Given vectors u = ⟨3, 4⟩ and v = ⟨4, 3⟩, what is the measure of the angle between the vectors?

0°
16.3°
163.7°
Undefined

Answer:

- 9/35

Step-by-step explanation:

The value of x is equal to 15°

In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

By substituting the given parameters, we have the following:

3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.

3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.

23x + 15 = 360°.

23x = 360 - 15

23x = 345

x = 345/23

x = 15°.

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Answer:

slope = - \(\frac{6}{5}\)

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (3, - 1 ) and (x₂, y₂ ) = (- 2, 5 )

m = \(\frac{5-(-1)}{-2-3}\) = \(\frac{5+1}{-5}\) = \(\frac{6}{-5}\) = - \(\frac{6}{5}\)

The midpoint of the line segment with the endpoints (5, 6) and (-5, -2) is (0, 2).Hence, the answer is: Midpoint = (0, 2).

The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is calculated using the formula:M = [(x1 + x2) / 2, (y1 + y2) / 2]where M is the midpoint.In the given problem, the endpoints are (5, 6) and (-5, -2).

So, we can find the midpoint by applying the formula mentioned above.Midpoint = [(5 + (-5)) / 2, (6 + (-2)) / 2]= [0/2, 4/2]= [0, 2]

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The formula to calculate the cost to rent Toyota Etios is R15 + R3 n.

The formula to calculate the cost to rent VW Polo Vivo is R11.50 + R3 n.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

We have the formula used to calculate the cost to rent the Ford Figo is cost (in rand)= R900 + R7 x n.

Now, Toyota Etios cost R15 per Km and per km charge will be R3.

So, the formula to calculate the cost to rent is

= R15 + R3 n

and, VW Polo Vivo cost R11.50 per Km and per km charge will be R3.

So, the formula to calculate the cost to rent is

= R11.50 + R3 n

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The given statement "no matter what the resource allocation is, area A will always have the highest resource availability," is not essentially true.

The term "area" generally refers to a specific region or part of a larger space. In the context of your question, area A represents a particular zone with resources allocated to it. Resource availability refers to the quantity and accessibility of resources in a given area.

To claim that area A will always have the highest resource availability regardless of resource allocation, it implies that there are factors inherent to area A that consistently make it the most resource-rich zone. This could be due to natural resource distribution, infrastructure, or other variables that ensure area A maintains the highest resource availability.

However, without additional information about area A and the specific resources in question, it is difficult to definitively state that area A will always have the highest resource availability.

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In the context of companies navigating an uncertain future, those who take the existing total industry structure and its future trajectory as given and decide where to compete are known as "strategic planners."

Strategic planners are entities that assess the prevailing industry structure and dynamics, acknowledging the uncertainty of the future but assuming that the industry will largely follow its expected trajectory. They carefully analyze the competitive landscape, including market conditions, customer preferences, technological advancements, and regulatory factors. By doing so, they identify areas where they can leverage their strengths and capabilities to outperform rivals.

Strategic planners understand that the industry structure may evolve over time due to various factors, such as technological disruptions, changing consumer behavior, or new market entrants. However, rather than attempting to reshape the industry or disrupt the status quo, they focus on identifying specific market segments or niches where they can excel within the existing industry framework.

These companies or individuals strategically position themselves by capitalizing on their unique strengths, whether it's cost leadership, differentiation through product innovation, superior customer service, or efficient supply chain management. They align their resources, capabilities, and competitive strategies to effectively compete in the chosen segments, while recognizing the need to adapt and evolve as the industry landscape changes.

By accepting the industry's structure and future trajectory as given, strategic planners mitigate risks associated with attempting to reshape the market or betting on uncertain outcomes. Instead, they concentrate their efforts on optimizing their performance within the existing industry context, thereby maximizing their chances of success in an uncertain future.

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We can see here that the volume of the cone is: D. 1,071.79 yd^3.

In geometry, a cone is a three-dimensional shape with a circular base that tapers smoothly to a single point called the apex or vertex. The axis of the cone is the line that connects the apex to the center of the base.

Cones are classified as either right or oblique depending on whether the axis is perpendicular to the base or not. A right cone has an apex directly above the center of its circular base and has a symmetrical taper. An oblique cone, on the other hand, has an apex that is not directly above the center of its base and has a slanted taper.

The formula of the volume of a cone: V=1/3hπr².

Where h = height of cone = 16yd

π = 3.14

r = 16/2 = 8yd

V = 1/3hπr² = 1/3 × 16 × 3.14 × 8²

= 1,071.78667

≅ 1,071.79yd³

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Hence, if yοu utilise the entire match, yοur accοunt will be credited with $8,000 befοre the end οf the year. Thus, option A is correct.

Fοr the purpοse οf resοlving prοpοrtiοnality issues, mathematicians emplοy the unitary methοd. It is predicated οn the nοtiοn that if we are aware οf the relatiοnship between twο quantities fοr οne unit οf measurement, we may utilise that relatiοnship tο determine the relatiοnship between the same twο values fοr any οther unit οf measurement.

When we need tο determine the value οf οne quantity based οn the value οf anοther quantity and the twο quantities are related tο οne anοther prοpοrtiοnally, we frequently emplοy the unitary technique in practical circumstances. The unitary technique can be used, fοr instance, tο determine the price οf five apples if we knοw that three apples cοst $2.

given,

If yοur emplοyer matches yοur retirement cοntributiοns dοllar fοr dοllar up tο a maximum οf $4,000, this implies that fοr every dοllar yοu put in, yοur emplοyer will put in an additiοnal dοllar, up tο a tοtal οf $4,000 in matching funds.

Yοur emplοyer will cοntribute an additiοnal $4,000 if yοu cοntribute the whοle $4,000, fοr a tοtal οf $8,000 in cοntributiοns tο yοur accοunt by the end οf the year.

Hence, if yοu utilise the entire match, yοur accοunt will be credited with $8,000 befοre the end οf the year.

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If your employer matches your retirement contributions on a dollar-for-dollar basis up to $4,000, how much will be contributed to your account by the end of the year if you take advantage of the entire match?

a. $8,000

b. $8,800

c. $8,100

d. $9,800

Yes, there will be a collision between Speedy Sue's car and the slow-moving van in the tunnel. The collision will occur at a distance of approximately 146.5 meters into the tunnel, and the time of the collision will be around 7.72 seconds.

To determine whether there will be a collision, we need to calculate the time it takes for Speedy Sue to reach the van and compare it with the time it takes for the van to exit the tunnel.

First, we calculate the time it takes for Sue to reach the van. The relative velocity between Sue and the van is (33.0 m/s - 5.40 m/s) = 27.6 m/s. Using the formula time = distance / velocity, the time it takes for Sue to reach the van is approximately 175 m / 27.6 m/s ≈ 6.34 seconds.

Next, we calculate the time it takes for the van to exit the tunnel. The distance the van needs to travel to exit the tunnel is the sum of the distance from its initial position to the end of the tunnel and the distance Sue needs to travel to reach the end of the tunnel. The total distance is 175 m + 175 m = 350 m. The velocity of the van is 5.40 m/s. Using the formula time = distance / velocity, the time it takes for the van to exit the tunnel is approximately 350 m / 5.40 m/s ≈ 64.81 seconds.

Since 6.34 seconds is less than 64.81 seconds, Sue will collide with the van before it exits the tunnel. To determine the distance into the tunnel where the collision occurs, we subtract the distance Sue travels in 6.34 seconds from the initial distance between Sue and the van. The distance Sue travels is (33.0 m/s - 1.90 m/s^2 * 6.34 s^2 / 2) * 6.34 s ≈ 146.5 meters.

Therefore, the collision between Sue's car and the van will occur at a distance of approximately 146.5 meters into the tunnel, and the time of the collision will be around 7.72 seconds.

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Answer:

-5x

Step-by-step explanation:

if f(4) = -5x+ 10 then f(x) + f(4) is;

-5x+10-10 = -5x

The ratio of John's money to Peter's money is 5/4. This means if John has a total amount of 5 then Peter will have a total of 4 as his amount.

Let's assume John has 'x' amount of  money, Peter has 'y' amount of money, The money John saved is 'p' and the money Peter saved is 'q'

So,

p = x - 80x/100                (equation 1)

q = y - 75y/100                (equation 2)

According to the given question, the amount John saved is equal to the amount Peter saved. Hence, we can equate equations 1 and 2.

p = q

x- 80x/100 = y - 75y/100

x - 0.8x = y - 0.75y

0.2x = 0.25y

x =  0.25y/0.2

x/y = 0.25/0.2

x/y = 25/20

x/y = 5/4

Hence, the ratio of John's money to Peter's money is 5/4.

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Answer:

x = 5

Step-by-step explanation:

15-x=2x

Add x to each side

15-x+x = 2x+x

15 = 3x

Divide each side by 3

15/3 = 3x/3

5 =x

Answer:

5

Step-by-step explanation:

15=3x

5=x

Therefore, the probability that a European New Zealander chosen at random is either positive in both systems or negative in both systems is approximately 0.2396.

To find the probability that a European New Zealander is either positive in both systems or negative in both systems, we can use the principle of multiplication for independent events.

Given:

Probability of being Rh+ (positive in the Rh system) = 81%

= 0.81

Probability of being Rh- (negative in the Rh system) = 1 - 0.81

= 0.19

Probability of being K+ (positive in the Kell system) = 8%

= 0.08

Probability of being K- (negative in the Kell system) = 1 - 0.08

= 0.92

Since the blood types in each system are independent, we can multiply the probabilities to find the joint probability of being positive in both systems or negative in both systems:

Probability of being positive in both systems = P(Rh+ and K+)

= P(Rh+) * P(K+)

= 0.81 * 0.08

= 0.0648

Probability of being negative in both systems = P(Rh- and K-)

= P(Rh-) * P(K-)

= 0.19 * 0.92

= 0.1748

To find the total probability, we sum the probabilities of being positive in both systems or negative in both systems:

Probability of being either positive in both systems or negative in both systems = P(Rh+ and K+) + P(Rh- and K-)

= 0.0648 + 0.1748

≈ 0.2396

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Ans:

(x+5)(x+1)+8

Step by step explanation:

-5 was mentioned as the 0 of the first root: (x+5). Then with some maneuvering we can plot (-3,4) then add (x+1) because they land on the same y axis. then we add 8 to get it right on the vertex.

As per the given 4 x 5 matrix, the reduced row echelon form of A is \(\left[\begin{array}{ccc}1&2&0\\0&0&1\\0&0&0\end{array}\right]\)

The term matrix in math refers a set of numbers arranged in rows and columns so as to form a rectangular array.

Here we have the 4 x 5 matrix.

And here we also know that a1,a2,a4 are linearly independent and the value of a3=a1+2a² and a5=2a1-a²+3a⁴.

Now, we have to apply the value of

a1 = 1, a2 = 0, a3 = 0, a4 = 0, a5 = 1, a6 = 0, a7 = 0, a8 = 0, and a9 = 1.

Then we get the matrix of 3 x 3 looks like the following,

\(\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]\)

Now, we have to do the following steps in order to get the reduced row echelon form of A,

The first and foremost steps is to take the non-zero number in the first row is the number 1.

Then we have to place any non-zero rows are placed at the bottom of the matrix.

This steps are repeated until the final row becomes zero.

Then we get the resulting matrix as \(\left[\begin{array}{ccc}1&2&0\\0&0&1\\0&0&0\end{array}\right]\)

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Answer:

y=1/6x+2

Step-by-step explanation:

To start, you know what m is; it's just the slope, which you said was 1/6. So you can right away fill in the equation for a line somewhat to read:

y=1/6x+b.

Now, what about b, the y-intercept?

To find b, think about what your (x,y) point means:

(12,4). When x of the line is 12, y of the line must be 4.

Because you said the line passes through this point, right?

Now, look at our line's equation so far: . b is what we want, the 1/6 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the the point (12,4).

So, why not plug in for x the number 12 and for y the number 4? This will allow us to solve for b for the particular line that passes through the point you gave!.

(12,4). y=mx+b or 4=1/6 × 12+b, or solving for b: b=4-(1/6)(12). b=2.

Answer:X=12/7

Step-by-step explanation:

Y \(\alpha\) X

⇒Y=KX

Where K is the constant

From the question,k=7

⇒ When Y=12,

y=KX

12=7X

X=12/7

Answer:

\(x = 2\)

Step-by-step explanation:

Given

Conjecture: \(x + 3 < x^2\) --- (Missing)

Required

Which value of x prove the conjecture otherwise

To do this , we simply substitute the values of x in the options

\(1.\ x = -\frac{1}{3}\)

This is negative;

So, there is no need to check

\(2.\ x = -3\)

This is also negative;

So, there is no need to check

\(3.\ x = 2\)

\(x + 3 < x^2\)

\(2 + 3 < 2^2\)

\(5 < 4\)

This value of x is false because 5 is not less than 4

\(4.\ x = 3\)

\(x + 3 < x^2\)

\(3 + 3 < 3^2\)

\(6 < 9\)

9514 1404 393

Answer:

  (√5)/2

Step-by-step explanation:

Of the several ways I can think of to do this, using a graphing calculator is about the easiest. It shows the minimum to be ...

  f(1) = √1.25 = (√5)/2

__

Using the distance formula, you have ...

  f(x) = √((x -(-2))² +((x² +2)-5/2)²)

  f(x) = √(x² +4x +4 +x⁴ -x² +1/4) = √(x⁴ +4x +17/4)

The minimum is found where the derivative is zero.

  f'(x) = (2x³ +2)/√(x⁴ +4x +17/4) = 0

  x³ = -1 . . . . . f'(x) is zero when the numerator is zero

  x = -1 . . . . . cube root

Then the minimum value of f(x) is ...

  f(-1) = √(x⁴ +4x +17/4) = √((-1)⁴ +4(-1) +17/4) = √(1 -4 +17/4) = √(5/4)

  f(-1) = (√5)/2 . . . . minimum value of f(x)

__

The graph shows f²(x) in red and its minimum of 1.25 = 5/4. The curve (x, x²+2) and the point (-2, 5/2) are also shown, for reference. (The slope of the curve at x=-1 is -2, and the normal to the curve at that point has slope 1/2. The normal goes through the point (-2, 5/2), consistent with f(x) being a minimum at x=-1.)

Check the picture below.

so the area of it, is really the area of a 16x16 square and four triangles with a base of 16 and a height of 15.

\(\stackrel{ \textit{\LARGE Areas}}{\stackrel{ square }{(16)(16)}~~ + ~~\stackrel{ \textit{four triangles} }{4\left[\cfrac{1}{2}(16)(15) \right]}}\implies 256~~ + ~~480\implies \text{\LARGE 736}~cm^2\)

Answer:

B, C, E

Step-by-step explanation:

right on edge

Answer:

x = - \(\frac{80}{7}\)

Step-by-step explanation:

Given

\(\frac{3}{7}\) - \(\frac{2}{5}\) x = 5

Multiply through by 35 ( the lcm of 7 and 5 ) to clear the fractions

15 - 14x = 175 ( subtract 15 from both sides )

- 14x = 160 ( divide both sides by - 14 )

x = \(\frac{160}{-14}\) = - \(\frac{80}{7}\)  

Answer:

.6

Step-by-step explanation:

-2.1-.6=-1.5 / -1 1/2

Answer:

Step-by-step explanation:

The loop will run an infinite number of times

Answer:

What is 3 5 with a denominator of 10?

As you can see, the answer to the question "what is 3/5 of 10?" as a number is 6.

Answer:

Step-by-step explanation:

Correct option is A)