If
f
(
x
)
=
2
x
4
−
3
x
+
3
f(x)=2x
4
−3x+3, then what is the remainder when
f
(
x
)
f(x) is divided by
x
−
1
x−1?

Therefore , the solution of the given problem of equation comes out to be x = 11 and y =-9.

The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.

Here,

Given  :

=> -x-y=-2

=>  5x + 7y= 28

So ,

=>x = 2-y

thus,

=> 5(2-y) + 7y =28

=> 10 -5y + 7y =28

=> 10 -2y = 28

=> -2y = 18

=> y =-9

and

=> x  = 2 - (-9)

=> x  = 11

Therefore , the solution of the given problem of equation comes out to be x = 11 and y =-9.

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You can sand 14.4 yd² of wood in 3.2 hours.

A ratio is used to compare two or more like quantities or numbers with the same units. It is often written with a colon, and when used in words, we say the ratio of one quantity "to" the second quantity. A rate is a ratio that compares two different quantities which have different units.

9:2

x:3.2

therefore;

x = (3.2 x 9)/2

x = 28.8/2

x = 14.4 yd² of wood

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Answer:

7

Step-by-step explanation:

In order to find the answer to the equation, you must substitute the given values into the equation.

A^3 - C + B

We know that A = 3, B = 6, and C = 8

(3)^3 - (8) + (6)

9 - 8 + 6

1 + 6

7

Therefore , the solution of the given problem of domain is The range of f(x) is a subset of this range, which is the range of -3x-2 (-14,), after answering the given question.

A function's domain is the set of values that can be sent into it. This collection represents all x values in a function like f. (x). A function's range is the set of possible values that it can accept. This collection includes the values that the return statement when we enter an x value. Assume that x and y are indeed the independent and dependent variables of a function with the formula y = f(x). If a function f provides a way to generate a single value y successfully while using a value of x .

Here,

In this case, f(x)=-3x-2 x < 4

3/4x-1 x≥ 4

Domain

This range, which is the range of -3x-2 (-14,), is a subset of the range of f(x).

Therefore , the solution of the given problem is The range of f(x) is a subset of this range, which is the range of -3x-2 (-14,), after answering the given question.

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Two equations that have the same solution as the given equation are;

2.3p – 10.1 =  6.49p – 4

230p – 1010 = 650p – 400 – p

Both sides of an equation will remain equal, when both sides are

multiplied by the same amount.

The given equation: 2.3·p - 10.1 = 6.5·p - 4 - 0.01·p

Simplifying the above equation by collecting like terms gives;

2.3·p - 10.1 = 6.5·p - 0.01·p - 4 = 6.49·p - 4

2.3·p - 10.1 = 6.49·p - 4

Multiplying both sides of the original equation by 100 gives

100 × (2.3·p - 10.1) = 100 × (6.5·p - 4 - 0.01·p)

230·p - 1010 = 650·p - 400 - p

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Answer:

  x = 3

Step-by-step explanation:

You want to know the value of x, given that NM = 5x-1 and QP = 3x+5 in congruent triangles NMQ and QPN.

Corresponding parts of congruent triangles are congruent, so we have ...

  NM = QP

  5x -1 = 3x +5

  2x = 6 . . . . . . . . . . add 1-3x

  x = 3 . . . . . . . . . . divide by 2

Answer:

$30 per sweater is how much profit the store will make

Step-by-step explanation:

The cost of 1 sweater (for the store) is $6.

The store sells the sweater for $36 (504/14).

The store is making $30 per sweater.

Answer:

0.95meters

Step-by-step explanation:

last year her was 0.45m tall

this past year he is 0.5m

Total = 0.45 + 0.5 = 0.95

Answer: 0.95

Step-by-step explanation: add 0.45+0.5=0.95

Answer:

To graph an arithmetic sequence, you can start by plotting the first few terms of the sequence on the coordinate plane. The x-axis represents the term number, and the y-axis represents the value of the term.

In this case, we are given that the fourth term is 20 and the common difference is -1/5 times the first term. Let's say the first term is x. Then, the second term is x - (1/5)x = 4/5x, the third term is 4/5x - (1/5)x = 3/5x, and the fourth term is 3/5x - (1/5)x = 2/5x.

Therefore, the first four terms of the sequence are x, 4/5x, 3/5x, and 2/5x. If we plot these terms on the coordinate plane, we get the following graph:

(0, x)

(1, 4/5x)

(2, 3/5x)

(3, 2/5x)

This graph represents the first four terms of the arithmetic sequence. To find the fifth term, we can use the formula for the nth term of an arithmetic sequence: a_n = a_1 + (n - 1)d, where a_1 is the first term, d is the common difference, and n is the term number.

For this sequence, the fifth term is x + (-1/5)x = 4/5x. To find the sixth term, we can use the same formula: a_6 = x + (-1/5)x = 3/5x.

By continuing this process, we can plot the rest of the terms of the arithmetic sequence on the coordinate plane.

Step-by-step explanation:

The nearest integer that is a solution, gotten through graphing of the quadratic function x² + 2x - 2 = 5, is x = -4

Quadratic equations when plotted on a graph follows a parabolic path.

To plot the functions there will be table of values that is used in making the graph. The table of values is solved as follows

x² + 2x - 2 = 5 rearranging the equation will result to x² + 2x - 7 = 0

For x = -20,  y = (-20)² + 2 * -20 - 7 = 353

For x = 0,  y = (0)² + 2 * 0 - 7 = -7

For x = 20,  y = (20)² + 2 * 20 - 7 = 433

x      y

-20  353

0      -7

20    433

The graph is plotted and attached. From the graph the solution is

x = -3.828, to the nearest integer = -4

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Answer:

9.6 hours

Step-by-step explanation:

12×8 would equal the amount of hours it takes to complete the job in 12 days so you simply divide that number by 10 which will give you 9.6h

Answer:

6.67 hour per day

Step-by-step explanation:

If

=8 hours a day = 12 days

then

= ? = 10 days

= 10/12 × 8hours per

= 6.67 hours per day.

Answer:

7/12 (seven over twelve)

Step-by-step explanation:

1/3 -1/4 =4/12- 3/12=1/12

1/2+1/12=6/12+1/12=7/12

so the answer is 7/12

hopefully this helps

Answer:

17/5÷23/8= 1  21/115

The answer is 1  21/115

Answer:

The area of a rectangle is given by the formula:

area = length * breadth

In this case, the length of the rectangle is (x+2) cm and the breadth is (x) cm, so the area is:

area = (x+2) cm * (x) cm

= x^2 + 2x cm^2

We know that the area of the rectangle is 15 cm^2, so we can set up the following equation:

x^2 + 2x cm^2 = 15 cm^2

We can solve for x by using the quadratic formula:

x = (-2 +/- sqrt(4 - 41(-15))) / (2*1)

= (-2 +/- sqrt(64)) / 2

= (-2 +/- 8) / 2

= (-4, 2)

We have two solutions for x, so we need to consider both of them to find the dimensions of the rectangle.

If x=-4, then the length of the rectangle is (x+2) cm = (-4+2) cm = (-2) cm and the breadth is (x) cm = (-4) cm. Since the length and breadth of a rectangle must both be positive, this solution is not valid.

If x=2, then the length of the rectangle is (x+2) cm = (2+2) cm = 4 cm and the breadth is (x) cm = 2 cm. These dimensions give us a valid rectangle with an area of 15 cm^2.

The perimeter of the rectangle is the sum of all four sides, so the perimeter is 2 cm + 2 cm + 4 cm + 4 cm = 12 cm.

Therefore, the value of x that gives us a rectangle with an area of 15 cm^2 and a perimeter of 12 cm is x=2.

Answer:

n = -4/9

Step-by-step explanation:

first get rid of n on left side

-2 = 9n + 2

Get rid of 2 on right side

-4 = 9n

Make 9n into n

-4/9 = n

ans: n = -4/9

hope this helps :)

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

10,14,18

The equation of rational function is (c) g(x) = (2x + 4)/(x + 1).

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that,

The function g(x).

The graph of a function never touches the x = 1 line

At x = -1 there will be a vertical asymptote.

At x = -2 there will be a horizontal asymptote.

The equation of the function g(x) will be:

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

The equation of rational function is g(x) = (2x + 4)/(x + 1)

Therefore,  g(x) = (2x + 4)/(x + 1) is correct.

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No, 11^2 x 5^4 is not a factor of 11^3 x 5^4.

To see this, you can divide 11^3 x 5^4 by 11^2 x 5^4 and see that there is a remainder.

11^3 x 5^4 = (11 x 11 x 11) x (5 x 5 x 5 x 5)

= 121 x 625

= 75125

11^2 x 5^4 = (11 x 11) x (5 x 5 x 5 x 5)

= 121 x 625

= 75125

75125 / 75125 = 1 with a remainder of 0.

Therefore, 11^2 x 5^4 is not a factor of 11^3 x 5^4.

Answer:

x > -4

Step-by-step explanation:

This is solved just like as if it was an equation. Its a two-step equation (inequality) The only thing that's different is with an inequality, it is imperative that you flip the inequality symbol if you multiply or divide by a negative number.

Here, we'll subtract 4 from both sides. Then divide by -3 on both sides. Flip! the < to a >.

see image.

x > -4.

[tex]4-3x < 16[/tex]

[tex]4-3x-4 < 16-4\\ \\-3x < 12[/tex]

[tex]\frac{-3x}{-3} < \frac{12}{-3} \\ \\x > -4[/tex]

Important. See that we switched the inequality symbol from "<" to ">", and this is because the symbol of the coefficient of variable "x" changed from negative to positive when it was divided by "-3". This rule will always be true, any time the symbol of the variable changed, the inequality symbol changes.

If x >-4 is the correct answer, then substituting x by "-4" in the inequation should make the inequation return the same value on both sides of the inequality symbol (>).

[tex]4-3(-4) > 16\\ \\4-(-12) > 16\\ \\4+12 > 16\\ \\16 > 16[/tex]

That's correct! x > -4 is the correct answer.

The line segment AB is d = [tex]\sqrt{106}[/tex] in  length if (-5, 4) and (B), and A = (-5 , 0) .  A line segment is hence a section or component of a line with two endpoints.

A line segment in geometry is bordered by two separate points on a line. A line segment has two fixed or distinct endpoints, whereas a line has no endpoints and can stretch in both directions indefinitely. A line segment is hence a section or component of a line with two endpoints. A line segment, unlike a line, has a set length. Measuring the length of a line segment can be done using either metric measurements, such as millimeters or centimeters, or conventional measurements, such as feet or inches.

given

d = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]

(5 )2 + ( 9 ) 2 = d

d = 25 + 81

d = [tex]\sqrt{106}[/tex]

The line segment AB is d = [tex]\sqrt{106}[/tex] in  length if (-5, 4) and (B), and A = (-5 , 0)

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========================================================

Explanation:

The left-most rectangle spans from x = 0 to x = 2. It has base 2 and height 2, which means it has an area of 2*2 = 4 square units. Let A = 4 since we'll use it later.

The middle rectangle goes from x = 2 to x = 4. It has base 2 and height 3 (because it goes from y = 0 to y = -3). The area is B = 2*3 = 6

Draw a vertical line through 6 on the x axis. This forms the final rectangle we need. It has base 2 (because it goes from x = 4 to x = 6) and height 5. The area is C = 2*5 = 10.

The small sliver to the right of x = 6 is ignored completely.

--------------------

Summary so far:

Those represent the areas of the rectangles from left to right. We ignore the portion to the right of x = 6.

Since rectangle B is below the x axis, we treat this as a negative area, or we subtract off this area. The positive areas of rectangles A and C are added.

So,

A-B+C = 4-6+10 = 8 is the final answer

We can write [tex]\displaystyle \int_{0}^{6}f(\text{x})d\text{x} = \boldsymbol{8}[/tex]

Total Liabilities  + Equity = $220,000.

Total Assets = $220,000.

What is Ratio Analysis and Balance Sheet?

The relationship between the two separate components is established through ratio analysis. Utilizing figures from the income statement, balance sheet, statement of cash flows, and other financial statements, it is used to assess the company's financial performance.

One of a company's financial statements that is created at the end of the year is the balance sheet. It establishes the balance of a company's assets, liabilities, and stockholder equity at the end of the fiscal year.

Here we are given in the Question,

Assets

Cash = $45,000

Inventory = $41,000

Property = $134,000

Liabilities

Notes  = $55,000

Wages  = $56,000

and

Equity

Stock = $50,000

Investment = $59,000

Total Liabilities  + Equity = ( Notes + wages ) + (stock + Investment)

Total Liabilities  + Equity = ( $55,000 + $56,000) + ($50,000 + $59,000)

Total Liabilities  + Equity = $220,000.

Total Assets = Cash + Inventory + Property

Total Assets = $45,000 + $41,000 + $134,000

Total Assets = $220,000

Therefore,

Total Liabilities  + Equity = Total Assets.

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The modifications and their effects on the ecosystem include:

With the construction of the Los Angeles aqueduct, water was transported to the west such that many desert regions there became lush urban areas and farmlands.

Large high ways and the damming of the Colorado River did not have such a good impact however, as they both led to runoff and to water bodies in the Owen valley drying up.

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The length of x of a diagonal support is 13.8 feet.

The hypotenuse of a triangle is the length of the longest side of the triangle. So that it is always opposite to the measure of the largest angle of a triangle.

In the question given, divide the length of the footbridge into 2 parts.

So that,

Half of the footbridge = 25/ 2

                     = 12.5 ft

So that applying the appropriate trigonometric function to determine the value of x using any of the congruent triangles. We have;

Sin θ = opposite/ hypotenuse

Sin 65 = 12.5/ x

x = 12.5/ Sin 65

  = 12.5/ 0.90631

x = 13.792 feet

The length x of a diagonal support is 13.8 feet.

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Answer: To determine which store has the cheaper steak, you need to compare the price per pound of steak at each store. To do this, divide the total price by the number of pounds of steak at each store.

At Store A, the price per pound of steak is $6.38 because 25.50 / 4 = <<25.50/4=6.375>>6.375.

At Store B, the price per pound of steak is $6.71 because 40.25 / 6 = <<40.25/6=6.708>>6.708.

Therefore, Store A is cheaper because it has a lower price per pound of steak. The correct answer is Store A.

Step-by-step explanation:

The unbiased estimator of 1/p does not exist.

An estimate that deviates from the genuine population value is said to be biased. If the kind and extent of the bias are known, a biased sample may still be informative. When a sample's value matches the actual value of a population parameter, that is an unbiased estimator.

Given:

If the random variable X has the binomial.

1/p = 1 /{1-(1-p)} = 1 + (1-p) + (1-p)²/2! + ....

And let an unbiased estimator of 1/p exist.

[tex]\sum^n_k_=_0T(k)(^n_k)p^k(1-p)^k[/tex] = 1 + (1-p) + (1-p)²/2! + ....

The above series is finite on the LHS and infinite power series on the RHS.

That is contradiction.

The basic idea is that an unbiased estimator of 1/p would have to have the property that its expected value as a function of p would have to tend to infinity as p tends to 0.

But since Ep[U(x)] is bounded above by some function of n that is independent of p, no such estimator can exist.

Therefore, the unbiased estimator 1/p can not exist.

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Answer: q1=11 q2=15 q3=20

Step-by-step explanation:

Answer:

Step-by-step explanation:

Certainly! To set up the problem, we can consider the owner-manager's utility as a function of two variables: income (profit) and charitable contributions or civic expenditures. Let's call these variables x and y, respectively.

The owner-manager utility is given by the function U(x,y), where x is the income (profit) and y is the charitable contributions or civic expenditures.

The cost of obtaining this utility is given by the function C(x,y), where x is the income (profit) and y is the charitable contributions or civic expenditures.

To find the lowest possible cost at which the owner-manager can obtain a specific level of utility, we can use the following optimization conditions:

The cost function C(x,y) should be minimized subject to the constraint U(x,y) = k, where k is the specific level of utility that the owner-manager wishes to achieve.

The first-order necessary conditions for a minimum are:

∂C/∂x = λ ∂U/∂x

∂C/∂y = λ ∂U/∂y

where λ is a Lagrange multiplier.

These conditions are known as the Karush-Kuhn-Tucker (KKT) conditions.

These optimization conditions differ from the utility-maximizing conditions in that we are minimizing the cost function instead of maximizing the utility function. In addition, we have the constraint U(x,y) = k, which means that we are trying to achieve a specific level of utility rather than trying to maximize it.

Answer:

Step-by-step explanation: 55