shayla is buying a birthday present for her mother. she decides to buy a bracelel for 20$. the sales tax is 6%. what is the total cost of the bracelet.

It should be noted that f(x) is increasing on the intervals (-1/2, 0) and (0, ∞), and decreasing on the interval (-∞, -1/2).

The derivative of f(x) is denoted as:

f'(x) = 2x - 1 - 1/x

It should be noted that to determine the critical points, set f'(x) to equal 0 and solve for x:

2x - 1 - 1/x = 0

Multiplying by x gives:

2x^2 - x - 1 = 0

On the intervals (-1/2, 0) and (0, ∞), the function f(x) exhibits increasing behaviour; in (-∞, -1/2). it's decreasing.

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The value of x in the expression is y + 3

The expression given is written as

3x + 3= 3y + 6

collect the like terms

3x - 3y= 6-3

3x - 3y= 3

3x= 3 + 3y

x= 3 + 3y/3

x= 3 + y

x= y + 3

Hence the value of x in the expression is y + 3

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Answer:

The molar mass of a chemical compound is defined as the ratio between the mass and the amount of substance of any sample of said compound.

unit of measurement: g/mol.

A mole is the amount of substance that contains as many elementary entities as there are atoms in 12g of carbon-12.

Avogadro's number= 6.02*10^23 particles.

Answer:

d)367

Step-by-step explanation:

Given, Tn = 5n² - 4

To find the 5th term, substitute n = 5 in the equation Tn = 5n² - 4

T5 = 5(5)² - 4

T5 = 121

To find the 7th term, substitute n = 7 in the equation Tn = 5n² - 4

T7 = 5(7)² - 4

T7 = 241

Therefore, the sum of the 5th and 7th terms = T5 + T7 = 121 + 241 = 362.

Hence, the correct option is (d) 367.

Row 1 in the matrix multiplied by 1/4 will produce: 1/2, 0, and 3/4 respectively.

A rectangular array of numbers or mathematical objects which are arranged in rows and columns is called a matrix. Each row of a matrix is a horizontal sequence of numbers or objects that are separated by commas and enclosed within square brackets, and it represents a vector in the row space of the matrix.

row 1 of the given matrix are: 2, 0, and 3, multiplying row 1 with 1/4 gives;

1/4 × 2 = 1/2

1/4 × 0 = 0

1/4 × 3 = 3/4

Therefore, row 1 in the matrix multiplied by 1/4 will produce: 1/2, 0, and 3/4 respectively.

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The rate at which the college student is earning credits, given the semesters taken, would be E. 14 credits per Semester.

The formula to find the number of credits the student takes per semester, would be :

( total credits after 3 semesters - total credits at the start ) / number of semesters = credits per semester

total credits after 3 semesters = 54 credits

total credits at the start = 12 credits

The credits per semester is therefore;

= ( 54 - 12 ) / 3

= 42 / 3

= 14 credits per semester

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The complete question is:

Which of these expresses the rate at which she is earning credits? Select the correct answer below:

3 credits per semester

42 credits per semester

14 semesters per credit

12 credits per semester

14 credits per Semester

7 semesters per credit

An inequality that matches this graph include the following: B} x ≥ -5.

In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

Since the closed circle is at point -5 and increases to the right, an inequality that matches this graph is x ≥ -5.

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The total surface area of the cylinder with a radius of 8 units and a height of 5 units is 653.12 sq. units.

What is surface area?

The quantity of space enclosing a three-dimensional shape's exterior is its surface area. A three-dimensional shape with height, breadth, and depth is referred to as having three dimensions, and surface area is a measurement of the total area that the surface of that shape occupies. In other terms, the surface area is the sum of the areas of all an object's sides.

Here, we have

Given:

Radius of cylinder = 8 units

Height of cylinder = 5 units

Thus:

Total Surface Area of a cylinder = 2 × 3.14 × 8 (8 + 5)

Total Surface Area of a cylinder = 50.24(13) = 653.12 sq. units.

Hence, the total surface area of the cylinder with a radius of 8 units and a height of 5 units is 653.12 sq. units.

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Answer:

251.2 in

Step-by-step explanation:

Circumference of circle = 2 · π · r

π = 3.14

r = 40 in

Let's solve

2 · 3.14 · 40 = 251.2 in

So, the circumference of the circle is 251.2 in

The answer for given polynomial is 4,1,-1.

A polynomial is made up of two terms, namely Poly (which means "many") and Nominal (which means "terms."). An expression that consists of variables, constants, and exponents and that is combined using mathematical operations such as addition, subtraction, multiplication, and division (no division operation by a variable) is referred to as a polynomial. The expression is divided into three categories: monomial, binomial, and trinomial depending on how many terms are included in it.

The zeros of a function are the values of its variables that meet the equation and result in the function's value being equal to 0. The zeros of a function can be represented graphically as the x-coordinates (or x-intercepts) where the graph intersects the x-axis. The discriminant formula allows us to identify whether the zeros of a quadratic function are real, complex, or repeating. As a result, when a function f(x) = 0, its zeros are x values. Therefore, if f(a) = 0, then 'a' is a zero of f(x).

according to question,

(((([tex]x^{4}[/tex])-(3•(x³)))-5x²)+3x)+4  = 0

 (((([tex]x^{4}[/tex]) -  3x³) -  5x²) +  3x) +  4  = 0

Polynomial Long Division

Dividing :  x4-3x3-5x2+3x+4

                             ("Dividend")

By         :    x-4    ("Divisor")

dividend     x4  -  3x3  -  5x2  +  3x  +  4

- divisor  * x3     x4  -  4x3            

remainder         x3  -  5x2  +  3x  +  4

- divisor  * x2         x3  -  4x2        

remainder          -  x2  +  3x  +  4

- divisor  * -x1          -  x2  +  4x    

remainder              -  x  +  4

- divisor  * -x0              -  x  +  4

remainder                    0

Quotient :  x3+x2-x-1  Remainder:  0

the answer for the given polynomial by hit and trial method is 4,1,-1.

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The zeros of the polynomial is -1 , 1 and 4.

what is polynomial?

A polynomial is made up of two terms, namely Poly (which means "many") and Nominal (which means "terms."). An expression that consists of variables, constants, and exponents and that is combined using mathematical operations such as addition, subtraction, multiplication, and division (no division operation by a variable) is referred to as a polynomial. The expression is divided into three categories: monomial, binomial, and trinomial depending on how many terms are included in it.

Here the given polynomial is g(x) = [tex]x^4-3x^3-5x^2+3x+4[/tex]

To find zeros , take g(x) = 0 then

=> [tex]0=x^4-3x^3-5x^2+3x+4[/tex]

=> [tex]-x^4+3x^3+5x^2-3x-4=0\\[/tex]

=> [tex]-x^4+x^3+2x^3-2x^2+7x^2-7x+4x-4=0[/tex]

=> [tex]-x^3(x-1)+2x^2(x-1)+7x(x-1)+4(x-1)=0[/tex]

=> [tex]-(x-1)(x^3-2x^2-7x-4)=0[/tex]

=> [tex]-(x-1)(x^3+x^2-3x^2-3x-4x-4)=0[/tex]

=> [tex]-(x-1)(x^2(x+1)-3x(x+1)-4(x+1)=0[/tex]

=> [tex]-(x-1)(x+1)(x^2-3x-4)=0[/tex]

=> [tex]-(x-1)(x+1)(x^2+x-4x-4)=0[/tex]

=> -(x-1)(x+1)(x+1)(x-4)=0

=> x-1=0 , x+1=0 , x-4=0

=> x = -1,1,4

Hence the zeros of the polynomial is -1 , 1 and 4.

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Answer:

42, 41, 123

Step-by-step explanation:

3, 2, 6, 5, 15, 14

- 1 x3. - 1. x3. - 1

you just gotta look for the pattern thats the same in the sequence so the next three numbers would be x3, then - 1 then x3 again onto the numbers.

Answer:

The next three numbers are 42, 41, and 123

Step-by-step explanation:

3 - 1 = 2

2 * 3 = 6

6 - 1 = 5

5 * 3 = 15

15 - 1 = 14

The pattern is subtracting one and then multiplying by three.

14 * 3 = 42

42 - 1 = 41

41 * 3 = 123

The number of fewer students to get to school by skateboard than by car and bus combined would be 60 fewer students.

To find how many fewer students get to school by skateboard than by car and bus combined, we need to add the number of students who use car and bus and then subtract the number of students who use skateboard.

Car: 30 students

Bus: 40 students

Car + Bus = 30 + 40 = 70 students

Skateboard: 10 students

Difference = (Car + Bus) - Skateboard

Difference = 70 - 10 = 60 students

So, 60 fewer students get to school by skateboard than by car and bus combined.

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When you multiply an inequality by a positive number, the direction of the inequality does not change. So if 4 < 7, then:

what is inequality?

Inequality is a mathematical statement that describes a relationship between two values or expressions that are not equal. In an inequality, we use the symbols "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to) to indicate the relationship between the values or expressions.

For example, "x < 5" is an inequality that means "x is less than 5", and "y ≥ 10" is an inequality that means "y is greater than or equal to 10". Inequalities are often used in algebra and other branches of mathematics to express relationships between variables or to solve problems.

Multiplying both sides by

7 gives: 28 < 49

Multiplying both sides by

6 gives: 24 < 42

Multiplying both sides by

3 gives: 12 < 21

Multiplying both sides by

10 gives: 40 < 70

All of these inequalities are still true, because we are multiplying both sides by a positive number.

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The vertical measurement of the structure corresponds to an estimated value of 119.53 feet.

The dimensions of the building can be represented by the variable h, whereas the proximity of Jeanna to the building in her initial stance can be identified as x. Utilizing the principles of trigonometry, it is feasible to express the following:

The trigonometric function involving the angle of 35 degrees and its corresponding acute triangle can be written as an equation in the form of tan(35) = h/x, which is denoted as equation 1.

Upon moving a distance of 100 feet from her initial position, Jeanna's distance from the building can be represented as x - 100. Additionally, the angle at which she must look up to view the top of the building is now 40 degrees. Through the application of comparable trigonometric reasoning, it is possible to articulate the following statement:

Equation 2 can be expressed as tan(40) = h/(x - 100), where h and x represent the height and horizontal distance, respectively.

Equation 1 can be manipulated in such a way as to express the variable x in terms of h. The value of x is obtained by dividing h by the tangent of 35 degrees.

The substitution of the given expression for variable x in equation 2 leads to the following result:

The equation tan(40) = h/(h/tan(35) - 100) is amenable for rephrasing in a more academic style of writing.

Upon performing reduction on this mathematical expression, it results in:

The given mathematical equation can be represented in an academic manner as follows: The equation tan(40) = tan(35)h/(h - 100tan(35)) holds true, where h denotes the height of an object located at an angle of 40 degrees to the horizontal plane. This equation specifies the relationship between the tangent values of two distinct angles, 40 degrees and 35 degrees, and the height of the object.

The present equation can be expressed in a more formal academic style as follows: "The function h is defined as the difference between the tangent of 40 degrees and the tangent of 35 degrees, i.e., h = tan(40) - tan(35). This formula can be simplified, resulting in h = -100tan(35)tan(40)."

By dividing each side of the equation by (tan(40) - tan(35)), we are able to obtain the following result:

The following expression denotes the value of h, computed using mathematical operations: h = -100tan(35)tan(40)/(tan(40) - tan(35)).

The value of h is approximately equal to 119.53 feet.

Hence, the vertical measurement of the structure corresponds to an estimated value of 119.53 feet.

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Answer:

y = (5/3)x + 2/3

Step-by-step explanation:

find slope

rise/run

(4--1)/(2--1)

(5)/(3)

M = 5/3

then plug in a point to get the y-intercept

4 = (5/3) * 2 + b

4 = 10/3 + b

subtract 10/3 on both sides

2/3 = b

in y =mx +b the equation is

y = (5/3)x + 2/3

Area of the patio is -6x² + x + 2 square yards and perimeter of the patio is 6 - 2x yards.

A yard is a unit of measurement used to measure length or distance in both the US customary system and the British imperial system. One yard is equal to 3 feet or 36 inches. In the US customary system, a yard is equal to 0.9144 meters, while in the British imperial system, it is equal to 0.9144 meters or 3 feet. Yards are commonly used for measuring larger distances, such as in construction or landscaping, as well as in some sports like American football and cricket.

The area of the rectangular patio is given by multiplying its length by its width, so the area is:

A = (1 + 2x)(2 - 3x)

Now using distributive property we get,

A = 2 - 3x + 4x - 6x²

Simplifying further, we get:

A = -6x² + x + 2

Therefore, the area of the patio is described by the quadratic equation -6x² + x + 2.

To find the perimeter of the patio, we add up the lengths of all four sides. The length and width are given as (1 + 2x) and (2 - 3x), respectively, so the perimeter is:

P = 2(1 + 2x) + 2(2 - 3x)

Simplifying this expression, we get:

P = 2 + 4x + 4 - 6x

P = 6 - 2x

Therefore, the perimeter of the patio is described by the linear equation 6 - 2x.

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The total volume of the wall units is 108 cubic feet

The volume of the wall is solved by dividing the figure to give the various dimensions represented in the form length x width x depth

The volume of each is solved then added to get the total volume

first division: 4 x 4 x 8 = 96

second division: 3 x 2 x 2 = 12

The total volume is

= 96 + 12

= 108 cubic feet

so the total volume is solved to be 108 cubic feet

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Therefore , the solution of the given problem of expressions comes out to be points X(-2,4), Y(-4,4), and Z(4,2) would be X'(-2,4), Y'(-3,-1), and Z'(0,3).

Instead of using random estimates, shifting variable numbers should be employed instead, which can be growing, diminishing, or blocking. They could only help one another by transferring items like tools, knowledge, or solutions to issues. The explanations, components, or mathematical justifications for strategies like expanded argumentation, debunking, and blending may be included in the explanation of the reality equation.

Here,

Figure XYZ will be scaled down by 1/4, with the centres being X(-2,4), Y(-4,4), and Z(4,2)

=>  Old_x - Center_x - Scale_factor * New_x + Center_x

=>  Scale factor * (Old y - Centre y) + Centre y = New y

Regarding X:

=>  New_x = 1/4 * (-2 - (-2)) + (-2) = -2

=>  New_y = 1/4 * (4 - 4) + 4 = 4

Therefore, X'(-2,4) is the image of point X after dilation.

Regarding Y:

=>  New_x = 1/4 * (-4 - (-2)) + (-2) = -3

=>  New_y = 1/4 * (-4 - 4) + 4 = -1

Therefore, Y'(-3,-1) is the image of point Y following dilation.

Regarding Z:

=> New_x = 1/4 * (4 - (-2)) + (-2) = 0

=> New_y = 1/4 * (2 - 4) + 4 = 3

Therefore, Z'(0,3) is the image of point Z after dilation.

As a result, the image points for the dilated figure XYZ with the centre points X(-2,4), Y(-4,4), and Z(4,2) would be X'(-2,4), Y'(-3,-1), and Z'(0,3).

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The measure of the angle that turns through 3/10 of the circle is 108 degrees.

An angle is a geometric figure that is formed by two rays that share a common endpoint, which is called the vertex of the angle. The rays are referred to as the sides or legs of the angle. Angles are typically measured in degrees, with a full circle measuring 360 degrees.

Angles can be classified based on their degree of measurement: acute angles are less than 90 degrees, right angles are exactly 90 degrees, obtuse angles are greater than 90 degrees but less than 180 degrees, and straight angles are exactly 180 degrees.

Since a full circle has 360 degrees, 3/10 of the circle can be represented as:

(3/10) x 360 degrees = 108 degrees

Therefore, the measure of the angle that turns through 3/10 of the circle is 108 degrees.

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The complete question is :

The angle turns through 3/10 of the circle. What is the measure of the angle?

Answer:

x=4

y=5

Step-by-step explanation:

The simplest form of the expression "(14ab³)/(7a⁻²b⁻¹)" is represented by the expression (d) 2a³b⁴.

To simplify the expression (14ab³)/(7a⁻²b⁻¹), we first simplify the terms with the same base,

First, we simplify the coefficients "14" and "7" by dividing them to get:

⇒ (14ab³)/(7a⁻²b⁻¹) = 2ab³/a⁻²b⁻¹;

Next, we simplify the variables "a" and "b" by subtracting the exponents of "a" and "b" in the denominator respectively,

We get,

⇒ 2ab³/a⁻²b⁻¹ = 2a¹⁻⁽⁻²⁾b³⁻⁽⁻¹⁾ = 2a¹⁺²b³⁺¹ = 2a³b⁴,

Therefore, the simplest form of the expression (14ab³)/(7a⁻²b⁻¹) is 2a³b⁴, the correct option is (d).

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The given question is incomplete, the complete question is

Look at this expression. (14ab³)/(7a⁻²b⁻¹),

Which of the following is the simplest form of the expression above?

(a) 2a⁻²b⁻³

(b) 2a⁻¹b²

(c) 2[tex]a^{-\frac{1}{2} }[/tex]b⁻³

(d) 2a³b⁴.

Answer: 96 fifth grade students outside for exercise. 48 students playing soccer, 24 students playing basketball, 12 students jogging around the track, and 12 students tossing footballs.

Step-by-step explanation:

Let x be the total number of fifth grade students.

- 1/2x are on the soccer fields

- 1/4x are on the basketball courts

- 1/8x are jogging around the track

- 12 students are tossing footballs

x = 1/2x + 1/4x + 1/8x + 12

x = 4/8x + 2/8x + 1/8x + 12

x = 7/8x + 12

1/8x = 12

x = 12*8

x = 96

Therefore, there are 96 fifth grade students outside for exercise.

Soccer fields: 1/2x = 1/2 * 96 = 48 students

Basketball courts: 1/4x = 1/4 * 96 = 24 students

Jogging around the track: 1/8x = 1/8 * 96 = 12 students

Tossing footballs: 12 students (as given in the problem)

There are 48 students playing soccer, 24 students playing basketball, 12 students jogging around the track, and 12 students tossing footballs.

Answer:

96 students in general

Step-by-step explanation:

I drew an Euler circle to make it more clear. so we can see that 1/8 class = 12

so 1/4 class is 12×2=24

1/2 class is 12×4=48

12+12+24+48=96

I hope this helped

Answer:

76°

Step-by-step explanation:

The sum of the interior angles of any quadrilateral is 360°.

p = 360 - 60 - 134 - 90 = 76

Answer: 12

Step-by-step explanation: 2 x 6 = 12 = the third side

The sportsman has a final distance with respect to his home equal to 305 meters.

In this problem we must the final distance of the sportsman with respect to his home. This can be determined by the following expression:

X = ∑ xₙ, for n = {1, 2, 3, ..., N}

Where the sportsman goes far away for his home for x > 0, in meters.

Now we proceed to determine the final distance:

X = + 350 m - 125 m + 80 m

X = + 305 m

The final distance of the sportsman with respect to his home is 305 meters.

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Answer:

Step-by-step explanation:

1

The direct distance between Thom's house and his school, as the crow flies, is  7.21 miles.

To find the direct distance between Thom's house and his school, we can use the Law of Cosines.

The Law of Cosines is a formula used to find the length of one side of a triangle when the lengths of the other two sides and the angle between them are known. In this case, we have a triangle with sides of length 6 miles, 8 miles, and the angle between them is 60 degrees.

The Law of Cosines formula is:

c² = a² + b² - 2ab * cos(C)

where:

a and b are the lengths of the known sides of the triangle

C is the angle between those two sides

c is the length of the unknown side (the distance we want to find)

In this case:

a = 6 miles

b = 8 miles

C = 60 degrees

First, convert the angle from degrees to radians:

C (radians) = (60 degrees * π) / 180 = 1.047 radians

Now, apply the Law of Cosines:

c² = 6² + 8² - 2 x 6 x 8 x cos(1.047)

c² = 36 + 64 - 96 x cos(1.047)

c² ≈ 36 + 64 - 96 x 0.5

c² ≈ 36 + 64 - 48

c² = 52

Finally, find the square root to get the distance:

c = √52 = 7.21 miles

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Answer:

b

Step-by-step explanation:

b