Need help please guysssssss

(a) U is a subspace of L(V, W) (b) F is a linear map, and U is the null space of F. (c) The dimension of U is n - 1

The dimension of U is n - 1

(a) To demonstrate that U is a subspace of L(V, W), we must demonstrate that it meets the three subspace properties:

If T1 and T2 are in U, then T1 + T2 is in U as well, since if T1(v) = 0 and T2(v) = 0, then (T1 + T2)(v) = T1(v) + T2(v) = 0 + 0 = 0.

If T is in U and c is a scalar, then cT is in U, since if T(v) = 0, then (cT)(v) = c * T(v) = c * 0 = 0.

Containing the zero vector: Because 0(v) = 0, the zero transformation in L(V, W), indicated by 0, is in U.

As a result, U is a subspace of L. (V, W).

(b) To demonstrate that F is a linear map, we must demonstrate that it meets the following two properties:

Addition linearity: F(T1 + T2) = (T1 + T2)(v) = T1(v) + T2(v) = F(T1) + F(T2) (T2).

Homogeneity is defined as F(cT) = (cT)(v) = c * T(v) = c * F. (T).

As a result, F is a linear map. To demonstrate that U is the null space of F, we must first demonstrate that U is the set of all T in L(V, W) such that F(T) = 0. In other words, T(v) = 0.

(c) A basis for U can be used to calculate the dimension of U. Because U is a subspace of L(V, W), we may construct a basis for U by limiting a basis for L(V, W) to U. A basis for L(V, W) can be produced by designating as T1, T2,..., Tn the set of all transformations that send the standard basis vectors of V to the standard basis vectors of W. These transformations' constraints to U are T1, T2,..., Tn such that T1(v) = T2(v) =... = Tn(v) = 0. Because v = 0, T1, T2,..., Tn constitute a linearly independent set. As a result, dim(U) = n - 1.

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Answer:

Step-by-step explanation:

Perimeter:  

     \(P=(x+y+z) \ cm\)

Semi-perimeter:

     \(SP=\frac{1}{2} (x+y+z) \ cm\)

Answer:

Step-by-step explanation:

Since you haven't provided any algebra 2 questions I can only give you advice on how to get better with algebra 2. Algebra 1 is mainly about learning how to isolate the variables in order to solve for it. Algebra 2 implements these knowledge and applies it to a handful of already designed equations. Some of these include linear, quadratic equation, and slope intersect. Memorize these equations and the rest is simply applying what you learned in Algebra 1. The best way to get better is through practice. Use all the resources available such as books, videos, and tutor help.

Answer:

6

Step-by-step explanation:

Answer:

25 milliliters of 25% solution and 75 milliliters of 5% solution should be used.

Step-by-step explanation:

Since the druggist has to prepare 100 ml of a 10% solution, but has only 5% and 25% solutions, to determine the proportion of each solution that he must use to prepare the solution with the desired percentage, it is necessary to perform the following calculation:

25 x 1 + 5 x 0 = 25

25 x 0.9 + 5 x 0.1 = 23

25 x 0.8 + 5 x 0.2 = 21

25 x 0.7 + 5 x 0.3 = 19

25 x 0.6 + 5 x 0.4 = 17

25 x 0.5 + 5 x 0.5 = 15

25 x 0.4 + 5 x 0.6 = 13

25 x 0.3 + 5 x 0.7 = 11

25 x 0.2 + 5 x 0.8 = 9

Therefore, the percentage that the druggist must use will be between 20% and 30% of the 25% solution, and between 70% and 80% of the 5% solution, that is:

25 x 0.25 + 5 x 0.75 = 10

Therefore, the druggist should use a 25% solution at 25%, and a 75% solution at 5%: Thus, since 100 x 0.25 is equal to 25, 25 milliliters of 25% solution and 75 milliliters of 5% solution should be used.

The points on a parabola with the focal axis parallel to the abscissa axis, of parameter p and A, B is -12.

Since A and B are points on the parabola, write two equations using the general form of the parabolic equation:

(x - h)² = 4p(y - 1)

The focal axis is parallel to the x-axis, so the distance from the vertex to the focus is equal to p. Therefore, use the distance formula to write an equation for the distance between the vertex and point A:

√((13 - h)² + (a - 1)²) = p

Similarly, write an equation for the distance between the vertex and point B:

√((4 - h)² + (b - 1)²) = p

A and B lie on the line 2x - y - 13 = 0, so substitute the x and y coordinates of A and B into this equation and solve for a and b:

2(13) - a - 13 = 0

2(4) - b - 13 = 0

Solving these equations gives us a = 3 and b = -5.

Now three equations and three unknowns (a, b, and h):

√((13 - h)² + 4) = p + 1

√((4 - h)² + 36) = p + 1

2h - 3 - 13 = 0

The third equation simplifies to 2h = 16, or h = 8.

Substituting this value of h into the first two equations and squaring both sides:

(13 - 8)² + 4 = (p + 1)²

(4 - 8)² + 36 = (p + 1)²

Simplifying these equations and solving for p gives us p = 3.

Finally, find a" + bP by substituting the values found for a, b, and p:

a" + bP = 3 + (-5)(3) = -12

Therefore, the solution is a" + bP = -12.

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Step-by-step explanation:

11.

As all the exterior angles of a pentagon add up to 360, [ because exterior angle of a polygon = n(360/n) where n = no. Of sides, As the number of sides in a pentagon is 5, n=5. Thus, the sum of exterior angles of a pentagon = 5(360°/5) = 360°.]

THEN,

56 + 2x + 85 + 57 + 4x = 360

6x + 198 = 360

6x = 360 - 198

X = 162/6 = 27

Ans : x = 27

12.

Let the missing angle be x,

As we know that all exterior angles in a pentagon add up to 360 ( Write the same thing written above),

Then,

83 + 83 + 26 + 46 + x = 360

238 + x = 360

X= 360 - 238

X = 122

Answer : the fifth exterior angle = 122°

Hope this helps

Answer:

\( |d| = \sqrt{ {( - 6 - ( - 3))}^{2} + {( - 4 - ( - 4))}^{2} } \\ = \sqrt{ {( - 3)}^{2} + {0}^{2} } = \sqrt{9} \\ |d| = 3\)

\(\large{\rm{\underline{\underline{Answer:}}}}\)

For two given points, (x1,y1) and (x2, y2) the distance between the points can be calculated by,

Distance formula,

d=√((x2 - x1)²+(y2 - y1)²

Given points,

(x1, y1) = (-4, -3)

(x2, y2) = (-4, -6)

Put the values,

d = √(-4 + 4)² + (-6 + 3)²

d = √ 0 + (-3)²

d = √9

d = \( \pm\) 3

But distance is always positive. Hence, the distance between the pair of points. (-4,-3) and (-4,-6) is 3 units.

Answer:

1

Step-by-step explanation:

4-3=1. Because both numbers are positive, the absolute value has no effect.

Answer:

1

Step-by-step explanation:

The  |  | sign is used to get an absolute figure.

For example: |3 - 4| = 1

Under normal circumstances, 3 - 4 = -1 but the |  | sign changes whatever is in it to a positive value.

Hence, |p - 4| when p = 4:

|4 - 3| = 1

4 - 3 = 1 under normal circumstances so the | | sign won't affect anything

The time spent higher than 26 meters above the ground is 0.42 minutes. Answer: 0.42

A Ferris wheel is 30 meters in diameter and boarded from a platform that is 4 meters above the ground.

The six o'clock position on the Ferris wheel is level with the loading platform.

The wheel completes 1 full revolution in 2 minutes.

We have to find how many minutes of the ride are spent higher than 26 meters above the ground.

So, let's start with some given data,Consider the height of a person at the six o'clock position = 4 meters

So, the height of a person at the highest point = 4 + 15 = 19 meters (since the diameter is 30 meters, the radius will be 15 meters)

Also, the height of a person at the lowest point = 4 - 15 = -11 meters

Therefore, the Ferris wheel completes one cycle from the lowest point to the highest point and back to the lowest point.

So, the total distance travelled will be = 19 + 11 = 30 meters.

Also, we are given that the wheel completes 1 full revolution in 2 minutes.

We need to calculate the time spent higher than 26 meters above the ground.

So, the angle between the 6 o'clock position and 2 o'clock position will be equal to the angle between the 6 o'clock position and the highest point.

This angle can be calculated as follows:

Angle = Distance travelled by the Ferris wheel / Circumference of the Ferris wheel * 360 degrees

Angle = 30 / (pi * 30) * 360 degrees

Angle = 360 degrees / pi

= 114.59 degrees

So, the total angle between the 6 o'clock position and the highest point is 114.59 degrees.

Now, we need to find out how much time is spent at an angle greater than 114.59 degrees.

This can be calculated as follows:

Time = (Angle greater than 114.59 degrees / Total angle of the Ferris wheel) * Total time taken

Time = (180 - 114.59) / 360 * 2 minutes

Time = 0.42 minutes

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Answer:

4 1/4

Step-by-step explanation:

BRAINLIEST?!

the left side of this equation equal the right side through the process of completing the square that establishes the equality between the left side and the right side of the Gaussian integral equation.

using  completing the square method:

Starting with the left side of the equation:

∫\(e^(^-^x^2)\) dx

\(e^(^-^x^2) = (e^(^-x^2/2))^2\)

∫\((e^(^-^x^2/2))^2 dx\)

let  u = √(x²/2) =  x = √(2u²).

dx = √2u du.

∫ \((e^(^x^2/2))^2 dx\)

= ∫ \((e^(^-2u^2)\)) (√2u du)

The integral of \(e^(-2u^2)\)= √(π/2).

∫ \((e^(-x^2/2))^2\) dx

= ∫  (√2u du) \((e^(-2u^2))\\\)

= √(π/2) ∫ (√2u du)

We substitute back  u = √(x²/2), we obtain:

∫ \((e^(-x^2/2))^2\)dx

= √(π/2) (√(x²/2))²

= √(π/2) (x²/2)

= (√π/2) x²

A comparison  with the right side of the equation  shows that they are are equal.

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Answer:

\(\boxed{\sf x=12}\)

Step-by-step explanation:

By applying Similar Triangles Theorem:-

\(\sf \cfrac{x}{6} =\cfrac{6}{3}\)

We'll multiply both sides of the equation by 6, the LCM of 6,3.

\(\sf x=2 \times 6\)

\(\sf x=12\)

Considering the given p-value, it is found that the sample does not give enough evidence that the proportion has changed.

At the null hypothesis, it is tested if the proportion is still the same, that is:

\(H_0: p = 0.04\)

At the alternative hypothesis, it is tested if the proportion has changed, that is:

\(H_1: p \neq 0.04\).

Depends on if the p-value is less or more than the significance level:

In this problem, the p-value is of 0.25, which is more than the standard significance level of 0.05. Hence, the null hypothesis is not rejected, which means that the sample does not give enough evidence that the proportion has changed.

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Answer: Fail to reject

This isn't enough evidence to conclude that the return rate is no longer

4%

Step-by-step explanation:

Answer:

131,200 units

Step-by-step explanation:

The number of units transferred to Department 2 from Department 1 is the total units to be accounted for  which is 180,200 units minus the ending work in process of 49,000 units.

The logic here is that Department 1 is to account for 180,200 units ,part of which is the ending working process while the remainder which was transferred out is the difference between the two figures

units transferred to Department 2=180,200-49,000= 131,200.00  units

Answer:

The expectation is  \(E(1 )= -\$ 1\)

Step-by-step explanation:

From the question we are told that  

     The first offer is  \(x_1 = \$ 8000\)

     The second offer is  \(x_2 = \$ 4000\)

      The third offer is  \(\$ 1600\)

      The number of tickets is  \(n = 5000\)

      The  price of each ticket is  \(p= \$ 5\)

Generally expectation is mathematically represented as

             \(E(x)=\sum x * P(X = x )\)

     \(P(X = x_1 ) = \frac{1}{5000}\)    given that they just offer one

    \(P(X = x_1 ) = 0.0002\)    

 Now  

     \(P(X = x_2 ) = \frac{1}{5000}\)    given that they just offer one

     \(P(X = x_2 ) = 0.0002\)    

 Now  

      \(P(X = x_3 ) = \frac{5}{5000}\)    given that they offer five

       \(P(X = x_3 ) = 0.001\)

Hence the  expectation is evaluated as

       \(E(x)=8000 * 0.0002 + 4000 * 0.0002 + 1600 * 0.001\)

      \(E(x)=\$ 4\)

Now given that the price for a ticket is  \(\$ 5\)

The actual expectation when price of ticket has been removed is

      \(E(1 )= 4- 5\)

      \(E(1 )= -\$ 1\)

Answer:

A rate is two variables that relies on each other so a example would be a projectile and a cannon, in relation the cannon goes no where while the projectile is flying through the air

Step-by-step explanation:

5 because simple division

Answer:

1890ml<10litres

1.72m=172cm

Step-by-step explanation:

10 x 1000 = 10000 ml which is greater than 1890 ml.

1.72 x 100 = 172 cm

Answer:

The rate is 5 dollars per student.

Step-by-step explanation:

The rate per student can be found with \(\frac{dollars}{student}\):

\(\frac{150dollars}{30student}=5\frac{dollars}{student}\\\\\frac{350dollars}{70student}=5\frac{dollars}{student}\)

The rate is 5 dollars per student.

Answer: 118.54

Step-by-step explanation:

The reasonable range for the total cost of the tickets the groups

would pay  is {84, 126, 2163}.

The sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively, are the domain and range of a relation.

A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values.

Given:

The Function modeled for the situation is

f(x) = 21 x where x is the number of tickets sold.

So, For x= 4 Tickets

Fare, F(x) = 21 x 4= $84

and, For x= 6 Tickets

Fare, F(x) = 21 x 6 = $126

and, For x= 103 Tickets

Fare, F(x) = 21 x 103 = $2163.

Hence, the range is {84, 126, 2163}.

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The value of total weight of the fish Nicholas and his father caught, in pounds is,

⇒ 87/4 pounds

We have to given that;

Nicholas caught a fish that weighed 14 1/2 pounds.

And, His father caught a fish that weighed half as much as the fish Nicholas caught.

Hence, The weight of fish caught  by his father is,

⇒ 14 1/2 ÷ 2

⇒ 29/2 × 1/2

⇒ 29/4

Thus, The value of total weight of the fish Nicholas and his father caught, in pounds is,

⇒ 14 1/2 + 29/4

⇒ 29/2 + 29/4

⇒ 58/4 + 29/4

⇒ 87/4 pounds

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Answer:

its the first one you listed

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

5/9 to a decimal would be .5 repeated

The answer is .5 repeated

Do not put your answer as .5 because .5 is 5/10

A proper answer can be something like "0.5 repeated, 0.5555..., or .5 with a line over the 5"

Answer:

The expression means 15 minus the product of 5 times the difference of p minus 6. If p = 8, then the value of the expression is .