\(3x+5/4x^{2} +8x+8\)

Answer:

for ponits

Step-by-step explanation:

In order to determine the dimension of the subspace of R3 spanned by the given vectors, we need to find the number of linearly independent vectors in the set.

For example, if we have two vectors in R3, we can determine if they are linearly independent by checking if one vector is a scalar multiple of the other. If they are linearly independent, they span a two-dimensional subspace of R3.

If we have three vectors in R3, we can use the same method to check if they are linearly independent. If they are, they span a three-dimensional subspace of R3. If they are not linearly independent, we can use row reduction to find a linearly independent subset of the vectors, which will span a subspace of lower dimension.

In general, the dimension of the subspace of R3 spanned by n vectors will be at most n, and it will be exactly n if and only if the vectors are linearly independent.

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Answer:

\(\{(-6, -4), (4, -8), (-6, 9), (1, -3)\}\)

Step-by-step explanation:

Given

\(\{(5, -9), (6, -6), (-3, 8), (9, -6)\}\)

\(\{(-6, -4), (4, -8), (-6, 9), (1, -3)\}\)

\(\{(1, -1), (-5, 7), (4, -9), (-9, 7)\}\)

\(\{(8, -9), (-3, -6), (-4, 4), (1, -5)\}\)

Required

Which is not a function

An ordered pair is represented as:

\(\{(x_1,y_1),(x_2,y_2),(x_3,y_3),..........,(x_n,y_n)\}\)

However, for the ordered pair to be a function; all the x values must be unique (i.e. not repeated)

From options (a) to (d), option (b) has -6 repeated twice. Hence, it is not a function.

Answer:

#9       (x, y) = (6, 32)

#10      The meaning of the solution is that if you buy 6 kites from either store, the total cost will be the same and is $32

Step-by-step explanation:

The graph legend is missing so by looking at the graph alone we are unable to determine which color line corresponds to which kind of kite(Kites-R-Fun or Windy Kites)

However the associated table will help us determine this

The linear equation for a line is expressed as

y = mx + c

where m = slope of the line and b = y-intercept which is the y-value for the point where the line crosses the y-axis(at x = 0)

Slope m = rise/run = Δy/Δx = (y2 - y1)/(x2 - x1) for any two points (x1, y1) and (x2, y2) on the line

Let's take the two  x values as x1=0 and x2=1 and use the table

For Kites-R Fun

x1 = 0 ==> y1 = 8. This is also the y-intercept, b

We see that the red line corresponds to x = 0, y = 8

x2 = 1 ==> y2 = 12

y2 - y1 = rise = Δy =12 - 8 = 4

x2 -   x1 = Δx = 1 - 0 =1

Slope m = 4/1 = 4

Equation of Kites-R Fun is 4x + 8

For Windy Kites

x1 = 0 ==> y1 = 20

y-intercept = 20 or b = 20

x2 = 1 ==> y2 = 22

Rise = Δy =22 - 20 = 2

Run = Δx = 1 - 0 = 1

Slope = m, b = 20

Equation of blue line is

y = 2x + 20

The two equations are:

y = 4x + 8

y = 2x + 20

Equating right sides:

4x + 8 = 2x + 20

Move 2x to the left side and 8 to the right side:

4x + 2x + 8 - 8 = 2x - 2x + 20 -8

2x = 12

x = 6

For x = 6 the costs are the same

Plugging x = 6into equation y = 4x + 8:

y = 4(6) + 8 = 24 + 8 = 32

So the solution set is

(6, 32)

Looking at the graph we see the two lines intersect at this point

(Heck, we could have avoided all this work and just looked at the graph but I don't expect that was what they intended. You can add this as a side note)

On the second part

For Kites-R-US, each kite costs $4

The meaning of the solution is that if you buy 6 kites from either store, the total cost will be the same.

The percent change in the number of students who signed up for the trip is 18%. Therefore, the answer is (D) 18%.

To determine the percent change in the number of students who signed up for the summer trip, we need to calculate the difference between the two numbers and then divide it by the original number and multiply by 100 to get the answer in percent form.

In this case, the difference between 80 and 94 is 94-80 = 14. The percentage increase would be (14/80) * 100 = 17.5%. So, rounding to the nearest whole number, the percent change in the number of students who signed up for the trip is 18%. Therefore, the answer is (D) 18%.

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Answer:

y = -2x + 11

Step-by-step explanation:

When two lines are parallel, their gradients are the same. So the gradient of the line parallel to this equation will be -2 as well.

Now we substitute values from this point to find the rest of the equation :

y = -2x + c

3 = -2(4) + c

3 = -8 + c  

c = 11

So the equation of the line parallel will be y = -2x + 11

Hope this helped and have a good day

The statement "in trend projection, a negative regression slope is mathematically impossible" is false.

In trend projection, a negative regression slope is mathematically possible. Trend projection, also known as linear regression, is a statistical technique used to forecast future values based on past trends. It assumes a linear relationship between the independent variable (time) and the dependent variable (the variable being forecasted).

The regression slope represents the direction and magnitude of the relationship between the variables. A positive slope indicates an upward trend, while a negative slope indicates a downward trend. Therefore, a negative regression slope is indeed possible in trend projection.

However, it's important to note that the validity of the trend projection depends on the underlying data and assumptions made. If the data and assumptions are not appropriate, the trend projection may not accurately represent the relationship between the variables.

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Answer:

Least acceptable weight= 15.6 ounces

and Greatest acceptable weight=16.4 ounces

Step-by-step explanation:

A cereal company fills boxes with 16 ounces of cereal.

The acceptable percent error in filling a box is 2.5%.

i.e. the error in decimal is: 2.5/100 x 16 = 25/1000 x 16 = 0.4

Hence,

the least acceptable weight is obtained by subtracting the actual amount with the error.

16-0.4=15.6 ounces.

and the greatest acceptable weight is obtained by adding the error to the actual weight.

16+0.4=16.4 ounces

Hence,

Least acceptable weight= 15.6 ounces

and Greatest acceptable weight=16.4 ounces.

What are the term associated with set?

Now, According to the question:

Let's know:

What are Sets?

A set is a well-defined collection of objects. Sets are named and represented using a capital letter. In the set theory, the elements that a set comprises can be any kind of thing: people, letters of the alphabet, numbers, shapes, variables, etc.

Any collection of objects (elements), which may be mathematical (e.g., numbers and functions) or not. A set is commonly represented as a list of all its members enclosed in braces. The intuitive idea of a set is probably even older than that of number.

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Inversely proportion - The work out value of R and A is 3.6 and 2 respectively.

What is inversely proportion?

They are said to be inversely proportional when one quantity's value rises relative to another's decline or vice versa. It implies that the two quantities behave inherently differently. For instance, time and speed have an inverse relationship. The time decreases as you increase the speed. Inverse proportion, varying inversely, inverse variation, and reciprocal proportion are additional terms used here to describe this kind of proportion.

Given, R \(\alpha\) 1/A

R = k/A

When R = 12 and A = 1.5

12= k× 1.5

k= 18

Now, when A=5, R= 18/5 = 3.6

And when R= 9, A = 18/9=2

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Given: Differential equation of the form: \($\frac{dx}{dt}+ax=b$\)

This is a first-order, linear, ordinary differential equation with a constant coefficient. To solve this differential equation we need to follow the steps below:

First, find the homogeneous solution of the differential equation by setting \($b=0$.$\frac{dx}{dt}+ax=0$\)

Integrating factor, \($I=e^{\int a dt}=e^{at}$\)

Multiplying both sides of the differential equation by \($I$.$\frac{d}{dt}(xe^{at})=0$\)

Integrating both sides.\($xe^{at}=c_1$\)

Where \($c_1$\) is a constant.

Substituting the initial condition,\($x(0)=x_0$.$x=e^{-at}c_1$\)

Next, we need to find the particular solution of the differential equation with the constant \($b$.\)

In the present case, \($b=constant$\)

Therefore, the particular solution of the differential equation is also a constant.

Let this constant be \($c_2$.\)

Then, \($\frac{dx}{dt}+ax=b$ $\implies \frac{dc_2}{dt}+ac_2=b$ $\implies c_2=\frac{b}{a}$\)

Thus, the general solution of the differential equation is,\($x(t)=e^{-at}c_1+\frac{b}{a}$\)

Where\($c_1$\) is the constant obtained from the initial condition,

and \($e$\)is the exponential constant.

If the initial condition is \($x(t_0)=x_0$ then,$x(t)=e^{-a(t-t_0)}c_1+\frac{b}{a}$\)

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Answer: Answer is 4.25

Step-by-step explanation: Jus take you first number (2 over 8.50) and divide. You get 4.25. Now try to multiply or add for other numbers, and you find multiplying 4.25 by X will get you the answer of Y.

21.2 because you use the area of a circle formula which is pi times r squared and divide it by four to get each quarter and then multiply by three because there are 3 quarters of the circle.

The r function that the data analyst can use to do this automatically is the clean names function.

When it comes to data manipulation, R is an excellent tool. It enables the use of several preprocessed packages, making data manipulation much easier.

Janitor's clean names() function will make all of your variable names consistent in a single line of code.

In R, a data analyst is cleaning up their data. To avoid errors in their analysis, they want to ensure that their column names are unique and consistent. What R function can they use to automate this? The clean names() function will ensure that column names are both unique and consistent.

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Answer:

32.1

Step-by-step explanation:

You add the code chunk arrange(bill_length_mm) to sort the column bill_length_mm in ascending order. The correct code is penguins %>% arrange(bill_length_mm). Inside the parentheses of the arrange() function is the name of the variable you want to sort. The code returns a tibble that displays the data for bill_length_mm from shortest to longest. The shortest bill length is 32.1mm.

Answer:

Step-by-step explanation:

Your answer

X =0.35 p

Mark it as Brainlist. Follow me for more answer.

Answer:

D) 4 < x < 6

Step-by-step explanation:

The interval is decreasing when it is doing down in value  when x is increasing.

The graph is decreasing over the interval between the values of 4 and 6.

a) The length of Captain Jack's ship is: 95.17 m

b) The height above the deck of the Ship is: 34.64 m

a) In triangle ABC, we can say that:

tan 30 = AB/h

where:

h is height above deck of ship

We are give AB = 20 m and as such:

h = 20/tan 30

h = 34.64 m

b) To find the the length of Captain Jack's ship:

BC = h * tan 70

BC = 34.64 * tan 70

BC = 95.17 m

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The simplified form of the given expression is 9b

From the question, we are to simplify the given expression

The given expression is 3√b^2

This expression can be properly written as

(3√b)²

To simplify the expression,

First, we will expand the expression by applying one of the rules of exponents

(3√b)²

Applying the rule of exponent

3² × (√b)²

9 × b

= 9b

Hence,

The simplified expression is 9b

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SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the formula for the rate of change

STEP 2: Write the given intervals

STEP 3: Find the average rate of change of f(x)

We substitute the coordinates into the rate of change formula:

STEP 4: Find the rate of change of g(x)

STEP 5: Find the rate of change of h(x)

STEP 6: Write the average rates of change for the functions

The average rates of change in ascending order will be -8,-3,-1

Hence, the arrangement of the functions according to their ascending order of average rates of changes are:

Answer:

Olivia's puppy, it weighed 5 pounds.

Step-by-step explanation:

The functions y = 2 (1/5)^x - 5 and y = 4^x are compared as follows

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

Initial value:               2                                    1

base function:        1/5 = decay function       4 = growth function

Translation:             5 units down                    no transformation

A decay function is a mathematical function used in various fields such as physics, engineering, economics, and machine learning, to model the reduction or decline of a value over time.

It is a type of function that decreases at a rate proportional to its current value, so that it approaches zero as time progresses.

Decay function are exponential functions with the base function as

This is the opposite of growth function which has values greater than 1

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Becca made a total of 24 rolls and 12 biscuits.

Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product.

Becca made 2 trays of rolls and biscuits, with 12 rolls and 6 biscuits in each tray. To find the total number of rolls and biscuits, we need to multiply the number of rolls and biscuits per tray by the number of trays, and then add them together:

Total rolls = 2 trays × 12 rolls per tray = 24 rolls

Total biscuits = 2 trays × 6 biscuits per tray = 12 biscuits

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Answer:

Yes

Step-by-step explanation:

Cause the 1 is there for no reason

The angles in the triangle are as follows:

m∠1 = 51 degrees

m∠2 = 33 degrees

m∠3 = 123 degrees

m∠4 = 24 degrees

The sum of angles in a triangle is 180 degrees. A right angle triangle is a triangle with one of its angles as 90 degrees.

Therefore, let's find the missing angle of the triangle.

Hence,

m∠1 = 180 - 72 - 57(sum of angles in a triangle)

m∠1 = 51 degrees

m∠2 = 90 - 72

m∠2 = 33 degrees

m∠3 = 180 - 57(sum of angles on a straight line)

m∠3 = 123 degrees

m∠4 = 180 - 123 - 33

m∠4 = 24 degrees

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Answer:

R=12.56

Step-by-step explanation:

radius is the center to side or half of the circumference 25.12/2=12.56

We will break apart the figure into triangles, rectangles, squares etc. We will then find area of each individual figure and sum it.

We can break apart the figure as shown below:

The domain of the function is\((0, +∞)\)and the range is\((-∞, +∞).\)

To find the domain and range of the function y = x^3/log_10(x), we need to consider the restrictions on the variables involved.

Domain:

The logarithm function\(log_10(x)\)is defined only for positive values of x. Additionally, the denominator cannot be zero. Therefore, the domain of the function is given by the set of positive real numbers excluding zero:

Domain: \((0, +∞)\)

Range:

To determine the range of the function, we need to analyze its behavior as x approaches different values.

As x approaches positive infinity, both\(x^3 and log_10(x)\) grow without bound. Therefore, the function\(y = x^3/log_10(x)\)approaches positive infinity as x approaches infinity.

As x approaches zero, the function approaches negative infinity. This is because the denominator \(log_10(x)\)approaches negative infinity while \(x^3\) remains finite.

Therefore, the range of the function \(y = x^3/log_10(x) is:\)

Range:\((-∞, +∞)\)

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Given a vector of length x=3a1 2a2 5a3 and a newly created coordinate system (b1,b2,b3) derived from (a1,a2,a3), the 3-2-1 sequence with angles of 30, 45, and 15 is used. The components of x in b1,b2,b3 is:  x_b = Rx(30°) * Ry(45°) * Rz(15°) * (3a1 + 2a2 + 5a3)

To find the components of vector x in the new coordinate system (b1, b2, b3) obtained from (a1, a2, a3) using the 3-2-1 sequence with angles 30°, 45°, and 15°, we can apply a series of rotation matrices.

First, we rotate the coordinate system around the z-axis (a3-axis) by 15°. This can be represented by the following rotation matrix:

Rz(15°) = | cos(15°) -sin(15°) 0 |

         | sin(15°) cos(15°)  0 |

         |   0         0        1 |

Next, we rotate the coordinate system around the new y-axis (b2-axis) by 45°. This rotation matrix is:

Ry(45°) = | cos(45°)   0   sin(45°) |

         |    0       1      0     |

         | -sin(45°)   0   cos(45°) |

Finally, we rotate the coordinate system around the new x-axis (b1-axis) by 30°. This rotation matrix is:

Rx(30°) = | 1    0         0      |

         | 0  cos(30°) -sin(30°) |

         | 0  sin(30°)  cos(30°) |

To find the components of vector x in the new coordinate system, we multiply the rotation matrices with vector x:

x_b = Rx(30°) * Ry(45°) * Rz(15°) * x

Given that x = 3a1 + 2a2 + 5a3, we substitute the values and perform the matrix multiplications:

x_b = Rx(30°) * Ry(45°) * Rz(15°) * (3a1 + 2a2 + 5a3)

Therefore, Calculating the matrix multiplication will yield the components of vector x in the (b1, b2, b3) coordinate system.

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