Given f(x) = x + 2 and g(x) = x2 – 4, find the function (g/f)(x).

Answer:

Negative nonlinear association.

Step-by-step explanation:

The value of [m] = 5 cm and [n] = 12 cm.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.

We have the perimeter of the rectangle is 34 cm. The perimeter of the triangle is 30 cm.

We can write -

2(m + n) = 34

m + n + (n + 1) = 30

Now -

m + n = 17

2n + m = 29

We can write -

m = 17 - n

then -

2n + 17 - n = 29

n = 29 - 17

n = 12 cm

so -

m = 17 - 12

m = 5 cm

Therefore, we get, the value of [m] = 5 cm and [n] = 12 cm.

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Answer:

792 ways

Step-by-step explanation:

To simplify 1/(5 + √3), multiply both numerator and denominator by the conjugate of the denominator, which is 5 - √3. This results in (5 - √3)/22, which is the simplified form of the expression.

The student has asked to evaluate the expression 1/(5 + √3). To simplify this expression, we can multiply both the numerator and the denominator by the conjugate of the denominator to get rid of the square root in the denominator. The conjugate of 5 + √3 is 5 - √3. So, we multiply the expression by (5 - √3)/(5 - √3).

The resulting expression after multiplication:

So our final answer after simplification is:

(5 - √3)/22

complete question given below:

Evaluate 1/(5+ square root of 3)

Answer:

The nth term for the geometric sequence is given by:

[tex]a_n = a_1 \cdot r^{n-1}[/tex]

where,

[tex]a_1[/tex] is the first term

r is the common ratio of the terms.

As per the statement:

Given the sequence

-12,__,__, -324

here, [tex]a_1 = -12[/tex] and [tex]a_4 = -324[/tex]

Solve for r:

By definition we have;

[tex]a_4 = a_1 \cdot r^3[/tex]

⇒[tex]-324 = -12 \cdot r^3[/tex]

Divide both sides by -12 we have;

[tex]27 = r^3[/tex]

⇒[tex]r = \sqrt[3]{27} =\sqrt[3]{3^3} = 3[/tex]

We have to find the missing terms [tex]a_2, a_3[/tex]

[tex]a_2=a_1 \cdot r[/tex]

⇒[tex]a_2 = -12 \cdot 3 = -36[/tex]

[tex]a_3=a_1 \cdot r^2[/tex]

⇒[tex]a_2 = -12 \cdot 3^2 = -12 \cdot 9 = -108[/tex]

therefore, the missing terms in the following geometric sequence is,

-12,_-36_,_-108_, -324

Answer:

-21 I think

I hope i helped you!

Answer:

D

Step-by-step explanation:

Correct on A P E X

Answer:

The game gives each player an initial amount of $5,000 in virtual money. After that, a player gets $500 in virtual money for each race won. This $5000 is fixed.

Let the races won be x

So, the function that represents the amount of virtual money a player has in terms of the number of races won becomes :

[tex]f(x)=500x+5000[/tex]

The independent quantity (x) is : the number of races won

And the dependent quantity f(x) or y is : the total virtual money earned

Answer: (A) The first option is the right answer.

Step-by-step explanation:

l ≤ 12

2l + 2w < 30

The following terms are defined below:

a. Whole number, b. Digit, c. Place value, d. Rounded number, and e. Equals.

a. Whole Number: A whole number is a positive integer not having any fractional or decimal parts. Whole numbers include the set of natural numbers(non-negative integers) along with zero.

b. Digit:  A digit, in mathematics, means any of the numerical symbols used to denote numbers in the decimal numeral system.

c. Place value: Place values are the values of a digit in a number based on its position or place within that number. Based on powers of ten, in the decimal numeral system, each digit's position determines its place value.

d. Rounded number: An approximation of a numerical value having been adjusted or approximated to a certain level of precision or a specific place value is called a "rounded number".

e. Equals: Mathematically, the term "equals" is utilized to represent that two quantities or expressions have the same value. The equals sign (=) is a symbol used to indicate equality between two mathematical expressions.

Thus, the above terms are defined.

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Final answer:

Whole numbers are counting numbers without fractions or decimals, digits are symbols used to represent numbers, place value is the value of a digit based on its position, a rounded number is simplified for ease of use, and equals shows that two quantities have the same value.

Explanation:

In the field of mathematics, the terms mentioned refer to basic concepts essential for understanding numbers and arithmetic operations.

a. Whole number

Whole numbers are the basic counting numbers starting from 0 and including all positive integers (1, 2, 3, ...). They do not include fractions, decimals, or negative numbers.

b. Digit

A digit is any one of the ten symbols used to write numbers. These symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

c. Place value

Place value refers to the value of a digit based on its position in a number. For instance, in the number 231.45, the place value of the digit '3' is tens, meaning it represents thirty.

d. Rounded number

A rounded number has been altered to a nearby, often simpler number. Rounding is done to make numbers easier to work with, especially when precision is not crucial.

e. Equals

The term 'equals' is used to signify that two quantities are the same in value, often represented by the symbol '='.

Only one statement is correct:

B ) The function is increasing from x = 0 to x = 1

Explanation: g ( 0 ) = 2, g ( 1 ) = 17,  2 < 17.

Final answer:

The question seeks the correct translation rule for the movement of quadrilateral ABCD to A'B'C'D'. Translation in geometry involves moving a shape in a consistent direction and distance. Given option A is incorrect, and considering directionality, T <-3,2> (ABCD) is another possibility for the translation.

Explanation:

The question asks for the rule that describes the translation of quadrilateral ABCD to A'B'C'D'. A translation in geometry is a type of transformation that moves every point of a shape the same distance in the same direction. Since option A, which is T <3,-2> (ABCD), is given as incorrect, let's analyze the remaining options.

To determine the correct rule for translation, we need to look at the relative position of the original points and their corresponding points after the translation. For example, if point A were at (x,y) and A' is at (x+3, y-2), this would correspond to a translation of 3 units to the right and 2 units down, which is described by the vector <3, -2>.

Since option A is incorrect and we know that the transformation corresponds to a translation and not a reflection or rotation, let's consider the other options. Looking at option D, T <-3,2> (ABCD), this would imply that every point of quadrilateral ABCD is moved 3 units to the left (because of -3) and 2 units up (because of 2), which would be the reverse of what is described in option A.

a)

Reflection over x-axis.

We know that when any point is reflected over the x-axis, then the rule of transformation that is applied is:

               (x,y) → (x,-y)

Hence,

         A (2,5)→ A'(2,-5)

         B (4,6) → B'(4,-6)

and  C (3,1) → C'(3,-1)

b)

 Reflection about the line y=3

We know that any point after reflection is at a fixed distance from the line as it was before reflection.

Hence,

         A (2,5)→ A'(2,1)

         B (4,6) → B'(4,0)

and  C (3,1) → C'(3,5)

c)

T<-2,5>

The rule that is applied to this translation is:

         (x,y) → (x-2,y+5)

Hence,

         A (2,5)→ A'(0,10)

         B (4,6) → B'(2,11)

and  C (3,1) → C'(1,6)

d)

                    T<3,-6>

The rule that is applied to this translation is:

                  (x,y) → (x+3,y-6)

Hence,

         A (2,5)→ A'(5,-1)

         B (4,6) → B'(7,0)

and  C (3,1) → C'(6,-5)

e)

    r(90◦, o)    

It is  a rotation of a point 90 degree clockwise about the origin.

Hence, the rule that describes this transformation is:

           (x,y) → (y,-x)

Hence,

         A (2,5)→ A'(5,-2)

         B (4,6) → B'(6,-4)

and  C (3,1) → C'(1,-3)

50 x 32 = 1600square feet

area of a square is S^2 so the length of the side of a square would be 1600 =S^2

S=sqrt(1600) = 40 feet long

 perimeter of a square is 40 x 4 = 160 feet