer:0.45

Step-by-step explanation:

Answer:

24%

Step-by-step explanation:

x-(11/100)x

89/100x

followed by

89/100x-13/100x

76/100x

so the total decrease is calculated as

x-76/100x

(24/100)x

i.e 24% decrease