Help me pls with this! :)

The remainder and factor of the given algebraic expression \(\frac{5x^{5} -4x^{3} -11x^{2} +12}{x+1}\) is \((5x^{4} -5x^{3} +x^{2} -12x+12)(x+1)\) and \(0\)

As per the given question, we are supposed to find out the factor and remainder of the given algebraic expression \(\frac{5x^{5} -4x^{3} -11x^{2} +12}{x+1}\) using remainder theorem concept.

Before solving this, we need to know the concept of remainder theorem.

According to which "When a polynomial is divided by a linear polynomial, the remainder theorem is used to get the remaining. We are aware that long division of polynomials can be used to find the remainder after dividing one polynomial by another. The remainder can instead be discovered using the remainder theorem."

Hence using the same concept we can conclude that the factors are \((5x^{4} -5x^{3} +x^{2} -12x+12)(x+1)\) and remainder is \(0\)

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Answer:

40.50

Step-by-step explanation:

you take 600.00 and multiply it by 2.25 you will get 1,350 divide 1,350 by 100 you will get 13.50 multiply 13.50 times 3 you get 40.50 that is interest for 3 years

The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.

Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.

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The length of the rectangular garden given the area and width is 8/7 miles

A rectangle is a form of quadrilateral having opposing sides parallel and four right angles. The area of a rectangle can be calculated by multiplying the length by width.

Area of a rectangular garden = length × width

16 = x × 14

16 = 14x

x = 16 / 14

x = 8/7 miles

Therefore, the length of the rectangular garden given the area and width is 8/7 miles.

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Answer:

Angles 1 and 8 because they are vertically aline

Answer:

Angles 1 and 8

Step-by-step explanation:

i took the test

Answer:

0.5

Step-by-step explanation:

2.2 is approximately 2.

2 divided by 4 is 0.5, so 2.2 divided by 4 must be close to 0.5.

Answer: 0.5

Answer:

4005

Step-by-step explanation:

3,998 - (-7) = ?

Two negative signs will make a positive sign.

3,998 - (-7) = 3998 + 7 = 4005

So, the answer is 4005

the denominator will be zero when. \(x=-2\)or \(x=-7.\) Therefore, the domain of the expression is all real numbers except \(x=-2\) and \(x=-7\).

In mathematics, factoring refers to the process of finding the factors of a given number or expression. Factors are numbers or expressions that can be multiplied together to obtain the original number or expression. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because these are the numbers that can be multiplied in pairs to obtain 12 (e.g. 2 x 6 = 12).

In algebra, factoring involves breaking down an algebraic expression into simpler expressions that can be multiplied together. This is done by finding common factors or using techniques such as difference of squares, perfect squares, or grouping. Factoring is an important tool in algebra, as it can help simplify complex expressions and solve equations.

To simplify a rational expression, follow these steps:

Step 1: Factor both the numerator and denominator if possible. For example, in the expression you provided, the numerator can be factored as\((2x+5)(x+4)\)and the denominator can be factored as \((2x+15)(x+2)\).

Step 2: Cancel out any common factors in the numerator and denominator. In this case, both the numerator and denominator have a common factor of (2x+5), which can be cancelled out.

Step 3: Simplify the remaining expression. After cancelling out the common factor, the simplified expression becomes:

\((2x+5)(x+4) / (2x+15)(x+2) = (x+4) / (x+2)(2x+15)\)

Domain restrictions occur when a value of x makes the denominator equal to zero, because division by zero is undefined. In this case, the denominator will be zero when x=-2 or x=-7. Therefore, the domain of the expression is all real numbers except x=-2 and x=-7.

It is important to identify any domain restrictions before simplifying a rational expression to ensure that the final expression is valid for all values of x in its domain.

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Answer:

16/33

Step-by-step explanation:

Tổng của cả 4 tấm thẻ là một số lẻ khi:

Có 1 thẻ là lẻ, 3 thẻ còn lại là chẵn, có: 6C1.5C3=60 cách

Có 3 thẻ là lẻ, 1 thẻ là chẵn, có: 5C1.6C3=100 cách

Suy ra có 160/11C4=16/33 cách

The z-value obtained from the test was 2.25, and the p-value was less than 0.02.

What is probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

Based on the experiment described, a two-sample z-test for the difference in proportions was conducted to determine if there is a significant difference between the proportion of rats that succeeded in the maze after being given substance m and the proportion of rats in the control group that succeeded in the maze.

This suggests that the difference in proportions between the two groups is statistically significant at the 0.05 level of significance (since the p-value is less than 0.05).

In other words, the results of the experiment suggest that substance m may be effective in helping to restore memory, as a greater proportion of rats in the substance m group succeeded in the maze compared to the control group. However, it's important to note that further experiments and analyses would be necessary to confirm these findings and determine the extent of the effect of substance m on memory restoration.

Therefore, The z-value obtained from the test was 2.25, and the p-value was less than 0.02.

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Answer:

hope this helps you

Note that the roots of the equation Unequal and rational (Option D)

The roots of the equation   (x - 3)² = 4 can be found by taking the square root of both sidesof the equation.

x - 3 = ±√4

⇒ x - 3 = ±2

Solve for x

For the positive square root.

x - 3 = 2

x = 2 + 3

x = 5

For the negative square root.

x - 3 = -2

x = -2 + 3

x = 1

Since the equation has two roots, x = 5 and x = 1. These roots are unequal and rational. (Option D)

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Full Question:

Although part of your question is missing, you might be referring to this full question:

The roots of the equation (x - 3)² = 4 are

A.Unequal and irrational.

B.Equal and rational.

C.  Equal and irrational.

D.  Unequal and rational.

Answer:

It's option B, (f • g)(x) = 3x^3 + 6x^2 - 5x - 10

Step-by-step explanation:

In this problem, we are dealing with a branch of functions called composite functions. What the difference is between normal and composite functions is that we instead of defining a value for f(x), take two functions, f(x) and g(x), in the form of f and g. For instance, h(x) = g.

• Take the products of both functions.

f(x)g(x) = 3x²+5 • x-2

• Next, expand the functions. We expand by combining like terms.

= 3x^3 - 6x^2 + 5x - 10

Since the function cannot be simplified further, this leads to option B being our answer.

Hope this helps!

Answer: False, A map is a function that takes a point as an input and produces a point as an output

Step-by-step explanation:

The system of inequalities to represent this real-world scenario is

\(\left \{ {{x + y \leq 450} \atop {7x + 4y \leq 1150}} \right.\)

Given data :

Let  x be the number of adults and y be the number of campers.

There are rooms for 450 people, so

x+y≤450.

Each adult costs $7, then x adults cost $7x.

Each camper costs $4, then y campers cost $4y.

There is a maximum budget of $1,150, so

7x+4y≤1,150

Hence, you get the system of two inequalities:

 \(\left \{ {{x + y \leq 450} \atop {7x + 4y \leq 1150}} \right.\)

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Given, the circumference of the circle, C=12π.

The circumference of a circle can be expressed as,

Here, r is the radius of the circle.

Put C=12π in the above equation to find radius r.

The diameter of the circle is,

Therefore, the radius of the circle is 6 and the diameter of the circle is 12.

Answer:

C

Step-by-step explanation:

-27 -(-38)

when you subtract a negative it turns into addition

-27+38

Answer:

c) -27 +38

Step-by-step explanation:

the reason is because when a number is in parentheses, especially if they are negatives, they become the opposite which in this case is + so -(-38) can be the same as saying -1 × -38 and since they are both negatives, the sign becomes positive and it's just 38 while the 27 isn't affected because there's nothing in front of it I hope I helped.

Solution :

Demand for cola : 100 – 34x + 5y

Demand for cola : 50 + 3x – 16y

Therefore, total revenue :

x(100 – 34x + 5y) + y(50 + 3x – 16y)

R(x,y)  = \($100x-34x^2+5xy+50y+3xy-16y^2$\)

\($R(x,y) = 100x-34x^2+8xy+50y-16y^2$\)

In order to maximize the revenue, set

\($R_x=0, \ \ \ R_y=0$\)

\($R_x=\frac{dR }{dx} = 100-68x+8y$\)

\($R_x=0$\)

\($68x-8y=100$\)  .............(i)

\($R_y=\frac{dR }{dx} = 50-32x+8y$\)

\($R_y=0$\)

\($8x-32y=-50$\)  .............(ii)

Solving (i) and (ii),

4 x (i)    ⇒       272x - 32y = 400

     (ii)   ⇒   (-)     8x - 32y = -50  

                        264x        = 450

∴   \($x=\frac{450}{264}=\frac{75}{44}$\)

     \($y=\frac{175}{88}$\)

So, x ≈  $ 1.70      and    y = $ 1.99

    R(1.70, 1.99) = $ 134.94

Thus, 1.70 dollars per cola

          1.99 dollars per iced ted to maximize the revenue.

Maximum revenue = $ 134.94

There are 4 cups of brown sugar are required for every 12 cups of white sugar.

A recipe calls for 2 cups of brown sugar for every 6 cups of white sugar. We can set up a proportion to find the relationship between the two quantities:

2 cups brown sugar / 6 cups white sugar = x cups brown sugar / 12 cups white sugar

To find the number of cups of brown sugar required for 12 cups of white sugar, we can cross-multiply and then solve for x:

2 cups brown sugar × 12 cups white sugar = 6 cups white sugar × x cups brown sugar

24 cups brown sugar = 6x cups brown sugar

x = 24/6

x = 4

So, 4 cups of brown sugar are required for every 12 cups of white sugar.

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Answer:

Tilt your head back and allow your mouth to hang open widely.

Contract the back of the throat and breathe deeply through your mouth.

Inhale and exhale completely while relaxing the shoulders.

When the yawn comes “reach and extend into it” to stretch the jaw muscles.

Step-by-step explanation:

Answer:

7n-10

Step-by-step explanation:

=(5n-3) - (-2n) -7 [Bracket Opens]

=5n - 3 +2n -7 [- × - = +]

=7n - 10 [ addition]

Answer:

576cm³

Step-by-step explanation:

8×6=48

48×12=576

A graph of the given piecewise-defined function is shown in the image below.

In Mathematics and Geometry, a piecewise-defined function simply refers to a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of this piecewise-defined function, we can reasonably infer and logically deduce that it is constant over several intervals or domains such as x > 2 and x < -2.

In conclusion, this piecewise-defined function has a removable discontinuity.

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Based on the calculations using unit pricing, Toilet paper B has a lower unit price and is the better deal between the two. Customers will save more money if they purchase toilet paper B rather than toilet paper A because the price per mega roll is lower. (option b)

Saving money while shopping is one of the best ways to reduce your expenses and have more disposable income for other things. Unit pricing is a pricing system that displays prices in standard units, allowing customers to compare prices across different brands and package sizes and save money. To determine which toilet paper deal is better, we can use the unit price method, which divides the price by the number of units in the package. The toilet paper with the lower unit price is the better deal.
The formula for unit pricing is as follows:
Unit price = total price ÷ number of units
Using the above formula, we can calculate the unit price of toilet paper A and toilet paper B as follows:
For Toilet paper A:
Unit price = $4.59 ÷ 6 mega rolls
Unit price = $0.765 per mega roll
For Toilet paper B:
Unit price = $9.02 ÷ 12 mega rolls
Unit price = $0.751 per mega roll
Therefore, based on the calculations, Toilet paper B has a lower unit price and is the better deal between the two. Customers will save more money if they purchase toilet paper B rather than toilet paper A because the price per mega roll is lower. (option b)
Unit pricing is a great way to compare prices, and consumers should always use it to determine the better deal between two products, as this will help them save money and stick to their budget.

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The value of the variable a in the equation is a = 10

A linear equation is any equation with a constant rate

The equation is given as

5(a - 5) = 25

Open the brackets in the above equation

So, we have the following equation

5a - 5 * 5 = 25

Evaluate the products in the above equation

So, we have the following equation

5a - 25 = 25

Add 25 to both sides of the equation

So, we have the following equation

5a - 25 + 25 = 25 + 25

Evaluate the sum in the above equation

So, we have the following equation

5a = 50

Divide both sides by 5

So, we have

5a/5 = 50/5

Evaluate the quotient

a = 50/5

Evaluate the quotient

a = 10

Hence, the solution to the equation is a = 10

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The solution of the given quadratic equation -5 = -36 / m + m is,

 m = - 9 or  m = 4

The given equation is

-5 = -36 / m + m

After re arranging it we get,

m² + 5m - 36 = 0

This is nothing but quadratic equation,

Since we know that,

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:

ax² + bx + c = 0

So now we can write,

⇒ m² + 9m - 4m - 36 = 0

⇒ m(m + 9) - 4(m + 9) = 0

⇒ (m + 9)(m - 4) = 0

Therefore,

⇒ (m + 9) = 0 or (m - 4) = 0

⇒ m = - 9 or  m = 4

Thus,

The solution of the given expression is

m = - 9 or  m = 4

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The value of angle LAF in the intersecting chords is determined as  104⁰.

The value of angle LAF is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.

m∠LAF = ¹/₂ (arc LF + arc YS)

From the diagram, we have arc LF = 160⁰ and YS = 48⁰

m∠LAF = ¹/₂ (160 + 48)

m∠LAF = 104⁰

Thus, the value of angle LAF is calculated by applying intersecting chord theorem.

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Alternatively, the gcf of 12 and 56 can be found using the prime factorization of 12 and 56:

The prime factorization of 12 is: 2 x 2 x 3.

The prime factorization of 56 is: 2 x 2 x 2 x 7.

The prime factors and multiplicities 12 and 56 have in common are: 2 x 2.

2 x 2 is the gcf of 12 and 56.

gcf(12,56) = 4.