Find the absolute maximum and minimum, if either exists, for: 1. f(x)=x²-12x+6 12. f(x) = 9x³-1 3. f(x)=8x4-3

The sum of the given two vectors A and B is found to be R = 3i + 3j. The magnitude of vector R is found to be 3√2 and its direction is 45°.

The sum of the two vectors A and B is given by: R = A + B

Here, vector A = i + 4j And, vector B = 2i - j

Now, to find R, we will add the respective components of the two vectors, i.e,

R = (i + 4j) + (2i - j)

= 3i + 3j

The magnitude of vector R is given by the formula:

|R| = \(\sqrt{(R_x^2 + R_y^2)}\)

Substituting the values,

|R| = √(3² + 3²) = √18 = 3√2

The direction of vector R is given by the formula:

θ = tan⁻¹(\(R_y/R_x\))

θ = tan⁻¹(3/3)

θ = 45°

Therefore, the magnitude of vector R is 3√2 and its direction is 45°.

The sum of the given two vectors A and B is found to be R = 3i + 3j. The magnitude of vector R is found to be 3√2 and its direction is 45°.

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Answer:

The answer is given below

Step-by-step explanation:

In triangle EFG, let a = EG, A = ∠f, b= 1.3 in, B = ∠G, c = 2.4 in C = ∠E = 48°

Using cosine rule:

\(c^2=a^2+b^2-2ab*cos(C)\\a^2-2ab*cos(C)=c^2-b^2\\Substituting:\\a^2-2a(1.3)cos(48)=2.4^2-1.3^2\\a^2-1.74a=4.07\\a^2-1.74a-4.07=0\\a=3\ or\ -1.34\\a=EG=3\ inches\)

EG = 3 inches

Using sine rule,

\(\frac{b}{sin(B)} =\frac{c}{sin(C)}\\ Substituting:\\\frac{1.3}{sin(B)} =\frac{2.4}{sin(48)}\\sin(B)=\frac{sin(48)*1.3}{2.4}=0.4025\\ B=sin^{-1}(0.4025)=23.7^0\)

∠G = B = 23.7°

Given ΔXYZ ≅ ΔEGF,

Therefore: ZX = EF = 1.3 inches, m∠X = m∠G =23.7 °, m∠Z = m∠F = 107°

ZY = FG = 2.4

Answer:

ZX = 1.3 in.

EG = 3 in.

m∠X = 48°

m∠G = 25°

Step-by-step explanation:

ΔXYZ ≅ ΔEGF

107 + 48 = 155

m∠G = 180 - 155 = 25

Answer:

14

Step-by-step explanation:

Since the stretch of highway is 12 1/4 kilometers long and has speed limit signs every 7/8 of a kilometer, we'll divide the values given. This will be:

= 12 1/4 ÷ 7/8

= 14

Therefore, there'll be 14 speed limits.

According to the question, srs is a simple random sample whose size consists of individuals from the population and chosen in such a way that every set of individuals has an equal chance to be sampled.

What is Stratified random samples?

For stratified random samples, initially classify the population into the groups of similar individuals which is called as “strata”. Later choose simple random samples and combine them to form a full sample.

As per question, srs of \(200\) of the \(25000\) undergraduate students and the srs of \(100\) of the \(500\) graduate students. This overall sample is a stratified sample.

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Step-by-step explanation:

When x increases by 1, y decreases by 1.

The sum of x and y has a constant value of -2.

Hence the function is x + y = -2.

Therefore, the given set is the function of ordered pairs.

What is the ordered pairs?

An ordered pair is a pair of two elements that is of the form (x, y) where the order of the elements \(x\) and \(y\) is important.

Here given ordered pair is

\((1, -3), (2,-4), (3,-5), (4,-6)\)

The given set is \((1, -3), (2,-4), (3,-5), (4,-6)\) so consider the set which represents the function with \((x,y)\) values. So, the equation is

\(y=x+1\)

As per the given set the domain part is \((1,2,3,4)\) and the range is \((-3,-4,-5,-6)\).

Hence, the given set is the function of ordered pairs.

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According to the information, we can infer that the number of ounces of water, x, that Will could have put in each cup is 8 ounces.

Will initially had a cooler filled with 144 ounces of water. After using 16 ounces to fill his water bottle, there were 144 - 16 = 128 ounces of water remaining in the cooler.

Will then took out 16 plastic cups for his teammates. Since the same amount of water was put in each cup, the remaining amount of water, 128 ounces, needs to be divided equally among the cups.

Dividing 128 ounces by 16 cups gives us 8 ounces of water for each cup.

So, Will could have put 8 ounces of water in each cup.

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Answer:

7/54  or 0.1296

Step-by-step explanation:

Answer:

0.1296296296

Step-by-step explanation:

that is your answer

Answer:

x= 1 and y =4

Step-by-step explanation:

5 x 1=5- 4 = 1.

To solve the equation above, one should find all the values of variable  such as  is the correct identity.

Graphically, the roots of some equation  are the abscisses of the intersection points of function  with axis :herefore, from the above plot of some function , we immediately can conclude that the values  are the roots of equation .

There are infinity number of different equations (linear, quadratic, cubic, trigonometric, equations with powers and radical, ect.) depending on concrete form of function .

Answer:

Slope - 5
Y-intercept - (0,1)

Step-by-step explanation:

// Solve equation [2] for the variable  y

[2]    y = -5x

// Plug this in for variable  y  in equation [1]

  [1]    5x - (-5x) = -1

  [1]    10x = -1

// Solve equation [1] for the variable  x

  [1]    10x = - 1

  [1]    x = - 1/10

// By now we know this much :

   x = -1/10

   y = -5x

// Use the  x  value to solve for  y

   y = -5(-1/10) = 1/2


Hope this helps.

Answer:

0

Step-by-step explanation:

Piecewise functions are like recycling bins. They give you a piece of information for whatever value you may encounter on your graph. So, all you need to do is sort out the value they give you into the correct "bin," so to speak.

The first equation they give you is for any value less than zero. So, anything from -0.9999999 (you get the idea) onwards will use the equation on the right. So, if you have a value less than zero, then you will plug the x-value into the equation (-x - 2). Therefore, let's say your value was f(-1). You'd do: (-(-1) - 2). The negative cancel on your -1 and you're left with 1. Then, 1 - 2 = -1. So, in this example, your answer would be f(-1) = -1.

The second equation gives you a possible range for any numbers between zero and anything less than three. Notice how in this one, the zero is included. This is because when you actually go to draw a piecewise function, your values can't repeat, or else it wouldn't be a function. So, since the problem asks you to find f(0), you need to use the second equation since it is the one that includes zero in its possible values. Thus, you plug in your number. In this case, the number is 0, so x = 0. The answer is to f(0) = 0

Lastly, the third equation is for any values that are three or bigger. This one includes the three in its possible values. If they gave you a value like f(4), you just do the same as in the last examples. 4^2 - 1 = 15. So, f(4) = 15.

And that's all there is to it. Just plug in the value they give you into the appropriate equation, and you'll be good to go. Hope this helped!

Answer:

12+6 = 6(2+1)

16+4=4(4+1)

12+8=4(3+2)

18+12=6(3+2)

Step-by-step explanation:

Answer:

12+6 = 4(3+2)

16+4=4(4+1)

12+8=6(2+1)

18+12=6(3+2)

Step-by-step explanation:

The value of c that makes f(x) a valid density function over [0, 2] is c = 1/4.

The function given to us is f(x) = cx, and we are asked to find the value of c that makes this a valid density function over the interval [0, 2]. To be a valid density function, a function must satisfy two properties:

The function must be non-negative over the interval.

The integral of the function over the interval must be equal to 1.

Let's first check the first property. For f(x) to be non-negative over the interval [0, 2], c must be non-negative as well. This is because x³ is always non-negative, and multiplying it by a negative value of c would make f(x) negative for some values of x.

So, we can conclude that c ≥ 0.

Now let's check the second property. We need to find the value of c that makes the integral of f(x) over [0, 2] equal to 1:

∫₀² cx³ dx = 1

We can solve this integral using the power rule of integration:

(c/4) [x⁴]₀² = 1

(c/4) (2⁴ - 0⁴) = 1

16c/4 = 1

4c = 1

c = 1/4

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Answer:

He failed to check for extraneous solutions

Step-by-step explanation:

sqrt(x+6) -4 =x

Add 4 to each side

sqrt(x+6) -4+4 =x+4

sqrt(x+6)  =x+4

Sqaure each side

(sqrt(x+6))^2  =(x+4)^2

x+6 = x^2 +8x+16

Subtract 6 from each side

x = x^2 +8x +10

Subtract x from each side

0 = x^2 +7x +10

Factor

0 = (x+5) (x+2)

Using the zero product property

x=-5  x=-2

Check the solutions

sqrt(-5+6) -4 =-5

sqrt(1) -4 = -5

1-4 =-5

-3 does not equal -5 not a solution

sqrt(-2+6) -4 =-2

sqrt(4) -4 = -2

2-4 =-2  is a solution

Todd must purchase 300 copies of his resume to have enough resumes for 245 schools.

Todd plans to send resumes to 245 schools, so he needs at least 245 copies of his resume.

The local printer sells copies in sets of 100

so Todd must purchase at least the nearest multiple of 100 that is greater than or equal to 245.

Divide 245 by 100

245 ÷ 100 = 2.45

The nearest multiple of 100 that is greater than or equal to 2.45 is 3. Therefore, Todd needs to purchase 3 sets of 100 copies.

3 sets × 100 copies = 300 copies

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The answer is B, which is to find the common denominator.

In solving a rational equation, the first step is usually to find a common denominator for all the fractions in the equation. This allows us to combine the fractions into a single fraction and simplify the equation.

To find the common denominator, we need to identify the factors of the denominators and determine the least common multiple (LCM) of these factors. Then, we multiply each fraction by the appropriate factor(s) to get the common denominator. For example, if we have the equation:

(3/x) + (4/2x) = 1/4

The denominators are x and 2x, which have factors of x and 2. The LCM of these factors is 2x, so we need to multiply the first fraction by 2 and the second fraction by 1 to get:

(6/2x) + (4/2x) = 1/4

Then we can combine the fractions and simplify the equation to get:

(10/2x) = 1/4

From here, we can continue to solve for x by cross multiplying and manipulating the equation.

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Answer:

-2

Step-by-step explanation:

(-6,3) (-4,-1)

change in y-coordinate/change in x-coordinate=-1-3/-4--6=

-4/2=-2

=-2

The equation of the line will be y = -2x - 9. Then the gradient of the line segment will be negative 2.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the gradient of the line and c is the y-intercept of the line.

The two points are given below.

(-6, 3) and (-4, -1)

The equation of the line that passes through (-6, 3) and (-4, -1) will be given as,

(y + 1) = [(- 1 - 3) / (- 4 + 6)](x + 4)

y + 1 = -2(x + 4)

y + 1 = -2x - 8

y = - 2x - 9

The equation of the line will be y = -2x - 9. Then the gradient of the line segment will be negative 2.

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The maximum profit if the profits per acre are $75 for corn and $40 for soybeans is $371,255.83. Therefore, the correct option is c.

To find the maximum profit from planting corn and soybeans, we can use linear programming. Let's first define the variables and write the constraints.

Let x be the number of acres of corn and y be the number of acres of soybeans.

1. Total acre constraint: x + y ≤ 6,000

2. Fertilizer/herbicide constraint: 9x + 3y ≤ 40,501

3. Labor constraint: 0.75x + y ≤ 5,250

The objective function to maximize is the profit function: P(x,y) = 75x + 40y

Now, we will use the Solver to find the maximum profit:

Step 1: Set up a spreadsheet with the constraints and the objective function.

Step 2: Go to the Data tab and click on Solver. If Solver is not available, you may need to add it in Excel Options.

Step 3: Set the objective function by selecting the cell with the profit function.

Step 4: Choose "Max" for the objective.

Step 5: Add the constraints by selecting the corresponding cells.

Step 6: Click on "Solve" and the Solver will find the optimal values for x and y.

After using Solver, we find that the optimal values are x = 4,363.89 (corn) and y = 1,636.11 (soybeans), which yields a maximum profit of $371,255.83. Therefore, the correct answer is c: $371,255.83

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Answer:

\(x<-24\)

Step-by-step explanation:

You are correct, you do add 5 to both sides and get

\(\frac{x}{8} <-3\)

Then you multiply by 8 on both sides to get

\(x<-24\)

The correct option is D. Asking 80 owners their attitude toward a new design would be an example of a sample.

If a target population is defined as all 2,134 pickup truck owners residing in Tippecanoe County, then asking 80 owners their attitude toward a new design would be an example of a sample.

Because the survey is conducted on a limited group of people who represent the larger population. Therefore, the survey conducted on the sample represents the population as a whole. The sample is a representative subset of the entire population, which can be used to infer statistics and characteristics of the whole population. A statistical frame is a technique used to choose a representative sample of the population.

Asking only owners listed in the telephone directory would not be an example of a statistical frame. Instead, it would be an example of a bias selection because it excludes owners who are not listed in the telephone directory. Asking 100 owners their attitude toward a new truck style would not be an example of a consensus as consensus is a general agreement among the people.

However, the survey conducted on a sample can be used to find out a general consensus. Universal testing is not feasible because it would involve surveying each and every member of the population, which is both time-consuming and expensive.

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The complete question is:

Answer:

  19 units

Step-by-step explanation:

You want the period of the cosine function shown on the graph.

The period is the horizontal distance between points where the graph repeats itself. It is convenient to use midline crossings or peaks as points that are easily identified as corresponding.

Here, the peaks appear on grid lines, so we have used those to identify the period. The first peak is at x=1, and the second is at x=20. The difference of these coordinates is the period.

The period of this function is 19 units.

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The two cars will meet in 14.5 hours.

To find out how long it will take for the two cars to meet, we need to determine the time it takes for Car A and Car B to cover the remaining distance between them.

Let's calculate the distance Car A has to travel until they meet. The total distance between the two cars is 580 km, and Car A has already traveled 130 km. Therefore, Car A has to cover a distance of 580 km - 130 km = 450 km.

Now, we can calculate the time it will take for Car A to cover this distance. Car A's speed is 50 km/h, so the time it takes is:

Time = Distance / Speed = 450 km / 50 km/h = 9 hours.

Since Car B took off after Car A traveled 130 km, it means that Car B has to cover the entire distance of 580 km.

Now, we know that Car B's speed is 40 km/h. The time it will take for Car B to cover the distance is:

Time = Distance / Speed = 580 km / 40 km/h = 14.5 hours.

Therefore, the total time it will take for the two cars to meet is the maximum of the times for Car A and Car B, which is 14.5 hours.

Final answer: It will take the two cars 14.5 hours to meet.

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Answer:

I'm in an elementary schools how I'm I suppose to know???? no answer

lolololo

The shape on the left is a square with side length of 12 cm

This means the height of the triangle is 12cm.

Knowing the height and the hypotenuse using the Pythagorean you can solve for the base.

20^2 = 12^2 + x^2

400 = 144 + x^2

Subtract 144 from both sides:

256 = x^2

Take the square root of both sides

X = sqrt(256)

X = 16

X = 16

Answer:

y= -7/9 x+70

Step-by-step explanation:

28x+36y=2520

36y=-28x+2520

y= -7/9 x+70

Answer: The answer is C. The rest of the answers make no sense and do not work.

Step-by-step explanation:

The answer is C

A b and D are all incorrect

Answer:

gsatygrdfyuhtzrtftsrvg

Step-by-step explanation:

gay

Answer: A (1.156x10(6)

Step-by-step explanation: IM DOING THE INTERIM TOOOOOO

Difference in the population of two countries will be 1.156 × 10⁶.

 Given in the question,

Estimated population of two different countries in year 2030,

Difference in population of both the countries = 1300,000,000 - 144,000,000 = 1156,000,000

Scientific notation of the population difference → 1.156 × 10⁶

    Therefore, difference in the population of two different countries will be 1.156 × 10⁶.

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The number of ways that a cook can arrange 8 of 12 spice jars on a spice rack is; 495 ways.

We want to find the number of ways that a cook can arrange 8 of 12 spice jars on a spice rack.

This is a Combination Problem which follows the formula;

nCr = n!/(r!(n - r)!

12C8 = 12!/(8!(12 - 8)!

Solving this gives;

12C8 = 495 ways

Thus, the number of ways that a cook can arrange 8 of 12 spice jars on a spice rack is 495 ways.

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Answer:

The correct answer is: 19,958,400.

Step-by-step explanation:

I hope this helps! :)

Answer:

f(5) = 9

Step-by-step explanation:

To evaluate f(5) substitute x = 5 into f(x), that is

f(5) = (5 - 2)² = 3² = 9

Answer:

Step-by-step explanation:

f(x) = ( x - 2)²

To find f(5) substitute the value of x that's 5 into f(x). That's for every x in f (x) replace it with 5

That's

f(5) = ( 5 - 2)²

= 3²

We have the final answer as

Hope this helps you

Answer:

Probability (Roulette ball not landing on red) = 10 / 19

Step-by-step explanation:

Given:

Number of total slots = 38

Number of red slots = 18

Number of black slots = 18

Number of green slots = 2

Find:

Probability (Roulette ball not landing on red)

Computation:

Probability (Roulette ball not landing on red) = 1 - Probability (Roulette ball landing on red)

Probability (Roulette ball not landing on red) = 1 - (18 / 38)

Probability (Roulette ball not landing on red) = 20 / 38

Probability (Roulette ball not landing on red) = 10 / 19