whats find the sum mean

The values of 'x' in |3x + 4| > 6, is, x > 3/2 or x < - 10/3.

We know the absolute value function of the modulus function always outputs a positive value irrespective of the sign of the input.

In piecewise terms  | x | = x for x ≥ 0 and | x | = - x for x < 0.

We know, If |x| > a, Then x > a or x < - a.

Given, |3x + 4| > 6.

Therefore,

3x + 4 > 6 or 3x + 4 < - 6.

3x > 2 or 3x < - 10.

x > 3/2 or x < - 10/3.

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Answer:

[tex]\left(x-\frac{5}{2}\right)^2=\frac{25}{2}[/tex]

Step-by-step explanation:

I am not completely sure if you just wanted me to write it in square form, so I will show the process of writing it in square form and how to find the solution.

[tex]-4x^2+20x=-25[/tex]    start by moving 25 to the right side

[tex]\frac{-4x^2+20x}{-4}=\frac{-25}{-4}[/tex]         divide both sides by -4

= [tex]x^2-5x=\frac{25}{4}[/tex]    

Now we rewrite the equation in the form [tex]\:x^2+2ax+a^2[/tex]

= [tex]x^2-5x+\left(-\frac{5}{2}\right)^2=\frac{25}{2}[/tex]  apply perfect square formula: [tex]\left(a-b\right)^2=a^2-2ab+b^2[/tex]

= [tex]\left(x-\frac{5}{2}\right)^2=\frac{25}{2}[/tex]   -- square form

Solutions to the quadratic equation:

Possible solutions: [tex]x=\frac{5}{\sqrt{2}}+\frac{5}{2}[/tex]    and [tex]\:x=-\frac{5}{\sqrt{2}}+\frac{5}{2}[/tex]

Answer:

A: 24, B: 12, C: 28, D: 24. Hope this helps

Step-by-step explanation:

Part A:

168/3 = 56

Therefore, Chad is driving the car in 56 mph.

672/56 = 12

Therefore, Chad drives 672 miles in 12 hours.

308/11 = 28

Therefore, Chad drives 28 miles per gallon of gas.

672/28 = 24

Therefore, Chad uses 24 gallons of gas to drive 672 miles.

Part B:

12 hours, you can use proportions, miles/hours.

[tex]\frac{56}{1}[/tex]= [tex]\frac{672}{x}[/tex]

x = 12

Part C:

divide the miles driven by Chad (308 miles ) by the number of gallons used (11 gallons).

308 miles / 11 gallons =28 miles per gallon

Chad's car gets 28 miles per gallon.

Part D:

[tex]\frac{28}{1} = \frac{672}{x} \\[/tex]

28x = 672

x = 672/28 = 24

24 gallons

Answer: A=56 B=12 C=28 and D=24

Step-by-step explanation:

A. Chad drove 168 miles in 3 hours

    In 1 hour he drove          168÷3

                                          = 56 Miles

B. We know,

    Covering 56 miles takes 1 hour

    So, It will take to cover 672 miles
                                           = 672÷56

                                           = 12 Hours

C. We know,

    Chad drove 308 miles with 11 gallons of gas

    So, miles per gallon chads car gave him 308÷11

                                                                       = 28 Miles Per Gallon.

D. We know,

   Chad car gives him 28 miles per gallon

   So, To cover 672 miles

   Chad needs                                            = 672÷28

                                                                    = 24 Gallons.

NOTE: Its simple math kiddo, do better in school

The total expected cost of Alice's train ride will be 20 Euro with a fine of 300 Euro if ticket checked and 0 fine if ticket not checked.

It is known to us that Alice is riding the train, and that she accidentally purchased a ticket for zone 4, although she has to be traveling to zone 5,

with this we need to find how much money can Alice expect to pay

since we know that there is a 5 percent chance that the transit authorities will check tickets,

Probability to check ticket = 5/100 = 0.05

fine = 300 euro

probability to not check ticket = 1 - 0.05 = 0.95

we know that she has already spent 5 Euro on the ticket,

there is a 300 Euro fine if ticket checked,

and 0 fine if ticket not checked,

Expected cost to pay = 5 + 0.05 × 300 + 0.95 × 0

= 5 + 15 + 0

= 20 Euro

Alice Expected to Pay = 20 Euro

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So, the coefficient of the x^(2) term in the expression 5x-4x^(2)+2 is -4.

The coefficient of the x^(2) term in the expression 5x-4x^(2)+2 is -4.

A coefficient is the number that is multiplied by a variable in an expression. In this case, the x^(2) term is -4x^(2), so the coefficient is -4.

To find the coefficient of a specific term in an expression, you can simply look at the number that is directly in front of the variable and its exponent. For example, in the term 5x, the coefficient is 5, and in the term 2, the coefficient is 2 (since there is no variable, the coefficient is simply the number itself).

In the expression 5x-4x^(2)+2, the x^(2) term is -4x^(2), so the coefficient is -4. This means that the x^(2) term is being multiplied by -4 in the expression.

So, the coefficient of the x^(2) term in the expression 5x-4x^(2)+2 is -4.

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Answer:

Step-by-step explanation:

12/13=0.92307692307

The number of residents in a city is a discrete variable with ratio level of measurement. Therefore, the correct option is option 3. When a pair of dice are rolled, the pair of mutually exclusive events are getting an odd number on the first die; getting a 4 on the second die. Therefore, the correct option is option 2.

The number of residents in a city is a discrete variable because it can only take on whole number values. The level of measurement for this variable is ratio level because there is a true zero point (a city with zero residents) and the differences between values are meaningful. Therefore, the correct answer is discrete, ratio level which is the third option.

Mutually exclusive events are events that cannot occur at the same time. In the case of rolling a pair of dice, the pair of mutually exclusive events is "Getting an odd number on the first die; getting a 4 on the second die." This is because if the first die is an odd number, the second die cannot be a 4 at the same time.

The other options are not mutually exclusive because they can occur at the same time. For example, it is possible to get an even number on the first die and a double 5 at the same time. Therefore, the correct answer is "Getting an odd number on the first die; getting a 4 on the second die" which is the second option.

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We can use the proportion (1000 grams )/(1 kilogram ) = (x grams )/(5 kilograms ) to convert 5 kilograms into grams.

The right proportion to use to convert 5 kilograms to grams is (1,000 grams)/(1 kilogram) = ( x grams)/(5 kilograms). This is because there are 1,000 grams in 1 kilogram, so we can use this ratio to find the number of grams in 5 kilograms. To solve for the unknown value, we can cross multiply and then divide.

The proportion is solved as:

So, the answer is 5,000 grams. Therefore, 5 kilograms is equal to 5,000 grams.

In conclusion, the correct proportion is (1000 grams )/(1 kilogram ) = (x grams )/(5 kilograms ).

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Isosceles trapezoid MNOP where MO = a + 13 and NP = 2a - 1,  The value of a 13.

A trapezoid, also known as a trapezium, is a four-sided polygon with two parallel sides, also called the bases. The non-parallel sides are called legs, and they can have different lengths. The parallel sides are perpendicular to the legs

In an isosceles trapezoid, the nonparallel sides are congruent, so we have MN = OP.

Also, the diagonal PN divides the trapezoid into two congruent right triangles, so we have:

[tex]MN^2 = (NP - MO)^2 + (MP)^2[/tex]

Substituting the given values, we get:

[tex]MN^2 = (2a - 1 - (a + 13))^2 + MP^2[/tex]

[tex]MN^2 = (a - 14)^2 + MP^2[/tex]

But since MN =OP and MO = NP - MN, we have:

[tex]OP = NP - MO = (2a - 1) - (a + 13) = a - 12[/tex]

So we also have:

[tex]OP^2 = (a - 12)^2 + MP^2[/tex]

Since MN = OP, we can set these two equations equal to each other:

[tex](a - 14)^2 + MP^2 = (a - 12)^2 + MP^2[/tex]

Simplifying and solving for a, we get:

[tex]a^2 - 28a + 197 = a^2 - 24a + 144[/tex]

[tex]4a = 53[/tex]

[tex]a = 13.25[/tex]

Therefore, the value of a is 13.25.

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Answer:

That is true.

Answer: True

Step-by-step explanation:

due to the fact that its 2 and every time you multiply by the factor itll equal a even number

Answer:

80%

Step-by-step explanation:

96.3 - 53.5 = 42.8

42.8 / 53.5 = 0.8

0.8 × 100 = 80%

Answer:

Step-by-step explanation:

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Answer:

1

Step-by-step explanation:

3 - 2 = 1

For the equation -3/2x² = x + 1 the solution set is option D: {(-1 + √5)/3, (-1 - √5)/3}.

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 ("=").

To solve the equation -3/2x² = x + 1, we need to move all the terms to one side to get a quadratic equation in standard form.

We can do this by adding 3/2x² and subtracting 1 from both sides -

-3/2x² - x - 1 = 0

To solve this quadratic equation, we can use the quadratic formula -

x = (-b ± √(b² - 4ac)) / 2a

where a = -3/2, b = -1, and c = -1.

Substituting these values, we get -

x = (-(-1) ± √((-1)² - 4(-3/2)(-1))) / 2(-3/2)

x = (1 ± √(1 - 6)) / (-3)

x = (1 ± √5) / (-3)

So the set of solutions for the equation is -

{(-1 ± √5) / 3, (-1 ± √5) / 3}

Therefore, the answer is option {(-1 + √5)/3, (-1 - √5)/3}.

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By answering the above question, we may state that Hence, [tex]xy{(-4)}[/tex]is x exponents divided by y raised to the power of 4.

The mathematical process of exponentiation, frequently referred to as "b raised to the nth power," is symbolised by the symbol bn and includes two numbers: a base number, b, and an exponent, or power, n. Exponents demonstrate the number of times that a number has been multiplied by itself. For example, 2-3 (written as 23) means: 2 x 2 x 2 = 8. 2 + 3 does not equal 6, nor does 23. Remember that an integer whose power is one is equal to itself. Exponents can be used as a way to express large numbers as powers. Therefore, the exponent is the measurement that shows how many times a number has been multiplied by itself. For instance, multiplying 6 by 4 results in the values 6 x 6 x 6.  .

Considering that the phrase is:

[tex]xy^{-4}[/tex]

We may simplify the case when x and y both have positive exponents as follows:

[tex]xy^{(-4)} = x / y^4[/tex]

This is due to the negative exponents rule, which claims that y(-n) = 1/yn, which indicates that [tex]y(-n) = 1/yn.[/tex]

Hence, [tex]xy{(-4)}[/tex]is x divided by y raised to the power of 4.

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G is linear.

To show that g:V→F defined by g(x)=⟨x,y⟩ for all x∈V is linear, we need to prove that g satisfies the following two properties:

1) g(x+z)=g(x)+g(z) for all x,z∈V
2) g(αx)=αg(x) for all x∈V and α∈F

Proof:

1) Let x,z∈V. Then g(x+z)=⟨x+z,y⟩=⟨x,y⟩+⟨z,y⟩=g(x)+g(z) by the distributive property of the inner product.

2) Let x∈V and α∈F. Then g(αx)=⟨αx,y⟩=α⟨x,y⟩=αg(x) by the scalar multiplication property of the inner product.

Therefore, g is linear.

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A cluster sample will: b. Seek views from a homogeneous group in the population

A cluster sample is a type of sampling method where the entire population is divided into groups, or clusters, and a random sample of these clusters are selected for the study. Each cluster is typically a homogeneous group, meaning that the individuals within the cluster are similar to each other in some way. For example, a cluster sample might be used to study the opinions of students at a particular school, where each class is a cluster and a random sample of classes are selected for the study. By selecting a homogeneous group, the researcher can ensure that the sample is representative of the population and can generalize the results to the larger population.

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Standard form of a polynomial expression is a way of writing the expression in descending order of the powers of the variable, starting with the highest power and ending with the constant. In this case, the polynomial expression is - 6 - 7x ^ (2) + 8x ^ (5).

In standard form, this expression can be written as 8x ^ (5) -7x ^ (2) - 6. This expression indicates that 8 is the coefficient of the highest power, x ^ (5). The coefficient of the second highest power, x ^ (2) is -7, and the coefficient of the constant, the term with no variable, is -6.

Standard form is useful for simplifying polynomial expressions, as it helps to clearly illustrate the coefficients of each term. It is also useful for graphing polynomials, as the order of the terms can be clearly seen.

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In half an hour, Ellie can cover 12 books.

To find out how many books Ellie can cover in half an hour, we need to use proportions.

We know that Ellie can cover 2 books in 5 minutes, so we can set up a proportion like this:
2 books / 5 minutes = x books / 30 minutes

Cross-multiplying and solving for x, we get:
5 minutes * x books = 2 books * 30 minutes
5x = 60
x = 12

So, Ellie can cover 12 books in half an hour.

To summarize, if Ellie can cover 2 books in 5 minutes, we can find out how many books she can cover in half an hour by dividing the total time (30 minutes) by the time it takes her to cover 2 books (5 minutes) and then multiplying the result by the number of books she can cover in 5 minutes (2). This gives us 12 books, which is the number of books Ellie can cover in half an hour.

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B is the right response: (6 + 4) 2 = 20.

We must analyse each expression and compare them in order to determine which number statement is correct.

starting with the formula A (6 + 4 2 = 6 + 8 = 14)

Let's now assess expression B:

(6 + 4) × 2 = 10 × 2 = 20

Expression in C: 6 + 4 2 = 6 + 2 =

The final expression is D (6 + 4) 2 = 10 2 = 5.

The values of the expressions can now be compared to determine which number sentence is correct.

As can be seen, expression B is the real number sentence because it has the highest value of all the expressions. As a result, B is the right response: (6 + 4) 2 = 20.

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The value of CB and DB are 3.25 and 5.2

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

CA = √ 4²+3²

CA = √ 16+9

CA = √ 25

CA = 5

represent DB by x

5/3+x = 4/5

25 = 4(3+x)

3+x = 25/4

3+x = 6.25

x = 6.25 - 3

x = 3.25

represent CB by y

y² = 3.25² + 4²

y²= 10.56+16

y² = 26.56

y = √ 26.56

y = 5.2

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Yes, the equation y = 3/4(x) represent a proportional relationship because its line passes through the origin.

In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Generally speaking, the graph of any proportional relationship such as the linear equation is characterized by a straight line that passes through all the points and the origin, which is denoted by the ordered pair (0, 0).

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By the squeeze theοrem, lim f(x) = 0 as x apprοaches -5.

The squeeze theοrem, alsο knοwn as the sandwich theοrem, is a theοrem in calculus that allοws us tο find the limit οf a functiοn using the limits οf twο οther functiοns that "squeeze" the οriginal functiοn between them.

We have the inequality:

-2x² - 20x - 51 ≤ f(x) ≤ 2x² + 20x + 49

We can rewrite this inequality as:

-2(x+5)(x+4.5) ≤ f(x) ≤ 2(x+5)(x+4.5) + 1

Nοte that we have factοred -2x² - 20x - 51 as -2(x+5)(x+4.5) and 2x² + 20x + 49 as 2(x+5)(x+4.5) + 1.

As x apprοaches -5, we can see that (x+5) and (x+4.5) apprοach 0, sο we have:

-2(0)(0) ≤ lim f(x) ≤ 2(0)(0) + 1

0 ≤ lim f(x) ≤ 1

Therefοre, by the squeeze theοrem, we have:

lim f(x) = 0 as x apprοaches -5.

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Therefore , the solution of the given problem of equation comes out to be equation y = -2x in standard notation

The very same variable letter is frequently used in mathematical formulas to attempt to impose harmony between two assertions. Mathematical equations, also referred to as assertions, are used to demonstrate the equality of many academic figures. Utilizing y + 6 as such an example, the normalise multiplies b + 6 in place of dividing 12 into two portions. The link integer among each sign component and the line length can be found. A symbol's meaning typically runs counter to itself.

Here,

The x element needs to be moved to the left and the equation needs to be written with integer coefficients in order to change the equation y = -2x in to other standard form (Ax + By = C).

With y = -2x as a starting point, we can add 2x to both sides to get:

2x + y = 0

With A = 2, B = 1, and C = 0, we now have the equation Ax Plus By = C. By multiplying both sides by -1, we can make the factors integers:

-2x - y = 0

This is the equation y = -2x in standard notation.

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The sοlutiοn οf the given prοblem οf equatiοn cοmes οut tο be equatiοn 2x + y = 0 in standard nοtatiοn. Thus, the correct option is 1.

The very same variable letter is frequently used in mathematical fοrmulas tο attempt tο impοse harmοny between twο assertiοns. Mathematical equatiοns, alsο referred tο as assertiοns, are used tο demοnstrate the equality οf many academic figures. Utilizing y + 6 as such an example, the nοrmalise multiplies b + 6 in place οf dividing 12 intο twο pοrtiοns. The link integer amοng each sign cοmpοnent and the line length can be fοund. A symbοl's meaning typically runs cοunter tο itself.

Here,

The x element needs tο be mοved tο the left and the equatiοn needs tο be written with integer cοefficients in οrder tο change the equatiοn y = -2x in tο οther standard fοrm (Ax + By = C).

With y = -2x as a starting pοint, we can add 2x tο bοth sides tο get:

2x + y = 0

With A = 2, B = 1, and C = 0, we nοw have the equatiοn Ax Plus By = C. By multiplying bοth sides by -1, we can make the factοrs integers:

2x + y = 0

This is the equatiοn 2x + y = 0 in standard nοtatiοn.

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Complete question:

Convert the following equation into standard form.

y = -2x.

[select from given choices]

The possible number of positive real zeros for the given polynomial function is 2 or 0.

To determine how many positive real zeros the polynomial function may have, we can use Descartes' Rule of Signs.

Descartes' Rule of Signs states that the number of positive real zeros of a polynomial function is equal to the number of sign changes in the coefficients of the terms, or less than that number by an even integer.

In the given polynomial function, f(x)=-7x^(7)+x^(3)-x^(2)+1, there are two sign changes in the coefficients of the terms: from -7 to +1 and from +1 to -1.

Therefore, the polynomial function may have 2 positive real zeros or 2-2=0 positive real zeros.

So, the possible number of positive real zeros for the given polynomial function is 2 or 0.

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[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$3200\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\dotfill &4 \end{cases} \\\\\\ I = (3200)(0.07)(4) \implies I = 896[/tex]

Answer:

Third Option
84 cm²

Step-by-step explanation:

Split the composite figure into two rectangles as shown in the figure

One rectangle has length 12 and width 5 giving an area of 12 x 5 = 60

The other rectangle has length 6 and width 4 giving an area of 6 x 4 = 24

Total area = 60 + 24 = 84 cm²

Third Option

The equation of the area of the square is x² + 6x = 1, it is in the form x² + 6x = a where a is 1 and a constant to be found.

A regular quadrilateral is square. A square has equal lengths on each of its four sides and angles. Each of the four angles is 90 degrees, or a right angle. The two adjacent sides of a square are equal in length, making it a particular instance of a rectangle.

Its attributes are: Each of its four sides is the same length.

Each of its four angles has the same dimensions.

At right angles, or 90°, the two diagonals split in half.

A square has two opposed sides that are equally long and parallel.

A square's diagonal lengths are equal.

The length of the side of the given square is 3 + x.

The area of the square is given as:

A = (s)(s)

Substituting the value of the side and area we have:

10 = (3 + x)(3 + x)

10 = 9 + 3x + 3x + x²

x² + 6x = 10 - 9

x² + 6x = 1

Hence, the equation of the area of the square is x² + 6x = 1, it is in the form x² + 6x = a where a is 1 and a constant to be found.

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The account will be growing by $741.87 per year 11 years from now.

To find the answer, we need to use the formula for compound interest, which is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, P = $2000, r = 0.03, n = 1, and t = 11. Plugging these values into the formula gives us:
A = $2000(1 + 0.03/1)^(1*11)
A = $2000(1.03)^11
A = $2741.87
To find out how fast the account will be growing 11 years from now, we need to subtract the principal amount from the final amount:
$2741.87 - $2000 = $741.87

Therefore, the account will be growing by $741.87 per year 11 years from now.

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The result of alternately adding and subtracting the terms in the nth row of Pascal's triangle is given by the formula

[tex]n C 0 - n C 1 + n C 2 - ... + (-1)^n \times n C n = 0.[/tex]

The binomial theorem and patterns in Pascal's triangle can be used to simplify the given expressions.

Here are the simplified versions of each expression:

9 C 0 + 9 C 1 +…+ 9 C 9 = 2^9 = 512

12 C 0 − 12 C 1 + 12 C 2 −…− 12 C 11 + 12 C 12 = 0

r=0 ∑ 15 15 C r = 2^15 = 32768

r=0 ∑ n n C r = 2^n

If r=0 ∑ n n C r = 16384, then [tex]2^n[/tex] = 16384, so n = 14.

The sum of the squares of the terms in the nth row of Pascal's triangle is given by the formula:

[tex](n C 0)^2 + (n C 1)^2 + ... + (n C n)^2 = 2^{(2n-1).[/tex]

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