What is (f + g)(x)? f(x) = -3x² + 6x g(x) = -X Write your answer as a polynomial or a rational in simplest form​

Answer:

Step-by-step explanation:

for (i = 0; i < dataPoints.size(); ++i) {

     if (dataPoints.at(i) > maxVal) {

        dataPoints.at(i) = dataPoints.at(i) - 4;

     }

  }

Answer:

\(344 {cm}^{2} \)

Step-by-step explanation:

\(area \: of \: the \: square \\ = 40cm \times 40cm \\ = 1600 {cm}^{3} \\ \)

\(area \: of \: the \: circle \\ = \pi {r}^{2} \\ = 3.14 \times {(20)}^{2} \\ = 3.14 \times 400 \\ = 1256 {cm}^{2} \\ \)

\(area \: of \: shaded \: region \\ = 1600 {cm}^{2} - 1256 {cm}^{2} \\ = 344 {cm}^{2} \\ \)

Using graphical method to solve the system of linear inequalities, the solution are (x, y) 3, 13.

A system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.

To solve this, we can write out the equations as

x + y ≤ 16 ...eq(i)

650x + 150y ≥ 3900 ...eq(ii)

Solving both equations with a graph.

Kindly find the attached graph to the problem.

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Answer:

the answer is D or A

Step-by-step explanation:

step-by-step explanation

I hope this helps

The mean squared error equals to c.) 6.

The mean squared error is a measure of the accuracy of a forecast model, indicating the average squared difference between the forecasted values and the actual values in a time series. In this case, a three-period moving average forecast is used.

To compute the mean squared error, we need to calculate the squared difference between each forecasted value and the corresponding actual value, and then take the average of these squared differences.

Using the given time series values and the three-period moving average forecast, we can calculate the squared differences as follows:

(23 - 17)² = 36

(17 - 17)² = 0

(17 - 26)² = 81

(26 - 11)² = 225

(11 - 23)² = 144

(23 - 17)² = 36

(17 - 17)² = 0

Taking the average of these squared differences, we get:

(36 + 0 + 81 + 225 + 144 + 36 + 0) / 7 = 522 / 7 ≈ 74.57

Therefore, the mean squared error is approximately 74.57.

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Answer:

52.5 feet

Step-by-step explanation:

3.5x2.5x2=52.5

Answer:

You'd get 25.3333 or you could also express 76/3 as a mixed fraction: 25 1/3.

                         ↑  

                  the arrow pointing shows what the remainder means

remainder is the one which is down

Answer:

Step-by-step explanation:

each pencil costs $8.33.

12÷$1.44=$8.33.

hope this helps!

mark me brainliest as well please.

p(1, 2) is false.

p(1, 1) is false.

p(3, 3) is false.

p(2, 1) ∨ p(3, 1) is true.

p(1, 3) ∧ p(2, 3) is true.

¬p(2, 2) is true.

We are given the predicate p(x, y) and the universe for the variables x and y is {1, 2, 3}. The truth values of p(x, y) are explicitly given for specific values of x and y.

p(1, 2): Since we don't have this specific value given in the provided information, we assume it is false.

p(1, 1): Similarly, since we don't have this specific value given, we assume it is false.

p(3, 3): Again, since we don't have this specific value given, we assume it is false.

p(2, 1) ∨ p(3, 1): We check the truth value of both statements individually and apply the logical OR operation. From the given information, p(2, 1) is true and p(3, 1) is true. So, the overall statement is true.

p(1, 3) ∧ p(2, 3): We check the truth value of both statements individually and apply the logical AND operation. From the given information, p(1, 3) is true and p(2, 3) is false. So, the overall statement is false.

¬p(2, 2): The negation of p(2, 2) is evaluated. Since p(2, 2) is true according to the given information, its negation is false.

p(1, 2) is false.

p(1, 1) is false.

p(3, 3) is false.

p(2, 1) ∨ p(3, 1) is true.

p(1, 3) ∧ p(2, 3) is false.

¬p(2, 2) is false.

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Answer:

-8 + 8 + -2 = -2

If you need more help use Algebra Calculator - MathPapa

Answer:

-8 + 8 + -2 = -2

Step-by-step explanation:

-8 + 8 + -2

Follow the PEMDAS order of operations

Add and subtract (left to right)

-8 + 8 = 0

= 0 + (-2)

Apply rule: For example, + (-a) = -a

+ (-2) = -2

= 0 - 2

0 - 2 = -2

So the answer would be -2

I hope that helped you understand how to solve it :)

Answer:

√89

Step-by-step explanation:

The solutions of the equation f(x) = g(x) include the following: B. -3, 0, 2, -4.

In Mathematics and Geometry, a point of intersection simply refers to the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.

By critically observing the graph of the lines representing the given system of equations, we can reasonably and logically deduce that the correct solution set lies in both Quadrant II and IV and it is denoted by the point of intersection of both the x-coordinate (x-axis) and y-coordinate (y-axis), which is given by this ordered pair (-3, 0) and (2, -4).

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The points of inflection on the graph of f is (a) three

From the question, we have the following parameters that can be used in our computation:

The first derivative, \(f'(x) = x - 4e^{-\sin(2x)\)

So, we have

\(f'(x) = x - 4e^{-\sin(2x)\)

Set the function to 0

\(x - 4e^{-\sin(2x)} = 0\)

So, we have

\(x =4e^{-\sin(2x)}\)

Rewrite the equation as

y = x

\(y =4e^{-\sin(2x)}\)

Next, we plot the graph of both functions (see attachment)

From the graph, we have the number of intersection points to be 3 on the interval

This means that the points of inflection on the graph of f are 3

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The colored chips they used to represent each vacation option are:

Hawaii:  14 blue chips

New York: 10 yellow chips

California: 10 red chips

Alaska: 6 green chips

The radio station awarded 40 different colored chips to 100% winners.

To know how many colored chips should they use to represent each vacation option the following steps are taken:

Hawaii = ( 35/100) × 40

= 14 blue chips

New York = (25/100) ×40

= 10 yellow chips

California = (25/100)  ×40

= 10 red chips

Alaska = (15/100)  × 40

= 6 green chips

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Answer:

The fraction of the trip completed is ³/₈

The fraction of the trip completed in decimal form is 0.375

Step-by-step explanation:

Given;

total trip to be completed by Tora, = 320 miles

distance completed by Tora, = 120 miles

The fraction of the race that Tora has completed is given as;

\(= \frac{distance \ completed}{total \ distance} \\\\= \frac{120}{320}\\\\= \frac{12}{32} \ (divide \ both \ numerator \ and \ denominator \ by \ 4)\\\\= \frac{3}{8}\)

As a decimal the fraction is written as;

\(\frac{3}{8} = 0.375\)

There is no specific number pattern for the sequence { 6, 1, 8,4, 2, 7} but to determine the next term of sequence we can use the following patterns

1) for even place terms pattern is

aₙ = aₙ₋₂ + 3.

2) for odd place terms pattern is first aₙ

= aₙ₋₂ + 2 and for next aₙ₊₂ = aₙ - 6, where n is odd number.

A pattern is a series or sequence of repetitions. A number pattern is a series of numbers that follow a specific order in mathematics. Patterns usually describe inverse relationships between numbers.

A sequence of numbers can also be called a pattern. The types of number patterns are classified as

We need to write a pattern for 6, 1, 8, 4, 2, 7. Now the sequence is 6, 1, 8, 4, 2, 7,

First term = 6

Second term = 1

Break this sequence down into odd and even terms or enteries. The order of odd entries is 6,8,2,.. So the pattern here is 2 and -6, i.e. 7ᵗʰ entry = 2 + 2 = 4 and 9ᵗʰ entry = 4+ 6 = 10 and so on. Now for Evan's bit term, 1,4,7,.. The pattern here is aₙ = aₙ₋₂ + 3. where n is an even number. So the entire sequence has no pattern, but the odd and even elements can be determined by different patterns.

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The correct statements are:

There are four ways to choose the committee.

There are three ways to form the committee if person D must be on it.

If persons B and C must be on the committee, there are two ways to form the committee.

It is given that:

A membership committee of three is formed from four eligible members.

1)

There are four ways to choose the committee.

This statement is true.

since we have to choose 3 members out of the 4 members so we can use the method of combination.

2)

There are three ways to form the committee if person D must be on it.

This statement is also true.

since D has to be in the committee, this means we have to choose 2 more people out of the three people to form the committee.

3)

If seven members are eligible next year, then there will be fewer combinations.

This statement is wrong.

Since we have to choose 3 members out of 7 members so the number of possible combinations will be:

i.e. there are 35 combinations possible.

4)

If persons B and C must be on the committee, there are two ways to form the committee.

if B and C have to be in the committee then we have to choose just one person out of the two people left.

Hence, the statement is true.

5)

If persons A and C must be on the committee, then there is only one way to form the committee.

If A and C have to be in the committee then as in last option we have to choose any one of the two person left.

so possible number of ways are 2.

Hence, the statement is false.

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Answer:

A square is defined as a quadrilateral with 4 sides of the same length and 4 right angles. To verify the lengths of the sides, you can use the distance formula. To find the angles, you can use the slopes of the line segments and make sure sides that form an angle have opposite reciprocal slopes.

Step-by-step explanation:

First, find the coordinates of each point. You're provided with the scale and you can just count, but to make it easier, you can label the axes.

A: (0,8)

B: (6,6)

C: (4,0)

D: (-2,2)

The distance formula is used to find the distance between any two points on the coordinate form. Here it is:

d=sqrt((y2-y1)^2 + (x2-x1)^2)

d=distance, and (x1, y1) and (x2, y2) are the points.

Find the length of each side. I'll demonstrate with two sides, AB and BC.

AB: (x1,y1)=(0,8) and (x2,y2)=(6,6)

d=sqrt((6-8)^2 + (6-0)^2)

 =sqrt((-2)^2 + 6^2)

 =sqrt(4+36)

 =sqrt(40)=2sqrt10

BC: (x1,y1)=(6,6) and (x2,y2)=(4,0)

d=sqrt((4-6)^2 + (0-6)^2)

 =sqrt((-2)^2 + (-6)^2)

 =sqrt(4+36)

 =sqrt(40)=2sqrt10

Do the same thing with sides CD and AD, you'll see that they both also have a length of 2sqrt10 inches. (You don't really have to simplify, I just like to.)

To verify if the sides are perpendicular, you need to find the slopes of the sides and make sure that the product of the slopes of each pair of sides that form a vertex is -1. In other words, each pair of sides that form a vertex have to have opposite reciprocal slopes. I'll demonstrate with 2 vertecies, A and B.

To find the slope, you have to use the formula m=(y2-y1)/(x2-x1). m is the slope, and again, (x1, y1) and (x2, y2) are the points you're plugging in.

To find the measure of angle A, you need to find the slopes of sides AD and AB. (These are the sides that meet to form the angle.)

AD: (x1,y1)=(0,8) and (x2,y2)=(-2,2)

m = (2 - 8)/(-2 - 0)

   = -6/-2

   = 3

AB: (x1,y1)=(0,8) and (x2,y2)=(6,6)

m = (6 - 8)/(6 - 0)

   = -2/6

   = -1/3

So AD has a slope of 3 and AB has a slope of -1/3. Now you need to make sure they have a product of -1.

-1/3 * 3 = -1

So yes, it works! As I mentioned before, you can also think of them as opposite reciprocals.

The reciprocal of 3 is 1/3. The opposite of 1/3 is -1/3. So yes, the sides are perpendicular.

Let's do it again with angle B. We have to find the slope of BC now, since we already know the slope of AB.

BC: (x1,y1)=(6,6) and (x2,y2)=(4,0)

m = (0 - 6)/(4-6)

   = -6/-2

   =3

So the slope is exactly the same as the slope of AD. A square is a parallelogram, so it has two pairs of opposite parallel sides. We already verified that 3 and -1/3 are opposite reciprocals, so we now know that angle B has a measure of 90 degrees as well. You can do the same for angles C and D. That way, you'll have proven that all the sides have the same length and all the angles measure 90 degrees-- so the quadrilateral ABCD matches the definition of a square.

Hope this helped!

Answer:

12x -7

Step-by-step explanation:

Hence, (a) the hematite content in the ore will be 40% . (b) Volume recovery is 49.8%. (c) 8.7 million ft3. (d) 128,424 short ton. (e)  65.6 million short tons. (f) $3.936 billion

a. The hematite content of the hematite ore being mined in percent:

Given, The ore contains 40% iron (Fe).Therefore, the hematite content in the ore will be 40%.

b. The average bank density of the hematite ore being mined in lbs/ft3:

The average bank density can be calculated as follows:

Average bank density = (Mass of ore) / (Volume of ore)To calculate the mass of the ore, we first need to calculate the amount of hematite ore being mined every year. 4 million short tons of ore containing 40% iron is being mined every year.

Therefore, the mass of hematite ore being mined every year is:

Mass of hematite ore = 4 million short tons x 0.4 = 1.6 million short tons

We can calculate the volume of the ore by dividing the mass of the ore by its density.

The density of the ore can be calculated by using the mass and volume recovery values.

Volume recovery = 100% - 50.2%

= 49.8%

Mass recovery = 82%

Therefore, Mass of feed to concentration plant = (Mass of concentrate) / 0.82

= (1.6 x 106 short tons) / 0.82

= 1.951 x 106 short tons

Density of feed = 1.951 x 106 short tons / 11.19 x 106 ft3 = 0.174 short tons/ft3

Average bank density = (Mass of ore) / (Volume of ore)

= (1.6 million short tons) / (0.174 million ft3)

= 9.20 lbs/ft3

c. The total volume of ore mined over the 50 years of operations in ft3:

Volume of ore mined in 50 years = 50 x 0.174 million ft3

= 8.7 million ft3

d. The amount of silica in the final concentrate in percent:

The amount of silica in the concentrate can be calculated as follows:

Mass of silica in concentrate = Mass of feed x (1 - Mass recovery) x (Silica content in feed / 100)

Mass of feed = (Mass of concentrate) / Mass recovery

= (1.6 x 106 short tons) / 0.82 = 1.951 x 106 short tons

Silica content in feed = 100% - 40%

= 60%

Mass of silica in concentrate = (1.951 x 106) x (1 - 0.82) x (60 / 100)

= 128,424 short ton

Silica content in the concentrate = (Mass of silica in concentrate) / (Mass of concentrate) x 100

= (128,424 short ton) / (1.142 x 106 short ton) x 100 = 11.2%

e. The total amount of hematite concentrate produced over the 50 years of operation (short tons):

The amount of hematite concentrate produced every year is:

Mass of hematite concentrate = Mass of feed x Mass recovery

= (1.6 x 106 short tons) x 0.82 = 1.312 x 106 short tons

Total amount of hematite concentrate produced over 50 years = 50 x 1.312 million short tons

= 65.6 million short tons

f. The overall value of hematite concentrate produced over the 50 years of operation (U.S. dollars):

The overall value of the hematite concentrate produced can be calculated as follows:

Overall value of concentrate = Total amount of concentrate produced x Price per short ton

= 65.6 million short tons x $60 per short ton

= $3.936 billion

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Answer:

sorry I cant speak spanish

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

415 is closer to 400, so just divide that by 8 to get 50.

Answer:

it's 12 because

2×6=12

3×4=12

4×3=12

and all of them have twelve

Answer:

Step-by-step explanation:

2×6=12

3×4=12

4×3=12

Answer: the answer is 2 14/15

Step-by-step explanation:

The solution of the expressions will be 0.44.

What is Number system?

A system of writing to express the number is called number system.

Given that;

The expressions are,

⇒ −[−1 2/5 ÷ 0.7 (1.8) ] − 2/3

Now,

Solve the expression as;

⇒ −[−1 2/5 ÷ 0.7 (1.8) ] − 2/3

Using the BODMAS rule to solve the expressions as;

⇒ −[−1 2/5 ÷ 0.7 (1.8) ] − 2/3

⇒ −[−1 2/5 ÷ 1.26 ] − 2/3

⇒ - [ - 7 / 5 ÷ 1.26 ] − 2/3

⇒ - [ - 7 / 5 x 1 / 1.26 ] - 2 / 3

⇒ - [ - 7 / 6.3 ] - 2/3

⇒ 1.1 - 2/3

⇒ 1.1 - 0.66

⇒ 0.44

Therefore,

The solution of the expressions will be 0.44.

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