If ƒ (x ) = 3x2 - x, find ƒ (-2).

Using the points A(1,5), B(1,-4), C(-3,5), D(-3,-4) the following are matched:

Distance between points B and C = √97.

Distance between points A and B = 9.

Midpoint between points  B and C = (-1, 1/2).

Midpoint between C and D = (-3, 1/2).

Slope of the line through B and D = 0.

The distance between two points of a line is given as:

Distance = \(\sqrt{c - a)^2 + (d - b)^2}\)

We have,

A(1,5), B(1,-4), C(-3,5) and D(-3,-4).

The distance between A and B.

= \(\sqrt{(1 - 1)^2 + (-4 - 5)^2}\)

= √81

= 9

The distance between B and C.

= \(\sqrt{(-3 - 1)^2 + (5 + 4)^2}\)

= √(16 + 81)

= √97

The midpoint (x, y) between B and C.

x = (1 - 3)/2 = -1

y = (-4 + 5) / 2 = 1/2

The midpoint (x, y) between C and D.

x = (-3 -3) / 2 = -6/2 = -3

y = (5 - 4) / 2 = 1/2

The slope of the line through points B and D.

= (-4 + 4) / (-3 - 1)

= 0/ -4

= 0

Thus,

The distance between A and B is 9.

The distance between B and C is √97.

The midpoint between B and C is (-1, 1/2).

The midpoint between C and D is (-3, 1/2).

The slope of the line through B and D is 0.

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Answer:

y = - \(\frac{3}{2}\)x - \(\frac{8}{3}\)

Step-by-step explanation:

2x-3y=8

rewrite, solve for y

3y = 2x - 8

divide by 3

y = \(\frac{2}{3}\)x - \(\frac{8}{3}\)

perpendicular = negative reciprocal slope = - \(\frac{3}{2}\)

9514 1404 393

Answer:

  $20,020

Step-by-step explanation:

The future value formula is helpful.

  FV = P(1 +r)^t

  $80,000 = P(1.08^18) = 3.9960195P

  P = $80,000/3.9960195 = $20,019.92

They should invest about $20,020 now.

Given that the particle is in equilibrium, the value of p = 2.5 and the value of q = -1.5

To answer the question, we need to know what force are

A force that thing which cause a change in motion of an object

Since there are three forces (15i + j) N, (5qi – pj) N and (-3pi - qj) N, where p and q are constants, act on a particle. Given that the particle is in equilibrium, the resultant force on the particle is zero.

A resultant force is a vector sum of two or more forces

So,  (15i + j) N + (5qi – pj) N + (-3pi - qj) N = 0i + 0j

15i + 5qi - 3pi + j - pj - qj = 0i + 0j

(15 + 5q - 3p)i + (1 - p - q)j = 0i + 0j

Equating components, we have

15 + 5q - 3p = 0 and 1 - p - q = 0

5q - 3p = -15 (1) and - p - q = -1

5q - 3p = -15 (1) and p + q = 1 (2)

From equation (2), p = 1 - q (3).

Substituting p into (1), we have

5q - 3p = -15 (1)

5q - 3(1 - q) = -15

5q - 3 + 3q = -15

5q + 3q = -15 + 3

8q = -12

q = -12/8

q = -3/2

q = - 1.5

Substituing q into (3), we have

p = 1 - q

p = 1 - (-3/2)

p = 1 + 3/2

p = (2 + 3)/2

p = 5/2

p = 2.5

So, the value of p = 2.5 and the value of q = -1.5

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3x - 14 here, 2x + 10 here. Consequently, X has a value of 14. In algebra, the letter "x" is frequently used to denote a value that is still unknown. It is referred to as a "variable" or "unknown" at times.

In algebra, the letter "x" is frequently used to denote a value that is still unknown. The term "variable" or "unknown" is used to describe it. x in x+2=7 is a variable. Not only can a variable be "y," "w," or any other letter, name, or symbol, it can also be "x." Examine: Variable

Bring the variable to one side of the equation, and then move all the other values to the other side by performing arithmetic operations on both sides of the equation to find the value of x. To determine the answer, simplify the values.

An experiment's independent variable is a variable that stands in for a variable that is being altered. In equations, the independent variable is frequently denoted by the variable x. X is the variable here.

\($$3 x-14-(2 x)=0$$\\\)

We shift every term to the left:

\($3 x-14-(2 x)=0$\)

We combine all the numbers and all the variables.

\($$x-14=0$$\)

All terms containing x are shifted to the left, and all other terms are shifted to the right.

\($$x=14$$\)

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Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

Answer: The function G(x) = [x] returns the greatest integer less than or equal to x. This means that for any value of x, G(x) will be the largest integer that is less than or equal to x. For example, G(3.5) = 3 and G(5) = 5.

The function R(x) = x/+2, x is any real number, this function returns the value of x incremented by 2. In other words, it is the result of adding 2 to x.

On the other hand, the graph of R(x) is a line that goes through the point (0, 2) and has a slope of 1, this means that for every change of 1 unit in the x-axis, the y-axis will change by 1 unit as well.

When we compare the two graphs, we can see that the graph of R(x) is shifted up 2 units from the graph of G(x) . If the graph of G(x) is thought of as the "ground", the graph of R(x) is "floating" two units above it. Also, the graph of R(x) is continuous while the graph of G(x) is not.

To sum up:

-The graph of G(x) is a step function, which start at the negative infinity and jumps up to the next integer at every point.

The graph of R(x) is a line that goes through the point (0, 2) and has a slope of 1

-R(x) is always two units above G(x) , and is a continuous function, while G(x) is not.

Step-by-step explanation:

Answer:

1) μ = 8000

2)  H0:  μ ≥8000

3)   Ha: μ  < 8000

4)  α= 0.10

5)  If the sample size is at least 15 a student's t test can be used.And we assume that the variances of the two independent groups are almost equal.

6) t= x`- μ/ s.d/ √n  = -0.816

7) The P- value = 0.214083.

8) The critical region is [-∞, -1.345]

9) Fail to Reject the Null Hypothesis

Step-by-step explanation:

1) The population characteristic is the population mean =μ = 8000

2) The claim is that the  addition of nitrates results in a decrease in the mean rate of uptake i.e μ < 8000

The null hypothesis is that  μ ≥ 8000

2) Null hypothesis: H0:  μ ≥8000

3) Alternative hypothesis:  Ha: μ  < 8000

4) The significance level alpha = α= 0.10

5)  If the sample size is at least 15 a student's t test can be used.And we assume that the variances of the two independent groups are almost equal.

Calculating mean and standard deviation using a calculator

Sample Size, n: 15

Mean= ∑ x/n = x`=: 7788.8

∑ x/n= 116832/15

St Dev, s.d(n-1) : 1002.4307

6) Test Statistic: student's t Test with d.f = n-1 = 14

t= x`- μ/ s.d/ √n  

t= 7788.8-8000/1002.4307/√15

t= -0.816

7) The P- value for the observed t value  is 0.214083.

The result is not significant at p < 0.10. H0 is accepted.

8) The Critical value for one sided t test at α =0.1 with 14 d.f is  less than t=  -1.3406

Hence the critical region is [-∞, -1.345]

Since the calculated t -0.816  value does not fall in the critical region  [-∞, -1.345] there is not sufficient evidence to reject H0

9) Fail to Reject the Null Hypothesis

Sample does not provide enough evidence to support the null hypothesis and conclude that  the data suggest that the addition of nitrates do not  result in a decrease in the mean rate of uptake. The claim is rejected.

Answer:

The growth model that represents the population of this city is not linear--it is exponential:

\(f(t) = 10000( {1.025}^{t} )\)

\(t = 0 \: represents \: 2010\)

Answer: answer is step by step

Step-by-step explanation:

A one-step equation is an algebraic equation you can solve in only one step. Once you've solved it, you've found the value of the variable that makes the equation true.

Hello there! I hope my answer will help you!

Look:

x+2=0

x=0-2

x=-2

Actually, it's Mental Math! :)

\(GraceRosalia\)

An attempt to divide by zero gives a contradictory result

A rule of algebra broken is dividing by zero (leading to a contradiction) and stating a finite result

Reason:

The given calculation is presented as follows;

1. a > 0, b > 0 given

2. a = b given

3. a·b = b²

4. a·b - a² = b² - a²

5. a·(b - a) = (b + a)·(b - a)

6. a = b + a

7. 0 = b

8. b = 2·b

9. 1 = 2

From line 4, the result are;

4. a·b - a² = b² - a² = 0

5. a·(b - a) = (b + a)·(b - a) = 0

On line 6, both sides where divided by (b - a) = 0, which should given an infinite result

Therefore, one rule of algebra broken is dividing by zero to get a finite result

In line 7, we have;

7. 0 = b

From 6. a = b + a, and a = b, we have;

8. b = 2·b

Therefore, line 9 should be;

9. 0 = 2·0; 0 = 0, given that we have;

1 × 0 = 0

2 × 0 = 0

∴ 1 × 0 = 2 × 0

However

In line 9., by dividing by b = 0, again, we have;

Therefore, one rule of algebra that is broken is dividing by zero and having a finite result

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9514 1404 393

Answer:

Step-by-step explanation:

You know the general term of an AP is ...

  an = a1 +d(n-1)

Here, a1 = k. The common difference is ...

  2k/3 -k = -k/3

So, the general term is ...

  an = k +(k/3)(n -1) . . . . the general term

__

The 6th term is then ...

  a6 = k + (k/3)(6 -1) = (3k +5k)/3 = 8k/3 . . . . 6th term

__

The 20th term is ...

  a20 = k + (k/3)(20 -1) = 22k/3

If this is 15, then the value of k is ...

  22k/3 = 15

  22k = 45

  k = 45/22 . . . . value of k for a20 = 15

Answer:

1,00,900,987 would be the answer

Question:

Flight 4581 travels daily from Pittsburgh to San Antonio. The flight is due into San Antonio at 5:07 p.m. The following list gives the Flight 4581 arrival time relative to 5:07 p.m. (in minutes) for a selection of 9 days. (A negative number means that the flight arrived early.) 21, 39, 37, 25, 6,-6, -4, 40, 37 Send data to Excel

(a) What is the mean of this data set? If your answer is not an integer, round your answer to one decimal place. an integer, round your answer to one decimal place.

b) How many modes does the data set have? and what are their values

Answer:

a) 21.2

b) Value of mode = 37

It contains just one mode

Step-by-step explanation:

Given:

x = 21, 39, 37, 25, 6,-6, -4, 40, 37

n = 9

a) Find the mean

Mean is the average value of a dataset.

Mean = Σx/n

Mean = \( \frac{21+39+37+25+6+(-6)+(-4)+40+37}{n} \)

\( = \frac{195}{9} \)

\( = 21.667 \)

The question says one decimal place.

Therefore, mean = 21.7

b) The mode of a dataset is the value that appears most frequently.

We have the following datasets:

21, 39, 37, 25, 6,-6, -4, 40, 37

The value that appears most frequently here is 37.

37 appeared twice while the rest appeared just once.

Therefore the dataset contains just one mode

The square root of 9 by long division method will give an answer of 3.

1: Group the digits of 9 into pairs from right to left. Since 9 is a single-digit number, we can consider it as a pair by itself.

2: Find the largest number whose square is less than or equal to the leftmost pair. In this case, the largest number whose square is less than or equal to 9 is 3.

3: Write 3 as the divisor on the left, and the quotient on the top right.

3 √ 9 |  0

4: Multiply the divisor (3) by the quotient (3), and write the result under the 9.

3 √ 9 |  0

      - 9

5: Subtract the result (9) from the leftmost pair (9), and write the difference (0) below the line.

3 √ 9 |  0

      - 9

       0

6: Bring down the next pair (0) to the right of the difference.

3 √ 9 |  0

      - 9

       0

     -----

7: Double the quotient (3) and write a blank space to the right.

3 √ 9 |  0

      - 9

       0

     -----

       0

      ?

8: Find a digit to fill in the blank space, such that when the new divisor (37) is multiplied by the digit, the result is less than or equal to the current dividend (0). In this case, the largest digit we can use is 0.

9: Write the digit (0) as the new quotient, and write the product of the new divisor (37) and the new quotient (0) below the line.

3 √ 9 |  0

      - 9

       0

     -----

       0

      0

10: Subtract the product (0) from the current dividend (0), and write the difference (0) below the line.

3 √ 9 |  0

      - 9

       0

     -----

       0

      0

      - 0

11: Since there are no more pairs to bring down, we have reached the end of the division. The square root of 9 is 3.

√9 = 3.

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Answer:

17157.28

Step-by-step explanation:

If we know that the volume of a sphere is equal to V=4/3πr3, then we can assume this.

The radius of the sphere is 16, so 16 cubed is 4096. 4096 x pi is 12867.96

12867.96 x 4/3 is 17157.28

Answer:

h = 0.962 cm

Step-by-step explanation:

Given that,

Mass of a solid cylinder, m = 26.05 g

The diameter of a cylinder, D = 3.56 cm

Radius, r = 1.78 cm

The density of a cylinder is 2.72 g/cm³

We need to find the height of the cylinder. Let it is h. We know that mass per unit volume is equal to density of an object. It can be given by :

\(d=\dfrac{m}{V}\\\\d=\dfrac{m}{\pi r^2 h}\\\\h=\dfrac{26.05}{\pi \times (1.78)^2\times 2.72}\\\\h=0.962\ cm\)

So, the height of the cylinder is 0.962 cm.

Answer:

5/9

Step-by-step explanation:

Answer:

I think you're looking for the term linear equation in 2 variables

The interest formula is :

where I = interest

P = Principal amount

r = interest rate

t = time in years

From the problem, Susan invested twice the amount at 6% as she does at 5%.

If she invested P to 5%, the amount she invested to 6% will be 2P

Using the formula to calculate the two interests.

For 5% :

For 6% :

The sum of the interests is $510

This will be :

She invested $3000 for 5% and $6000 for 6%

The answers are :

5% : $3000

6% : $6000

So, by taking the perfect square, option D is accurate and  √27·√6 is equal to either  3·√18 0r 9√2.

The square root of a number in mathematics is a quantity that, when multiplied by itself, yields the initial number. It is also known as a radical and is denoted by the sign "". For instance, since 3 times 3 = 9, the square root of 9 is 3. The symbol for the square root function is: √x = y, which states that y is equal to x squared. The phrase "the square base of x" should be read as "x". Since the sum of two negative integers is positive, the square root can either be positive or negative. However, the square root is typically only considered to have positive values,

given

Using the square root property, which states that the square root of a product is equivalent to the product of the square roots, we can simplify the product √27·√6 :

√27·√6 = √(27·6)

Now that we have factored out any perfect squares, we can simplify the equation under the radical sign. Since 3 has no perfect square factors and 27 can be factored as 9 3, we can write:

√(27·6) = √(9·3·6)

Taking the perfect square 9 out of this equation will further simplify it:

√(9·3·6) = √9 · √(3·6) = 3 · √18

So, by taking the perfect square, option D is accurate and  √27·√6 is equal to either  3·√18 0r 9√2.

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9514 1404 393

Answer:

  476 +598 = 1074

Step-by-step explanation:

In order for the sum to be smallest, the two most-significant digits must be the smallest possible. That is, they must be 4 and 5.

The two least-significant digits must be even. The remaining even digits are 6 and 8. Then the tens digits are the digits left over: 7 and 9.

Possible sums are ...

  476 +598 = 1074

  478 +596 = 1074

  496 +578 = 1074

  498 +576 = 1074

The sum is 1074.

Answer:

Step-by-step explanation:

There are two methods of doing this

one is in the pin and another:

3 2/7 =23/7

7 5/14= 103/14

23/7 + 103/14 = Lcm 14

23/7 *2= 46/14

46/14 + 103/14 =149/14

149/14 = 10 9/14

Answer:

Step 1: Write your hypotheses and plan your research design

Step 2: Collect data from a sample

Step 3: Summarize your data with descriptive statistics

Step 4: Test hypotheses or make estimates with inferential statistics

Step 5: Interpret your results

Step-by-step explanation:

We substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

The given system of equations are 2x-1/3y = -2...(1)

3x+y=1...(2)

We solve this system of equations by using substitution method.

Let us solve for x in equation to substitute it in equation (2).

2x=-2+1/3y

Divide both sides of equation by 2.

x=-1+1/6y

Now plug in the value of x in equation 2.

Hence, we substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

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Answer:

65 packets and 4 stamps

Step-by-step explanation:

The first thing we see is that the stamps are mixed... which means they must be added.

208 + 186 = 394 stamps total

Now we see that each packet has 6 stamps. So we divide the number of stamps in total by 6.

394/6= 65.66667

Now we see from that number that the stamps can't quite make 66 packets, so there are 65 packets.

Now we find the number of stamps left over by multiplying the number of packets by 6.

65 x 6= 390

Now we take the total number of stamps minus the number of stamps in packets.

394 - 390 = 4

Therefore, there are four stamps left over.

Hope this helps!