explain why two lines through the origin that meet at a right angle can be considered orthogonal subspaces of r2 but two planes through the origin that meet at a right angle can not be considered orthogonal subspaces of r3.

Answer:

See below ~

Step-by-step explanation:

Finding the discriminant

⇒ The discriminant is -27.

⇒ Because the discriminant is less than 0, the two roots are complex.

Answer:

23, 50, 64

Step-by-step explanation:

137 = 23 + 50 + 64

Let the first number be x

Second number: 2x+4

Third number: 3x-5

Write the equation:

x + (2x + 4) + (3x-5) = 137

Solve for "x"

6x - 1 = 137

6x = 138

x = 23

Plug x (23) into the equation:

x + (2x + 4) + (3x-5) = 137

23 + 2(23) + 4 + 3(23) - 5 = 137

(23 + 46 + 4 + 69) - 5 = 137

142 - 5 = 137

Answer:

f(g(x)) =

Just plug in g(x) in the x of x^2 + 3

((x-2)^1/2))^2 + 3

x - 2 + 3

x + 1

f(g(x)) = x + 1

so, the third choice.

Answer:

40+5q

Step-by-step explanation:

Distributive property is multiplying each number inside the parentheses by the number outside the parentheses.

For example: a(b+c) would be ab+ac

Knowing that all you have to do now is multiply:

5x8=40

5xq=5q

Put them together and you get 40+5q!

I hope this helps, and have a great day! :)

It is not possible to determine how many other tasks are delayed or how late the project will be delayed without more information.

We would need to know the original schedule and deadlines for the tasks and project in order to calculate the delays. Additionally, it is unclear if t1 and t2 are the only tasks that are delayed or if there are others. Therefore, an approximate answer cannot be provided without more information.

We could assume that only 2 tasks are missing in the whole project to add a maximum of 2+3 = 5 days, but this would not be a realistic estimate.

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Answer:

Measure of angle 2 and angle 4 is 42°.

Step-by-step explanation:

From the figure attached,

m∠ABC = 42°

m(∠ABD) = 90°

m(∠ABD) = m(∠ABC) + m(∠DBC)

90° = 43° + m(∠DBC)

m(∠DBC) = 90 - 43 = 47°

Since ∠ABC ≅ ∠4 [Vertical angles]

m∠ABC = m∠4 = 42°

Since, m∠3 + m∠4 = 90° [Complimentary angles]

m∠3 + 42° = 90°

m∠3 = 90° - 42°

        = 48°

Since, ∠5 ≅ ∠3 [Vertical angles]

m∠5 = m∠3 = 48°

m∠3 + m∠2 = 90° [given that m∠2 + m∠3 = 90°]

m∠2 + 48° = 90°

m∠2 = 90 - 48 = 42°

m∠3+ m∠4 = 90° [Since, ∠3 and ∠4 are the complimentary angles]

48° + m∠4 = 90°

m∠4 = 90 - 48 = 42°

Therefore, ∠2 and ∠4 measure 42°.

Answer:

h is the function name; t is the input, or independent variable; h(t) is the output, or dependent variable.

The tangent of the angle between vectors v and w is 2√(21) / 9

We can use the dot product and cross-product formulas to find the angle between two vectors.

The dot product of two vectors v and w is given by:

v · w = ||v|| ||w|| cos(θ)

where ||v|| and ||w|| are the magnitudes of the vectors v and w, and θ is the angle between them.

The cross product of two vectors v and w is given by:

v × w = ||v|| ||w|| sin(θ) k

where k is a unit vector in the direction of the cross product.

Since v × w = 6i - 7j + 9k and v · w = 9, we can find the angle between v and w as follows:

\(\theta = sin^{-1}\frac{||v \times w||}{||v|| \ ||w||} = sin^{-1}\frac{||6i - 7j + 9k||}{||v|| \ ||w||}\)

We can find the magnitude of v × w by using the formula for the magnitude of a cross-product:

\(||v \times w|| = ||6i - 7j + 9k|| \\\\= \sqrt{6^2 + (-7)^2 + 9^2} = \sqrt{6^2 + 49 + 9^2}\\\\=\sqrt{84} = \sqrt(2^2 \times 3 \times 7) = 2\sqrt{(3 \times 7)\)

We can find the magnitude of v and w using the given dot product formula:

v · w = ||v|| ||w|| cos(θ) = 9

||v|| ||w|| = 9 / cos(θ)

Since we know that ||v|| and ||w|| are positive, we can square both sides to obtain:

\((||v|| \ ||w||)^2 = \frac{9 }{cos(\theta))^2} \\\\||v||^2 \ ||w||^2 = \frac{81}{cos^2(\theta)}\)

Finally, using the tangent formula, we can find tanθ:

tan(θ) = sin(θ) / cos(θ) = ||v × w|| / ||v·w|| = 2√(3 × 7) / 9 = 2√(21) / 9.

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Answer:

5.35?

Step-by-step explanation:

use a calculator and check it

Answer:

The car must have a speed of 25 kilometres per hour to stop after moving 7 metres.

Step-by-step explanation:

Let be \(d(s) = 0.0056\cdot s^{2} + 0.14\cdot s\), where \(d\) is the stopping distance measured in metres and \(s\) is the speed measured in kilometres per hour. The second-order polynomial is drawn with the help of a graphing tool and whose outcome is presented below as attachment.

The procedure to find the speed related to the given stopping distance is described below:

1) Construct the graph of \(d(s)\).

2) Add the function \(d = 7\,m\).

3) The point of intersection between both curves contains the speed related to given stopping distance.

In consequence, the car must have a speed of 25 kilometres per hour to stop after moving 7 metres.

Answer:

x=17 degrees

Step-by-step explanation:

All 3 angles = 180 degrees

So 90 + 54 + (x+19) = 180

Combine like terms

163 + x = 180

Subtract 163 from both sides

x = 180-163

x = 17

One possibility could be :

y = x - 3

wherein:

x : number of apples on Monday

y : number of apples on Tuesday, the day after

Hope I helped you! :)

Have a great day/night!!

In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.

The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.

We have to find the product of tan A and tan C.

In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.

So, we have, tan A = tan C

Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.

Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.

Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.

Answer: `(BC)^2/(AB)^2`.

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Sample Space (S) = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

To illustrate all possible outcomes of tossing a dime 3 times, we can create a tree diagram. We'll represent a Head as "H" and a Tail as "T".

Here's the tree diagram:

         H

      /     \

  H       T

 /  \    /  \

H    T  H    T

         T

      /     \

  H       T

 /  \    /  \

H    T  H    T

Using the tree diagram, we can write out the sample space as a set of all possible outcomes:

Sample Space (S) = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

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Answer:

A to B is a scale of 1.2

Step-by-step explanation:

Answer:

The answer is 1.2

The system of linear inequalities to model the situation is 10x + 20y ≤ 100 and y > 2x

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

Using the following representations:

We have the following system of inequalities from the given statements

10x + 20y ≤ 100

y > 2x

Hence, the system of inequalities is 10x + 20y ≤ 100 and y > 2x

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Answer:

3). x > -3 and x <=2

4) x >7 and x < 14

5) x <= -7 or x > = - 4

6) x <= 4 or x >6

7. p < 6 and p >2

6 > p > 2

8. n <= -7 or n > 12

- 7 <= n > 12

Step-by-step explanation:

how much is in the spice mix? context is necessary

Answer:

25 and 54

Step-by-step explanation:

(a)

6z² - 2z + 5 ← substitute z = 2

= 6(2)² - 2(2) + 5

= 6(4) - 4 + 5

= 24 - 4 + 5

= 20 + 5

= 25

(b)

64 - 5z ← substitute z = 2

= 64 - 5(2)

= 64 - 10

= 54

Using the formula of volume of rectangular prism;

1. The volume of the rectangular prism is 3672cm³

2. The volume of the rectangular prism is 630in³

3. The volume of the rectangular prism is  3744ft³

The volume of a rectangular prism can be calculated by multiplying its length (l), width (w), and height (h). The formula for the volume of a rectangular prism is:

Volume = length × width × height

V = l × w × h

By substituting the given values for the length, width, and height into the formula, you can calculate the volume of the rectangular prism.

1. To find the volume of the rectangular prism, we have to substitute the value into the formula;

v = 9 * 24 * 17

v = 3672cm³

2. The volume of the rectangular prism is given as;

v = 4.5 * 14 * 10

v = 630in³

3. The volume of the rectangular prism is given as;

v = 8 * 12 * 39

v = 3744ft³

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Answer:

D(0,5) F(-3, -4) E(4, -3)

Step-by-step explanation:

3 units horizontally means that you should add 3 to each of the respective x coordinates. since D looks to be at (-3, 5) then you would make the new point (I'll call it D1) at D1 (-3 + 3, 5) or (0, 5). Do the same for all other points!

Hey there!
When you are translating something on a graph, things can get complicated. I'm here to help!

Translating 3 points horizontally means that every point on this triangle stated in this graph moves 3 points to the left or right, since horizontal means that. The problem doesn't reiterate whether a direction is included, so let's just worry about the right.

Moving 3 points to the right means that the x coordinate of the points gain 3.
D-> (-3, 5) -> Add 3 to the x coordinate -> D' -> (0, 5)
E-> (1, -3) -> Add 3 to the x coordinate -> E' -> (4, -3)
F-> (-6, -4) -> Add 3 to the x coordinate -> F' -> (-3, -4)

Note that the y-coordinate of the points remain unchanged and the altered translated points are labelled with the prime symbol, shown as ' which means that they are translated from the original graph.

Attached is the image that you should be getting when finished with your translations.

Hope this helped!

It should take approximately 1.98 hours, or around 1 hour and 59 minutes, to cook a 5.17 pound beef rib roast based on the recommended guideline of 23 minutes per pound at a 325°F oven setting.

To calculate the cooking time for a 5.17 pound roast, we can use the recommended guideline of 23 minutes per pound. First, we need to convert the weight from pounds to minutes, and then convert minutes to hours.

Cooking time in minutes = 5.17 pounds * 23 minutes/pound

Cooking time in minutes = 118.91 minutes

To convert minutes to hours, we divide the total minutes by 60:

Cooking time in hours = 118.91 minutes / 60

Cooking time in hours ≈ 1.98 hours

Therefore, it should take approximately 1.98 hours to cook a 5.17 pound beef rib roast based on the recommended guideline of 23 minutes per pound at a 325°F oven setting.

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Answer:

i think your answer would be d

Step-by-step explanation:

hope this helps!

The answer to the question is (i) the measurement of angles and distances in accordance with specific procedures.

A survey is a method used to gather information about a particular population or sample group. It involves collecting data through various means such as questionnaires, interviews, and observations. The purpose of a survey is to obtain information about a particular topic or issue that can be used for analysis, decision-making, or research purposes.

The items listed in options (ii), (iii), and (iv) all pertain to information that may be included in a land survey, which is a type of survey used to determine the boundaries, size, and characteristics of a piece of land. A professional measurement of a tract of land, the type of improvements best suited for the land, and the total area of the land with its mapped boundaries and elevation are all important pieces of information that may be gathered during a land survey.

On the other hand, the measurement of angles and distances in accordance with specific procedures is not typically part of a survey, as it is more closely related to a surveying technique known as triangulation. Triangulation is a method used to determine the location of a point by measuring angles and distances from fixed points. While similar in name, surveying and triangulation are distinct practices.

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(a) The sum of everyone's utilities is highest when 2,000 people go After and the rest go Before is not a Nash Equilibrium beacuse it doesn’t meet the criteria for Nash Equilibrium.

(b) The Nash equilibrium number of After 7am drivers is 4000.

(c) A congestion charge of 20 for drivers going after can solve the discrepancy between a and b, as the Nash equilibrium is now met with the 2000 drivers entering after 7 am, and 4000 entering before 7 am.

a) No, it is not a Nash Equilibrium.

Nash Equilibrium is a set of strategies that make sure that no player can improve their own utility by unilaterally changing their strategy.

Therefore, let’s say that all players choose to follow the strategy of entering After 7 am, given that N>4000 people want to drive into Central London. In this scenario, everyone’s utility would be as follows:

u(After) = 50 – 0.01N

However, if a single person changes his strategy and chooses to enter Before 7 am instead, his utility would be 10 instead of the previous 0 (as he is still affected by the congestion even if he enters after).

Thus, the new utility for the person who switched would be greater than what they would have gotten before.

Therefore, this scenario doesn’t meet the criteria for Nash Equilibrium.

b) The Nash equilibrium number of drivers entering after 7 am can be found by the following formula:

50-0.01N=10

40=0.01N

N=4000

which means 4000 people should choose to go Before 7 am, and the rest should go After 7 am.

c) A congestion charge of 20 for drivers going after can solve the discrepancy between a and b.

Let’s say the congestion charge is C. In this case, the utility of entering After 7 am would be

u(After)

=30-0.01(N-A)+20

= 50-0.01N+20-0.01A-20 50-0.01N-0.01A-20 30-0.01N-0.01A

Thus, the Nash Equilibrium number of drivers entering after 7 am would be as follows:

30-0.01N-0.01A=10

20=0.01A

A=2000

N = 4000+2000

N = 6000

Therefore, a congestion charge of 20 for drivers going after can solve the discrepancy between a and b, as the Nash equilibrium is now met with the 2000 drivers entering after 7 am, and 4000 entering before 7 am.

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Answer:

I think it -2 then -7

The current through the inductor to reach one-half of its maximum value after closing the switch is approximately 12.5 microseconds.

To determine the time it takes for the current through the inductor to reach one-half of its maximum value, we can use the time constant formula for an RL circuit:

t = (1/2)(L/R)

Given:

Plugging in the values, we have:

t = (1/2)(0.00125 H) / (50.0 Ω)

Simplifying the equation, we find:

t = 0.0000125 s or 12.5 μs

Therefore, the current through the inductor will reach one-half of its maximum value approximately 12.5 microseconds after closing the switch.

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Answer:

1. -7

2. -31

3. 122

Step-by-step explanation:

Those are your answers.