Willy Wonka makes a 13 metre chocolate bar as he believes that chocolate is best made as a giant piece rather than small packaged pieces. The chocolate bar is then cut into 4/11 of a metre. How many bars does this make?

The area of the shaded region is calculated as: 6.88 yd²

The area of the shaded region in the diagram = area of rectangle - area of semicircle.

Given the following:

Area of the semicircle = 1/2(πr²) = 1/2 × 3.14 × 4² = 25.12 yd²

Area of the rectangle = length × width = 8 × 4 = 32 yd²

The area of the shaded region = 32 - 25.12 = 6.88 yd²

Learn more about the area of shaded region on:

https://brainly.com/question/14989383

#SPJ1

The system of linear equations have variable unique solutions, infinitely many solutions and no solutions.

In algebra, a system of equations comprises two or more equations and seeks common solutions to the equations. "A system of linear equations is a set of equations which are satisfied by the same set of variables."

A system of equations as discussed above is a set of equations that seek a common solution for the variables included.

1.

y = -2x + 3 ...eq(i)

y = 1/2x - 7 ...eq(ii)

The solutions to the linear equations (x,y) are (4, -5)

2.

y = 2x - 7 ...eq(i)

y = 5x + 5 ...eq(ii)

The solutions to the linear equations (x,y) are (-4, -15)

3.

3y = -12x + 6 ...eq(i)

y = -4x + 2 ...eq(ii)

The linear equations (x, y) have infinitely many solutions

4.

y = -2x + 3 ...eq(i)

y = 2x - 1 ...eq(ii)

The linear equations (x,y) have solutions of (1, 1)

5.

y = 5x + 4 ...eq(i)

y = 5x - 2 ...eq(ii)

The linear equations have no solutions

Learn more on system of linear equation here;

https://brainly.com/question/13729904

#SPJ1

Answer: I hope this is helpful mark me brainlist if this apply to you

Step-by-step explanation:

The square meter, also called the meter squared, is the International System of Units (SI) unit of area. The symbol for square meters is m2. Less formally, square meter is sometimes abbreviated as sq m.A metre square is a square with sides one metre in length – it refers to the shape and the side length, not the area. By contrast, a square metre is an area and can be any shape.The basic unit of length is the meter and is denoted as. In geometry, can be used as a variable to denote a line and can be used to name a point. In algebra, denotes the slope of a line in the equation y = m x + c .

a) The function velocity of the particle is v(t) = 0.5 · t² + 6 · t + 7, b) The distance traveled by the particle is 467 feet.

In this problem we have the equation that represents the acceleration of a particle. The function velocity (v) is obtained by integrating the function acceleration (a) and the function position is obtained by integrating the function velocity. Now we present the definitions of each function:

Velocity

v(t) = ∫ a(t) + C

Position

s(t) = ∫ v(t) + C

Where C is the integration constant.

The distance traveled during the time interval is found means of definite integrals:

Δs = [tex]\int\limits^b_a {v(x)} \, dx[/tex]= s(b) - s(a)

a) First, determine the function velocity of the particle:

v(t) = ∫ (t + 6) dt + C

v(t) = 0.5 · t² + 6 · t + C

7 = C

v(t) = 0.5 · t² + 6 · t + 7

b) Second, determine the distance traveled in the given time interval:

Δs = s(10) - s(0)

Δs = 0.167 · 10³ + 3 · 10² + 7 - 0.167 · 0³ - 3 · 0² - 7

Δs = 467

To learn more on definite integrals: https://brainly.com/question/14279102

#SPJ1

It is Growing Exponential function because the base is greater than 1 and the exponent has a positive sign.

What is exponential decay function?

A exponential decay is a function that, as the name implies, decays exponentially. So it decays fast at the beginning and slower as the value of the variable increases.

[tex]y=5^x[/tex]

It is a function called "Exponential function". The base determines the growth or decay of the function.

If  base > 1, then the function grows, otherwise if base is between 0 and 1, the function decays.

Here, the  base is positive and it's not 1 or 0.

If we have

[tex]y=5^{-x}[/tex]

this function can be rewritten in this way:

[tex]y=(1/5)^x[/tex]

Here, base between 0 and 1, the function decays

To learn more about the exponential decay function from the given link

brainly.com/question/19599469

#SPJ4

Answer:

m<8=1024

Step-by-step explanation:

Since they are asking for m<8, we do 128*8=1024.

The value of the variable x and the measures of each side of the triangle ΔDEF found using the definition of an isosceles triangle are;

x = 9

DE = 13

EF = 28

DF = 28

An isosceles triangle is a triangle that has two angles in the triangle that are congruent  and two congruent sides.

The specified parameters are;

∠D is congruent to ∠E in triangle ΔDEF

The length of the segments of ΔDEF are;

DE = x + 4

EF = 4·x - 8

DF = 7·x - 35

The (base) angles ∠D and ∠F of ΔDEF are congruent, therefore, ΔDEF is an isosceles triangle (definition)

Therefore;

EF = DF (Definition of an isosceles triangle)

4·x - 8 = 7·x - 35

7·x - 4·x = 3·x = 35 - 8 = 27

3·x = 27

x = 27 ÷ 3 = 9

x = 9

DE = x + 4

Therefore;

DE = 9 + 4 = 13

EF = 4·x - 8

Therefore;

EF = 4 × 9 - 8 = 28

DF = 7·x - 35

Therefore;

DF = 7 × 9 - 35 = 28

Learn more about isosceles triangles in geometry here:

https://brainly.com/question/29618252

#SPJ1

By using a linear combination, we can write our number using only hundreds and ones as:

2,857 = 28*100 + 57*1

To write the number using only hundreds and ones we need to write our number as a linear combination of ones and hundreds, so we can write:

2,857 = a*100 + b*1

There are multiple solutions for this, we can use b to cover the ones and the tens, so:

57 = b*1

57 = b

And we can use a to cover the hundreds and thousands, so:

2,800 = a*100

2,800/100 = a

28 = a

Then we can write our number using only hundreds and ones as:

2,857 = 28*100 + 57*1

Learn more about linear combinations:

https://brainly.com/question/4658834

#SPJ1

Answer: 1.41 meters

Step-by-step explanation:

14.1 decimeters to meters
Decimeters are 10 times smaller than meters, so you divide the value by 10 to get meters
14.1/10 = 1.41
1.41 meters

Answer:

8%

Step-by-step explanation:

1. Subtract:

  55000 - 50600 = 4400

2. Divide:

   4400/55000 = 0.08

The algebraic expression √((x²-1)²) simplifies to x²-1

An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.

Given: sqrt((x^(2)-1)^(2))=x^(2)-1

√((x²-1)²)

The square root will cancel out the square:

Thus, √((x²-1)²)  = x²-1

Therefore,  √((x²-1)²) simplifies to x²-1

Learn more about algebraic expressions on:

https://brainly.com/question/4344214

#SPJ1

The solution to the inequality expression is x ≥ - 5

what is inequality expressions ?

Both equations and inequalities are mathematical phrases created by connecting two expressions. The two expressions are regarded as being equivalent in an equation.

solution:

The given expression - 4(x + 3) ≤ –2 – 2x

                                     - 4x - 12  ≤ -2 - 2x

                                      -4x + 2x  ≤ -2 + 12

                                              -2x  ≤  10

                                               -x  ≤ 5

Multiply  both sides by - 1

Then x ≥ - 5

Hence the solution to the inequality expression is x ≥ - 5

To learn more about inequality expression from the given link

https://brainly.com/question/25275758

#SPJ4

Hence, yes we can solve the triangle with the help of Law of Cosines.

What is trigonometry?

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Here given that,

Some people are saying it is possible to use the Law of Cosines to solve a triangle if given only three angles, and some are saying it is not possible.

Yes, with the help of Law of Cosines we can solve the triangle and the formula for it is

[tex]c^2=a^2+b^2-2abcos(C)[/tex]

where, [tex]a,b,c[/tex] are the side lengths of the triangle and [tex]C[/tex] is the angle.

Hence, yes we can solve the triangle with the help of Law of Cosines.

To know more about the trigonometry

https://brainly.com/question/10283811

#SPJ1

Answer:

Step-by-step explanation:

3< 0 + 2

3 < 2

the inequality is false because 3 is greater than 2, so the ordered pair (0,3) can’t be a solution of the inequality

Answer:

(0, 3) is not a solution to y < x + 2.

Step-by-step explanation:

Plug the given coordinates in to the inequality:

(0, 3)  →  x = 0,  y = 3

y < x + 2

3 < 0 + 2

3 ≮ 2

(0, 3) is not a solution to y < x + 2.

Answer:

D. The longest side is twice as long as the shortest side.

Step-by-step explanation:

Given one angle is 30° and another is 60°, the third must be 90°, making a Special 30-60-90 triangle. In a 30-60-90 triangle, the hypotenuse (longest side) is twice (two times) as long as the shortest side.

Answer:

this 1

Step-by-step explanation:

same doubt pease any help

Answer:

Rate = 72 km per hour
Distance traveled in 2 hours = 144 km

Step-by-step explanation:

The car speed is given as 20 meters per second

There are 3600 seconds in an hour

So in 1 hour the car would travel 20 x 3600 = 72,000 meters. This is equivalent to 72,000 meters per hour

There are 1000 meters in a kilometer

So, in terms of kilometers, the car would travel 72,000/1000 = 72 km i one hour. This is equivalent to a speed of 72 km per hour

In 2 hours the car would travel 72 x 2 = 144 km

Answer:

25 people

Step-by-step explanation:

10 people will be vaccinated for 2hrs

10 = 2

y people will be vaccinated for 5hrs

y = 5

(To find y we need to cross multiply)

10 = 2

y = 5

2y= 50

y=50/2

y=25

:- 25 people will be vaccinated in 5hrs.

Lets check if our answer is correct let us make 5 hrs our unknown x

10 = 2

25 = x

(cross multiply)

25×2=10x

50=10x

x=5hrs

so our answer is correct.

please rate as brainliest

The two quantities have proportional relationship and it's slope is 333.33

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

In this case, we have to determine is there's a uniform increase or decrease of the quantity.

The formula of proportionality is often given as

y = kx

Let's take two points and check if they share the same constant of proportionality

2000 = k(6)

k = 333.33

1000 = k(3)

k = 333.33

The relationship between sales and day is proportional.

The slope of the graph is given as

m = y₂ - y₁ / x₂ - x₁

m = 2000 - 1000 / 6 - 3

m = 333.33

NB: The slope and constant of proportionality in this case are the same quantity.

Learn more on proportions here;

https://brainly.com/question/18437927

#SPJ1

The points of a triangle are known as vertices, and various triangle points are centroid, circumcenter, incenter and orthocenter.

A triangle is a three-sided polygon.

The triangle's three points are known as vertices.

Several triangle-related points:

Thus, the points of a triangle are known as vertices, and various triangle points are centroid, circumcenter, incenter and orthocenter.

To learn more about points of triangle refer here

https://brainly.com/question/10273861

#SPJ4

To match equivalent expression is the fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.

In mathematics, equivalent fractions are those with the same denominator and differing numerators.

According to equivalent fractions, two or more fractions are considered to be equal if both provide the same fraction following simplification. Let's imagine that two fractions, a/b and c/d, were simplified to provide comparable fractions, e/f. In this case, the two fractions are equal to one another.

For instance, if we simplify 5/15, we get a fraction that is equal to 1/3, which is equal to 5/15.

We have to find how do we match equivalent expression.

To learn more about fraction visit: https://brainly.com/question/10354322

#SPJ4

The value of x in the Algebraic expressions is x = w / (56+r).

What is Algebra?

Algebra is a branch of mathematics focused on the study of mathematical symbols and the rules for manipulating those symbols. In algebra, letters and other symbols represent numbers, which can be manipulated and combined to solve equations and other mathematical problems. Algebra is used in a variety of different fields, from engineering to economics, and is essential for anyone studying mathematics. Algebra can be used to solve problems involving linear equations, quadratic equations, polynomials, and more. Algebra also provides an important foundation for more advanced fields of mathematics, such as calculus. By learning the basics of algebra, students can gain an understanding of key mathematical concepts and gain the skills necessary to solve complex problems.

The solution is,

given:        19x + rx  = -37x + w

            ( 19x + 37x) = w - rx

                56x + rx  = w

                 x(56+r )  = w

                             x = w / (56+r)

Therefore the value of x in the algebraic expression is  x = w / (56+r).

To learn more about Algebra from the given link,

https://brainly.com/question/4344214

#SPJ9

Answer:

[tex]\begin{aligned}\textsf{(a)} \quad y&=-6x^2\\y&=4x^2-2\end{aligned}[/tex]

[tex]\textsf{(b)} \quad x=\dfrac{1}{4}y^2[/tex]

Step-by-step explanation:

A graph is symmetric with respect to the y-axis if for every point (a, b) on the graph, there is also a point (-a, b) on the graph.

Linear functions are not symmetric with respect to the y-axis.

Quadratic functions are symmetric with respect to the y-axis if the y-axis is their axis of symmetry, so when the variable x is squared.

Cubic functions are not symmetric about the y-axis.

Square root functions are not symmetric about the y-axis.

There are two quadratic functions with x² in the given answer options.

Test to see if they are symmetric with respect to the y-axis.

Test for symmetry

To determine if a graph is symmetric with respect to the y-axis, replace all the x's with (−x).  If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the y-axis.

Given function:

[tex]y=-6x^2[/tex]

Replace x with (-x):

[tex]\implies y=-6(-x)^2[/tex]

[tex]\implies y=-6x^2[/tex]

Therefore, as the function is equal to the original function, this function is symmetric with respect to the y-axis.

Given function:

[tex]y=4x^2-2[/tex]

Replace y with (-y) and x with (-x):

[tex]\implies y=4(-x)^2-2[/tex]

[tex]\implies y=4x^2-2[/tex]

Therefore, as the function is equal to the original function, this function is symmetric with respect to the y-axis.

A graph is symmetric with respect to the x-axis if for every point (a, b) on the graph, there is also a point (a, -b) on the graph.

Linear functions are not symmetric with respect to the x-axis.

Quadratic functions are symmetric with respect to the x-axis if the x-axis is their axis of symmetry, so when the variable y is squared.

Cubic functions are not symmetric about the x-axis.

Square root functions are not symmetric about the x-axis.

There is one quadratic functions with y² in the given answer options.

Test to see if it is symmetric with respect to the x-axis.

Test for symmetry

To determine if a graph is symmetric with respect to the x-axis, replace all the y's with (−y).  If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the x-axis.

Given function:

[tex]x=\dfrac{1}{4}y^2[/tex]

Replace y with (-y):

[tex]\implies x=\dfrac{1}{4}(-y)^2[/tex]

[tex]\implies x=\dfrac{1}{4}y^2[/tex]

Therefore, as the function is equal to the original function, this function is symmetric with respect to the x-axis.

The expression written in terms of sinx and cosx is

sinx· cos7π/4 - cosx ·sin7π/4

What is an algebraic expression?

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression.

The given expression is sin(x - 7π/4).

Use the formula for sin(A-B) to rewrite the expression:

sin(x - 7π/4)

= sinx· cos7π/4 - cosx ·sin7π/4

Hence, the expression written in terms of sinx and cosx is sinx· cos7π/4 - cosx ·sin7π/4

Learn more about algebraic expressions here:

https://brainly.com/question/953809

#SPJ1

The maximum value of the parabola is represented by y-vertex whose value is 9.

What is a Quadratic Function?

The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

For solving a quadratic function you should find the discriminant: Δ=b²-4ac . And after that you should apply the discriminant in the formula:[tex]x=\frac{-b\pm\sqrt{\Delta} }{2a}[/tex] .

The question gives a quadratic equation and two points, but you do not know some coefficients. Then, you should find the unknown coefficients and after that, you should find the y-vertex of the parabola ([tex]y_v=\frac{-{\Delta} }{4a}[/tex]).

             y = a(x - 1)² + k  ->  points (2, 6.5) and (-1, -1), thus

            6.5=a(2-1)² + k (1)

            -1=a(-1-1)² + k   (2)

         Simplifying the equations

             6.5=a(1)² + k  ( 1 )

            -1=a(-2)² + k  (2)

            6.5=a+ k      ( 1 )

            -1=4a+ k      (2)

         Multiply equation 1 by -1

            -6.5=-a- k    ( 1 )

            -1=4a+ k      (2)

          Sum equations 1 and 2

           -7.5=3a

              a= -2.5

        If a= -2.5, from equation 1, you have

            -6.5=-a- k    

            -6.5=-(-2.5)- k  

            -6.5=2.5- k

            k=2.5+6.5

            k=9

Then , the parabola equation is y= -2.5 (x-1)² +9. You can rewrite it as:

y=-2.5(x²-2x+1)+9

y= -2.5x²+5x-2.5+9

y= -2.5x²+5x+6.5

[tex]y_v=\frac{-{\Delta} }{4a}=y_v=\frac{-{(b^2-4ac)} }{4a}=\frac{-{(5^2-4*(-2.5)*(6.5))} }{4*(-2.5)}=\frac{-90}{-10} =9[/tex]

Learn more about the quadratic function here:

brainly.com/question/1497716

#SPJ1

We are interested in values that make the quadratic expression negative if the quadratic expression is less than, equal to, or greater than 0. We are interested in numbers that make our quadratic expression positive if the quadratic expression is more than, greater than, or equal to 0.

An discriminant value definition ?

The discriminant is the expression b2 - 4ac for the quadratic equation ax2 + bx + c = 0. The discriminant's value reveals how many roots f(x) has: - The quadratic function has two unique real roots if b2 - 4ac > 0, otherwise it does not. The quadratic function has one repeating real root if b2 - 4ac = 0.

Find out more information on discriminant at brainly.com/question/2507588

#SPJ4

Answer:

Glitzy Generalizations , Card Arranging , Plain people , Testimonial , Bandwagon , Using names are the six techniques used by propaganda.

Step-by-step explanation:

Information—especially that which is slanted or deceptive—used to advance or publicize a specific political cause or point of view.

Glitzy Generalizations

Use expressions or words that sound appealing and are widely accepted.

Card Arranging

Using only those ideas and facts that support your argument.

Plain people

Tell voters that you are a normal person with same needs and beliefs as theirs.

Testimonial

Persuades people to do something by leveraging their popularity as a celebrity or athlete.

Bandwagon

Encourages a tendency to follow the crowd

Using names

Put a bad name on your opponent.

Glitzy Generalizations , Card Arranging , Plain people , Testimonial , Bandwagon , Using names are the six techniques used by propaganda.

To know more about Propaganda

https://brainly.com/question/2696849

#SPJ4

The height of the cedars when they were planted by André, found using the formulas for arithmetic progression is 1.32 meters

An arithmetic progression is a number sequence that consists of numbers that have a constant or common difference between consecutive term of the sequence.

The year André planted the cedar hedge tree = 15 years ago

The present height of the hedge = 3 meters = 300 cm

The average rate at which the cedars grew = 12 cm per year

The height of the cedar hedge when André initially planted the them can be found by representing the situation using an arithmetic progression formula or as follows;

The nth term of an arithmetic progression, aₙ, can be found using the formula; aₙ = a₁ + (n - 1)·d

Where;

a₁ = The initial height of the tree

d = The amount the tree grows each year = 12 cm

n = The number of years ago, the tree was planted

When n = 15, we get;

a₁₅ = 3 meters = 300 cm

Therefore;

300 = a₁ + (15 - 1) × 12

a₁ = 300 - (15 - 1) × 12 = 132

Learn more about arithmetic progression in mathematics here:

https://brainly.com/question/13911455

#SPJ1

The permutation and combination expressions have their values to be ⁸C₇ = 8 and ¹¹P₅ = 55440

From the question, we have

⁸C₇ and ¹¹P₅

The combination expression: ⁸C₇

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 8 and r = 7

Substitute the known values in the above equation

Total = ⁸C₇

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

⁸C₇ = 8!/7!1!

Evaluate

⁸C₇ = 8

(b) The permutation expression: ¹¹P₅

The number of ways of selection could be drawn is calculated using the following permutation formula

Total = ⁿPᵣ

Where

n = 11 and r = 5

Substitute the known values in the above equation

Total = ¹¹P₅

Apply the permutation formula

ⁿPᵣ = n!/(n - r)

So, we have

¹¹P₅ = 11!/6!

Evaluate

¹¹P₅ = 55440

Hence, the values are 8 and 55440

Read more about permutation and combination at

brainly.com/question/11732255

#SPJ1