Checkerboards A checkerboard consists of eight rows and eight columns of squares as shown in the following figure. Starting at the top left square of a checkerboard, how many possible paths will end at the bottom right square if the only way a player can legally move is right one square or down one square from the current position?

Since, AB and BC are not perpendicular,

No, Points A(-2,1), B(4,7), and C(1,4) cannot be three vertices of rectangle ABCD.

The correct option is A.

A rectangle is a quadrilateral in which all the angles are equal and the opposite sides are equal and parallel.

A rectangle is a closed two-dimensional figure with four sides, all the angles of a rectangle are equal to 90°.

Given points

A(-2,1),

B(4,7), and

C(1,4)

For being vertices of rectangle

Angle between line segment AB and BC should be 90°.

Slope of line AB

m = (y - y')/(x-x')

m = (7 - 1)/(4 - -2)

m = 6/6

m = 1

Slope of line BC

m' = (y - y")/(x - x")

m' = (7 - 4)/(4-1)

m' = 3/3 = 1

Since slope of the two lines is same that is both are parallel, which is only possible when A, B, C are in a straight line.

Hence,  points A(-2,1), B(4,7), and C(1,4) cannot be three vertices of rectangle ABCD.

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Answer:

Isabella can buy together 5 paintbrushes ( p ) and jars of paint ( p ) : j + p = 5, She can`t buy 4 items ( because 4 * $0.99 = $3.96 < $4.87 ) and she also can`t buy 6 items ( 6 * $0.95 = $5.70 > $4.87 ). So: p = 5 - j. Another equation is: 0.95 * ( 5 - j ) + 0.99 j = 4.87, 4.75 - 0.95 j + 0.99 j = 4.87; 0.04 j = 0.12; j = 0.12 : 0.04; j = 3, p = 5 - 3 = 2. We can prove it: 0.95 * 2 + 0.99 * 3 = 1.90 + 2.97 = 4.87. Answer: Isabella buys 2 paintbrushes and 3 jars of paint.

Answer:

40%

Step-by-step explanation:

no of children = 16

no of adult = 24

total = 40

percentage of people who are children =

[tex] \frac{16 \\ }{40} \times 100\%[/tex]

[tex] = \frac{1600 \\ }{40} \%[/tex]

[tex]40\% \\ [/tex]

i hope this helped

For the given bi-quadratic polynomial with 4 terms, the constant is -1/6, the leading term is -9x⁴ and the leading coefficient is -9.

When two or more algebraic terms are added, subtracted, or multiplied (no division), the result is a mathematical expression known as a polynomial. Constants, positive exponents, and at least one variable are all commonly present in polynomial expressions.

Consider the given polynomial,

The highest power of the variable is 4. Therefore this type of polynomial is called a bi-quadratic polynomial.

The portions of the equation that are often separated by "+" or "-" signs are known as polynomial terms. The number of terms in the above equation is 4.

The term which does not contain any variables are called constant. For the given polynomial the constant is -1/6.

The term with the largest power of the variable is the leading term. The leading term's coefficient is the leading coefficient.

For the above polynomial, the leading term is -9x⁴ and the leading coefficient is -9.

Therefore the above for the given bi-quadratic polynomial with 4 terms, the constant is -1/6, the leading term is -9x⁴ and the leading coefficient is -9.

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Answer:

[tex]-3 \frac{1}{3}t+6[/tex]

Step-by-step explanation:

Given expression:

[tex]\sf 7\frac{1}{3}t-\left(10 \frac{2}{3}t-6\right)[/tex]

Remove the parentheses:

[tex]\implies \sf 7\frac{1}{3}t-10 \frac{2}{3}t+6[/tex]

Factor out the common term t:

[tex]\implies \sf \left(7\frac{1}{3}-10 \frac{2}{3}\right)t+6[/tex]

Change the mixed numbers into improper fractions:

[tex]\implies \sf \left(\dfrac{7 \cdot 3+1}{3}-\dfrac{10 \cdot 3+2}{3}\right)t+6[/tex]

[tex]\implies \sf \left(\dfrac{22}{3}-\dfrac{32}{3}\right)t+6[/tex]

Subtract the fractions:

[tex]\implies \sf \left(\dfrac{22-32}{3}\right)t+6[/tex]

[tex]\implies \sf \left(\dfrac{-10}{3}\right)t+6[/tex]

Convert the improper fraction back into a mixed number:

[tex]\implies -3 \frac{1}{3}t+6[/tex]

A chemical element's atom is a particular type of particle of substance. A positively charged electron or many negatively charged electrons encircle the central nucleus of an atom.

Electrons: If an electron leaves an atom, it is said to be ionized. Ionization can occur through various processes, such as collision with another particle or exposure to electromagnetic radiation.

Protons: Protons are found in the nucleus of an atom, and are held in place by the strong nuclear force. If a proton were to leave the nucleus, it would no longer be a stable atom and it would become an ion.

Neutrons: Neutrons are also found in the nucleus of an atom and are held in place by the strong nuclear force. If a neutron were to leave the nucleus, it would no longer be a stable atom, and it would become a different element.

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An inequality is a mathematically explicable relationship between two expressions that can be represented by any of the following symbols: >, <, ≤, ≥, and ≠.

A mathematical statement known as an inequality uses the inequality symbol to represent the connection between two expressions. The terms on each side are not equal when there is an inequality sign present.

It suggests that the left and right expressions should be greater or smaller than one another, or the opposite. Literal inequalities are ones where the inequality symbols indicate the connection between two algebraic expressions.

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Using linear equations, it is 3570metre  from the post office to the

library

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

Length of each block=275 meter

let's Create a linear equation from this i.e. 275x where x=number of blocks.

No. of blocks from  post office to the library = 13 (x=13)

so, distance of  post office to the library= 275*13

                                                                    =3575meter

                                                        ≈3570 meter (round to nearest 10th)

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The value of k in the given equation is -0.104839

Evaluate

[tex]\frac{31}{2}[/tex]k + [tex]\frac{3}{4}[/tex] = - [tex]\frac{7}{8}[/tex]

Move the constant to the right side

[tex]\frac{31}{2}[/tex]k = [tex]-\frac{7}{8} - \frac{3}{4}[/tex]

Subtract the terms

[tex]\frac{31}{2}[/tex]k = [tex]-\frac{13}{8}[/tex]

Multiply both sides

[tex]\frac{31}{2}[/tex]k x [tex]\frac{2}{31} = - \frac{13}{8} * \frac{2}{31}[/tex]

k = [tex]-\frac{13}{124}[/tex]

k = - 0.104839

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A virus spreading around Brookfield will infect 988 people in the next 3 days.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

Number of people infected by the virus = 685

The rate at which the virus is infecting = 13%

The virus is spreading at 13% rate each day.

To deduce the number of people who will get infected in next 3 days.

The final equation will be -

= 685 × ( 1 + 13%)³

= 685 × (113/100)³

= 685 × (1.13)³

= 685 × 1.442

= 987.77 ≈ 988

Therefore, the number of people who will get infected is 988.

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The average rate of change is 19   3 ≤19 ≤15

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The polynomial for x2 -4 in function notation is (x+2)(x-2) since a function produces an output from an input.

Mathematics deals with numbers and their variants, equations and related structures, shapes and their locations, and locations where they might be found. The term "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is an association between inputs and outputs where each input results in a single, unique output. A domain and a codomain, or scope, are assigned to each function.The input is an x. On functions, one-to-one functions, many-to-one functions, within functions, and on functions are the four main categories of functions that are available.

given

A function creates an output from an input.

The name of the function, f (x) f(x) f(x)f, left parenthesis, x, right parenthesis, and the output, f (x) f(x) f(x)f, left parenthesis, x, right parenthesis, are all enclosed in parentheses.

x2 -4

(x2 - 2*2)

= (x+2)(x-2)

The polynomial for x2 -4 in function notation is (x+2)(x-2) since a function produces an output from an input.

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The equation that must be true for event C and D to be independent are P(C│D) = P(C) and

P(D│C ) = P(D).

Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B)

For two events C and D. For the two events to be independent events then;

P(C│D) = P(C∩ D)/ P(D) = P(C)

or

P(D│C) = P(D∩ C)/ P(C) = P(D)

For example if a fair die is rolled,

P(D ) = Probability of getting a 3

P(C) = Probability of getting an even number

P(C│D) = P(C∩ D)/ P(D)

P(C∩ D)= 1/3 × 1/2 = 1/6

P(C│D) = P(C∩ D)/ P(C) = 1/6 ÷ 1/3 = 1/2

therefore P(C│D) = P(C) and

P(D│C ) = P(D).

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The product of a, b and c would be 6.

What is an expression?

An expression is a mathematical phrase that can contain numbers, variables, and operators. Expressions do not contain an equal sign and they can't be solved for a single value. They are used to represent a value or a set of values.

The given expression is     [tex]\frac{\sqrt[4]{16xy^4}}{x^{\frac{1}{2}}y^{\frac{1}{2}}}[/tex]

In order to write the expression in the form of [tex]ax^by^c[/tex], we need to simplify it.

First, we simplify the fourth root of [tex]16xy^4[/tex] by taking the fourth root of 16, which is 2. So, the expression becomes

[tex]2\frac{xy^4}{x^{\frac{1}{2}}y^{\frac{1}{2}}}[/tex]

Next, we simplify the fraction by canceling out the[tex]x^{\frac{1}{2}} $$ and $ y^{\frac{1}{2}}[/tex] from the numerator and denominator. This gives us [tex]2xy^3[/tex]

So the expression in the form of [tex]ax^by^c[/tex] is [tex]2xy^3[/tex], where a = 2, b=1, and c=3.

the product of a, b, and c is 2 * 1 * 3 = 6.

Hence, the product of a, b and c would be 6.

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first

Semi perimeter (S)=(2+4+3)/2

=9/2=4.5

now

area=

[tex] \sqrt{4.5(4.5 \times 2)(4.5 \times 4)(4.5 \times 3)} [/tex]

[tex] \sqrt{s( s- a)( s-b )( s- c)} [/tex]

which is equal to

99.20

Answer:

[tex]\frac{1}{81}[/tex]

Step-by-step explanation:

using the property of exponents

• [tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]\frac{1}{a^{(n-m)} }[/tex] , then

[tex]\frac{9^{-6} }{9^{-4} }[/tex]

= [tex]\frac{1}{9^{(-4-(-6))} }[/tex]

= [tex]\frac{1}{9^{(-4+6)} }[/tex]

= [tex]\frac{1}{9^2}[/tex]

= [tex]\frac{1}{81}[/tex]

Answer:

1/81

Steps:

move 9^-6 to the denominator using the negative exponent rule

b^-n=1/b^n

1/9^-4 x 9^6

Multiply 9^-4 by 9^6 by adding the exponents

1/9^2

Raise 9 to the power of 2

1/81

Answer:the temperature at 2:00 am is 2C and drops 2 each hour for X hours

Step-by-step explanation:

Since the function g is given in three equivalent forms, a form which most quickly reveals the vertex is: C. g(x) = 3(x + 1)² - 12.

The vertex is equal to (-1, -12).

In this exercise, you are required to determine and select the vertex form of a function g that is written in three equivalent forms. Mathematically, the vertex form of a quadratic equation is given by this formula:

y = a(x - h)² + k

Where:

Based on the information provided, we can reasonably infer and logically deduce that a mathematical expression which quickly reveals the vertex of the quadratic equation is given by g(x) = 3(x + 1)² - 12.

Since the directrix is horizontal, the axis of symmetry would be vertical. Additionally, the distance (a) from directrix to vertex on the axis of symmetry is equal to 3.

In conclusion, the vertex of this quadratic equation is given by the ordered pair (-1, -12).

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Since two triangle are considered to be congruency if each of their 3 sides, and Mario is correct, the correct response is SSS.

If a triangle's size and shape are a perfect match, it is said to be congruent. The symbol is contained in the word "congruent". The three sides and three angles of two triangle are said to be congruent when their three sides and three angles coincide.

Here,

As illustrated below, start by writing the names of the triangles' vertices, starting with triangles DAB and BCD.

AB = CD

DA = BC

Side BD is the same in both triangles, therefore

BD = BD

The fact that the triangle DAB & BCD have the same number of angles on each side indicates that they are congruent and utilise the SSS property of a congruence triangle.

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Answer:

Step-by-step explanation:

watch the other parralleles cotés

The Pythagorean Theorem, one of the most well-known mathematical formulas, tells us how a right triangle's sides relate to one another. The hypotenuse, along with the two legs, make up a right triangle. The hypotenuse, the longest side of the right triangle and the side opposite the right angle, is where the two legs of a right triangle come together at a 90° angle.

Equation to represent the length -

a2  + b2 = c2

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The amount of numbers that are greater than 3 is given as follows:

Infinity.

The four inequality symbols, along with their meaning, are presented as follows:

The inequality for this problem is defined as follows:

x > 3.

Meaning that the graph is composed by all the values that are greater than 3.

Perhaps the biggest difference between an equality and an inequality is the number of solutions. While an equality has a fixed number of solutions, an inequality has infinity solutions, as all the values in the solution set are solutions to the inequality.

(the solution set in this problem is all the values to the right of x = 3).

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The solution for this scenario is,

⇒ 53 t-shirts and 55 yearbooks

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The band is selling t-shirts for $22 and yearbooks for $23.

And, The goal is to sell at least $2,400 in merchandise.

Now, Let  x = number of $22 t-shirt

Let y = number of $23 yearbook

Hence, We can formulate;

⇒ 22x + 23y ≥ 2400

By option 4;

There are 53 t-shirts and 55 yearbooks.

Hence, Substitute x = 53 and y = 55 in above equation,

⇒ 22x + 23y ≥ 2400

⇒ 22×53 + 23×55 ≥ 2400

⇒ 1166 + 1265 ≥ 2400

⇒ 2431 ≥ 2400

Thus, The correct option is,

⇒ 53 t-shirts and 55 yearbooks

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Answer:

Yes, he can

Step-by-step explanation:

We have to find the total of Chocolate milk Alex has by taking

2 1/2 = 5/2

2/4 + 5/2 = 2/4 + 10/4 = 12/4 = 3 quarts of chocolate milk

1 gallon = 4 quart

And here, Alex only has 3 quarts of chocolate milk, so he can pour the milk from both jugs into a third jug.

Answer:

3/4 + 1/3 = 13/12 = 1 1/2

Step-by-step explanation:

Answer:

[tex]r=-2[/tex]

Step-by-step explanation:

First, apply the distributive property: A(B + C) = AB + AC

[tex]-8r-3(-6-5r)=8-5(4-2r)[/tex]

[tex]-8r+18+15r=8-20+10r[/tex]

Then, get all of the r's on one side.

[tex]-8r+18+15r=8-20+10r[/tex]

↓ subtract 18 from both sides

[tex]-8r+15r=8-2+10r[/tex]

↓ subtract 10r from both sides

[tex]-8r+5r=8-2[/tex]

Finally, solve for r by combining like terms, then dividing by -3.

[tex]-3r = \ 6\\\overline{\, -3 \: } \ \ \ \ \overline{-3}[/tex]

[tex]r = -2[/tex]

To find the length of a line segment given the coordinates of the midpoint and one endpoint, you can use the distance formula. The distance formula is:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Where (x1, y1) and (x2, y2) are the coordinates of two points, and d is the distance between the points.

Given the midpoint (mx, my) and one endpoint (ex, ey) you can use the following steps to find the length of the segment:

For example, if the midpoint of a segment is (5,7) and one endpoint is (7,10), the length of the segment is:

d = √((7-5)^2 + (10-7)^2)

d = √((2)^2 + (3)^2)

d = √(4+9)

d = √13

the length of the segment is √13 units.

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The addition of the algebraic expression is = [tex]\frac{6}{5} t - \frac{4}{3}[/tex], so option (d) is correct.

Given that,

The expression (-4/5t + 5/3) and (-3 + 2t)

The addition of algebraic expressions requires categorizing the terms in an algebraic expression into two types - like and unlike terms.

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). ...

These expressions are represented with the help of unknown variables, constants and coefficients.

Then, take up the like terms and add them.

The addition of algebraic expression is;

= [tex]-\frac{4}{5} t + \frac{5}{3} -3+2t[/tex]

= [tex]-\frac{4}{5} t+2t+\frac{5}{3} -3[/tex]

= -0.8t + 2t + 1.66 - 3

= 1.2t - 1.34

= [tex]\frac{6}{5} t - \frac{4}{3}[/tex]

Therefore,

The addition of the algebraic expression is = [tex]\frac{6}{5} t - \frac{4}{3}[/tex], so option (d) is correct.

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