Find the average rate of change of g(x) = 3x³ + 1 from æ =
- 1 to x = 4.

Answer:

Hello,

Step-by-step explanation:

0=x²+17x+72=x²+8x+9x+72=x(x+8)+9(x+8)=(x+8)(x+9)

x=[-9,-8]

Answer:

[tex]x = - 8 \: - 9[/tex]

Step-by-step explanation:

[tex]1. \: {x}^{2} + 72 + 17x = 0 \\ 2. \: (x + 8)(x + 9) = 0 \\ 3. \: x = - 8 \: - 9[/tex]

When the product of a number m and 1.7 is 6.63 the required value of m is 3.9

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

Now the given statement is,

The product of a number m and 1.7 is 6.63

Thus, converting it into numerical form we get,

1.7m = 6.63

Dividing both the side by 1.7 we get,

1.7m/1.7 = 6.63/1.7

Solving we get,

m = 3.9

this is the required value of m.

Thus, when the product of a number m and 1.7 is 6.63 the required value of m is 3.9

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The equation representing the relationship between the area of the circle and the radius is given by A = π ( r + 16 )².

We are given that:

Waves travels at a rate of 16 feet / second.

Now, let the radius of circle be r.

Now, we know that the area of a circle is given by:

A = π r²

Now, radius increases by 16 feet every second.

So, the equation of the area will become:

A = π ( r + 16 )²

Therefore, the equation representing the relationship between the area of the circle and the radius is given by A = π ( r + 16 )².

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Each roommate have to pay $68.85 equally.

Given, the TV costs = $275.40 including tax.

number of roommates who wants to buy a Tv with equal pay = 4

Divide the total amount of the TV among the number of roommates.

One of the four fundamental mathematical operations—the others being addition, subtraction, and multiplication—is division. Simply said, division is the process of dividing a large group into smaller groups so that each group contains an equal number of elements. In mathematics, it is an operation that is used for equal distribution and equal grouping.

⇒ 275.40 ÷ 4

= 68.85

Hence each roommate have to pay $68.85 equally to buy a TV which costs $275.50.

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The coordinates of the midpoint M of the segment AD is ( -1, 1 ).

Hence, option A)( -1, 1 ) is the correct option.

The midpoint formula is expressed as;

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

Given the data in the question;

Point A(3,−2)

Point D(−5,4)

To determine the midpoint, plug the given points into the formula above and simplify.

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

M = ( ( 3 + (-5) )/2, ( (-2) + 4)/2 )

M = ( ( 3 - 5 )/2, ( -2 + 4)/2 )

M = ( ( -2 )/2, ( 2)/2 )

M = ( -1, 1 )

The coordinates of the midpoint M of the segment AD is ( -1, 1 ).

Hence, option A)( -1, 1 ) is the correct option.

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Using proportions, it is found that 7.2q and q/6 are different terms, due to the different numeric coefficients.

A fraction is converted to decimal by the division of the numerator by the denominator, that is, we apply the proportion of the numerator by the denominator.

For this problem, we have two terms, given as follows:

7.2q and q/6.

To verify if they are equal terms, we have to look at the numeric coefficients, hence:

Hence 7.2q and q/6 are different terms, due to the different numeric coefficients.

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Step-by-step explanation:

f (x) = 7

Slope: 0

y-intercept: (0,7)

x   y

0   7

1    7

Graph x

Slope: 1

y-intercept: (0,0)

x   y

0  0

1    1

Plot each graph on the same coordinate system.

f (x) = 7

x

The equation of the line that passes through (2, -6) and is perpendicular to the given line is y = -x -4

From the question, we are to determine the equation of a line that passes through (2, -6) and it perpendicular to y = x + 4

If two lines are perpendicular, the product of their slope is -1.

That is,

m₁m₂ = -1

First,

We will determine the slope of the line that the equation was given

y = x + 4

Comparing with the slope-intercept form of the equation of a straight line

y = mx + b

Where m is the slope

and b is the y-intercept

By comparison

m = 1

The slope of the line that the equation was given is 1

Thus,

The slope of the line that is perpendicular to this line is -1

From the given information,

The line passes through the point (2, -6)

Using the point-slope form of the equation of a line

y - y₁ = m(x - x₁)

Then,

y - -6 = -1(x - 2)

y + 6 = -x + 2

y = -x + 2 - 6

y= -x -4

Hence, the equation of the described line is y = -x -4

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Answer:

y = -x -4

Step-by-step explanation:

The inverse function returns the original value for which the output of a function was given.

[tex]y^{-1}[/tex] = -1 ± √(x - 5) /2 be the inverse the function y = (1 - 2x)² + 5.

The inverse function returns the original value for which the output of a function was given. When it comes to functions, f and g are inverse, with f(g(x)) = g(f(x)) = x. A function that is made up of its inverse returns the original value. The inverse of f is then g(y) = (y - 5)/2 = x.

An inverse in mathematics is a function that serves to "undo" another function. That is, if f(x) produces y, then putting y into the inverse of f yields x. Invertible functions are those that have an inverse, which is denoted by f1.

Let the equation be y = (1 - 2x)² + 5

simplifying the above equation, we get

√(x - 5) y = (1 - 2x)² + 5

x = (1 - 2y)² + 5

The function of x be x = (1 - 2y)² + 5

x - 5 = (1 - 2x)²

± √(x - 5) = (1 - 2y)

± √(x - 5) - 1 = 2y

Divide both sides of the equation by 2, we get

[± √(x - 5) - 1]/2 = 2y/2

[± √(x - 5) -1] /2 = y

[tex]y^{-1}[/tex] = -1 ± √(x - 5) /2

Therefore, the inverse of the function be [tex]y^{-1}[/tex] = -1 ± √(x - 5) /2.

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The new function for f(x) = (x – 3) is g(x) = x/2 – 3

Given,

The function, f(x) = (x – 3)

Horizontal stretch by a factor of 2

The quadratic parent function f(x) = (x – 3) is the simplest form of a quadratic function.

If the function is multiplied by the factor b and:

|b| > 0  the function is stretched.

If 0 < |b| < 1 the function is compressed.

Then the new function will be in the form:

g(x) = (1/b)x - 3

Therefore, keeping the above on mind, if b=2, then the new function is:

g(x) = (1/2)x - 3

g(x) = x/2 - 3

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value of the median in the situation = 49

Solution :

Median :

A Median is defined as the middle value in a given set of numbers or data. In Mathematics, there are three different measures, which are used to find the average value for a given set of numbers. They are mean, median, and mode. These three measures are called the measures of central tendency. The average value of the given data is given by mean. The middle value of the given data is defined by a median. The repeated value of the given data is defined by mode.

Mean :

The mean is estimated by dividing the sum of all the numbers by the count of the numbers.

Median Formula

Based on the definition, the formula to find the median of the dataset is given by:

If the given number of observations/data is odd, then the formula to calculate the median is:

Median = {(n+1)/2}th term

If the given number of observations is even, then the formula to find the median is given by:

Median = [(n/2)th term + {(n/2)+1}th term]/2

Where,

“n” is the number of observations.

Count of variety A  = 10

Median = [(n/2)th term + {(n/2)+1}th term]/2

Median = [(10/2)th term + {(10/2)+1}th term]/2

Median = [5th term + {6th term}]/2

Median = [49 + 49]/2

Median = [98]/2

Median = 98/2 = 49

value of the median in the situation = 49

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answer is 36

Step-by-step explanation:

good right?

Answer:

I'm from California I'm new to this

Answer:

Step-by-step explanation:

325

Number of people probably wore sandals at the mall = 9 people

Let 's' denote the total number of people Amelia counted at the mall.

Let x be the number of people wearing sandals out of them.

The equation developed by Amelia according to this is,

 s = 35x + 12

This is a linear equation written with s in terms of x .

Total people counted by Amelia = 325

So we have to find the value of x when s = 325.

Substituting s = 325 to the equation,

325 = 35x + 12

⇒ 325 - 12 = 35x

⇒ x = (325 - 12)/35

⇒ x = 8.9 ≈ 9

Since x denote the number of people wearing sandals, we take x = 9

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The answer to the given logarithm expression is log₄₉7  = 1/2

Another technique to clarify exponents in mathematics is through logarithms. A base number's logarithm equals another number.

For instance, log10 100 = 2 if 102 = 100. A logarithm is defined as an influence by which variety must be raised to receive another value. this is often the foremost convenient thanks to represent large numbers. Logarithms have several important properties that prove that logarithmic multiplication and division is written because the logarithm of addition and subtraction. The log is named the logarithm of base e. The logarithm is represented by ln or loge. where 'e' represents Euler's constant,  approximately capable 2.71828. as an example, the log of 76 is written as ln 76. The log defines what percentage times 'e' must be multiplied to induce the required output.

We need to evaluate log₄₉7

Using Property

logₙ (a) = 1 / logₐ (n)

log₄₉7 = 1/ log₇ 49

Using the properties of log again logₐ (mⁿ) = n logₐ m

49 = 7²log₇ 49

can be written as

log₇ 49 = 2 log₇ 7

We know that logₐ a = 12 log₇ 7= 2

Value of log₄₉7 = 1/ log₇ 49= 1/ 2 log₇ 7= 1/2

Hence,  we evaluated the logarithm which is log₄₉7  = 1/2

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Answer:

B. 8 x 10^3

Step-by-step explanation:

(1.6 x 10^5)/(0.2 x 10^2)

= (1.6/0.2)x(10^5/10^2)

= 8x10^(5-2)

= 8 x 10^3

Answer: The value is −34.234

Step-by-step explanation:

Based on the expression the number of grid squares in a character of size 7 is 55

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression for the number of grid squares in a character of size s is given as

6 + s^2

Rewrite the expression as a function

So, we have

f(s) = 6 + s^2

To find the number of grid squares in a character of size 7, we set s to 7

i.e. s = 7

So, we have

f(7) = 6 + 7^2

Evaluate the exponent

So, we have

f(7) = 6 + 49

Evaluate the sum

So, we have

f(7) = 55

Hence, the number of grid squares in a character of size 7 is 55

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The expanded form of the expression log m² n⁵ is

2 log m +5 log n.

Given that the expression is log m² n⁵.

We are required to find the expansion form of the given expression.

Product property of logarithm says that the logarithm of a product is equal to a sum of logarithms. Because logs are exponents, and we multiply like bases, we have to add the exponents.

The expression is log m² n⁵.

log m² n⁵=log [tex]m^{2}[/tex]+ log [tex]n^{5}[/tex]

=2 log m +5 log n

Hence the expanded form of the expression log m² n⁵ is

2 log m +5 log n.

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The rate of falling temperature is 5 1/3 degrees per hour.

What do you mean by the rate of temperature?

This indicates the sensitivity of the reaction to change in temperature.

Given that;

The temperature fell 4 degrees in 3/4 of an hour.

So, we can set up a proportion to see how much temperature fell in an hour,

[tex]\frac{4}{3/4} = \frac{x}{1}[/tex]

4 /0.75 = x

x = 5 1/3

Hence, The rate of falling temperature is 5 1/3 degrees per hour.

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Answer:(1,800 - 12g) / 30 = m

Step-by-step explanation:

1. Trouvez la différence commune

Trouvez la différence commune en soustrayant n'importe quel terme de la séquence du terme qui le suit.

La différence de la séquence est constante et est égale à la différence entre deux termes consécutifs.

2. Trouvez la somme

3. Trouver le formulaire explicite

4. Trouver la forme récursive

5. Trouvez le neuvième élément

^^ <3

Answer:

They are not equal

Step-by-step explanation:

the first one equals 0

the second one equals 12

Answer: yes

Step-by-step explanation: In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y.

Answer:

Yes it is a function bc no number repeats 2x

Step-by-step explanation:

Y

Answer:

4.: 15.84

5.: 193.2

6.: 10.7*5, 8.4*6, 7.5*7.5, 2.1*24

7.: 6, 5.75

Step-by-step explanation:

4.: 6.6*2.4=15.84

5.: 27.6*7=193.2

6.: 10.7*5=53.5, 8.4*6=50.4, 7.33*6=43.98, 7.5*7.5=56.25, 2.1*24=50.4

7.: 1.6*6.25=10, all numbers higher than 6.25 will return products higher than 10, all numbers lower than 6.25 will return products lower than 10.

Step-by-step explanation:

The sum of ypur ages is

=F+B

in three years your ages will both grow by 3

= (F+3)+(B+3)

For the difference of ages we know tha B is older than F

=B-F

Given that you are in the 88th percentile for GPA, there are 72 students that have a GPA greater than or equal to yours.

Percentile refers to the measure used to indicate the value below which a certain percentage of data lies.

If a data is said to be in the nth percentile, this means that n% of the data in the distribution are equal to or lower than that data.

If you are in the 88th percentile, then 88% of all the 600 students have a GPA equal or lower than yours.

88% of 600 = 0.88(600) = 528

students that have a GPA greater than or equal to yours = 600 - 528

students that have a GPA greater than or equal to yours = 72

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Two expressions with an equal sign is called as Equation. If the difference between two numbers is 12. The first number is 5 less than twice the second number then the two numbers are 29 and 17.

Two expressions with an equal sign is called as Equation.

Let the two numbers be a and b.

Given equation is a-b=12 .....(1) and

The first number is 5 less than twice the second number i.e a=2b-5

Substitute a in (1)

2b-5-b=12

b-5=12

b=17

b=17 is the second number.

Now we have to find first number so

a=2b-5...(2)

Substitute b=17 in (2)

a=2(17)-5

=34-5

=29

Therefore the two numbers are 29 and 17.

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Answer:

A all values are solutions

Step-by-step explanation:

we have the absolute value of an expression (in this case 13x).

that means the result is always (ALWAYS) positive, no matter what happens in the included expression.

the minimum result value is 0.

it cannot get below 0.

so, |13x| > -5 is always true, no matter what value you pick for x.