Cutting (chess) boards. Suppose we are given a standard 8 x 8 checkerboard and given a standard 8 x 8 checkerboard and an immense supply of dominoes. Each domino can cover exactly two adjacent squares on the checkerboard below). As a warm-up, verify that the checkerboard can be covered completely dominoes where each domino covers exactly two squares and the dominoes do not overlapon another. Assume next that two squares of the checkerboard have been cut off as shown (second checkerboard). Your challenge now is to determine if you can cover this cut checkerboard winnon overlapping dominoes so that again, each domino covers exactly two squares. Finally, your last challenge is to consider the same question for the truncated checkerboard (last checkerboard). Does your answer change? Justify your answers.

Answer:

|(-12) - 6| (If you could mark as brainliest that would be great!)

Step-by-step explanation:

Since the points g and h are in the same vertical line, the distance between them is simply the absolute value of the difference in their y-coordinates.

Therefore, the absolute value expression to represent the distance between point g and point h is:

|(-12) - 6| = |-18| = 18

Answer:The correct answer is |-12| + |6|

Step-by-step explanation: Because the distance between point G and point H is 18, the equation -12 + 6 = 18 so that’ll be your answer. <3

To find the four second-order partial derivatives of the function f(x, y) = 4x^4y - 5xy + 2y, we first differentiate the function with respect to x and y to obtain the first-order partial derivatives.

The first-order partial derivatives are:

f_x(x, y) = 16x^3y - 5y, and

f_y(x, y) = 4x^4 + 2. Now, we differentiate the first-order partial derivatives with respect to x and y to find the second-order partial derivatives:

1. The second-order partial derivative f_xx(x, y) is obtained by differentiating f_x(x, y) with respect to x:

f_xx(x, y) = (d/dx)(16x^3y - 5y) = 48x^2y.

2. The second-order partial derivative f_xy(x, y) is obtained by differentiating f_x(x, y) with respect to y:

f_xy(x, y) = (d/dy)(16x^3y - 5y) = 16x^3 - 5.

3. The second-order partial derivative f_yx(x, y) is obtained by differentiating f_y(x, y) with respect to x:

f_yx(x, y) = (d/dx)(4x^4 + 2) = 16x^3.

4. The second-order partial derivative f_yy(x, y) is obtained by differentiating f_y(x, y) with respect to y:

f_yy(x, y) = (d/dy)(4x^4 + 2) = 0 (since the derivative of a constant term with respect to y is zero).

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Answer:

1. 19.375 inches taller

2. 8.808 km farther

Step-by-step explanation:

Answer:

Step-by-step explanation:

1.19.375

2.8.808

for the reasoning you just show that you subtracted

Answer:

\(\fbox{\begin{minipage}{16em}Option D: y = (4/7)x + 8 is correct\end{minipage}}\)

Step-by-step explanation:

(1) A typical form of equation of a line is:

\(y = Mx + b\)

with, \(M\) is slope and \(b\) is y-intercept.

(2) Another straight line has equation in form of:

\(y = Nx + c\)

with \(N\) is slope and \(c\) is y-intercept

(3) If these two lines are perpendicular, according to the property of two perpendicular lines on the two-dimensional plane, we have:

\(M\) x \(N\) = -1

(4) Transform the given equation of original line into typical form:

      \(7x + 4y = -24\\\)

<=> \(4y = -7x - 24\)

<=>  \(y = (\frac{-7}{4})x - \frac{24}{4}\)

<=> \(y = (\frac{-7}{4})x - 6\)

=> \(M = \frac{-7}{4}\)

=> \(N = \frac{-1}{M} = \frac{-1}{\frac{-7}{4} } = \frac{-4}{-7} = \frac{4}{7}\)

=> Option D: \(y = (\frac{4}{7})x + 8\) is correct (Slope = \(\frac{4}{7}\))

Hope this helps!

:)

Answer:

14.14in cubed

Step-by-step explanation:

formula for volume of sphere is 4/3 x pi x radius to the power of three.

Since the diameter is 3, to find the radius we need to divide 3 by 2. So the radius is 1.5.

plug 1.5 in formula:

4/3 x pi x 1.5 to the power of 3

anwser: 14.14 or in terms of pi is 4.5pi inches cubed

Answer:

9?

Step-by-step explanation:

uhhhhhhhhhhhhhhhhhhhhhhhhhhh

Answer:

D.) $320

Step-by-step explanation:

4% of 8,000

so

0.04 x 8,000

= 320

In a Linear Programming problem, the objective function line is moved in the direction that reduces cost.

Linear Programming (LP) is an operation research approach used to determine the best outcomes, such as optimum profit, minimum cost, or maximum yield, given a set of constraints represented as linear relationships. Linear programming's fundamental idea is to find the best value of a linear objective function that takes into account a variety of constraints that are linear inequalities or equations. The goal of the constraints is to restrict the values of the decision variables. A linear programming problem consists of a linear objective function and linear inequality constraints, as well as decision variables. In a Linear Programming problem, we try to maximize or minimize a linear objective function, which represents our target. This objective function is expressed as a linear equation consisting of decision variables, each of which has a coefficient. Linear programming's ultimate goal is to find values of the decision variables that maximize or minimize the objective function while still satisfying the system of constraints we're working with. In this case, the objective function line is moved in the direction that reduces cost, which means we are minimizing the cost. We do this by moving the objective function line down towards the minimum point. This is the point where the objective function has the smallest possible value that meets all of the constraints.

Thus, in a Linear Programming problem, the objective function line is moved in the direction that reduces cost.

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Answer:

b

Step-by-step explanation:

2 consecutive integers have a difference of 1 between them, example 5, 6

let m be the first integer then m + 1 is the second and their product is

m(m + 1) → b

Given :-

To Find :-

Solution :-

Let ,

Their product ,

Hence option b is correct .

1) Let's find the equation of the line. firstly calculating the slope

2) Now that we have found the slope, let's find the linear coefficient

by plugging into the slope-intercept form, one of those points. Usually with the least value.

(3,6)

y=mx+b

6=6(3)+b

6=18+b

6-18=b

b=-12

3) Writing that as a function, we have:

f(x) =6x-12

Answer:

The minimum force required would be 50-N!

Answer:

The factored form is,

\((4a^2+2a+1)(4a^2-2a-1)\)

Step-by-step explanation:

We have,

\(16a^4-4a^2-4a-1\\factoring,\\We\ can \ write \ 16a^4 \ as \ (4a^2)^2\\Also,\\then we have,\\(4a^2)^2-(4a^2+4a+1)\\Now, 4a^2 + 4a + 1 \ is \ a \ perfect \ square,\\4a^2 + 4a + 1 = (2a)^2 + 2(2a) + 1\\= (2a + 1)^2\\so, we \ have,\\(4a^2)^2 - (2a + 1)^2\\\)

Using the difference of square formula,

\(x^2 - y^2 = (x+y)(x-y)\\with,\\x = 4a^2,\\y = 2a+1,\\we \ get,\\(4a^2+2a+1)(4a^2-2a-1)\)

Which is the factored form,

{(3,1), (-3,1), (4, 3), (-4,3)}this one is function

{(3,3), (-2,-2), (0, 0), (-4,4)}this one is function

{(1,4), (2,4), (3, 4), (4,4)this ones a function}

{(3,1), (3,2), (3, 3), (3,4)} not a function

{(3,1), (3,3), (3, 2), (2,3)}​not a function

HOPE THIS HELPS

mark brainliest if helpful

Answer:

\(h=6\)

\(k=2.5\)

\(m=\sqrt{21}\)

\(n=3\sqrt{10}\)

\(p=\sqrt{17}\)

Step-by-step explanation:

We can use the Pythagorean Theorem in each case.

Pythagorean Theorem:

\(a^{2} +b^{2} =c^{2}\)

Where \(a\) and \(b\) are two sides of a right-angle triangle and \(c\) is Hypotenuse (the longest side opposite to the right angle)

For \(h\):

\(h^{2} +8^{2} =10^{2}\)

\(h^{2} +64=100\)

Subtract 64 from both sides:

\(h^{2} =100-64\)

\(h^{2} =36\\\)

\(h=\sqrt{36}\)

\(h=6\)

We follow the same process to find  \(k,m,n\) and \(p\).

Answer:

$5.00 per ounce

Step-by-step explanation:

18/3.6

5

Answer:

Please check explanations

Step-by-step explanation:

Mathematically, the area of a triangle

A = 1/2 * b * h

b is base, h is height

For 12 square units, we can have a base of 6 and a height of 4

By tripling the dimensions for the second triangle, we will have a triangle of 18 by 12

So the new area is;

A = 1/2 * 12 * 18

That was how we got 108 square units

The following is true about the study: e. It has one factor (medication) blocked by age.

In statistics, when a factor (independent variable) is blocked by another factor, it means that the effect of the first factor is controlled or eliminated by the second factor.

In this case, the factor that is blocked is the medication, which means that the effect of medication on the outcome variable is controlled by age.

Blocking a factor is often done in experimental design to remove the effects of extraneous variables or to control the influence of certain factors on the outcome variable.

In this case, age is considered a blocking variable because it is not of interest in the study, but it may have an effect on the outcome variable. By blocking the effect of medication by age, the study can better isolate the effect of medication on the outcome variable.

In summary, the statement e. "It has one factor (medication) blocked by age" is correct which means that the study controlled for the effect of age on the outcome variable by blocking the effect of medication by age.

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Answer:

only the expression -5x + 4x + 3 contains like terms.

Step-by-step explanation:

Like terms in algebra refer to terms that have the same variables raised to the same powers.

1. 3x - 3y: This set consists of two terms, 3x and -3y. These terms are not like terms because they have different variables (x and y). Like terms must have the same variable(s) raised to the same power(s).

2. 64/8: This is a single number, 64 divided by 8. Since it is not an algebraic expression with multiple terms, there are no like terms in this set.

3. -5x + 4x + 3: This set contains three terms, -5x, 4x, and 3. The terms -5x and 4x are like terms because they have the same variable (x) raised to the same power (1). Like terms can be combined by adding or subtracting their coefficients while keeping the variable and its exponent unchanged.

4. 5b(4b): This is an algebraic expression that simplifies to 20b^2. Since it contains only one term, there are no like terms in this set.

In summary, among the given sets of numbers, only the expression -5x + 4x + 3 contains like terms, namely -5x and 4x. These terms can be combined by adding their coefficients to give -x + 3.

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con·gru·ent

adjective

1. in agreement or harmony.

"the rules may not be congruent with the requirements of the law"

2. GEOMETRY: (of figures) identical in form; coinciding exactly when superimposed.

Answer:

its 1/3 of the volume of a cyinder with the same base

Step-by-step explanation:

a pyramid has the same policy with prisms of the same base

Volume is a three-dimensional scalar quantity. If the radius and the height of a cone and a cylinder are the same, then the volume of the cylinder is thrice the volume of the cone.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

Assume a cone and a cylinder such that the radius of the base of both the figures is r units, while the height of the cone and cylinder both is h units.

The volume of the cone with radius r units and height h units now can be written as,

Volume of the cone = (1/3) × π × r² × h units³

The volume of the cylinder with a radius of r units and the height of h units now can be written as,

Volume of the Cylinder = π × r² × h units³

Taking the ratio of the volume of the cone and the volume of the cylinder,

Volume of the cone/Volume of the cylinder = (1/3)πr²h units³ / πr²h units³

Volume of the cone/Volume of the cylinder = 1/3

Volume of the cylinder = 3 × Volume of the cone

Hence, if the radius and the height of a cone and a cylinder are the same, then the volume of the cylinder is thrice the volume of the cone.

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Answer:

38

Step-by-step explanation:

It is 4,10,6,6,6,6 feet so add it up and it is 38

Answer:

Approximate between two whole numbers by finding the perfect squares nearest to the target number. Identify which value the non-perfect square root is closest to, then use the iterative process to approximate further to the tenths place, and then further to the hundredths place.

Step-by-step explanation:

The difference between 141.2 and 79.83 is as follows:141.2 - 79.83 = 61.37The sum of 141.2 and 79.83 is:141.2 + 79.83 = 221.03The product of 141.2 and 79.83 is:141.2 × 79.83 = 11250.996 The quotient when 141.2 is divided by 79.83 is:141.2 ÷ 79.83 = 1.7696655174 (approx. 1.77)

Thus, the sum of 141.2 and 79.83 is 221.03. The difference between 141.2 and 79.83 is 61.37. The product of 141.2 and 79.83 is 11250.996. The quotient when 141.2 is divided by 79.83 is approximately 1.77.Thus, the solution can be summarized as follows: Given the two numbers 141.2 and 79.83, we are to find their sum, difference, product, and quotient.

After performing the necessary arithmetic operations, we get that their sum is 221.03, their difference is 61.37, their product is 11250.996, and their quotient is approximately 1.77.

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Answer:

The difference between the area of the original triangle and the area of the new triangle is 5(3x + 7)(5x - 1)/2

Step-by-step explanation:

We know that the area of a triangle A = 1/2bh where b = base and h = height.

Let A be the area of triangle 1 with base (3x + 7) and height (5x - 1).

So its area A = (3x + 7)(5x - 1)/2.

Now for the second triangle, the base is tripled, so its base is 3(3x + 7) and its height is doubled, so its height is 2(5x - 1)

So its area is A' = 3(3x + 7) × 2(5x - 1)/2 = 3(3x + 7)(5x - 1)

So the difference between the area of the original triangle and the new triangle is

A' - A = 3(3x + 7)(5x - 1) - (3x + 7)(5x - 1)/2

= (3x + 7)(5x - 1)(3 - 1/2)

= 5(3x + 7)(5x - 1)/2

So the difference between the area of the original triangle and the area of the new triangle is 5(3x + 7)(5x - 1)/2

The value of the angle m∠DAC is 74° as AB bisects ∠DAC .

We know from the properties of angles that the angle bisector will bisect the angle into two equal parts.

∠DAC is bisected by the straight line AB. This forms two angles ∠DAB and ∠BAC .

∠DAC =∠DAB + ∠BAC

now, ∠DAB = ∠BAC

given that ∠DAB = 37

Hence m∠BAC = 37

now,

∠DAC = ∠DAB + ∠BAC

m∠DAC = 37° + 37°

m∠DAC = 74°

A line that divides an angle into two equal angles is known as an angle bisector in geometry. A device that splits an object or form into two equal halves is referred to as a "bisector." A ray that divides a given angle into two identical segments of the same length is called an angle bisector.

Therefore the value of m∠DAC is 74° .

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It takes Levi's dad 1.67 hours to wash the car by himself.

When Levi and his dad work together, they are able to wash the car in one hour. To find out how long it takes for Levi's dad to wash the car alone, we can use the work rate formula, which is (Work rate of Levi) + (Work rate of Levi's dad) = (Work rate of both together).

Levi takes 2.5 hours to wash the car alone, so his work rate is 1/2.5 = 0.4 cars per hour. We know that when they work together, they can wash one car in one hour, so their combined work rate is 1 car per hour. Let's denote Levi's dad's work rate as "x." We can now set up the equation:

0.4 + x = 1

To solve for x, we simply subtract 0.4 from both sides of the equation:

x = 1 - 0.4
x = 0.6 cars per hour

Now, to find out how long it takes for Levi's dad to wash the car alone, we need to find the reciprocal of his work rate:

1 / 0.6 = 1.67 hours

Therefore, it takes Levi's dad 1.67 hours to wash the car by himself.

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Answer: 1,2,3,4

Step-by-step explanation:

The domain consists of every x value

Any k-cycle (a1.....ak) can be written as a product of (k-1) 2-cycles. Therefore, any permutation can be written as a product of some number of 2-cycles.

To prove that any k-cycle can be written as a product of (k-1) 2-cycles, we use induction on k.

Base case: For k=2, the 2-cycle (a1 a2) is already a product of (2-1) = 1 2-cycle.

Inductive step: Assume that any (k-1)-cycle can be written as a product of (k-2) 2-cycles. Consider a k-cycle (a1 a2 ... ak).

First, we can write this k-cycle as a product of two cycles: (a1 ak) and (a1 a2 ... ak-1).

Then, by the induction hypothesis, the cycle (a1 a2 ... ak-1) can be written as a product of (k-2) 2-cycles.

Finally, we can express the original k-cycle as a product of (k-1) 2-cycles:

(a1 a2)(a2 a3)...(ak-2 ak-1)(ak-1 ak)(a1 ak)

Therefore, any k-cycle can be written as a product of (k-1) 2-cycles.

Since any permutation can be written as a product of cycles, and each cycle can be written as a product of 2-cycles, it follows that any permutation can be written as a product of some number of 2-cycles.

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