Given the function f(x)=3x2+8x-6, evaluate each of the following
f(0) =
f(1) =
f(-1) =
f(2) =
f(-3) =

The first equation is incorrect.

The second equation is correct.

The third equation is correct.

Let's go through each equation and determine whether it is correct or incorrect:

(b²+7b-9)+(4b-6b²) = -8b² + 14b-9

To determine if this equation is correct, we need to simplify both sides and check if they are equal.

On the left side:

(b²+7b-9)+(4b-6b²) = b² - 6b² + 7b + 4b - 9 = -5b² + 11b - 9

On the right side:

-8b² + 14b - 9

Comparing both sides, we can see that -5b² + 11b - 9 is not equal to -8b² + 14b - 9. Therefore, the equation is incorrect.

(4a+6)-(3a²-9a+1)=-3a²+ 13a +5

Again, we need to simplify both sides of the equation and check if they are equal.

On the left side:

(4a+6)-(3a²-9a+1) = 4a + 6 - 3a² + 9a - 1 = -3a² + 13a + 5

On the right side:

-3a² + 13a + 5

Comparing both sides, we can see that -3a² + 13a + 5 is equal to -3a² + 13a + 5. Therefore, the equation is correct.

(12c-8c²)+(5c²- 10c) = -3c²+2c

Again, let's simplify both sides and compare them.

On the left side:

(12c-8c²)+(5c²- 10c) = 12c - 8c² + 5c² - 10c = -3c² + 2c

On the right side:

-3c² + 2c

Comparing both sides, we can see that -3c² + 2c is equal to -3c² + 2c. Therefore, the equation is correct.

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Answer:

\(12x^{6} y^{6} z^{2}\)

Step-by-step explanation:

Answer:

12x6y6z2

Step-by-step explanation:

Multiply (–3x4y3z)(–4x2y3z). = 12x6y6z2

Answer:

x = 10

Step-by-step explanation:

3x - 9 = 21

add 9 on both sides:

⇒ 3x - 9 + 9 = 21 + 9

⇒ 3x = 30

divide 3 on both sides:

⇒ \(\frac{3x}{x} = \frac{30}{3}\)

⇒ x = 10

to check answer, substitute x by 10 on the original equation:

⇒ 3x - 9 = 21

⇒ 3 x 10 - 9 = 21

⇒30 - 9 = 21

⇒ 21 = 21

Answer:

C

Step-by-step explanation:

9514 1404 393

Answer:

  (-4√494)/13i +(6√494)/13k ≈ -6.8388i +0j +10.2585k

Step-by-step explanation:

To answer this question, you need to know two things:

  1) the direction of vector v

  2) the magnitude of vector u

__

direction of v

A direction is specified by a "unit vector", one with the proper ratio of components, and a magnitude of 1. It is found from a given vector by dividing that vector by its magnitude.

The unit vector in the v direction is ...

  v/|v| = (-2i +3k)/(√((-2)² +3²) = (-2i +3k)/√13

__

magnitude of u

The magnitude of vector u is ...

  |u| = √(5² +(-2)² +3²) = √38

__

Then the desired vector is ...

  (2|u|)(v/|v|) = 2√38(-2i+3k)/√13 = (-4√494)/13i +(6√494)/13k

_____

Additional comment

We have chosen to "rationalize the denominator" by writing √(38/13) as (√494)/13.

Answer:

P=17×4=68mm

...........

Answer: 9

Step-by-step explanation:

Use the pythagorean thrm, a^2+b^2=c^2.

x^2+12^2=15^2 so x=sqrt(15^2-12^2)=9

Answer:

The answer to your problem is, B. 9 feet

Step-by-step explanation:

The pythagoras' theorem states that:

Hyp² = base² + perp²

Which can only be applicable for a right-angle triangle.

So by the ‘ Pythagoras' theorem ‘

Hyp² = base² + perp²

Base² = Hyp² - perp²

Base² = 15² - 12²

Base² = 225 - 144

Base² = 81

Base = 9

9 being the answer.

Thus the answer to your problem is, B. 9 feet

Answer:

Step-by-step explanation:

ss

The value of x is 9 cm, and angle O is 0 degrees.

To solve the triangle LMN and find the values of x and angle O, we can use the Law of Cosines and the Law of Sines. Let's go step by step:

(i) To find the value of x, we can use the Law of Cosines. According to the Law of Cosines, in a triangle with sides a, b, and c, and angle C opposite to side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we want to find side NM (x), which is opposite to angle N. The given sides and angles are:

LN = 12 cm

NK = 6 cm

KM = 8 cm

Let's denote angle N as angle C, side LN as side a, side NK as side b, and side KM as side c.

Using the Law of Cosines, we can write the equation for side NM (x):

x^2 = 12^2 + 6^2 - 2 * 12 * 6 * cos(N)

We don't know the value of angle N yet, so we need to find it using the Law of Sines.

(ii) To find angle O, we can use the Law of Sines. According to the Law of Sines, in a triangle with sides a, b, and c, and angles A, B, and C, the following equation holds:

sin(A) / a = sin(B) / b = sin(C) / c

In our case, we know angle N and side NK, and we want to find angle O. Let's denote angle O as angle A and side KM as side b.

We can write the equation for angle O:

sin(O) / 8 = sin(N) / 6

Now, let's solve these equations step by step to find the values of x and angle O.

To find angle N, we can use the Law of Sines:

sin(N) / 12 = sin(180 - N - O) / x

Since we know that the angles in a triangle add up to 180 degrees, we can rewrite the equation:

sin(N) / 12 = sin(O) / x

Now, we can substitute the equation for sin(O) from the Law of Sines into the equation for sin(N):

sin(N) / 12 = (6 / 8) * sin(N) / x

Now, we can solve this equation for x:

x = (12 * 6) / 8 = 9 cm

So, the value of x is 9 cm.

To find angle O, we can substitute the value of x into the equation for sin(O) from the Law of Sines:

sin(O) / 8 = sin(N) / 6

sin(O) / 8 = sin(O) / 9

9 * sin(O) = 8 * sin(O)

sin(O) = 0

This implies that angle O is 0 degrees.

Therefore, the value of x is 9 cm, and angle O is 0 degrees.

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The figure for the given question is provided here :

The 70 meters by 50 meters rectangular field having a path with an area of 104 m² around it indicates that the width of the path, found using the quadratic formula is about 0.43 meters.

The quadratic formula is a formula that is used to find the values of x that are the solutions to the the the quadratic equation of the form, a·x² + b·x + c = 0.

The length of the rectangular field = 70 meters

The width of the rectangular field = 50 meters

The width of the path around the field = Uniform width

Area of the path around the field = 104 m²

Let x represent the width of the path, we get;

(70 + 2·x) × (50 + 2·x) - 70 × 50 = 104

4·x² + 240·x = 104

4·x² + 240·x - 104 = 0

The quadratic formula which can be used to find the value of x in the equation a·x² + b·x + c = 0, is presented as follows;

\(x = \dfrac{-b\pm \sqrt{b^2-4\cdot a \cdot c} }{2\cdot a}\)

Comparing the equation 4·x² + 240·x - 104 = 0 to the quadratic equation for the quadratic formula; a·x² + b·x + c = 0, we get;

a = 4, b = 240, c = -104

Therefore;

\(x = \dfrac{-240\pm \sqrt{240^2-4\times 4 \times (-104)} }{2\times 4}\)

x ≈ 0.430 or x ≈ -60.4

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Answer:

\(\frac{1}{2}\)

Step-by-step explanation:

If the equation of a line is \(y=mx+b\), the slope is \(m\) and the \(y\)-intercept is \(b\).

A juvenile court could not hear a case involving a contract dispute because it lacks subject matte jurisdiction.

Because a court does not have the legal authority to rule on a case if it does not have jurisdiction over it, jurisdiction is crucial.

The question of whether a particular court has the authority to hear a particular case or controversy is known as subject matter jurisdiction. In this instance, that is unimportant. Brooks is currently being tried in Waukesha County, Wisconsin, before a circuit court judge.

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Answer:

c is the answer to this

Step-by-step explanation:

Answer:

-2.33

Step-by-step explanation:

Let the number be denoted as "x"

-45x + 12 = 117

-45x = 117-12

-45x = 105

x = 105/-45

x= -2.33

Answer:

(0, -3) and (1, -2)

Step-by-step explanation:

This question essentially asks at which points do these two quadratic functions intersect. By looking at the graph, the two points of intersection are at (0, -3) and (1, -2)

Answer:

The solutions are (0, -3) and (1, -2).

Step-by-step explanation:

The solutions to a graphed system of equations are the points of intersections.

Points of intersection refer to the coordinates where the graphs of the equations intersect on a coordinate plane.

From inspection of the given graphs, we can observe that the blue and red curves intersect at points (0, -3) and (1, -2).

Therefore, the solutions are (0, -3) and (1, -2).

Yes, Timothy is correct because triangle AKLM was dilated by using a scale factor of 1.5 centered at the origin.

In Mathematics, dilation can be defined as a type of transformation that is typically used for enlarging or reducing the size of a geometric object but not its shape, based on the scale factor.

For the given coordinates of the preimage triangle KLM, the dilation with a scale factor of 1.5 from the origin (0, 0) would be calculated as follows:

Coordinate K (-1, 3) → Coordinate K' (-1 × 1.5, 3 × 1.5) = Coordinate K' (-1.5, 4.5).

Coordinate L (8, 4) → Coordinate L' (8 × 1.5, 4 × 1.5) = Coordinate L' (12, 6).

Coordinate M (10, -3) → Coordinate M' (10 × 1.5, -3 × 1.5) = Coordinate M' (15, -4.5).

In conclusion, the coordinates of the image triangle K'L'M after a dilation with a scale factor of 1.5 from the origin are (-1.5, 4.5), (12, 6), and (15, -4.5) as shown in the graph above, therefore, Timothy is correct.

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Answer:

2,4 3,5

Step-by-step explanation:

Answer:

f(x) * g(x) is 8x^2 + 8x -6

f(x) - g(x) is -2x + 5

Step-by-step explanation:

When finding the answer, we can notice they already give the values for the needed answers.

The first one requires f(x) and g(x). At the beginning of the question it shows that f(x) is equal to 2x+3. Meaning we can plug in 2x+3 for f(x).

The same goes for g(x). At the begginning of the question, it shows that g(x) is equal to 4x-2. Meaning we can plug in 4x-2 for g(x).

f(x) * g(x)

(2x+3) * (4x-2)

To find the answer, we need to distibute the 2x+3 into 4x-2.

To distribute, we do :

2x * (4x-2)   +   3 * (4x-2)

First we distribute the 2x

2x * 4x  =  8x^2        and        2x * -2  =  -4x

8x^2 - 4x

Next we distibute the 3

3 * 4x  =  12x        and        3 * -2 = -6

12x - 6

Now we can combine them by adding like terms to get the asnwer:

8x^2 = 8x^2

-4x + 12x = 8x

-6 = -6

The first answer is 8x^2 + 8x -6

Second question:

Since we already know the values for f(x) and g(x), all we have to do is plug in the values.

(2x+3) - (4x-2)

This time, since we are subtracting, all we have to do is subtract like terms.

2x - 4x = -2x

3 - (-2) = 5

The second answer is -2x + 5

Answer:

c and d

Step-by-step explanation:

cause

Answer:

C & D

Step-by-step explanation:

Because all the others are going like 4,12, u get what i mean, and the other go by, 5,10,15,20 thats what they mean by propertional realtionship lol, hope this helps l

Answer:

y=2x+6

Step-by-step explanation:

Answer: \(0\leq x\leq 2\)

Step-by-step explanation:

\(460-270.71-3.09*4-33.71=143.22\)

After all his purchases, he has $143.22 left. Outfits cost $68.20 each.

\(143.22/68.20=2.1\)

He has enough to buy at most, 2 outfits.

So, your inequality would be

\(0\leq x\leq 2\)

Answer:

v

Step-by-step explanation:

v

Answer:

20%

Step-by-step explanation:

E(x) for the given data is  6.6 and p(x=0) =0.22 and variance is = 15.26

The Poisson distribution is a discrete probability function that means the variable can only take specific values in a given list of numbers, probably infinite. A Poisson distribution measures how many times an event is likely to occur within an “x” period of time. In other words, we can define it as the probability distribution that results from the Poisson experiment. A Poisson experiment is a statistical experiment that classifies the experiment into two categories, such as success or failure. Poisson distribution is a limiting process of the binomial distribution.

mean = 9 on a rainy day

mean=3 on a dry day.

Let X denote the number of traffic accidents tomorrow. If it will rain tomorrow with a probability of 0.6,

a)

E[x]= E[X|R]+E[X|D}

E[X]=0.6*9-0.4*3

=5.4-12=6.6

B)

X is equal to zero. Why is it called a small way?

P(Y)=e^(-9*0.6+3*0.4).

P(X=0)=0.22

part C.

He had variance affected also missing. So I will calculate that,

V(x)=x2-E(x) =15.26.

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For the given two - dimensional function, we can write -

In mathematical analysis, the maximum and minimum of a function, known generically as extremum are the largest and smallest value of the function, either within a given range (the local or relative extrema), or on the entire domain.

Given is calculate the relative maxima and minima for the function -

2x⁴ + y² - 3yx²

For the given two - dimensional function, we can write -

Relative Maxima  →  No relative maxima.

Relative Minima  →  No relative minima.

Saddle Points  →  No saddle points.

Therefore, for the given two - dimensional function, we can write -

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{Question in english -

Calculate the relative maxima and minima of the function.

f(x, y)=2x^4+y^2-3yx^2}

Answer:

4c+6≤−10

4c+6−6≤−10−6 ... subtract 6

4c≤−16...divide both sides by 4

final: c≤−4

5c-3>2

5c-3>2...add 3

5c>5...divide by 5

c>1

Answer:

Step-by-step explanation:

1st 10 days - 8 GB

2nd 10 days - 8 GB

3rd 10 days - 8 GB

________________

30 days    -  24 GB

The dimensions of the rug would be 27 feet long and 19 feet wide with a 6 foot space around the carpet uniformly.

She wants to buy a rug for a room that is 25 ft wide and 33 ft long.

She wants  to leave a uniform strip of floor around the rug.

she can afford to buy 513 square feet of carpeting.

Cynthia room area = lw

where

Therefore,

Cynthia room area = 25 × 33

Cynthia room area = 825 ft²

She wants to leave a uniform strip of floor all around the rug and has affordability to buy 513 square feet of carpet.

Therefore, the dimension the rug should have is as follows:

(25 - 6) (33 - 6) = 513

19 × 27 = 513 ft²

Therefore, the dimensions of the rug would be 27 feet long and 19 feet wide with a 6 foot space around the carpet uniformly.

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The results of operations between vectors are, respectively:

Case A: u + w = <- 3, - 1>

Case B: - 6 · v = <6, 6>

Case C: 3 · v - 6 · w = <- 21, - 15>

Case D: 4 · w + 3 · v - 5 · u = <39, 4>

Case E: |w - v| = √(4² + 3²) = 5

In this problem we must determine the operations between vectors, this can be done by following definitions:

Vector addition

v + u = (x, y) + (x', y') = (x + x', y + y')

Scalar multiplication

α · v = α · (x, y) = (α · x, α · y)

Norm of a vector

|u| = √(x² + y²)

Now we proceed to determine the result of each operation:

Case A:

u + w = <- 6, - 3> + <3, 2>

u + w = <- 3, - 1>

Case B:

- 6 · v = - 6 · <- 1, - 1>

- 6 · v = <6, 6>

Case C:

3 · v - 6 · w = 3 · <- 1, - 1> - 6 · <3, 2>

3 · v - 6 · w = <- 3, - 3> + <- 18, - 12>

3 · v - 6 · w = <- 21, - 15>

Case D:

4 · w + 3 · v - 5 · u = 4 · <3, - 2> + 3 · <- 1, - 1> - 5 · <- 6, - 3>

4 · w + 3 · v - 5 · u = <12, - 8> + <- 3, - 3> + <30, 15>

4 · w + 3 · v - 5 · u = <39, 4>

Case E:

|w - v| = |<3, 2> - <- 1, - 1>|

|w - v| = |<4, 3>|

|w - v| = √(4² + 3²) = 5

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Answer:

5p

Step-by-step explanation: