The graph of a cubic polynomial function
has horizontal tangent lines at (1, −2) and (−1, 2). Find
an equation for the function and sketch its graph.

Answers

Answer 1

Answer: A cubic polynomial function has the form f(x) = ax^3 + bx^2 + cx + d.

A horizontal tangent line is a line that is parallel to the x-axis and it occurs at a critical point of the function, where the derivative of the function is 0.

We know that a cubic function has 3 critical points and thus 3 derivative that could be 0, so to find the equation of the cubic function we will use these two points to find the value of a, b, c, and d.

We know that the critical points of a cubic function are found by solving f'(x) = 0, where f'(x) is the derivative of the function, so we have:

f'(x) = 3ax^2 + 2bx + c = 0

Now we can use the two points to find the value of a, b, c, and d.

We know that the point (1,-2) is on the graph of the function, so we can substitute it into the equation to find d:

f(1) = a + b + c + d = -2

And we know that the point (-1,2) is on the graph of the function, so we can substitute it into the equation to find d:

f(-1) = -a + b - c + d = 2

Now we can use these two equations to find the value of a, b, and c:

a + b + c + d = -2

-a + b - c + d = 2

2a + 2d = 0

a = -d

-a + b - c + d = 2

b - c = 4

3ax^2 + 2bx + c = 0

3(-d)x^2 + 2bx - c = 0

Now we can use these equations and the critical points to find the value of a, b, c, and d

3(-d)x^2 + 2bx - c = 0, (1,-2) => 3d+2b-c = 0

3(-d)x^2 + 2bx - c = 0, (-1,2) => 3d-2b+c = 0

b-c = 4

Solving these equations, we have:

a = -1/3

b = 1

c = -5/3

d = -2

And the equation for the function is:

f(x) = -1/3x^3 + x^2 - 5/3x - 2

We can now sketch the graph of the function by using the information that we have. The cubic function will have an vertex of symmetry at (0,-2) and two horizontal tangent lines at (1,-2) and (-1,2) .

Since a < 0, the function is concave down, so the graph will be opened downwards and will have a local minimum at (0,-2) .

It is important to note that this is one possible equation for a cubic function that has horizontal tangent lines at (1, −2) and (−1, 2), but there may be other possibilities.

Step-by-step explanation:


Related Questions

in the graph below, what best describes the average acceleration from 40 to 70 s?

Answers

The typical increase in speed from 40 to 70 seconds The magnitude is lower than the initial acceleration and is positive.

How do you describe average acceleration?

The velocity change's average acceleration is referred to as this. To calculate any object's average acceleration, we divide the change in velocity by the amount of time that has passed. As a result, it is clear that the average acceleration is defined as the ratio of the change in velocity to the change in time over a certain interval.

The average acceleration is the velocity change divided by the time that has passed. A marble's average acceleration is 20 cm/s, for instance, if its velocity increases from 0 to 60 cm/s in three seconds. The marble's speed will increase by 20 cm/s every second as a result. The ball will therefore have an upwards-moving terminal velocity of 20 m/s after two seconds.

To learn more about average acceleration refer to :

https://brainly.com/question/26246639

#SPJ1

The height in feet of a firework t seconds after it is launched is modeled by h(t) --16r2 + 105t + 10. Find its average speed from l to 3 seconds.

Answers

The change in height divided by the change in time yields the firework's average speed from t=1 to t=3 seconds.

Average change speed is equal to (h(3) – h(1)) (3 - 1)

h(3) = 16*32 + 105*3 + 10 = 536

h(1) = 16*12 + 105*1 + 10 = 126

Average speed = (536 - 126)/(3 - 1) = 410/2 = 205 ft/sec

h(t) = 16r2 + 105t + 10 models the height of a firework t seconds after it is released. We must determine the change in height divided by the change in time in order to get its average speed between t=1 and t=3 seconds.

By entering t = 3 into h(t), we can determine the height at 3 seconds, which gives us h(3) = 16*32 + 105*3 + 10 = 536. We can figure out the height.

Learn more about average here

https://brainly.com/question/24057012

#SPJ4

Oil is spilled onto a kitchen floor. The area covered by the oil at time t is given by the function A, where A(t) is measured in square centimeters and tis measured in seconds. Which of the following gives the rate at which the area covered by the oil is changing at time t=10? A A(10) B A(11) – A(9) с A(10) 10 A' (10)

Answers

The rate at which the area covered by the oil is changing at time t = 10 is  A'(10).

Oil is spilled onto a kitchen floor. The function A, where A(t) is measured in square centimeters and t is measured in seconds, gives the area covered by the oil at time t.

Given that the region that was covered in oil at time t = A(t)

We must differentiate A(t) with respect to time t in order to calculate the rate of change in the area covered by the oil over time.

By differentiation:

[tex]\frac{dA}{dt}=A'(t)[/tex]

The rate at which the oily area is transforming is t = 10

[tex]\frac{dA}{dt}|_{t=10}=A'(t)|_{t=10}[/tex]

[tex]\frac{dA}{dt}=A'(10)[/tex]

Hence, the rate at which the area covered by the oil is changing at time t = 10 is  A'(10).

To learn more about rate here:

https://brainly.com/question/23634231

#SPJ4

Part B: What is the probability that a randomly chosen person is a child? (3 points)

Part C: What is the probability that a randomly chosen person prefers running and is a child? (3 points)

Part D: What is the probability that a person prefers running given that the person is a child? (3 points)

Part E Are being a child and preferring running independent events? Explain. (5 points)

Answers

The probability  that a randomly chosen person is a child, that a randomly chosen person prefers running and is a child  is 12/25 , 1/ 6  respectively.

What is probability ?

Probability can be defined as the ratio of number of favourable outcomes  and number of total outcomes.

Given in the table ,

Probability that a randomly chosen person is a child

= 48 / 100

= 12/25

Probability that a randomly chosen person prefers running and is a child

= 6/48

= 1/8

Probability that a person prefers running given that the person is a child

= 6/48

=1/8

Therefore, The probability  that a randomly chosen person is a child, that a randomly chosen person prefers running and is a child  is 12/25 , 1/ 6  respectively.

To learn more about Probability from the given link.

https://brainly.com/question/30034780

#SPJ1

the measure of the angle represented by the expression (7x+12)=1.?

Answers

The measure of the angle represented by the expression (7x+12) is 61°.

What is the measure of the angle represented by the expression (7x+12)?

The measure of the angle represented by the expression (7x+12) is determined as follows:

The same-side interior angles are supplementary and their sum is 180°.

7x + 12 and 17x are same-side interior angles and are, therefore, supplementary.

7x + 12 + 17x = 180°

solving for x by summing similar terms:

24x + 12 = 180

24x = 168

Dividing both sides by 24

x = 7

Therefore,

7x + 12 = 7 * 7 + 12

7x + 12 = 61°

Learn more about same-side interior angles at: https://brainly.com/question/11346339

#SPJ1

a number n is said to be squarefree is the largest square that divides n is 1. show that any square-free integer can be uniquely written as the product of a squarefree integer and a square

Answers

Any square-free integer can be expressed as the product of a square-free integer (which has no square  factors) and a perfect square (which has only square factors). This product is unique for any given square-free integer.

Any square-free integer can be expressed as the product of a square-free integer and a perfect square. This is because a square-free integer has no square factors, so the product of a square-free integer and a perfect square would have only square factors, and thus be square-free. To show that this product is unique for any given square-free integer, we can use the fact that any integer can be expressed as the product of its prime factors and that a square-free integer has no square factors. This means the prime factors of the square-free integer are all distinct, and thus the product of the square-free integer and the perfect square can be expressed as the product of the prime factors of the square-free integer and the prime factors of the perfect square. Since the prime factors of the perfect square are all the same, the product is uniquely determined by the prime factors of the square-free integer. Thus, the product of a square-free integer and a perfect square is unique for any given square-free integer.

Learn more about square here

https://brainly.com/question/14198272

#SPJ4

Two trains leave towns 476 kilometers apart at the same time and travel toward each other. One train travels 22 km/h faster than the other. If they meet in 2 hours, what is the rate of each train?

Answers

Answer:

Train 1: 130 km/h

Train 2: 108 km/h

Step-by-step explanation:

Let train 1 be the faster train.

Train 1:

distance = d

speed = s

time = 2 hours

Train 2:

distance = 476 - d

speed = s - 22

time = 2 hours

speed = distance/time

distance = speed × time

Train 1:

d = 2s

Train 2:

476 - d = 2(s - 22)

d = 2s

476 - d = 2s - 44

d = 2s

476 - 2s = 2s - 44

520 = 4s

s = 130

s - 22 = 108

Train 1: 130 km/h

Train 2: 108 km/h

Which ordered pair is a solution to the linear system?
2x + y = 5

x – y = 13

Answers

It’s 2x + y = 5
I hope this is Right
Also I hope this helps!


Consider the following sample data.
14 9 19 18 5
8
Calculate the z-score for the following values.
a. 12
b. 6
c. 15
d. 13
a. The z-score for 12 is.
(Round to two decimal places as needed.)

Answers

The z-score for the given values is - 0280, -1.08, 0.49, 0.147 respectively.

What do z-scores mean?

The z-score of a data point defines this precise distance in terms of standard deviations above or below the mean.

This formula is used to determine a z-score:

mean standard deviation for each data point

Means of the data points with a standard deviation of z

Below is the same equation in symbol form:

z= x−μ / σ

Here are some noteworthy z-score details:

When the z-score is high, the data point is.

A negative z-score indicates that a data point is below average.

If the z-score is close to 0.00, the data point is thought to be around average.

For the given data set,

14 9 19 18 5 8

Mean of the data =sum of observations / no. of observations =  73/6 = 12.16

Mean of the data is 12.16

Standard deviation = √∑(x - μ)² / n-1

= ​5.70

a) The z- score of 12 is

z=  x−μ / σ

z = 12 - 12.16 / 5.70

z = - 0280

b) x = 6,

z = 6 - 12.16/5.70

z = -1.08

c) x = 15

z = 15 - 12.16/5.70

z = 0.49

d) x = 13

z = 13 - 12.16 / 5.70

z = 0.147

To Learn more About z-scores Refer To:

brainly.com/question/25638875

#SPJ1

Solve pls this equation

Answers

Hey there!

If you are solving for x, then your final solutions are [tex]x=\sqrt{-y},-\sqrt{-y}[/tex].

Hope this helps!

Answer:

Step-by-step explanation:
first of all, you have to let that ,
Put,
x=0 => y=0
x=1 => y=( -1 )
x=2 => y= ( -2 )
And
x=(-1) => y= (-1 )
Plot or mark the points on graph
That is ur correct ans of your question
If you want detailed ans on paper then send me ("i want detailed answer")
ty ts

A family has two cars. The first car has a fuel efficiency of 15 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas. During one particular week, the two cars went a combined total of 975 miles, for a total gas consumption of 45 gallons. How many gallons were consumed by each of the two cars that week?

Answers

Answer:  We can start by using algebra to represent the information given in the problem. Let x be the number of gallons consumed by the first car and y be the number of gallons consumed by the second car.

We know that:

x + y = 45 (the total number of gallons consumed by both cars)

15x + 30y = 975 (the total number of miles driven by both cars, given the fuel efficiency of each car)

We have two equations and two unknowns, so we can use these equations to solve for the value of x and y.

From the first equation, we can solve for x:

x = 45 - y

We can substitute this expression of x into the second equation:

15(45 - y) + 30y = 975

Simplifying the left side of the equation:

675 - 15y + 30y = 975

Subtracting 675 from both sides:

15y = 300

And finally divide both sides by 15:

y = 20

So the second car consumed 20 gallons of gas that week.

We can substitute this value of y back into the equation x = 45 - y to find the value of x

x = 45 - 20 = 25

So the first car consumed 25 gallons of gas that week.

Step-by-step explanation:

which model can be used to find 4/5 1/10

Answers

Can you post a picture?

Which quadrilaterals have diagonal that bisect their angles?

Answers

Rhombus and Square are the quadrilaterals where diagonals are equal and bisect each other at 90°.

What is quadrilateral?

A quadrilateral is a four-sided closed shape, where sum of the interior angles equals 180°.

Here,
For the quadrilateral there are only two quadrilaterals where diagonals bisect each other at 90° and will be of equal length of measure are square and rhombus.

Thus, Rhombus and Square are the quadrilaterals where diagonals are equal and bisect each other at 90°.

Learn more about quadrilateral here: https://brainly.com/question/13805601
#SPJ1

Which of the following are properties of a kite? Choose ALL that apply.

Diagonals are perpendicular

Two pairs of consecutive sides are congruent

1 diagonal bisects the other

Opposite angles are congruent

Answers

Answer:

Diagonals are perpendicular

1 diagonal bisects the other

Opposite angles are congruent

the pressure gauge on a cylinder of gas registers the gauge pressure, which is the difference between the interior pressure and the exterior pressure p0. let's call the gauge pressure pg. when the cylinder is full, the mass of the gas in it is mi at a gauge pressure of pgi. assuming the temperature of the cylinder remains constant, show that the mass of the gas remaining in the cylinder when the pressure reading is pgf is given by mf

Answers

The gauge pressure, or the difference between the inner pressure and the external pressure p0, is what the pressure gauge on a gas cylinder measures. Give the gauge pressure the letter pg.

The gas in the cylinder weighs mi at pgi gauge pressure when it is full. We can apply the ideal gas formula, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature, assuming the cylinder's temperature stays constant.

We can assume that the product nRT is constant because the temperature is constant. Consequently, we can write:

(pgf + p0) = (pgi + p0)(Vi) (Vf)

where Vi is the cylinder's initial volume and Vf is the cylinder's final volume when the pressure is pgf.

We also know that the gas's mass, m, is determined by multiplying the number of moles, n, by the molar mass, M, or m = nM.

The ideal gas law can be used to express the number of moles in terms of volume and pressure:

m/M = P(V/RT) = n

Thus, mf = pgf(Vf/RT).

M equals (pgf + p0)(Vf/RT).

(Vi/RT) Mi (pgi + p0)

where mf is the mass of gas still present in the cylinder at pgf pressure.

To learn more about the ideal gas equation, refer to the link:brainly.com/question/28837405

#SPJ4

What is the linear velocity in miles per hour for a particle moving in a circular path at 200 revolutions per minute on a circle of radius 60 feet?

Answers

Answer: 1,200. None of the above.

Step-by-step explanation:

200 revolutions per minute times 60 feet. 1,200

Word Needed! *
The Bellah's pool is leaking. The pool leaked 3/4
gallon in 20 minutes, or 1/3hour. How many
gallons is the pool leaking each hour?

Answers

The pool is leaking 2 1/4 gallons an hour. We got this by finding out how many 20 mins make an hours which is 3. 3*20mins=60mins=1hr. Now we can add 3/4+3/4+3/4 or do 0.75*3. We get 2 1/4. Another way we could do this is by fractions. We could do 0.75 gal/20mins=x gal/60mins. Then cross multiply to get 60*0.75=20x then divide to get the answer.

[tex]\frac{csc x -1}{cot x} = \frac{cot x}{csc x + 1}[/tex]

Answers

Answer:

The equation [tex]\frac{csc x -1}{cot x} = \frac{cot x}{csc x + 1}[/tex] can be simplified by cross-multiplying the fractions and then solving for x. This will result in the equation [tex]csc^2 x - 1 = 0[/tex], which can be simplified to [tex]csc x = 1[/tex], and thus [tex]x = \frac{\pi}{2} + n\pi[/tex], where n is any integer.

give me brainiest

Rewrite 8.24 x 10 6 in standard form
A 824,000
B 8,240,000
C 8,240,000,000
D 82,400,000

Answers

Answer:

answer is B) 8 240 000

(: have a nice day

Answer:

B 8,240,000

Step-by-step explanation:

your welcome

Enter the equation for the graph y=[?] cos([?]x)

Answers

The equation for the graph will be

[tex]y=1 cos(3x)[/tex]

Define the function y = cos(2x + π/4) ?

The function y = cos(2x + π/4) is a cosine function where the independent variable x is multiplied by 2 and then has π/4 added to it before the cosine is applied. The amplitude of this function is 1 and the period is π.

In this question

[tex]we assume, \\y=acos(bx)\\\\when x=0y=1\\\\y=acos(bx)\\\\1=acos0\\\\a=1\\so y=cos(bx)\\\\when x=\pi/3 y=-1\\y=cos(b.\pi/3)\\-1=cos1b.pi/3=cos(pi)\\b=3[/tex]

[tex]y=acosbx[/tex]

[tex]so, y=1.cos(3x)[/tex]

To know more about the cosine function  visit:

https://brainly.com/question/17954123

#SPJ1

To friends shop for fresh fruit. Jaxson buys a watermelon for $8.25 and 3 pounds of cherries. Tim buys a pineapple for $3.15 and 2 pounds of cherries. Use the variable P to represent the price in dollars per pound of cherries. write and simplify an expression to represent how much more Jaxson spent.

Answers

If two friends shop for fresh fruit. Jaxson buys a watermelon for $8.25 and 3 pounds of cherries. The expression to represent how much more Jaxson spent is :5.1 +p.

How to find the expression?

P = price of the cherries per pound

Price of cherries bought by Jaxson= $3p

Total amount spent by Jaxson =  $8.25 + $ 3p

Price of cherries bought by Tim = $2p

Total amount spent by Tim = $3.15 + $ 2p

Now let find how much more Jaxson spent.

8.25 + 3p - 3.15 + 2p

5.1 + 3p - 2p

Combine like terms

5.1 +1p

Multiply by 1

5.1 + p

Therefore the expression to represent how much more Jaxson spent is :5.1 +p.

Learn more about expression here:https://brainly.com/question/3255078

#SPJ1

A fashion store is planning its end–of–season sale. It sells 40 of its signature jeans every week at $175 per pair. Last year, the store's sales increased to 60 pairs per week when the price was dropped by $25. By what amount should the store discount the price this year to maximize its revenue?

A. $112.50
B. $103.50
C. $62.50
D. $71.50

Answers

Answer:

A

Step-by-step explanation:

Every $1 decrease in price corresponds to a 0.8 increase in the number of pairs of jeans sold.

So, if [tex]x[/tex] pairs of jeans are sold, the revenue in dollars is [tex](175-x)(40+0.8x)[/tex].

The roots of this function are [tex]x=175[/tex] and [tex]x=-50[/tex]. The maximum is achieved halfway between these roots at [tex]x=62.5[/tex].

When 62.5 pairs of jeans are sold, the price is $112.50.

Based on the information, the store should discount $112.50 from the price to maximize its revenue.

How to calculate the amount of discount that the store should make?

To calculate the amount of discount that the store must make to maximize its profits we must perform the following mathematical operation:

First we have to analyze the available data which are:

40 exclusive jeans/week ($175 each)60 exclusive jeans/week ($150 each)

According to the above information, the problem could be answered with the following mathematical formula:

(175 - x)(40 + 0.8x)

x = 175

x = -50

x = 62.50.

According to the above, the correct answer is $112.50 (option A).

Learn more about discounts in: https://brainly.com/question/3541148

#SPJ1

Robin paid a $120 a month on a credit card. She was late on a payment so her monthly bill was raised to $150 a month. which of these shows how Robin can calculate the percent increase she was charged

Answers

Answer: One way to calculate the percent increase in Robin's monthly bill is to use the following formula:

% increase = (new amount - original amount) / original amount x 100

In this case, the original amount is $120 and the new amount is $150. So, the calculation would be:

% increase = (150 - 120) / 120 x 100 = 30 / 120 x 100 = 0.25 x 100 = 25

Therefore, the percent increase in Robin's monthly bill is 25%.

Another way to calculate the percent increase is to use the formula:

(New amount - original amount) / original amount

In this case: (150-120)/120 = 0.25, and multiply by 100 to get 25%

So, both formula gives the same answer 25%

Step-by-step explanation:

whoever can get this i will mark them brainiest

Answers

The first diagram of the triangle DEF correctly represents the transformation.

What are transformations?

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

The preimage of the triangle is ABC and the image is DEF.

Therefore, ∠A = ∠D, ∠B = ∠E and ∠C = ∠F>

A 90° rotation counterclockwise will rotate the vertex C one-quarter left of a complete circle.

Therefore, The first triangle represents the correct transformation.

learn more about transformations here :

https://brainly.com/question/29194193

#SPJ1

Suppose P dollars is invested with an annual interest rate of​ 3.5% compounded semiannually. Use the laws of exponents to find the equivalent annual rate.

Answers

Answer:

3.53%

Step-by-step explanation:

annual 3.5%

So half a year =1.75% and compound twice a year.

equivalent annual rate is (1+1.75%)^2 -1 =.0353 =3.53%


Find an equation of the sphere with center (2,-6,4) and radius 5.
Describe its intersection with each of the coordinate planes.

Answers

The equation of a sphere with center (a, b, c) and radius r is given by:

[tex](x - a)^2 + (y - b)^2 + (z - c)^2 = r^2[/tex]

Given the center (2,-6,4) and radius 5, we can substitute these values into the equation to find the equation of the sphere:

[tex](x - 2)^2 + (y + 6)^2 + (z - 4)^2 = 5^2[/tex]

So, the equation of the sphere is:

[tex](x-2)^2 + (y+6)^2 + (z-4)^2 = 25[/tex]

The sphere will intersect each of the coordinate planes in circles.

Intersection with the XY-plane:

The sphere intersects the XY-plane when z = 4.

Then, the equation of the circle on the XY-plane is [tex](x-2)^2 + (y+6)^2 = 5^2[/tex]

Intersection with the XZ-plane:

The sphere intersects the XZ-plane when y = -6.

Then, the equation of the circle on the XZ-plane is [tex](x-2)^2 + (z-4)^2 = 5^2[/tex]

Intersection with the YZ-plane:

The sphere intersects the YZ-plane when x = 2.

Then, the equation of the circle on the YZ-plane is [tex](y+6)^2 + (z-4)^2 = 5^2[/tex]

The sphere with center (2,-6,4) and radius 5 intersects each of the coordinate planes at circles.

These circles are defined by the equations [tex](x-2)^2 + (y+6)^2 = 25[/tex] on the XY-plane, [tex](x-2)^2 + (z-4)^2 = 25[/tex]  on the XZ-plane, and  [tex](y+6)^2 + (z-4)^2 = 25[/tex]  on the YZ-plane.

To learn more about coordinate planes:

https://brainly.com/question/13854649

#SPJ4

Suppose a company has fixed costs of $40,800 and variable cost per unit of 1/3 x + 222 dollars, where x is the total number of units produced. Suppose further that the selling price of its product is 1946 − 2/3 x dollars per unit.

Answers

The break-even points at which the sum of the fixed and variable costs (40,800 + (1/3)·x + 222) is equivalent to the revenue (1946·x - (2/3)·x²) are; x = 21, 2897

What is a break-even point?

The break-even point in cost accounting is the point where the total cost of production is equivalent to the total revenue from the sale of the products.

The fixed cost of the company = $40,800

The variable cost = (1/3)·x + 222 Dollars

x = The total number of units sold

The selling price of the product = 1946 - (2/3)·x Dollars

A possible question, obtained from a similar question is the value of the number of units sold at break even point

The break even point where the cost and revenue are equivalent, can be found as follows;

Revenue = Selling price × Number of units sold, therefore;

Revenue = (1946 - (2/3)·x) × x = 1946·x - (2/3)·x²

At the break even point, we get;

Sum total of the cost = Revenue

Therefore;

Fixed cost + Variable cost = Revenue

40,800 + (1/3)·x + 222 = 1946·x - (2/3)·x²

1946·x - (2/3)·x² - (40,800 + (1/3)·x + 222) = 0

(-2·x² + 5837·x - 123066)/3 = 0

x = (-5837 ± √(5837² - 4×(-2)×(-123066)))/(2×(-2))

x = (-5837 ± √(33086041))/(-4)

x ≈ 21 or x ≈ 2897

The number of units produced at the break even point are; x = 21 units and 2897 units

Learn more about cost analysis here: https://brainly.com/question/17236115

#SPJ1

Identify the slope and y intercept of each graph. Drag the 3 points to the correct places on the graph drag and adjust the line so it goes through the points on the line
Y = 2x - 5
M =
B =

Answers

Answer:

slope: 2 , y-int: (0, -5)

Step-by-step explanation:

When u and v are nonzero vectors, Spanlu,v) contains only the line through u and the line through v and the origin.
A. False. Span(u,v) includes linear combinations of both u and v. B. False. Span(u,v) will not contain the origin. C. True. Span(u,v) is the set of all scalar multiples of u and all scalar multiples of v

Answers

Span(u,v) is the set of all linear combinations of u and v, including scalar multiples of both. It does not include the origin.

Span(u,v) is the set of all linear combinations of u and v, meaning any combination of u and v multiplied by scalars. This includes scalar multiples of both u and v, but does not include the origin. To calculate Span(u,v), first write u and v as vectors u = (u1,u2,...,un) and v = (v1,v2,...,vn). Then, any linear combination of u and v can be written as c1u + c2v, where c1 and c2 are scalars, and the set of all such linear combinations is Span(u,v). For example, if u = (1,2) and v = (3,4), then Span(u,v) = {(1,2), (3,4), (4,6), (5,8), (7,10), ...}. In other words, Span(u,v) is the set of all scalar multiples of u and all scalar multiples of v.

Learn more about linear here

https://brainly.com/question/28707677

#SPJ4

Choose the blanks
The linear relationship is or is not
And the graph passes or does not pass

Answers

Because the ratios between each set of numbers are equal, and the graph passes through the point, the linear relationship is proportionate (0,0).

What does the word "proportional" mean?

Proportional connections are those in which the ratios of the two variables are equal. Another way to think about them is that one variable is always a constant value multiplied by the other in a proportional relationship. The "constant of proportionality" is the name given to this variable.

The origin, points (2,14.5), (4,29), and (6,43.5) are provided (0,0).

We are aware that the ratios are equivalent in a proportional connection, i.e.

So,

⇒ 14.5/2 = 29/4 = 43.5/6 = 7.25

The linear relationship is a proportionate relationship since the ratios are equal.

The given situation's graph has been drawn, and it is evident that the graph passes through its origin, or "zero," which is (0,0)

Since the ratios between each set of data are equal, the linear relationship can only be a proportional relationship because the graph passes through the point (0,0).

To learn more about  linear relationship refer to:

https://brainly.com/question/30373083

#SPJ1

Other Questions
FILL IN THE BLANK In this episode, Vivaldi evokes the sound of singing birds through the use special effects like staccato notes, running scales, and ____. a car burns fuel with a density of 700 kg/m3 under atmospheric conditions that produce an air density of 1.2 kg/m3. the car has a fuel rating of 36 mpg (miles per gallon) at a speed of 60 mph (miles per hour) and a frontal cross-section of 4.5 feet by 2.5 feet. 1. calculate PLEASE HURRY I HAVE LIMITED TIME!Question- Find the standard form equation of a circle given a center of (7, 14) and a point on the circle of (4, 15).Answers- A.(x-7)^2 + ( y-14)^2 = 10B.(x-7)^2 + (y-14)^2 = 15 C.(x-7)^2 + (y-14)^2 = 25D.(x+7)^2 + (y+14)^2 = 2 . What did the Florida State's Attorney mean when he said that the case was very difficult to provebecause it was a "dry-bones" case? what problem is not a major issue for mexico Mr. Smith owns a car that is currently worth $8,000. The value of the car depreciates at the rate of 25% each year. Which of the following graphs represents the value of the car, y, in dollars, after x years? V a slice of pizza contain 20 grams of carbohydrates, 5 grams of proteins, 3 grams of fats, 240 mg of sodium, and 300 mg of potassium, how many kcals are provided by the slice of pizza? what are three truths about the nature of justice that are taught through the creation accounts in scripture? Technological improvements are more likely to occur ifa. the economy is centrally planned.b. entrepreneurs are compensated for taking risks with higher profits.c. economic decisions are made by politicians rather than entrepreneurs.d. companies face little competition in their markets. for this first part of the project you will be creating a faq (frequently asked questions) sheet highlighting utilitarianism and ethical egoism, which are two of the most well-known ethical theories. a faq sheet is a document that compiles a collection of information in the form of questions with their applicable answers. the goal of this sheet will be to provide some foundational information to the participants that they can take with them as they move through the diversity fair. it also works as a good conversational starter as people who visit your booth will be covering various aspects of ethics. positive charge is distributed uniformly on a plastic rod bent to form a quarter-circular arc (figure 1). figure1 of 1 a positively charged rod is bent so that it forms a concave rightward arc symmetrical about a horizontal dashed line going through the center of the rod. the center of curvature of the bent rod is marked with a black dot. part a what is the direction of the electric field at the center of the circle? What is the solution to StartFraction 5 over 6 EndFraction x minus one-third greater-than 1 and one-third?x > StartFraction 25 over 18 EndFractionx < StartFraction 25 over 18 EndFractionx > 2x < 2 over the last few years, an organization has brought up the need to replace old systems. while the organization has made these old systems function with various workarounds, custom middleware applications, and other methods to make up for their shortcomings, it has become increasingly apparent that they need to be replaced soon. which of the following security concerns does the company face if they continue to use the outdated systems? the age of the systems means they are accessible from virtually anywhere, making them vulnerable to security breaches from outside actors. the age of the systems means they run on outdated oss that are no longer supported, making security updates impossible to install. the age of the systems means they need numerous entry points from the outside, making the platforms' security impossible to configure. the age of the systems means they use insufficient hardware, making it impossible to secure communications between them and more modern devices. you would like to know whether silicon will float in mercury and you know that can determine this based on their densities. unfortunately, you have the density of mercury in units of kilogrammeter3 kilogram meter 3 and the density of silicon in other units: 2.33 2.33 gramcentimeter3 gram centimeter 3 . you decide to convert the density of silicon into units of kilogrammeter3 kilogram meter 3 to perform the comparison. by which combination of conversion factors will you multiply 2.33 2.33 gramcentimeter3 gram centimeter 3 to perform the unit conversion? a scientist make primer specift to a particular str fragment. these primers are used then used to amplify the str fragments from 10 diffrent elephants. would you expect the fragments to be the same size in all the elphants One company estimates same-day delivery as more than three less than half the total number of miles which graph represents the overall equation represented by the scenario or points may not apply to the scenario note that the graphs have similar miles for the independent variable on the X axis and the Y axis is a unit of time dependent on the number of miles write 2 use cases for the egrants project. you may use the requirements written in the simple sentence format for the egrants project developed in a previous assignment as a starting point to choose what requirement to use for your use cases. 30 points which of the following technologies describes how super-resolution imaging can track a single molecule inside of a cell, even though the resolution limit of light is much larger than the molecule being tracked? the system that maintains the human species from generation to generation is the system. True or False The supermarket has 20 aisles. 10 of the aisles are empty. What percentage of the aisles are empty?