a car travels 87 miles north and 114 miles west. what is the magnitude of the cars resultant vector

Answers

Answer 1

The magnitude of the resultant vector is 27 miles

How to determine the vector magnitude

Resultant vector = Distance of A - Distance of B

This is so because of the opposite direction of the car's movement

A = 87 miles

B = 114 miles

Resultant vector = 114 - 87

Resultant vector = 27 miles

Thus, the magnitude of the resultant vector is 27 miles

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Related Questions

If a linear function contains the pairs (5,7) and (9,11), which pairs should have the reciprocal function to this one?

Please choose an answer.

a.
(7.5) and (11.9)


b.
(5.7) and (11.9)


c.
(5.7) and (9.11)


d.
(7.5) and (9.11)

Answers

The pair of the reciprocal function will be (7, 5) and (11, 9). Then the correct option is A.

What is coordinate geometry?

Coordinate geometry is the study of geometry using the points in space.

If a linear function contains the pairs (5, 7) and (9, 11).

If the pairs should have the reciprocal function to this one. Then the coordinate gets swapped.

The pair of the reciprocal function will be (7, 5) and (11, 9).

Then the correct option is A.

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which statement accurately describes how to reflect point A (3,-1) over the y axis

Answers

The reflection over the y-axis only changes the sign of the x-component so the reflected point is A' (-3, -1)

How to reflect point A over the y-axis?

Here we can't see the options, so I will teach you how to reflect any point over the y-axis.

Any point on the X-Y plane is defined by its coordinates (x, y).

If we reflect this point over the y-plane, we only change the sign of the x-component of the point.

So after the reflection, we get the point (-x, y).

Then if we apply that reflection to point A (3, -1). We will get the reflected point:

A' (-3, -1)

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is translation a and b?

Answers

Translation Represented by a Column Vector or Matrix
where a is the number of units to move right or left along the x-axis and b is the number of units to move up or down along the y-axis.

la suma de dos ángulos internos es siempre mayor que la medida del tercer ángulo
verdadero o falso y por que

Answers

Utilizando el triangulo rectangulo como contraejemplo, veremos que esto es falso.

¿Es la propicición verdadera o falsa?

Primero, sabemos que para todo triangulo la suma de sus angulos internos es igual que 180°.

Ahora, vamos a el triangulo más comun. El triangulo rectangulo.

Este es el triangulo que tiene uno de sus angulos internos igual a 90°.

Digamos que los otros dos angulos internos son A y B, entonces tendriamos:

A + B + 90° = 180°

Despejando A + B obtenemos:

A + B = 180° - 90° = 90°

A + B = 90°

Entonces vemos que la suma de estos dos angulos internos es igual que el tercer angulo.

Encontramos un contraejemplo de la proposición, asi, concluimos que la proposición es falsa.

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A particular brand of cell phone case is available in four different styles and each style comes in three colors. How many different cases are available

Answers

Answer:

12

Step-by-step explanation:

the number of the available cases is :

3 × 4 = 12

What is the probability that , in a group of 200 random people , at least two of them have the same triple of initials (such as JTK for James Tiberius Kirk)

Answers

The probability is P(X >= 2).

200 random people, n = 200

Let us consider the Binomial expression

i.e.,

P(X = r) = nCr*p^r*q^(n-r)

Here we have to assume that the 3 initials are equally likely events.

i.e.,

p = 1/3

q = 1 - 1/3

= 2/3

Required probability = P(X >= 2)

= 1 - [P(X = 0) + P(X = 1)]

= 1 - [200C0*(1/3)^0*(2/3)^200 + 200C1*(1/3)^1*(2/3)^199]

= 1 - [1*1*(2/3)^200 + 200*(1/3)*(2/3)^199]

= 1 - [(2/3)^200 + 200*(1/3)*(2/3)^199]

= 1 - (2/3)^200 - 200*(1/3)*(2/3)^199

Probability is truly how possibly something is to happen. every time we're unsure about the final results of an event, we will talk about the possibilities of certain consequences and how probably they are. The evaluation of events ruled by means of possibility is called records.

3 styles of probability

ClassicalRelative Frequency Definition.Subjective possibility.

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Really short Question; Please help and Show your Work! I would rate you 5 stars or anything you like

Answers

Answer:

  about 94.41°

Step-by-step explanation:

The Law of Cosines can be used to find an angle in a triangle with three sides given.

Setup

The law of cosines relation generally relates the side opposite the angle to the other measures in the triangle:

  r² = p² +q² -2pq·cos(R)

Solution

We want to find the measure of angle R, so we solve the equation for that:

  2pq·cos(R) = p² +q² -r² . . . . . . add 2pq·cos(R)-r²

  cos(R) = (p² +q² -r²)/(2pq) . . . . divide by the coefficient of the cosine

We can fill in the given side lengths at this point:

  cos(R) = (13² +10² -17²)/(2·13·10) = -20/260 = -1/13

Then the angle can be found using the arccos function:

  R = arccos(-1/13) ≈ 94.41°

The measure of angle R is about 94.41°.

__

Additional comment

When you have done a few of these, you recognize that the angle opposite side 'c' is ...

  C = arccos((a² +b² -c²)/(2ab))

A calculator can make short work of this. The second attachment shows the evaluation of this expression with a=10, b=13, c=17. The calculator angle mode is set to degrees. The arccos function is the 2ND function of the Cos key.

Identify the line with an undefined slope

Answers

Answer:

d. vertical line

Step-by-step explanation:

A line with an undefined slope is a vertical line

Slope is the change in y over the change in x

When the slope is undefined, it means that the x does not change, which is a vertical line

Answer:

Line D

Step-by-step explanation:

Slope is defined as rise/run. Since a vertical line has zero run and infinite rise the equation is infinity/0 and anything divided by zero is undefined.

question on the image ​

Answers

Answer:

232.28°

Step-by-step explanation:

Using N = 0 degrees

Arctan ( 12.8 / 9.9)   = 52.28    degrees   ( this A to C )

   C to  A  would be  232.28  °    ( just add 180 degrees)

Answer:

16.2

pls give brainlest

explanation:

lets use pythagorean theorem

12.8^2+9.9^2

which is 163.84+98.01=261.85

261.85 square root = 16.181177

round 16.18=16.2

answer 16.2

Given that OA = 2x + 9y , OB = 4x + 8y and CD = 4x - 2y , explain the geometrical relationships between the straight line AB and CD.
It’s a 3 mark question sooo if someone could help then thanks.

Answers

The geometrical relationships between the straight lines AB and CD is that they are parallel to each other

How to determine the relationship

It is important to note the following;

A drawn from the origin and passes through point A (a , b), then the equation of OA = ax + byIf a line is drawn from the origin and passes through point B (c , d), then the equation of OB = cx + dy

We  find the equation of AB by subtracting OB from OA, thus AB = (c - a)x + (d - b)y

The slope of line AB =

⇒ OA= 2 x + 9 y

⇒ OA = 4 x + 8 y

⇒AB = OB - OA

⇒AB = (4 x + 8 y) - (2 x + 9 y)

⇒ AB = 4 x + 8 y - 2 x - 9 y

Collect like terms

⇒ AB = (4 x - 2 x) + (8 y - 9 y)

⇒AB = 2 x + -y

⇒ AB = 2 x - y

⇒ Coefficient of x = 2

⇒ Coefficient of y = -1

⇒ The slope of ab = [tex]\frac{-2}{-1}[/tex] = 2

For CD

⇒ CD = 4 x - 2 y

⇒Coefficient of x = -4

⇒ Coefficient of y = -2

⇒The slope of cd = [tex]\frac{-4}{-2}[/tex] = 2

Note that Parallel lines have same slopes

And Slope of ab = slope of cd

AB // CD

Therefore, the geometrical relationships between the straight lines AB and CD is that they are parallel to each other

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a textbook company ships its books in boxes that can hold 30 pounds. one particular order calls for a shipment of 800 books. if each book weighs 1.4 kilograms, how many boxes will be required to fulfill this order

Answers

83 boxes are required to carry 800 books.

According to the question:

One Box can hold weight = 30 pounds

We know that ,  1 pound= 0.45 kg

hence, 30 pounds = 30 x 0.45 = 13.5kg  

hence,  one box can carry 13.5 kg of weight.

Now,

Weight of 1 book = 1.4 kg

So, Total Weight of 800 books= 1.4 x 800 kg

And , No. of boxes required to carry 800 books = (1.4 x 800)/13.5 = 82.96

                                                                             or approximately 83 boxes

Hence, 83 boxes are required to carry 800 books.

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What is slope-intercept form

Answers

Answer:

y=mx+b

Step-by-step explanation:

Slope intercept form is y=mx+b where "m" should be substituted with the slope and "b" stands for the y-intercept value. "x" and "y" are your input and output values respectively.

Please help 15 points

Answers

Since in each option, each input is mapped to only one output, all the options are correct.

When a relationship represents a function?

A relationship represents a function when each input is mapped to only one output.

In this problem:

For the Venn sets, only one line departs each value of x, hence it is a function.For the ordered pairs, each value of x(2, 5 and -4), is mapped to only one value of y, hence it is a function.The graph has no vertically aligned points, hence it is a function.

Thus all the options are correct.

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Necesito saber

El cuádruplo de su anterior es igual al cubo de menos cuatro

Y tambien un ejercio aparte que dice

La tercera parte de su siguiente es igual al anterior de menos diez

Answers

Las expresiones matemáticas descritas son: (x-1)4=-4³ y 1/3(x+1)=(-10)-1.

¿Cómo identificar las expresiones matemáticas?

Para identificar las expresiones matemáticas debemos organizar los datos proporcionados en el fragmento de la siguiente manera:

El cuádruplo de su anterior es igual al cubo de menos cuatro: (x-1)4=-4³La tercera parte de su siguiente es igual al anterior de menos diez: 1/3(x+1)=(-10)-1

Luego debemos solucionar las expresiones matemáticas para encontrar el resultado final:

A. (x-1)4 = -4³

4x-4 = -64

4x = -64+4

4x = -60

x = -60/4

x = -15

B. 1/3(x+1) = (-10)-1

1/3x+1/3 = -11

1/3x = -11-1/3

1/3x = -32/3

x = -32/3•3

x = -32

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What are the four steps for multiply rational expressions as seen in the lesson

Answers

Answer:To multiply rational expressions:Completely factor all numerators and denominators.Reduce all common factors.Either multiply the denominators and numerators or leave the answer in factored form.

Therea re 8 kids at a birthday party. If there are 6 girls and 2 boys at the party, what draction of the kids are girls?

Answers

Answer:

3/4

Step-by-step explanation:

The total number of children is 8 and the number of girls is 6. This can be represented as 6/8.

You would then need to simplify...

6/2=3

8/2=4

which which lead you to 3/4!

pls help on algebra homework!! will mark brainliest!

Answers

Answer:

32

Step-by-step explanation:

YZ = ⅗XY.

XY = 20

20 / 5 x 3 = 12

YZ = 12

XZ = YZ + XY

XZ = 20 + 12

XZ = 32

Work is attached. Hope it helps!

the sum of lengths of two legs of a right angle triangle is 14 cm and its area is 24 cm square find the perimeter of the triangle​

Answers

The answer is 31.84cm

A rectangular plot is to be fenced off and divided into three parts/plots on land that borders a barn. If you do not fence the side along the barn, find the length and width of the plot that will maximize the area if you have 200 feet of fence. What is the largest area that can be enclosed

Answers

5000 square feet is the largest area that can be enclosed

It is given that a rectangular plot is to be fenced off and divided into three parts/plots on land that borders a barn there are and there is 200 feet of fence that is available.

One-fourth of the perimeter = 50

The other width also equals 50.

So the length of fencing = 200 - 50 - 50 = 100

So the area = 50 x 100 = 5000 square feet.

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math!! please please helppp!!!

What is the slope of the line below?

(i attached an image)


a) (0,4)

b) -1/3

c) (-1.5,0)

d) 3

e) 4

f) (0,4)

g) -3

h) 1/3

Answers

Answer:

The slope is 3

Step-by-step explanation:

it is 3 up and 1 across, which is 3/1 = 3

Answer:

3

Step-by-step explanation:

Look at the two lower dots shown on the line.

slope = rise/run

The vertical distance from the lower point to the higher point is 3. That is the rise.

The horizontal distance from the lower point to the higher point is 1. That is the run.

slope = 3/1 = 3

Answer: 3

The __________ states that as a procedure is repeated again and again and again and again, the probability tends to approach the actual probability.

Answers

Answer:

Law of large Numbers

Step-by-step explanation:

The Law of large numbers.

What is the Law of natural numbers?

The law of large numbers plays the main role in probability and statistics. It means that if you repeat an experiment independently so many times and average the result, what you get has to be close to the expected value.

An example of the Law of Large Numbers:

Let's assume that you rolled the dice three times and the outcomes were 6, 6, and 3. Then the average result is 5.

So, according to the law of the large numbers, if we roll the dice a large no. of times, then the average result should be closer to the expected value.

It also states that probability and statistics set a sample size that grows, and the mean of the sample size gets closer to the average of the entire population.

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A door delivery florist wishes to estimate the proportion of people in his city that will purchase his flowers. Suppose the true proportion is 0.07. If 289 are sampled, what is the probability that the sample proportion will differ from the population proportion by more than 0.03

Answers

The probability that the sample proportion will differ from the population proportion by more than 0.03 is 0.99968.

Given the true proportion is 0.07, sample size 289.

We have to calculate the probability that the sample proportion will differ from the population proportion by more than 0.03.

Probability is the likeliness or chance of happening an event among all the events possible. The probability lies between 0 and 1.

Probability=number of items/ total items.

True proportion=0.07

n=289

sample population mean=0.07

Sample proportion standard error=[tex]\sqrt{pq/n}[/tex]

=[tex]\sqrt{0.07*0.93)/289}[/tex]

=[tex]\sqrt{0.0651/289}[/tex]

=[tex]\sqrt{0.00022}[/tex]

=0.015

Probability that the sample proportion will differ from the population proportion by more than 0.03=P(I P-p I>0.03)

=P( I Z I>0.03*0.015)

=P ( I z I >0.0045)

=0.99968.

Hence the probability that the sample proportion will differ from the population proportion by more than 0.03 is 0.99968.

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Someone help, I need answers ASAP pls it’s urgent pls

Answers

its congruent lines

Select the correct answer from each drop-down menu. ∆ABC has vertices at A(11, 6), B(5, 6), and C(5, 17). ∆XYZ has vertices at X(-10, 5), Y(-12, -2), and Z(-4, 15). ∆MNO has vertices at M(-9, -4), N(-3, -4), and O(-3, -15). ∆JKL has vertices at J(17, -2), K(12, -2), and L(12, 7). ∆PQR has vertices at P(12, 3), Q(12, -2), and R(3, -2). can be shown to be congruent by a sequence of reflections and translations. can be shown to be congruent by a single rotation.

Answers

The option  that is shown to be congruent by a sequence of reflections and translations is Option B: Triangle ABC and Triangle MNO

Option  C:  Triangle JKL and Triangle PQR can be shown to be congruent by a single rotation.

How are they congruent?

Note that:

If ∆MNO  can be gotten  from ∆ABC  then ∆MNO ≅ ∆ABC  

To solve for Reflection (x axis), it will be:

The coordinate note for the reflection is (x, y) will be: (x,-y)

Since ∆MNO  M(-9, -4), N(-3, -4), and O(-3, -15).

Then the reflections will be:

M(-9, -4)- M1(-9,4)

N(-3, -4)- N1(-3,4)

O(-3,-15)-O1(-3,15)

To solve for Reflection (y axis), it will be:    

The coordinate note for the Reflection  is (x,y) will be (-x,y)

Since ∆M1N1O1  = M1(-9, 4), N1(-3, 4), and O1(-3, 15).

Then M1(-9, -4) - M2(9,4)

N1(-3, -4) - N2(3,4)

O1(-3,-15)- O2(3,15)

To solve for Translation

The coordinate note for the Translation is (x,y) will be (x+2,y+2)

Since ∆M2N2O2  = M2(9,4), N2(3,4), and O2(3, 15).

Then M2(9, 4) - M3(11,6)=A

N2(3,4) -  N3(5,6)=B

O2(3,15) - O3(5,17)=C

Hence  ∆MNO ≅ ∆ABC  

To know the congruent by a single rotation.

 If ∆JKL  can be gotten from ∆PQR

Then ∆JKL ≅ ∆PQR  

For Rotation of 90 degree in an anticlockwise position, then:

The coordinate note for the Rotation is (x,y) will be (-y, x)

So, ∆JKL  = J(17, -2), K(12, -2), and L(12, 7).

J(17, -2)-  J1(2,17)

K(12, -2) - K1(2,12)

L(12,7) - L1(-7,12)

To solve for translation

The coordinate note for the translation is (x,y) will be (x+10,y-14)

Then ∆J1K1L1 =  J1(2, 17), K1(2, 12), and L1(-7, 12).

Hence J1(2, 17) - J2(12,3) = P

K1(2, 12)- K2(12,-2) = Q

L1(-7, 12)- L2(3,-2) = R

So, ∆JKL ≅ ∆PQR.

So therefore, The option  that is shown to be congruent by a sequence of reflections and translations is Option B: Triangle ABC and Triangle MNO

Option  C:  Triangle JKL and Triangle PQR can be shown to be congruent by a single rotation.

See options below

___ can be shown to be congruent by a sequence of reflections and translations.

1)Pick one to go with the sentence.

a Triangle ABC and Triangle XYZ

b Triangle ABC and Triangle MNO

c Triangle JKL and Triangle ABC

d Triangle PQR and Triangle XYZ

___ can be shown to be congruent by a single rotation.

Pick one to go with the sentence.

a Triangle ABC and Triangle XYZ

b Triangle PQR and Triangle XYZ

c Triangle JKL and Triangle PQR

d Triangle JKL and Triangle XYZ

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On april 1 of the current year, a company purchased and placed in service a machine with a cost of $240,000. the company estimated the machine's useful life to be four years or 60,000 units of output with an estimated salvage value of $60,000. during the current year, 12,000 units were produced. prepare the necessary december 31 adjusting journal entry to record depreciation for the current year assuming the company uses: a. the straight-line method of depreciation b. the units-of-production method of depreciation c. the double-declining balance method of depreciation

Answers

The answers to the questions are:

a. $33,750b. $36000c. $90000

a. the straight-line method of depreciation

[tex]\frac{cost of machine - salvage}{useful life} * period[/tex]

= (240000 - 60000) / 4 * (9 / 12)

= $33,750

The debit is 33750 as well as the credit

b.  the units-of-production method of depreciation

(240000 - 60000) / 60000 * 12000

= $36000

c. the double-declining balance method of depreciation

(24000 *2 /4) * (9/12)

= $90000

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Please Answer Asap!!! Write the equation based on the graph of the following base 2 logarithmic function:

Answers

The graph of the logarithmic function that passes through (-2,-2) and (1,0) is [tex]\log_2(x+3)-2[/tex].

Suppose that the function is

[tex]f(x)=\log_2(x+c)+d[/tex]

Then there are two observations that we must consider from the figure

The graph must pass through (-2,-2) and (1,0)

So,

[tex]-2=\log_2(-2+c)+d[/tex]

[tex]\implies -2+c=e^{-2-d} ...~...~(1)[/tex]

And,

[tex]0=\log_2(1+c)+d\\\implies 1+c=e^{-d} ~...~...~(2)[/tex]

Observe the figure given below we see that the graph of

[tex]\log_2(x)[/tex] passes through (1,0) but does not pass through (-2,-2) and the graph is to the right of (-2,-2) hence, we need the graph to move left.

When we increase c the graph  [tex]\log_2(x+c)+d[/tex]  moves left and

When we decrease d then the graph  [tex]\log_2(x+c)+d[/tex]  moves down.

That makes the graph required to be   [tex]\log_2(x+3)-2[/tex].

Hence, the graph of the logarithmic function that passes through (-2,-2) and (1,0) is [tex]\log_2(x+3)-2[/tex].

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Question 6 The volumes of two similar solids are 729m3 and 125m3 The surface area of the larger solid is 324m2. What is the surface area of the smaller solid

Answers

Answer:

  100 m²

Step-by-step explanation:

The scale factor for volume of similar figures is the cube of the scale factor for linear dimensions. The scale factor for area is the square of that linear dimension scale factor.

Scale factor

If the ratio of volumes is the cube of the scale factor, then the scale factor for the smaller figure in terms of the larger is ...

  [tex]k=\sqrt[3]{\dfrac{125\text{ m}^3}{729\text{ m}^3}}=\sqrt[3]{\dfrac{5^3}{9^3}}=\dfrac{5}{9}[/tex]

Smaller area

The area of the smaller figure is found from ...

  [tex]\dfrac{A}{324\text{ m}^2}=\left(\dfrac{5}{9}\right)^2=\dfrac{25}{81}\\\\A=(324\text{ m}^2)\cdot\dfrac{25}{81}=\boxed{100\text{ m}^2}[/tex]

The surface area of the smaller solid is 100 square meters.

__

Additional comment

The least surface area for a given volume is that of a sphere. The larger volume given corresponds to a sphere with a radius of about 5.583 meters. Such a sphere will have an area of about 391.7 square meters. There is no known physical object with a volume of 729 m³ that can have a surface area as little as 324 m².

Avery solves the equation below by first squaring both sides of the equation.
√z^2+8 = 1 -2z
What extraneous solution does Avery obtain?
z= ?

Answers

[tex]\left(\sqrt{z^{2}+8} \right)^{2}=(1-2z)^{2}\\\\z^{2}+8=4z^{2}-4z+1\\\\0=3z^{2}-4z-7\\\\0=(z+1)(3z-7)\\\\z=-1, z=\frac{7}{3}[/tex]

We know that if z=7/3, the right-hand side will be negative, which means it is an extraneous solution as square roots cannot be negative.

There are 210 rabbits at the farm. For every 5 gray rabbits, there are 2 white rabbits. How many white rabbits are at the farm

Answers

The number of white rabbits that are at the farm is 60

Calculating quantity

From the question, we are to determine the number of white rabbits that are at the farm

From the given information,

There are 210 rabbits at the farm

and

For every 5 gray rabbits, there are 2 white rabbits

Then, we can write that

5x + 2x = 210

Where x is the number of groups of 5 gray rabbits and 2 white rabbits

Then,

7x = 210

x = 210/7

x = 30

The number of white rabbits is 2x

∴ Number of white rabbits = 2×30

Number of white rabbits = 60

Hence, the number of white rabbits that are at the farm is 60

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Which table or graph shows the value of y going up as the value of x goes up?
O A. x y
16
OB.
2
3
4
9896SHSN1
4
← PREVIOUS
12
18
24

Answers

The value of y is increasing for x values in Graph C, the correct option is C.

What is a Linear Graph?

A Linear Graph is the graphical representation of a Straight line equation.

From the graph attached with the answer, The x-y values for all the graphs are observed to determine the graph in which the y value goes up as the x value increases.

For the x value increasing, the value of y is decreasing in Graph A, B, and D.

The y value is rising only for Graph C.

Therefore, the correct option is C.

The complete question is attached with the answer.

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Other Questions
True or false: We can increase our reasoning ability by continuing to give ourselves cognitive challenges. The Fourteenth Amendment to the Constitution established which of thefollowing? The ______ is a theoretical model that explains and predicts what resource attributes underpin competitive advantage. It identifies which types of resources are key to firm performance. Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(7,5)B(7,6)C(4,6)D(4,5)Given these coordinates, what is the length of side CD of this rectangle? Find cos(A). Show your work and reduce the ratio if necessary A teacher takes her AP calculus class of 8 students to lunch. They sit around a circular dining table.a. How many seating arrangements are possible?b. How many seating arrangements are there if the teacher has to sit on the chair closest to the soda fountain?c. Among the students are one set of triplets. How many seating arrangements are there without all three of them sitting together? Can anyone please help this is due tomorrow Which equation are true A. 3^4)(3^5)=3^9B.8^6=1\-6C 43)Which power the President does NOT have?A) line item vetoB) sign international treatiesC) nominate Justices to the Supreme CourtD) Command the armed forces in a time of war. Which two European nations had a head start in the exploration during the "Age of Exploration?"Germany and ItalyAustria and HungarySpain and PortugualSwitzerland and the Netherlands The owner of a farm plants apple trees and mango trees in a ratio of 16:6. How many oak trees are planted if 198 mango trees are planted? Which of the following best describes how Brown v. Board of Education affected the United States?It forced the Southern states to desegregate their schools.It allowed Linda Brown to attend a better public school.It led to the end of the Southern Manifesto.It dealt a blow to segregation in public facilities. Which section of the project charter publicly acknowledges the commitment of the sponsor, managers and team members to the project Write a narrative about a character who experiences success or failure and learns a lesson. How do i solve f(x)=log3(x-2)-2 Opportunity cost is the amount of one thing you must give up in order to get more of another thing how many two-digit positive numbers are divisible by 3 or 5? In a video game, two objects move around the screen according to the equations r = 4cos() and r = 1 2cos(). which coordinates represent a possible collision point of the objects? Determine whether the geometric series 27 + 18 + 12 + 8 + ... converges or diverges, and identify the sum if it exists. The nursing student is teaching a class to second graders. The student would correctly identify that food moves down the esophagus via the process termed: