What does plotting the points tell us about the relationship between x and y?

The value of 'a' is equal to -12, the value of 'b' is equal to 5 and the value of 'k' is equal to -11.

The stationary points of a curve are those points at which the first derivative of the function f(x) becomes zero. At the stationary points, the nature of the function is neither increasing nor decreasing.

→ The stationary points of a curve can either be a local minima or a local maxima of the function.

→ If we plot the graph of the curve, then stationary points can be said to be those points at which the tangent to the curve becomes horizontal which means the tangent becomes parallel to the x-axis.

→ Therefore for a point (a,b) to be the stationary point of a function f(x): f'(a) must be equal to zero.

→ For the given question:

f(x) = y = x³ + ax + b

f'(x) = 3x² + a

(2, k) is a stationary point:

f'(2) = 0

f'(2) = 3(2)² + a = 0

a = -12

 The value of 'a' comes out to be equal to -12.

→ Hence the equation of the curve is: y = x³ - 12x + b

→ The stationary points (2, k) and (-2, 10-k) must be lying on the curve, hence they must satisfy the equation of the curve:

→ Putting (2, k) in the equation of the curve:

k = (2)³ - 12(2) + b

(k - b) = -16 - Equation (i)

→ Putting (-2, 10 - k) in the equation of the curve:

(10 - k) = (-2)³ -12(-2) + b

(10 - k) = -8 + 24 + b

b = -6 - k - Equation (ii)

→ Putting the value of 'b' from the equation (ii) in equation (i):

k - (-6 - k) = -16

k + 6 + k = -16

2k = -22

k = -11

∴ The value of 'k' comes out to be equal to -11.

→ Putting the value of 'k' in equation (i):

k - b = -16

-11 - b = -16

b = 5

∴ The value of 'b' comes out to be equal to 5.

Therefore, the value of 'a' is equal to -12, the value of 'b' is equal to 5 and the value of 'k' is equal to -11.

To know more about stationary points check the below link:

https://brainly.com/question/22575515

#SPJ1

A rigid body motion, also known as a rigid transformation, happens when a point or object travels while maintaining its size and shape.

While the image's size and shape are unaffected by rigid body motion, its location and orientation are. The three fundamental movements of a rigid body are translation, reflection, and rotation. Prior to movement, archetypes depict points or forms.

A rigid body motion, also known as a rigid transformation, happens when a point or object travels while maintaining its size and shape. Stretching and other non-rigid motions, which alter an object's size, are not comparable to this.

Area of triangle = 1/2 X b X h

b= 10

h=5

A = 1/2 X 10X 5

A = 25 unit sq.

To know more about rigid motion transformations visit:
https://brainly.com/question/29175049

#SPJ4

Answer:

Step-by-step explanation:

Rena Roosh,  fun name  :P  so,  just use  your algebra skillz

2x + 5x = 3x + 16

I'm wondering if there is an extra "x" on the right hand side,  

anyway

7x -3x = 16

4x = 16

x = 4

see??

Answer:

Step-by-step explanation: Perform any simplification of like terms if possible

7x=3x+16

Collect x terms on one side. Can use the left side for x terms. That means 3x must dissapear. To do this we need to take 3x from both sides.

7x-3x=3x-3x+16

4x=16

To solve for x we need to divide by 4 on both sides

4x/4=16/4

x=4

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

When the temperature T is 500, the pressure p is 400. If we let "k" represent the constant of proportionality that relates p and T, then we can write the relationship between p and T as:

p = k * T

Substituting the known values of p and T into this equation, we get:

400 = k * 500

Solving for the constant of proportionality k, we find that:

k = 400/500 = 0.8

Now that we know the value of the constant of proportionality k, we can use it to find the value of p when T = 600. Substituting this value of T into the equation above and solving for p, we get:

p = 0.8 * 600 = 480

Therefore, when T = 600, the pressure p is 480.

The valid statement regarding the truth value is B. The truth value of p → q is T.

A truth value, also known as a logical value, is a measure of how true a proposition is in logic and mathematics. In classical logic, there are only two possible truth values.

A proposition's attribute indicating whether it is true or false is the definition of a truth value. A statement or proposition's truth or falsehood determines its truth value. Every statement has one of the two truth values, true or false, according to our theory.

Since the truth values of p and q are both false, the truth value of p → q is T according to the truth table.The correct option is B.

Learn more about truth values on

https://brainly.com/question/9051197

#SPJ1

Complete question

If the truth values of both p and q are false, then which of the following is a valid statement?

The truth value of p → q is F.

The truth value of p → q is T.

The truth value of p → q cannot be determined without knowing what p and q represent.

The truth value of p → q could be either T or F.

The probability of having one white ball is 1/20 or approximately 0.05.

To find the probability of selecting one white ball out of three balls, you need to know the number of white balls in the box and the total number of balls in the box. You also need to know whether the balls are being selected randomly or not.

Assuming that there is only one white ball in the box and the rest are some other color, and that the balls are being selected randomly.

The probability of selecting one white ball out of three would be:

Probability = (number of ways to select one white ball out of three) / (total number of ways to select three balls)

Since there is only one white ball, there is only one way to select one white ball out of three. The total number of ways to select three balls out of six is 6 choose 3, which is equal to 20.

Therefore, the probability of selecting one white ball out of three would be

Probability = (number of ways to select one white ball out of three) / (total number of ways to select three balls)

Probability = 1/20

Probability = approximately 0.05.

Learn more about probability, here https://brainly.com/question/11234923

#SPJ4

Answer: 188.53$ in total.

$31.42 as hourly wage .

Step-by-step explanation:

Wage1 for 6hours = $12.4 * 6

Wage2 for 20minutes = $12.4 / 3

Since an Hour has three 20 minutes in it , so hourly wage $12.4 is divided by 3 to get the wage for a 20minute work.

Wage3 as Tips = $110

Total Wages for Tuesday = Wage1 + Wage2 + Wage3

                                           = $188.53

New hourly Wage = $188.53 / 6 = $31.42

The matrix B that organizes the data is given as follows:

B = [13, 36, 27,

      10, 15, 0,

       23, 51, 27].

The matrix that shows the total value of each cap size in each location is given as follows:

C = [247, 684, 513,

      190, 285, 0,

      437, 969, 513].

The matrix B is defined considering that it will have three rows and three columns, as follows:

Then the matrix B is defined as follows:

B = [13, 36, 27,

      10, 15, 0,

       23, 51, 27].

The cost of each baseball cap is of $19, thus the cost matrix is obtained multiplying the matrix B by the constant of 19.

When a matrix is multiplied by a constant, all the elements of the matrix are multiplied by the constant, hence the cost matrix is given as follows:

C = [247, 684, 513,

      190, 285, 0,

      437, 969, 513].

More can be learned about matrices at https://brainly.com/question/2456804

#SPJ1

As the sample size is large enough to assume so the sample proportion mentioned in the above question is approximately normally distributed.

It is a statistical expression used to determine an approximate value of some random variables.

we measure the approximately normal proportion by the outcome of the product of the size of population, n  and the proportion of population, p

p =X/n, where X is the sample size and n denote the size of population

If n×p ≥ 10 then the sampling distribution is approximately normal.

hence, as we have large proportion of sample, so it is approximately normal.

to read more about approximately normal distribution visit:

https://brainly.com/question/23418254

#SPJ4

The probability of having the sums that would exceed 100 has been calculated to be 0.5

We have the set or the sample space as:{1 , 5 , 10 , 100) It is said that two numbers would be able to be gotten from the set that we have. Given that the total numbers are 4, we would have ⁴C₂ = 6

The two numbers would be gotten from the set of 4 numbers in 6 different ways.

We are to find the numbers which when we add them up would be able to give us a sum that is greater than 100 these values are (100, 1), (100, 5), (100, 10)

Hence three pairs out of the given six that we already have would be able to give us values that are more than 10. We would have to divide through such that 3 / 6 = 1 / 2 = 0.5

Hence the probability that their values when summed would have to be greater than 100 is 0.5

Read more on probability here:

https://brainly.com/question/24756209

#SPJ1

Answer:

25.2 cm

Step-by-step explanation:

[tex]\angle S=180^{\circ}-165^{\circ}-13^{\circ}=2^{\circ} \\ \\ \frac{t}{\sin T}=\frac{s}{\sin S} \\ \\ \frac{t}{\sin 165^{\circ}}=\frac{3.4}{\sin 2^{\circ}} \\ \\ t=\frac{3.4\sin 165^{\circ}}{\sin 2^{\circ}} \\ \\ t \approx 25.2[/tex]

The general rule that describe 2 4 6 8 10 the sequence.

What exactly are sequence and example?

An ordered list of numbers is a sequence. To go forward in the defined pattern, three dots are shown. A phrase is used to describe each number in the series.

                       One is the first word, three is the second, five is the third, and so on, in the series 1, 3, 5, 7, 9,...

Which four forms of sequence are there?

Arithmetic sequences, geometric sequences, quadratic sequences, and special sequences are the four primary categories of distinct sequences you need to be familiar with.

Learn more about sequence

brainly.com/question/21961097

#SPJ4

Answer:

PR

Step-by-step explanation:

Because both triangles are equal to each other, so their sides will equal each other too!

The equation of the pyramid is as follow,

Volume is equal to one by third of the Area of the base into Height.

V=(1/3) X A X H, where A is area and H is height.

The sum of a pyramid's side faces makes up the lateral surface area.

LSA of the pyramid multiplied by the base's area gives the total surface area.

A pyramid is a 3D shape that has a base made of a polygon and faces that are all triangular and linked. The conventional form of a pyramid is created by joining each vertex of the base to a single common tip or apex. In this part, let's study more about pyramids.

The area encompassed between a pyramid's faces is referred to as the pyramid's volume. The formula for each pyramid varies based on the pyramid's foundation. The formula used to determine a pyramid's volume, which is expressed in cubic units, is as follows V=(1/3) X A X H.

Different forms of pyramids have varying amounts of surface area. The following formula is used to determine a pyramid's surface area:

Surface Area = Base Area + (½ × Perimeter of the base × Slant height)

Surface Area = Base Area + Lateral Area.

For more such question on pyramid equation.

https://brainly.com/question/21510592

#SPJ4

Step-by-step explanation:

I just answered this question. how often did you post it ?

in short again :

360 = 8x + 20 + 104 + arc angle KJP

arc angle KJP = 2× opposite angle of K and P =

= 2×(5x + 1)

so, together

360 = 8x + 124 + 2×(5x + 1) = 8x + 124 + 10x + 2 =

= 18x + 126

234 = 18x

x = 13

Answer:

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, the length of one side of a triangle must always be shorter than the sum of the lengths of the other two sides. This theorem is often used in geometry to determine whether or not a given set of lines can form a triangle.

When it comes to angles, the Triangle Inequality Theorem can be used to determine whether or not a triangle can be formed given the measures of its angles. For example, if the measures of two angles in a triangle are 45 degrees and 60 degrees, the measure of the third angle must be less than 180 degrees - 45 degrees - 60 degrees, or 75 degrees. If the measure of the third angle is greater than 75 degrees, it is not possible for the three angles to form a triangle.

Overall, the Triangle Inequality Theorem is a useful tool for understanding the relationships between the sides and angles of a triangle, and for determining whether or not a given set of lines or angles can form a triangle.

Step-by-step explanation:

So the mountain will be approximately 798.02 meters tall after 8 millennia.

The mountain loses 5% of its elevation every millennium, which is the same as losing 0.05 * its current elevation. Therefore, after 1 millennium, the mountain's elevation will be 1 - 0.05 = 0.95 times its current elevation. After 2 millennia, it will be 0.95 * 0.95 = 0.9025 times its current elevation, and so on.

After 8 millennia, the mountain's elevation will be 0.95^8 times its current elevation. We can calculate this as follows:

Elevation after 8 millennia = 1,300 meters * 0.95^8

= 1,300 meters * 0.6134

= approximately 798.02 meters

So the mountain will be approximately 798.02 meters tall after 8 millennia.

To learn more about Elevation,

visit; brainly.com/question/29477960

#SPJ4

After 8 millennia, the mountain's elevation will be 0.95^8 times its current elevation. We can calculate this as follows:

Elevation after 8 millennia = 1,300 meters * 0.95^8

= 1,300 meters * 0.6134

= approximately 798.02 meters

So the mountain will be approximately 798.02 meters tall after 8 millennia.

The height of the triangle is determined by the formula, 2 × Area / Base

Given,

Triangle;-

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

We have to find the formula for height of triangle;

According to theorem;

The  area of the triangle = 1/2 × base × height

Then,

Height of the triangle = 2 × Area / Base

That is,

The formula for the height of the triangle is 2 × Area / Base

Learn more about height of triangle here;

https://brainly.com/question/26093510

#SPJ4

Complete question is here;

What is the formula to find the height of a triangle?

She can only move a certain distance in three seconds, with a lower distance of 33.45 feet and a upper distance of 43.45 feet.

The first three seconds of a race saw a runner's speed rapidly grow.

The time is therefore 3 seconds.

The table provides her speed at half-second intervals.

We are aware,

Speed = Distance / Time

Similarly

Distance = Speed × Time

t equals 0.5 seconds

Then, the lower distance traveled overall is equal to 0.5(0 + 6.7 + 9.2 + 14.1 + 17.5 + 19.4).

Terms are multiplied and added.

= 0.5 × 66.9

= 33.45 feet

The upper distance traveled is equal to 0.5 (6.7 + 9.2 + 14.1 + 17.5 + 19.4 + 20)

= 0.5 × 86.9

= 43.45 feet

As a result, Her lower distance in three seconds is therefore 33.45 feet, and her upper distance in three seconds is 43.45 feet.

To learn more about speed visit:

brainly.com/question/12759408

#SPJ4

The average time spent in the system which consists three fax machines is 0.026470 hour. So, option (e) none of the above is right here.

The M/M/1 queuing system is a single-server, infinite-capacity system in which the arrival interval is exponentially distributed with the parameter lambda and the service time is also exponentially distributed with the parameter. If the number of servers is maximum and all are equal, this model is considered an M/M/C queue.

We have, total number of fax machine in a business school is equals to three.

The toner of each machine needs to be changed in 5 hours of use . Time taken by secretary to replace toner cartridge = 15 minutes

We have to calculate average time spent in the system. fax machines , k = 3

Service person , R = 1

Arrival rate, λ = 3/5per hour = 0.6/hour

Service rate, μ =( 60/15) per hour

= 4/hour

Now, using the equation of finite population model M/M/1, the average time spent to maintain the fax machines in system is ,

L = λ² /μ (μ - λ )

plugging the value of μ and λ in above formula we get, L = (0.6)²/4(4-0.6)

= 0.36/13.6 = 0.026470

So, required answer is 0.026470 hour .

To learn more about queuing system, refer:

https://brainly.com/question/15597528

#SPJ4

Answer: The image T(V) is defined as the set {k | k=T(v) for some v in V}. So x=T(y) where y is an element of T^-1(S). The preimage of S is the set {m | T(m) is in S}. Thus T(y) is in S, so since x=T(y), we have that x is in S.

Given a function f:A→B, and D⊆B, the preimage D of under f is defined as f−1(D)={x∈A∣f(x)∈D}. Hence, f−1(D) is the set of elements in the domain whose images are in C. The symbol f−1(D) is also pronounced as “f inverse of D.”

In geometry, figures in a plane can be transformed in a variety of ways, including shifts and scaling, to produce new shapes. The new (transformed) shapes are called images and the original, unaltered shapes are called preimages.

In geometry, figures in a plane can be transformed in a variety of ways, including shifts and scaling, to produce new shapes. The new (transformed) shapes are called images and the original, unaltered shapes are called preimages.

Step-by-step explanation:

The surface area of the cuboid is 148 cm².

The surface area of a cuboid is the total space occupied by it. A cuboid is a six-faced three-dimensional shape in which each face is in the shape of a rectangle.

Given that, a cuboid has volume of 120 cm³ and the area of the base of the cuboid is 30 cm².

We know that, the volume of cuboid is l×b×h.

Here, l×b=30

Now, 30×h=120

h=4 cm

We know that, surface area of the cuboid is 2(lb+bh+hl)

= 2(30+h(b+l))

= 2(30+4(b+l))

We have, l×b=30

Pair of factors of 30 are

2×15=30

3×10=30

5×6=30

So, the possible surface area is

2(30+4(2+17))

= 2×106

= 212 cm²

2(30+4(3+10))

= 2×82

= 164 cm²

2(30+4(5+6))

= 2×74

= 148 cm²

Therefore, the surface area of the cuboid is 148 cm².

Learn more about the surface area of a cuboid here:

https://brainly.com/question/26403859.

#SPJ1

2X + 4Y = 100 is the equation.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Let's assume that X is the quantity of multiple-choice questions and Y is the quantity of short-answer questions.

Given that the short-answer questions are worth four points and the multiple-choice questions are for two, the equation is 2X + 4Y = 100.

Thus the equation for 2 points each, and short-response questions are worth 4 points each. The assessment is worth 100 total points where x represent the number of multiple-choice questions, and let y represent the number of short-response questions.

2X + 4Y = 100.

To know more about equation please click the link:

brainly.com/question/29657983

#SPJ1

Answer: I don't believe the explanation above provides the correct answer. You would need to use the concept of proportions to solve this problem. The Answer I got is 2100.

Step-by-step explanation:

It is very simple all you have to do is setup a proportion with Reena's on top and Neha's on the bottom.

8/6 = 2800/x

Now cross multiply,

2800 * 6 = 8x

x=16800/8

x=2100

Now we can double-check by dividing the original ratio with the ratio we found.

8/6 = 1.3333333...

2800/2100 = 1.333333...

Thus, the answer is correct.

Answer:

When you roll a fair die you have an equal chance of getting each of the six numbers 1 to 6. The expected value of your die roll, however, is 3.5.

Step-by-step explanation:

hope this helps

mark me brainliest

Step-by-step explanation:

kya tablet side apply the side of the wall has 22 M and 20 m

Answer:

30

Step-by-step explanation:

30

The answer is x = 4

y = -1

z = -3

3x+2y+z=7

5x+5y+4z=3

3x+2y+3z=1

________

Let's take the first and the third equation, multiply the first one by (-1) and sum them up:

3x+2y+z=7

3x+2y+3z=1

____

-3x-2y-z=-7

3x+2y+3z=1

____

2z = -6

z = -6/2

z = -3

Substitute z in all equations:

3x+2y+z=7

5x+5y+4z=3

3x+2y+3z=1

______

3x + 2y - 3 = 7

5x + 5y - 12 = 3

3x + 2y - 9 = 1

______

3x + 2y = 10

5x + 5y = 15

3x + 2y = 10

The first and the third equations are the same, so one can be excluded:

3x + 2y = 10

5x + 5y = 15

Multiply the first equation by -5 and the second equation by 2 and sum them up:

-15x - 10y = -50

10x + 10y = 30

_________

-5x = -20

x = -20/-5

x = 4

Substitute x:

3x + 2y = 10

12 + 2y = 10

2y = 10 - 12

2y = -2

y = -2/2

y = -1

Learn more about equations to visit this link

https://brainly.com/question/29657988

#SPJ4