(3)/(x^(2)-2x-8)-(4)/(x^(2)-16) Simplify. Assume that all variables result in nonzero denominators.

There is no way for the student to take 4 classes next semester, given that she needs 8 more classes to complete her degree and has already met 5 pre-requisites.

Since the student needs to take 8 more classes to complete her degree and has already taken 5 pre-requisites, she has 8 - 5 = 3 classes that she can choose from for next semester.

To calculate the number of ways she can take 4 classes next semester, we can use the combination formula:

nCr = n / (r × (n-r))

where n is the number of classes she can choose from (which is 3), and r is the number of classes she will take next semester (which is 4).

Plugging in the values, we get:

3C4 = 3 / (4 × (3-4)) = 0

Since we cannot choose 4 classes from a set of 3 classes, the answer is 0.

Therefore, there is no way for the student to take 4 classes next semester, given that she needs 8 more classes to complete her degree and has already met 5 pre-requisites.

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7 x 4 = 28

than you need to do y + 5x

than you get you answer 6

The polynomial that must be added to x^(2)-2x+6 is 2x^(2) + 9x - 6.

To find the product of the two polynomials (2x^(4)y)(3x^(5)y^(8)), we need to use the distributive property and combine like terms.

The distributive property states that a(b+c) = ab+ac. So, we can distribute the first polynomial to each term in the second polynomial:

(2x^(4)y)(3x^(5)y^(8)) = (2x^(4)y)(3x^(5)) + (2x^(4)y)(y^(8))

Next, we can combine like terms by adding the exponents of the variables:

= 6x^(4+5)y^(1+8)

= 6x^(9)y^(9)

So, the product of the two polynomials is 6x^(9)y^(9).

To find the polynomial that must be added to x^(2)-2x+6 so that the sum is 3x^(2)+7x, we can set up an equation:

x^(2)-2x+6 + (a+bx+cx^(2)) = 3x^(2)+7x

Then, we can rearrange the equation to solve for the polynomial:

a+bx+cx^(2) = 3x^(2)+7x - x^(2) + 2x - 6

a+bx+cx^(2) = 2x^(2) + 9x - 6

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The total yards gained by Jordan's team is 4.

What is Expression ?

Mathematical statements called expressions must contain a minimum of two terms with either numbers, variables, or both, joined by an operator. The four different types of mathematical operators are addition, subtraction, multiplication, and division. For instance, the expression x + y is an expression where x and y are terms with an addition operator between them. Mathematical expressions can be divided into two categories: algebraic expressions, which include both numbers and variables, and numerical expressions, which solely contain numbers.

On first day, Jordan's football team gained 12 yards.

On second day, Jordan's football team lost 8 yards.

So, The total yards(net) would be :

= total yards gained by team - total yards lost by team

=  12 - 8

= 4 yards.

Here, total yards gained by team is the first expression while total yards lost by team is the second expression.

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Expressions A, B, and F are equivalent to (a²-16(a+4)).

Equivalent is a term that means equal in value, measure, force, effect, or significance. It can be used to describe two or more things that are of the same value or having the same characteristics. For example, a 1:1 ratio is said to be equivalent because it has the same value on both sides. Equivalent can also mean having the same or similar effect, such as two different treatments for a disease that have the same outcome.

The expressions A, B, and F are equivalent to (a²-16(a+4)). Expression A is equal to a² - 16a - 64. This expression can be rewritten as a³ - 64, which is equal to A. Expression B is equal to (a - 4)³. This expression can be rewritten as a³ - 64, which is equal to A. Expression F is equal to [(a)²-(4^2)](a+4). This expression can be rewritten as (a² - 16)(a+4), which is equal to A. Therefore, expressions A, B, and F are equivalent to (a²-16(a+4)).

Expression C is equal to (a+4)³, which is not equivalent to (a²-16(a+4)). Expression D is equal to (a+4)²(a-4), which is not equivalent to (a²-16(a+4)). Expression E is equal to (a-4)²(a+4), which is not equivalent to (a²-16(a+4)). Expression G is equal to(a-4)(a+4)(a+4), which is not equivalent to (a²-16(a+4)). Therefore, expressions C, D, E, and G are not equivalent to (a²-16(a+4)).

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Plotting the data and visually examining the connection between x and y equation is often the best method for identifying which equation best describes the line of best fit.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions.

Based on the above equations, y = x + 5 or y = x - 5 would be the most plausible contenders. Both of these equations have the typical slope for a linear connection, which is a straight line slope of 1.

While the y-intercept of the equation y = x + 15 has a significantly bigger value than would be predicted based on the other possibilities, the slope of the equation is 1. Similar to that, the slope of the equation y = 2x - 15 is 2.

Plotting the data and visually examining the connection between x and y is often the best method for identifying which equation best describes the line of best fit.

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The largest possible value x could take given that it must be an integer for x < 2 is 1.

The key distinction between an inequality and an equation is that an inequality describes a connection of inequality between two expressions, whereas an equation expresses equality between two expressions. In other words, an inequality shows that one expression is more or less than the other expression, but an equation shows that two expressions have the same value.

The highest number x might have is 1 if x must be an integer and x 2. This is due to the fact that any number higher than one would break the inequality x 2, and any number between one and two that is not an integer would also violate the stipulation that x must be an integer.

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The Surface Area of Container is 954. 56 inch².

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. Square units are used to measure it as well.

For each three-dimensional geometrical shape, surface area and volume are determined. The area or region that an object's surface occupies is known as its surface area.

As, we Know the Surface Area of Cylinder

= 2πr² + 2πrh

Radius of the base = 8 inches

Height of the cylinder = 11 inches.

Now, putting the values we get

= 2πr² + 2πrh

= 2 x 3.14 x 8 x 8 + 2 x 3.14 x 8 x 11

= 401.92 + 552.64

= 954. 56 inch²

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The graph of the quadratic function y = 1.5x² + 4x - 2 is given by the image shown at the end of the answer.

The function for this given problem is defined as follows:

y = 1.5x² + 4x - 2.

a 1.5, b 4, c -2.

By Solving the equation we get these values,

x = -3.09, hence function passes through the point (-3.09, 0).

x = 0.43, hence function passes through the point (0.43, 0).

The y-intercept of this function is given by coefficient c = -2, hence the function also passes through the point (0, -2).

The x-coordinate vertex is given as follows:

x = -b/2a = -4/3 = -1.33.

Hence the y-coordinate vertex is of:

y = 1.5(-1.33)² + 4(-1.33) - 2 = -4.67.

Missing Information

The problem asks for the graph of the following function is given below:

y = 1.5x² + 4x - 2.

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Answer:

C

Step-by-step explanation:

The equation that shows the whole amount of pizza Miah ate on Saturday is 3/32 of the whole pizza

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.

This word problem are interpreted to mathematical equation

The left over is calculated is 3/8

therefore 5/8 of the pizza is left for Saturday

On Saturday she ate 1/4 of the pizza

= 1/4 × 3/8

= 3/32

therefore Miah ate 3/32 of the whole pizza on Saturday.

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There is only one solution for this equation. v = 31/4 is the only solution to this equation.

To solve for v in the equation (3)/(4v)+(7)/(v)=1, we need to get a common denominator and then solve for v.

Step 1: Get a common denominator. The common denominator for 4v and v is 4v. So, we will multiply the second fraction by 4/4 to get a common denominator:
(3)/(4v)+(7*4)/(v*4)=1

Step 2: Simplify the fractions:
(3)/(4v)+(28)/(4v)=1

Step 3: Combine the fractions:
(3+28)/(4v)=1

Step 4: Simplify the numerator:
(31)/(4v)=1

Step 5: Cross-multiply to solve for v:
31=4v

Step 6: Divide both sides by 4 to get v:
v=31/4

The solution is v=31/4.

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Nicole has 8 nickels and 7 dimes.

A system of equations is simply two or more equations that share the same variables.

Let's use a system of equations to solve this problem:

Let x be the number of nickels, and y be the number of dimes.

From the problem, we know that:

x + y = 15 (equation 1) (the total number of coins is 15)

0.05x + 0.1y = 1.1 (equation 2) (the total value of the coins is $1.10)

To solve for x and y, we can use substitution or elimination. Let's use elimination:

Multiply equation 1 by 0.1:

0.1x + 0.1y = 1.5 (equation 3)

Subtract equation 3 from equation 2:

0.05x = 0.4

x = 8

Substitute x = 8 into equation 1:

8 + y = 15

y = 7

Therefore, Nicole has 8 nickels and 7 dimes.

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Milo is 8.09 miles from the dock.

Here we can use the Law of Cosines,

which states that c² = a² + b² - 2abcos(C),

Where c is the side opposite the angle C in a triangle.

Call the distance from the dock to the point where Milo changes direction "a", the distance Milo sails in the new direction "b", and the angle between these two sides "C".

We know that a = 7 miles and b = 4 miles.

To find C, we can use the fact that Milo changes direction by 5π/36 radians.

Since he turned to the right, we can say that he turned by,

⇒ 360 - 5π/36 = 355π/36 radians.

This is the angle between the two sides of the triangle.

Now we can plug these values into the Law of Cosines to find the distance from Milo to the dock:

⇒ c² = a² + b² - 2abcos(C)

⇒ c² = 7² + 4² - 2(7)(4)cos(355π/36)

⇒ c² = 49 + 16 - 56cos(355π/36)

⇒ c² = 65.47

Taking the square root of both sides, we get:

c = 8.09 miles (rounded to 2 decimal places)

Therefore, Milo is 8.09 miles from the dock.

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Answer:

The area of the whole rectangle is 28 cm^2

Step-by-step explanation:

since both triangles are congruent, they have the same area. 14 x 2 = 28

Answer: 515,783

Step-by-step explanation:  f(x)= a(1+r)^x      450,000(1+0.023)^6

The given set of vectors in R4 is linearly independent and  the vector u as a linear combination of the vectors v1, v2, and v3  can be written as u = (7,12,22)

a) To determine if the set of vectors in R4 is linearly independent or linearly dependent, we can use the rank of the matrix formed by these vectors. If the rank of the matrix is equal to the number of vectors, then the set is linearly independent. Otherwise, it is linearly dependent.

First, let's form the matrix using the vectors:

| 1 0 -1 0 |
| 1 1 0  2 |
| 0 3  1 -2 |
| 0 1 -1  2 |

Next, let's find the rank of the matrix. We can do this by using Gaussian elimination to reduce the matrix to row echelon form:

| 1 0 -1 0  |
| 0 1  1 -2 |
| 0 0  4 -6 |
| 0 0  0  4 |

The rank of the matrix is 4, which is equal to the number of vectors. Therefore, the set of vectors is linearly independent.

b) To write the vector u as a linear combination of the vectors v1, v2, and v3, we need to find the scalars a, b, and c such that:

u = av1 + bv2 + cv3

This gives us the following system of equations:

10 = 2a + b - 2c
1 = 3a + 2b + 2c
4 = 5a + 4b + 3c

We can use Gaussian elimination to solve this system of equations:

| 2  1 -2 | | a | = | 10 |
| 3  2  2 | | b | = |  1 |
| 5  4  3 | | c | = |  4 |

After reducing the matrix to row echelon form, we get:

| 1 0  1 | | a | = | 2 |
| 0 1 -2 | | b | = | 3 |
| 0 0  0 | | c | = | 0 |

From the third equation, we can see that c can be any value. Let's choose c = 0. Then, from the first two equations, we get:

a = 2
b = 3

Therefore, the vector u can be written as a linear combination of the vectors v1, v2, and v3 as follows:

u = 2v1 + 3v2 + 0v3

u = (2)(2,3,5) + (3)(1,2,4) + (0)(-2,2,3)

u = (4,6,10) + (3,6,12) + (0,0,0)

u = (7,12,22)

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LHS ≠ RHS and the equation is not an identity.

9. Simplify each expression:
a. √(1 + cos 76° / 2)
b. (sin 158.2°) / (1 + cos 158.2°)
10. Verify that each equation is an identity.
a. sin 2x / 2 sin x = cos^2 x/2 – sin^2 x/2
b. tan θ/2 = csc θ – cot θ

Answer:
9. a. √(1 + cos 76° / 2) = √(1 + 0.2419 / 2) = √(1 + 0.12095) = √(1.12095) = 1.0589
b. (sin 158.2°) / (1 + cos 158.2°) = (0.12088) / (1 + (-0.9927)) = 0.12088 / 0.0073 = 16.566
10. a. sin 2x / 2 sin x = cos^2 x/2 – sin^2 x/2
LHS = sin 2x / 2 sin x = 2 sin x cos x / 2 sin x = cos x
RHS = cos^2 x/2 – sin^2 x/2 = (cos x + sin x)(cos x - sin x) / 4 = (1)(cos x - sin x) / 4 = cos x - sin x / 4
Therefore, LHS ≠ RHS and the equation is not an identity.
b. tan θ/2 = csc θ – cot θ
LHS = tan θ/2 = sin θ/2 / cos θ/2
RHS = csc θ – cot θ = 1 / sin θ - 1 / cos θ = (cos θ - sin θ) / (sin θ cos θ)
Therefore, LHS ≠ RHS and the equation is not an identity.

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The measure of center that would best summarize the plot is given as follows: Median of 11.

The measure of variability is given as follows: IQR of 1.5.

A box and whisker plots shows these five features from a data-set, listed as follows:

From the plot, these features are given as follows:

The median is the best measure of center of the data-set.

There is an outlier at 16, hence the best measure of variability is the IQR, given by the difference between the Q3 and the Q1, hence:

IQR = 11.5 - 10

IQR = 1.5.

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The solution of linear equations is (x, y) = (-0.8905, 0.708).

To solve this system of linear equations by elimination, first multiply both equations by the same number so that when you add the equations together, one of the variables is eliminated. In this case, we'll multiply the first equation by 3 and the second equation by 8.

8(8x+3y=-5)

3(3y=x+4)

24x + 9y = -15

24y = 8x + 32

Now add the two equations together:

24x + 24y = -15 + 32

24x + 24y = 17

Simplifying this equation, we get:

24y = 17

y = 17/24

y = 0.708

Now, plug in the value of y into one of the original equations to solve for x. We'll use the first equation:

8x + 3(0.708) = -5

8x + 2.124 = -5

8x = -7.124

x = -7.124/8

x = -0.8905

Therefore, the solution to the system of linear equations is (x, y) = (-0.8905, 0.708).

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Check the picture below.

[tex]\boxed{4} \\\\\\ (x+3)^2~~ = ~~[(x-1)+10](x-1)\implies x^2+6x+9~~ = ~~(x+9)(x-1) \\\\\\ x^2+6x+9~~ = ~~x^2+8x-9\implies 6x+9=8x-9\implies 9=2x-9 \\\\\\ 18=2x\implies \cfrac{18}{2}=x\implies 9=x[/tex]

Answer:

Step-by-step explanation:

According to the Synthetic Division, the Quotient is equal to  7x² -4x + 5 and the Remainder is equal to 8.

Synthetic division can divide two polynomials more quickly than the standard long division algorithm.

With this method, the dividend and divisor polynomials are reduced to a set of numerical numbers.

Given:

(7x³-25x² +17x -7) ÷ (x-3).

So, Synthetic Division for this is as follows:                                    

                      (x-3) | (7x³-25x² +17x -7) | 7x² -4x + 5

                                                    7x³-21x²

                                                 _________

                                                           -4x² + 17x

                                                           -4x² + 12x        

                                                    _______________

                                                                        5x - 7              

                                                                        5x - 15

                                                                      ________

                                                                               8

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The correct equivalent form of 8⁵/8² is Adam made an error in step 2. The denominator should be 1, not 8¹. Option B is correct.

In step 2, Adam used the property of exponents that states: [tex]a^{(m-n)}[/tex] = [tex]a^{m}[/tex] / [tex]a^{n}[/tex]. However, he made a mistake by writing 8¹in the denominator instead of 1.

The correct expression after step 2 should be:

[tex]8^{5-2}[/tex] /1 = 8³

Then, in step 3, Adam used the property of exponents that states: [tex]a^{m}[/tex] / a =   [tex]a^{m-1}[/tex]. This step is correct, and the expression becomes:

[tex]8^{3/8}[/tex]

Finally, in step 4, Adam simplified the expression by dividing 8³ by 8². This step is also correct, and the expression simplifies to:

8¹ = 8

Therefore, the correct equivalent form of 8⁵/8² is 8.

Hence, B. Adam made an error in step 2. The denominator should be 1, not 8¹ is the correct option.

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--The given question is incomplete, the complete question is

"Adam is rewriting the expression 8^5/8^2 in equivalent form. His steps are shown: step 1: 8^5/8^2, step 2:  8^(5-2)/8^1, step 3: 8^3/8, step 4: /8^2. which statement describes the step and the error Adam made in that step? A) Adam made an error in step 2. The exponent in the numerator should be 5+2 B) Adam made an error in step 2. The denominator should be 1, not 8^1 C)  Adam made an error in step 3. The value of 8^1 is 1, not 8."--

According to the question the solution to the inequality is x < 6.

Inequality is the unequal distribution of resources, rights, and opportunities among individuals or groups in a society. It is a form of systemic injustice that can take on many forms, such as economic, social, and political. Economic inequality is when people have unequal access to resources such as wealth, income, and education; social inequality is when people have unequal access to social opportunities and resources such as political power, public services, and health care; and political inequality is when people have unequal access to the political process and decision-making, such as voting rights and other forms of representation.

To solve this inequality, we need to isolate the variable on one side. First, let's subtract 8 from both sides:
-4x + 8 > -16
-4x > -24
Now, divide both sides by -4:
-4x/-4 > -24/-4
x < 6
Therefore, the solution to the inequality is x < 6.

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Answer:

Step-by-step explanation:

lol sorry I know it but don’t know how up to right it sorry

The degree and terms of the polynomial are explained and an example is also discussed.

What are polynomials?

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. It is a mathematical expression made up of exponents, constants, and variables that are mixed using addition, subtraction, multiplication, and division (No division operation by a variable).

The expression's components that are divided up by the operators "+" or "-" are referred to as polynomial terms. In polynomials, like terms are ones that share the same variable and power. Unlike terms are those that have dissimilar variables and/or dissimilar powers.

The degree of a polynomial is the highest or biggest exponent of the variable in the polynomial. A polynomial equation's maximum number of solutions can be calculated using the degree.

The different types of polynomials based on terms are:

The different types of polynomials based on the degree are:

Example,

Consider a polynomial 3x² + 5x + 4

Number of terms = 3 (Trinomial)

Degree = 2 (Quadratic polynomial)

Therefore the degree and terms of the polynomial are explained and an example is also discussed.

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The answer is:

Work/explanation:

Here's how we classify polynomials based on the number of terms:

monomial - has only one term

binomial - has two terms

trinomial - has three terms

polynomial - has four terms or more

As for degrees, those are the highest exponents the polynomial.

Example: Classify [tex]\bf{2p^2+p}[/tex].

It has 2 terms so it's a binomial.

Its highest exponent is 2 so it's a second degree binomial.