Two children take turns breaking up a rectangular chocolate bar 6 squares wide by 8 squares long. They may break the bar only along the divisions between the squares. If the bar breaks into several pieces, they keep breaking the pieces up until only the individual squares remain. The player who cannot make a break loses the game. Who will win

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]5x+4y=16\implies 4y=-5x+16\implies y=\cfrac{-5x+16}{4} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{5}{4}}x+4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so we're really looking for the equation of a line whose slope is -5/4 and it passes through (8 , -7)

[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{5}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{- \cfrac{5}{4}}(x-\stackrel{x_1}{8}) \implies y +7= -\cfrac{5}{4} (x -8) \\\\\\ y+7=-\cfrac{5}{4}x+10\implies {\Large \begin{array}{llll} y=-\cfrac{5}{4}x+3 \end{array}}[/tex]

Translation is a rigid transformation. As such, it preserves sizes and angles. Isometric is an alternative way to say the size is preserved. Hence; B, C and E are the correct choices.

A triangle is a three-sided polygon. A closed shape consisting of three straight lines and three corners. The sum of the three angles of a triangle is always 180 degrees. Triangles come in a variety of shapes and sizes and can be classified according to their angles and sides. The most common type of triangle is the right triangle, which has 90 degree angles.

Translation is the transformation that happens when we move the image without changing anything in it. Therefore, the shape, size, and orientation remain the same.

In this case the triangle ABC has been transformed to A'B'C'. This means that the triangle has been moved in one direction to form a new triangle A'B'C' without changing its size or orientation. This is an example of translation transformation.

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The complete question is follows:

Triangle ABC was translated to form A’B’C’. Which describes the transformation? Check all that apply

A. It is non rigid

B. The size is preserved

C. It is rigid

D. The angles are not preserved

E. It is isometric

Answer: (0, 1), (2,3), (x,x), (-5,x) (I put x's in for the missing numbers)

Step-by-step explanation: Hope this helps!!

Here is the graph:

AC = 25 units is the length of AD.

The Geometric Mean (Altitude) Theorem (9.7) The hypotenuse of a right triangle is split into two pieces by the height from the right angle. The geometric mean of the lengths of the two hypotenuse segments determines how long the altitude is.

Length of BC = 10 units

Length of DC = 4 units

We will use geometric mean theorem in the given right triangle to get the length of side AC.

[tex]hypotenuse/leg=leg/projection\\AC/BC=BC/DC\\x/10=10/4\\x=25[/tex]

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An addition inequality to determine how much taller William must be to ride the coaster is, Height of William + x ≥ 42.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, Riders must be at least 42 inches tall to ride the coaster, and 'x' be the variable representing how much taller William should be.

Therefore, Height of William + x ≥ 42 is an inequality that may be used to calculate how much taller William has to be in order to ride the coaster.

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Answer:

Depending of the figure that you are trying to find perimeter on, you just add up all the sides of that figure.

Answer:

The perimeter is the distance around a figure.

Step-by-step explanation:

For example, if I have a square where each side is 5 inches.  The perimeter would be 20 inches.  5 + 5+ 5 + 5, a square has four sides and each side length is 5 inches.

The graph of the inverse variation equation is called a rectangular hyperbola.

A form of proportionality called inverse variation occurs when one number falls as the other rises or the other way around. This suggests that if one number rises while the other decreases, the magnitude or absolute value of the first quantity will decrease, resulting in a constant product. The constant of proportionality is another name for this item.

An inverse variation is a relationship between two variables in which the product is constant; as a result, while one of the variables changes, the other changes correspondingly to maintain the same value of the product. This connection has the form of a hyperbola.

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Answer: 1/7

Step-by-step explanation: Find the GCD (Greatest Common Denominator) of the numerator and denominator. The GCD of 22 and 154 is 22. Divide both the numerator and denominator by the GCD = 22 ÷ 22; 154 ÷ 22. Reduced fraction: 1/7. Therefore, 22/154 simplified to lowest terms is 1/7.

The average speed of Luna I is 1.78 x 10^-3 kilometers/minute.

To find the average speed of Luna I, we need to divide the total distance traveled (3.8 x 10^5 kilometers) by the total time it took to travel that distance (2.16 x 10^4 minutes). The quotient of these two numbers is 1.78 x 10^-3 kilometers/minute.

It's the ratio of distance covered to the time taken to cover that distance. The unit of speed is distance/time, which in this case is kilometers/minute. The speed of Luna I is in scientific notation, which is a way to express very large or very small numbers in a more manageable form.

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The inverse of the function f(x) =√x - 2 + 3 is (x - 3)² + 2 so, option B is correct.

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.

Given:

f(x)=√x - 2 + 3.

The inverse function can be found as shown below,

f⁻(x) = √(y - 2) + 3  (Replace x by y)

x = √(y - 2) + 3

solve the equation as shown below,

x - 3 = √(y - 2)

Squaring both sides,

(x - 3)² = [√(y - 2)]²

x² + 9 - 6x = y - 2

x² + 9 - 6x + 2 = y

y = x² - 6x + 11 or y = (x - 3)² + 2

Thus, the inverse of the function is  (x - 3)² + 2.

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The polynomials which, when added to the polynomial 3x²+3x-1, is equivalent to the following expressions: 1, 2x²-3, and x+5 include the following below:

This is referred to as algebraic expressions that consist of variables and coefficients.

For 1; it is calculated as:

3x²+3x-1 + P = 1.

P = 2 - 3x² -3x.

For 2x²-3, it is calculated as:

3x²+3x-1 + P = 2x²-3

P = -2 -x² -3x

For x +5; it is calculated as:

3x²+3x-1 + P = x +5

P = 6 -2x -3x².

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The full question is:

Find a polynomial which, when added to the polynomial 3x^2+3x-1, is equivalent to the following expressions: 1, 2x^2-3, and x+5

The description for the problem involving the linear function is given as follows:

The time it will take to make a total of 20 parts is of 6 minutes.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

In this problem, the function is defined as follows:

y = 2x + 8.

In which the variables are given as follows:

Hence the time needed to make 20 pieces is given as follows:

20 = 2x + 8

2x = 12

x = 12/2

x = 6 minutes.

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The expression that correctly shows the amount remaining in the piggy bank will be; 22d + 7n + 15q - (8d + 3n) = $4.85

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We are given that piggy bank contains 22 dimes, 7 nickels and 15 quarters. This morning you removed 8 dimes and 3 nickels.

LEt consider

→ dimes = d

→ nickels = n

→ quarters = q

Now the expression will be;

22 dimes + 7 nickels + 15 quarters - 8 dimes - 3 nickels

22d + 7n + 15q - 8d - 3n = $4.85

22d + 7n + 15q - (8d + 3n) = $4.85

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Answer: −2<x<0

Step-by-step explanation: 2<x+4<4 2+−4<x+4+−4<4+−4 −2<x<0

The coeficient of y² in the expression is the number 3

What is an algebraic expression?

An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

In the given expression we have the following:

3y² + 4x

As we are asked for the coefficient of the variable "y" then we must take the number that is just before the letter which in this case is the number 3.

3 is the coefficient of y²

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The measure of ∠S is 59.4° for trignometric identities

What are trigonometric identities?

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

ΔSTU:

s = 50 inches

t = 58 inches

u = 630 inches

Applying the cosines rule on ΔSTU.

s² = t² + u² - 2 x t x u x cos S

cos S = (t² + u² - s²) / 2tu

cos S = (58² + 27² - 50²) / (2 x 58  x 27)

cos S = (3364 + 729 - 2500) / 3132

cos S = 0.5086.

∠S = (0.5086)

∠S = 59.4°

Thus,

∠s angle value is  59.4°.

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Answer:

25x^6y^2

Step-by-step explanation:

Since it is a square all sides are the same. So you multiply 5x^3y and 5x^3y together to get the area. That would get you 25x^6y^2.

Answer:

Step-by-step explanation:

Depreciation means wearing and tearing in the value of an asset over the years

(a) Given:

p = initial value of an asset

i% = depreciation per year

n = number of years

Depreciation after n years (d) = [tex]p(1-\frac{1}{100} )^{n}[/tex]

Value of machine after n years = p-d

(b) Given:

p = RM100000

i% = 5

n = 10
Depreciation after 10 years = [tex]100000(1-\frac{5}{100} )^{10} = 59873.69392[/tex]

Value of machine after 10 years = p-d = RM100000 - RM59873.69392 = RM 40123.30608

Value of machine after 10 years to nearest ringgit = RM40123

Answer:

3(x + 2) and 3x + 6 are equivalent expressions because the value of both the expressions remains the same for any value of x. 3x + 6 = 3 × 4 + 6 = 18.

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The GCF of the given expressions is 4x⁷⁶

The greatest common factor, abbreviated as GCF, of two numbers is the largest number that is a factor of, or divides evenly into, both of the numbers. When two numbers are relatively small, we have a quick and simple way to calculate their greatest common factor. We do this by listing all of the factors of each number, and then identifying the largest number that is in both lists.

Given here, The expressions 20x⁷⁶ and 8x⁹² and GCF(20,8)=4

and x⁷⁶ is a factor of  8x⁹²

∴ GCF(20x⁷⁶ , 8x⁹²) =4x⁷⁶

Hence, The GCF of the given expressions is 4x⁷⁶

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Factor -20 x-5 y, where x+y=4 and x+y=5. Our prime numbers become much, much harder to factor as we add a few extra digits.

When you factor in mathematics, you divide a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the division of an amount into its factors or divisors. The factorization of the integer 12, for instance, might be 3 times 4 or something similar. [tex]N = X^{a} * Y^{b} * Z^{c}[/tex] is used to represent the general factorization formula. In this instance, X, Y, and Z stand for a number's factors. Get a polynomial's GCF (Greatest Common Factor).

GCFs of polynomials should be factored out. By grouping the terms, factor a polynomial with four terms. trinomial of the form, and factor it. The size of our goods and the size of the data we use to check mean that each check takes an average amount of time longer. It is clear from this that factoring the product becomes significantly more difficult when we add a few digits to our prime integers.

Therefore the correct answer is option A)5(4x+y)

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Answer:

A fraction is a mathematical expression that represents the division of two numbers, called the numerator and the denominator. The numerator represents the number of parts being considered, while the denominator represents the number of parts in the whole. A fraction with a numerator of 6 and a denominator of negative 8 can be simplified to -3/4. To find an equivalent fraction, we can multiply or divide both the numerator and denominator by the same number without changing the value of the fraction. In this case, the fraction with a numerator of negative 8 and a denominator of 6 is equivalent to -4/3.

Step-by-step explanation:

The length of the chord of the larger circle can be found by taking the square root  [tex](5r)^2 - (2r)^2[/tex] which is equal to r√21, where r is the radius of the smaller circle.

The given problem states that there are two concentric circles with radii in the ratio of 3:5. This means that the radius of the smaller circle is 3r and the radius of the larger circle is 5r. The distance between the center of these two circles is 2r.

Also, it is given that the length of the chord of the larger circle that is tangent to the smaller circle is 40 cm. Using this information, we can find the length of the chord of the larger circle by using the Pythagorean theorem.

The length of the chord of the larger circle is found by taking the square root of [tex](the radius of the larger circle)^2[/tex] - [tex](the distance between the two centers)^2[/tex] which is √21[tex]r^2[/tex]= r√21.

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The number of units that tile will he need to surround his pool is 19.82units.

this question is of quadratic equation ,

The number of units of tile simply refers to the perimeter.

So, we need to find all the sides of the rectangle.

Now, we have,

AB = 4.24 units

BD = 7.07 units.

So, we can find AD using pythagoras theorem.

So,

(AD)² + 4.24² = 7.07²

(AD)² + 17.978 = 49.985

(AD)² = 49.985 - 17.978

AD = √32.007

AD = 5.66 units

AD = BC = 5.66 units

Likewise, AB = DC = 4.24 units

Thus,

perimeter = 2(5.66) + 2(4.24) = 19.8 units.

The number of units that tile will he need to surround his pool is 19.82units.

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C) there is a 5% probability of rejecting a false null hypothesis

Simply put, probability is the likelihood that something will occur.

When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Testing hypotheses is a crucial component of empirical research and evidence-based medicine. A well-developed hypothesis is only half the solution to the research problem. Working understanding of fundamental statistical principles is preferred for this, as well as subject-specific knowledge gleaned through a thorough survey of the literature.

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The equation for dimensions of the rectangle is x(x - 3) = 10 and the width is 2 meters and the length is 5 meters.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Here,

x(x-3)=10

x²-3x=10

x²-3x-10=0

x²-5x+2x-10=0

(x-5)(x+2)=0

x=-2,5

x=5 units

x-3=5-2

=2 units

The rectangle's dimensions are x(x - 3) = 10, with a width of 2 meters and a length of 5 meters.

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The percent of the people surveyed who were completed satisfaction with the car will be 48%.

A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100. The percentage then refers to a component per hundred. The word percentage simply means per 100 and it is represented by %.

In this case, a survey was given to people who own a certain type of car. 24 out of 50 stated that they were satisfied with the car.

The percent of the people surveyed were completed satisfaction with the car will be:

= 24 / 50 × 100

= 48%

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Complete question

A survey was given to people who own a certain type of car. 24 out of 50 stated that they were satisfied with the car. what percent of the people surveyed were completed satisfaction with the car?

An indirect proof is an argument that begins with the assumption that a conclusion is false, then uses logical reasoning to show that the assumption leads to a contradiction.

a fact or assertion that contradicts what someone else said or that differs from another fact or assertion to the point where one of them must be incorrect.

A situation or set of ideas that contradict one another is called a contradiction. A contradiction would be saying out loud that you support the environment while never remembering to empty the recycling. A statement that contains opposing ideas is frequently referred to as a "contradiction in terms."

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