There are 260 eighth grade students at South Whitenardh middle school. All right grade students are required to enroll in either a music class or an art class. No students take both art and music classes. The number of students taking music classes is 14 more than twice the number taking art classes. Write an equation to represent the total number of eight grade students

Answer:

1st, 4th and 5th are correct.

Step-by-step explanation:

A reflection in the line y = -2 and then translation of 2 units right will create the same area so option (C) will be correct.

f we shift the triangle anywhere then there will be no change in the area but if we apply the scale factor then since the dimension changes so its area will also change.

In all options, there is a scale factor so it will change area but in option C

A reflection in the line y = -2 reflection gives a mirror image about y = -2 but no changes in area then translation of 2 units right will shift triangle 2 units right but no effect in the area.

Hence "A reflection in the line y = -2 and then translation of 2 units right will create the same area".

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The height of the mt. Everest in miles exists 5.499 miles.

By changing the unit of measurement, a quality can be expressed differently. In contrast to distance, which can be stated in miles, kilometers, feet, or any other unit of length, time can also be expressed in minutes rather than hours.

By multiplying or dividing a number, a conversion factor can be used to change one set of units to another. The right conversion factor to an equal value must be used when a conversion is required. The correct conversion factor, for instance, is 12 inches to 1 foot when converting between inches and feet.

The height of the mt. Everest is : 29035 feet.

The unit conversion is given as :

5280 feet = 1 mile

1 feet = 1/5280 mile

So, 29035 feet =29035 × 1/5280 miles

29035 feet = 29035/5280 miles

29035 feet = 5.499 miles

So, the height of the mt. Everest in miles is 5.499 miles.

The complete question is:

In the Himalaya mountains along the border of Tibet and Nepal, mount Everest reaches a record height of 29,035 feet. how high is mt. Everest in miles? use the conversion equivalency of 1 mile = 5280 feet.

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Answer:  The height of the Mount Everest in miles is 5.499 miles

Step-by-step explanation:

1 miles = 5,280 feet

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Answer:

[tex]\dfrac{3}{a-6}\quad \textsf{if}\;\;a \neq -6,a \neq 6[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{a}{a-6}-\dfrac{3}{a+6}+\dfrac{a^2}{36-a^2}[/tex]

Rewrite the third fraction:

[tex]\implies \dfrac{a^2}{36-a^2}=\dfrac{-a^2}{-(36-a^2)}=\dfrac{-a^2}{a^2-36}[/tex]

[tex]\boxed{\begin{minipage}{4 cm}\underline{Difference of two squares }\\\\$x^2-y^2=(x-y)(x+y)$\\\end{minipage}}[/tex]

Apply the difference of two squares to the denominator of the third fraction:

[tex]\implies a^2-36=a^2-6^2=(a-6)(a+6)[/tex]

Therefore the expression can be written as:

[tex]\implies \dfrac{a}{a-6}-\dfrac{3}{a+6}+\dfrac{-a^2}{(a-6)(a+6)}[/tex]

[tex]\implies \dfrac{a}{a-6}-\dfrac{3}{a+6}-\dfrac{a^2}{(a-6)(a+6)}[/tex]

The least common multiplier (LCM) of the denominator is (a - 6)(a + 6).

Adjust the fractions based on the LCM:

[tex]\implies \dfrac{a(a+6)}{(a-6)(a+6)}-\dfrac{3(a-6)}{(a-6)(a+6)}-\dfrac{a^2}{(a-6)(a+6)}[/tex]

Simplify:

[tex]\implies \dfrac{a^2+6a}{(a-6)(a+6)}-\dfrac{3a-18}{(a-6)(a+6)}-\dfrac{a^2}{(a-6)(a+6)}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}-\dfrac{d}{c}=\dfrac{a-b-d}{c}:[/tex]

[tex]\implies \dfrac{a^2+6a-(3a-18)-a^2}{(a-6)(a+6)}[/tex]

Simplify:

[tex]\implies \dfrac{3a+18}{(a-6)(a+6)}[/tex]

Factor out 3 from the numerator:

[tex]\implies \dfrac{3(a+6)}{(a-6)(a+6)}[/tex]

Cancel the common factor (a + 6):

[tex]\implies \dfrac{3}{a-6}[/tex]

Therefore:

[tex]\dfrac{a}{a-6}-\dfrac{3}{a+6}+\dfrac{a^2}{36-a^2}=\dfrac{3}{a-6}\quad \textsf{if}\;\;a \neq -6,a \neq 6[/tex]

 As per Given data,

The month in which the balance of two bank accounts A is become equal to the balance of account B is 30thmonths,

Unknown variables are used to find the unknown values of the problem using the algebraic expressions.

Month       Account A        Account B

 0                    $ 100                 $ 250  

  1                    $ 125                 $ 270

  2                   $ 150                 $ 290

Clearly

The amount in account A is growing with $25 each month. Thus, the amount in this account in nth month is,

100+25[tex]n[/tex]

The amount in account B is just growing with $20. Thus, the amount in this account in nth month is,

250+20[tex]n[/tex]

x month

balances of two

account becomes equal,

then

100 + 25x =250 + 20x

25x - 20x = 250 - 100

5x = 150

x =30

Therefore, in 30th month balance of account A equal to balance of account B

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Q. The table shows the balances of two bank accounts for 3 months. In 30th month will the balance of account A be equal to the balance of account B?

Month       Account A      Account B

   0               $100                $250

    1               $125                 $270

    2              $150                 $290

Step-by-step explanation:

i. AD = BC= 6cm (each two opposite sides are equal in length in parallelogram)

ii.DC=AB=9cm (each two opposite sides are equal in length in parallelogram)

iii.DCB=60 ,, bec DC and AB are parallel so their interior angles are supplementary their sum equals 180°

so DCB = 180-120=60°

iv.ADC=ABC = 120° because each two opposite angles are equal in measure in parallelogram

v. DAB=DCB =60° because each two opposite angles are equal in measure in parallelogram

vi. OC=AO =7cm because the diagonals of parallelogram bisect each other

vii. OB=DO=5cm because the diagonals of parallelogram bisect each other

viii . DAB=60° ,, CDA= 120 °

DAB+CDA =180°

or you could simply say that because DC and AB are parallel their interior angles are supplementary their sum is 180°

The equation y^ = -2.5x + 222.5 models the amount of cholesterol, LDL, for a person in mg/dl, where x is the time spent exercising per day in minutes.

What in mathematics is a quadratic equation?

Definitions: x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

To find the amount of cholesterol for a person exercising 20 minutes a day, we need to substitute x = 20 into the equation:

y^ = -2.5(20) + 222.5

Solving this equation, we get:

y^ = -50 + 222.5

y^ = 172.5

So, the amount of cholesterol for a person exercising 20 minutes a day is 172.5 mg/dl.

Therefore, the answer is 172.5 mg/dl

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The area of the garden is 625 square meters.

We know that the perimeter of a square is equal to the sum of all four sides. Since the gardener is using 100 meters of fencing to enclose the garden, and since the garden is a square, we can set the perimeter equal to 100 meters:

P = 4s

100 = 4s

Where P is the perimeter, and s is the length of one side of the square.

We can solve for s by dividing both sides of the equation by 4:

s = 100/4 = 25

Since the area of a square is equal to one side of the square squared, we can find the area of the garden by squaring the value of s:

A = s^2

A = 25^2

A = 625

So the area of the garden is 625 square meters.

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Answer:

6

Step-by-step explanation:

Call the bigger number a, smaller b
a + b = 10
b + 2 = a
a + b + 2 = a + a = 2a = 12
a = 12 : 2
a = 6

x = 5

AB = 6

BC = 13

A line can be defined as a straight set of points that extend in opposite directions, It has no ends in both directions(infinite). It has no thickness. It is one-dimensional.

Given,

AB = 2x - 4

BC = 3x - 2

AC = 19

By the figure

AB + BC = AC

2x - 4 + 3x - 2 = 19

5x - 6 = 19

5x = 25

x = 5

AB = 2 × 5 - 4 = 10 - 4 = 6

BC = 3 × 5 - 2 = 15 - 2 = 13

Hence the value of x, AB and BC is 5, 6, 13 respectively.

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The equation that models the height of the tent, h, in feet, with respect to the horizontal distance in feet from the left edge, d, is h = 1.5 d + h0.

The height of the tent is 22. 5 feet at a horizontal distance of 15 feet.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The height of the tent varies at a rate of 1. 5 feet with the horizontal distance from the left edge.

This can be written as -

h = 1.5 d, where d is the distance.

So, the equations that models the situation is -

h = 1.5 d + h0

The peak of the tent is at 30 feet and is at a horizontal distance of 20 feet from the left edge.

So, when d =20, then h =30.

Plugging the values in the equation -

30 = 1.5 (20) + h0

30 = 30 + h0

h0 = 0

The height of the tent is 22. 5 feet.

So, now h = 1.5 d and h = 22.5.

Equating these two -

22.5 = 1.5 d

d = 22.5/1.5

d = 15

Therefore, the distance value is obtained as 15 feet.

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Mama bear only ate (1/4) of the pie, leaving Goldilocks with the remaining (1/8) fraction.

The fraction is expressed in the form a/b, where an is referred to as the numerator and b is referred to as the denominator. The fraction is a rational number that only divides two integers.

Let the pie's largest portion be a.

Half of the pie was consumed by Papa Bear.

Papa Bear then consumed = (1/2)a.

Rest of the pie is equal to a- (1/2).

a= (1/2)a

Mama bear consumed (half) of the remaining pie.

Mother bear consumed (1/2)(1/2).

pie portion a= (1/4) pie portion after mom bear has eaten = (1/2)

a- (1/4)a= (1/4)a

Baby bear afterwards consumed (half) of the remaining pie.

Baby bear ate (1/2)(1/4), thus. After the young bear has finished eating, the remaining pie is equal to (1/4) a- (1/8)a= (1/8)

The remainder of the component was given to GoldLiocks.

As a result, mom bear only ate (1/4) of the pie, leaving Goldilocks with the remaining (1/8) portion.

The complete question is Papa Bear ate 1/2 of a pie. Mama Benr ate 1/2 of what was left Baby Bear ate 1/2 of what

was left after Mama Bear finished.

3) What fractional part of the pie did Mama Bear eat?

4) What fractional part of the pie was left for Goldilocks?

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The solution to the differential equation y'' + y = sin2x is y = -2sin2x + (Acos2x + Bsin2x).

This differential equation can be solved by the method of variation of parameters. This method involves finding two arbitrary functions, U and V, such that U' = V and V' = -U + sin2x, so that the general solution of the differential equation is y = U + V. Solving the two equations yields U = Acos2x + Bsin2x and V = -2sin2x, where A and B are arbitrary constants. Substituting U and V into the general solution of the differential equation yields the final solution y = -2sin2x + (Acos2x + Bsin2x).

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On solving the provided question, we can say that - The provided arithmetic sequence's 66th term is -950.

An arithmetic sequence is a set of integers that are ordered and have a common difference between each following word.An ordered group of integers with a shared difference between each word is known as an arithmetic sequence.

The given arithmetic sequence is,

25, 10, -5, .....

The sequence's initial word, a, equals 25, while the common difference, d, equals -15.

Use the formula nth term of arithmetic series = a+ (n-1)d to determine the 66th term of the sequence.

66th term =

[tex]25 + (66-1)(-15)\\ = 25 + 65× (-15)\\ = 25 - 975\\ = -950\\[/tex]

The 66th term of the arithmetic sequence is -950.

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The two (2) possible locations of point F include the following: F. [7, 9.5].

In this scenario, line ratio would be used to determine the coordinates of the point on the directed line segment that partitions the segment into a ratio of 5 to 3.

Mathematically, line ratio can be used to determine the coordinates of F and this is modeled by this mathematical expression:

F(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

Given the following parameters:

Point (x, y)= (4, 11)

Point (x, y) = (8, 9)

m:n = 3:1

Substituting the given parameters into the line ratio formula, we have;

F(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

F(x, y) = [(3(8) + 1(4))/(3 + 1)],  [(3(9) + 1(11))/(3 + 1)]

F(x, y) = [(24 + 4)/(3 + 1)],  [(27 + 11)/(3 + 1)]

F(x, y) = [(28)/(4)],  [(38)/(4)]

F(x, y) = [7, 9.5]

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Answer:

try -5

Step-by-step explanation:

mainly because it says -3 plus 5 and there's only 4 and 5 so It can't really go further

Answer:try -5

Step-by-step explanation:

mainly because it says -3 plus 5 and there's only 4 and 5 so It can't really go further

The slope of the straight line connecting the break's ends to the function's diagram.

For 0 < x < 4 will be -60

For 4 < x < 8 will be -31

The mathematical formula f (x) = [tex]$$a^{x[/tex] denotes an exponential function. a constant known as the function's base and a variable called x are present. The transcendental number e, roughly equivalent to 2.71828, is the most frequent exponential-function base.

When a positive constant other than 1 is raised to a variable exponent, the function is said to be exponential. Solving at a certain input value yields the evaluation of a function. If you know the growth rate and the starting point, you can find an exponential model.

We have to use the knowledge of functions to describe the average rates of each one of them, so:

For 0 < x < 4 will be -60

For 4 < x < 8 will be -31

It is a measurement of how much the function changed for one person on average throughout that interval. It results from the slope of the straight line connecting the break's ends to the function's diagram.

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The correct answer is that we cannot conclude that being able to read is beneficial for them as there can be various cause and effect relation.

A research is conducted to collect information about a specific topic for the purpose of study. A group of population is asked to fill a survey form or answer questions based on the research topic.

This data is collected and analyzed to get the required result.

Here, in this question kindergarten students are the population from whom data is collected . Here, the conclusion is that having the ability to read and write from before only doesn't means they will have academic intelligence later.

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The equation -15x + 4x + 2 - x = x has  solution and the solution is 2/13

From the question, we have the following parameters that can be used in our computation:

-15x+4x+2-x= x+

Express the equation properly

So, we have the following representation

-15x + 4x + 2 - x = x

Collect the like terms in the equation

This gives

-x - 15x + 4x - x = -2

Evaluate the like terms

So, we have the following representation

-13x = -2

Divide both sides by -13

This gives

x = 2/13

Hence, the solution is 2/13

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Answer:

simply do 70 divided by 12, then that divided by 3, in total it should take 1, 2, or 3 hours to read 3 books a month

Step-by-step explanation:

To find the zeros of a polynomial algebraically, you can use the following steps:

Write the polynomial in standard form, with the terms arranged in descending order of the degree of the term. For example, if the polynomial is 3x^2 - 2x + 5, it is already in standard form.

Set the polynomial equal to zero. For example, if the polynomial is 3x^2 - 2x + 5, you would set the equation equal to zero like this:

3x^2 - 2x + 5 = 0

Use the quadratic formula to find the solutions (i.e., the zeros) of the equation if the polynomial is a quadratic (degree 2). The quadratic formula is:

x = (-b +/- sqrt(b^2 - 4ac)) / (2a)

where a, b, and c are the coefficients of the polynomial, and sqrt represents the square root.

For example, if the polynomial is 3x^2 - 2x + 5, the solutions would be:

x = (-(-2) +/- sqrt((-2)^2 - 4 * 3 * 5)) / (2 * 3)

x = (2 +/- sqrt(4 - 60)) / 6

x = (2 +/- sqrt(-56)) / 6

Since the square root of a negative number is not a real number, there are no real solutions (zeros) for this polynomial.

Use the Rational Root Theorem to find the solutions of the equation if the polynomial is not a quadratic. The Rational Root Theorem states that if a polynomial of degree n has a rational root p/q (where p and q are integers and q is not equal to zero), then p must be a divisor of the constant term and q must be a divisor of the coefficient of the term of highest degree.

For example, if the polynomial is x^3 - 2x^2 + x - 6, the constant term is -6 and the coefficient of the term of highest degree is 1. The divisors of -6 are -6, -3, -2, -1, 1, 2, 3, and 6. The divisors of 1 are 1 and -1. Therefore, the possible rational roots of this polynomial are -6, -3, -2, -1, 1, 2, 3, and 6.

To find the actual roots, you can try each of these numbers as a root and see if it works. For example, if you try -6 as a root, you would get:

(-6)^3 - 2(-6)^2 + (-6) - 6 = 0

(-216) - (-72) + (-6) - 6 = 0

-144 - 6 - 6 = 0

-156 = 0

This equation is not true, so -6 is not a root of the polynomial. You can repeat this process for each of the other possible rational roots until you find all of the roots of the polynomial.

Answer:√17

              √81

                √27

This 3 numbers are irrational number

Answer:

17 and 27 are irrational

Step-by-step explanation:

Answer:

$720

Step-by-step explanation:

The formula is:

A = P(1 + rt)

We know

P = $6000

r = 3% = 0.03

t = 4 years

A = 6000( 1 + 0.03 x 4) = $6720

Now we have to find the interest by taking

$6720 - $6000 = $720

So, he earns $720 in interest in 4 years.

Answer:

C

Step-by-step explanation:

The angles at point A have to be congruent so that you have two congruent angles. and one congruent side, which give SAA.

From the image, we can see than angle B and angle D are congruent. We also know that line AC is congruent to itself since it shared between the two triangles. Since we need one more angle, that angle has to be angle A.

An expression to represent the sum of their ages is as follows.

g = 14 + L

If the ratio of the ages of X and Y is p:q and their sum is X, then the following formula can be used to calculate Y's age: Age of Y = Y/Total Ages x Total Ratios. Age of Y = (p+q) q x A.

Assume that L is Louannel's sister's age, m is Mark's age, and g is Gregory's age.

Gregory's age difference with his cousin Mark, who is 20 years older (m).

∴ g = 20 + m            .............(1)

Also given that Mark is 6 years younger than his sister Louanne(L)

∴ m = L - 6                ............(2)

Now, substituting m = L - 6 from (2) in (1),

∴ g = 20 + L - 6

∴ g = 14 + L

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So, on  solving the provided question, we can say that  to form a inequality - x * y > 8

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

here to form a inequality-

let x = goals by each player

y = no. of players

x * y > 8

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The equation of a line can be written in both slope-intercept form and standard form.

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Substitution method is a method used to solve equations. It involves replacing a variable with its given value, which helps to isolate it and solve for the unknown. For example, if we have the equation 2x+5=17, we can solve for x by substituting 17 for 2x+5 and then subtracting 5 from both sides to obtain x=12.

The substitution method is a technique used to solve systems of equations. An example of the substitution method would be solving the system of equations:

x + 2y = 5

3x + 6y = 15

First, solve the first equation for x:

x = 5 - 2y

Substitute the expression for x into the second equation:

3(5 - 2y) + 6y = 15

Simplify:

15 - 6y + 6y = 15

Solve for y:

15 = 15

Now substitute the value of y back into the expression for x:

x = 5 - 2(3)

Solve for x:

x = -1

Therefore, the solution to the system of equations is:

x = -1, y = 3

Substitute x in equation 1 into equation 2, solve, then substitute y back into equation 1.

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The Binomial Expression is defined as the type of algebraic expression that consists of exactly two terms .

What is Binomial Expression ?

The algebraic expression which contains exactly only two terms is termed as  binomial expression . It is called a two term polynomial.

the binomial is also called a sum or a difference between two or more monomials. Binomial is the simplest form of a polynomial.

Some Examples of Binomial Expression are ⇒ [tex]4x^{2} +6y^{2}[/tex] , [tex]xy^{3} +xy[/tex] ;

Various Mathematical Operations can be performed on Binomial Expression such as Addition , Subtraction , Multiplication and Division .

and The  Equation that contains one or more binomial expression is called as a Binomial Equation.

The given question is incomplete , the complete question is

What is a Binomial Expression ?

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The sum of two functions, f and g: (f + g)(x) = f (x) + g(x) and The difference of two functions f and g: (f - g)(x) = f (x) - g(x).

What is operation function ?

The operations function refers to all the activities that focus on producing goods and services for the customers. It includes the production process of converting raw material into final products. It helps to reduce costs and make process improvements.

Have given ,

Two function f and g then ,

There is one more way that functions can be combined. The fifth operation is called the composition of two functions. The composition of the functions f (x) and g(x) is symbolized this way: (fog)(x). It is equivalent to f (g(x)). It is read "f of g of x." The concept is simple. First, the value of g at x is taken, and then the value of f at that value is taken. Let's try an example to clear things up.

So , The sum of two functions, f and g: (f + g)(x) = f (x) + g(x) and The difference of two functions f and g: (f - g)(x) = f (x) - g(x).

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