What are the four important properties of a parallelogram?

The complete diagonal line WY is 3x² + 6x - 105.

A basic quadrilateral with two sets of parallel sides is known as a parallelogram. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.

The area of a parallelogram is base multiples by height as two triangles form a parallelogram.

Given, In parallelogram WXYZ, diagonals line WY intersect at point A.

WA = 3x² - 105 and AY = 6x, So the line Wy can be obtained by adding

WA and AY.

= 3x² - 105 + 6x.

= 3x² + 6x - 105.

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The required measure of the diagonal AY is given as 84 as per the given condition.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
WA = 3x²- 105,
AY = 6x

Since diagonals of parallelograms bisect each other,
3x²- 105 = 6x
3x² - 6x - 105 = 0
x² - 2x - 35 = 0
(x - 7)(x + 5) = 0
x = 7, -5

A negative value of x can be neglected.
So,
AY = 6x
     = 6×7 = 42

Now.
WY = 2AY = 2(42) = 84

Thus, the required measure of the diagonal AY is given as 84 as per the given condition.

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The phrases can be represented by the algebraic expression x + 14 are Option 2 (A number plus 14), Option 4 (Fourteen more than a number), and Option 5 (A number increased by 14).

Given that we have to find the phrases represented by algebraic expression

Given expression is:

x + 14

This expression means that "x" is increased by 14 or 14 is added to x

Let us check the options one by one

Option 1:

The quotient of a number and 14

So this expression is wrong, since it involves quotient which is not related to given expression

Option 2

A number plus 14

Writing it mathematically,

number + 14

If the number be "x", then we get x + 14

So this option is correct

Option 3

Fourteen less than a number

Writing it mathematically,

number - 14

If the number be "x", then we get x - 14

So this Option is wrong

Option 4

Fourteen more than a number

Here, "more than" means addition

Writing it mathematically,

14 + number

If the number be "x", then we get 14 + x which is same as x + 14

So this option is correct

Option 5

A number increased by 14

Here, "increased by" means addition

Writing it mathematically,

number + 14

If the number be "x", then we get x + 14

So this option is correct

Thus correct options of the algebraic expression x + 14 are option 2, 4, 5.

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Full Question:

Which phrases can be represented by the algebraic expression x + 14? Select three options.

1. the quotient of a number and 14

2. a number plus 14

3. fourteen less than a number

4. fourteen more than a number

5. a number increased by 14

The phrases can be represented by the algebraic expression x + 14 are Option 2 (A number plus 14), Option 4 (Fourteen more than a number), and Option 5 (A number increased by 14).

Given that we have to find the phrases represented by an algebraic expression

Given expression is:

x + 14

This expression means that "x" is increased by 14 or 14 is added to x

Let us check the options one by one

Option 1:

The quotient of a number and 14

So this expression is wrong since it involves a quotient which is not related to the given expression

Option 2

A number plus 14

Writing it mathematically,

number + 14

If the number be "x", then we get x + 14

So this option is correct

Option 3

Fourteen less than a number

Writing it mathematically,

number - 14

If the number be "x", then we get x - 14

So this option is wrong

Option 4

Fourteen more than a number

Here, "more than" means addition

Writing it mathematically,

14 + number

If the number be "x", then we get 14 + x which is same as x + 14

So this option is correct

Option 5

The number increased by 14

Here, "increased by" means the addition

Writing it mathematically,

number + 14

If the number be "x", then we get x + 14

So this option is correct

Thus correct options of the algebraic expression x + 14 are option 2, 4, 5.

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Full Question:

Which phrases can be represented by the algebraic expression x + 14? Select three options.

1. the quotient of a number and 14

2. a number plus 14

3. fourteen less than a number

4. fourteen more than a number

5. a number increased by 14

Constructing the four lines that intersect the circumference of the circle and form the square.

To construct a circle inscribed in a square, first draw a square with the desired side length.

Next, draw two diagonals from opposite corners of the square. This will divide the square into four quadrants. Measure the length of each diagonal.

Divide the length of each diagonal by two and mark the midpoints of each diagonal.

This will create four points which will define the circle. Connect each of the midpoints with a curved line to form a circle inscribed in the square.

Finally, use a compass to adjust the curve of the circle until it is perfectly symmetrical.

The circle should be perfectly centered in the square and tangent to each of its sides.

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Answer: (A) Set compass to the diameter of the circle.

Step-by-step explanation:

"cX" is a function that takes two inputs and returns a scalar result and the value of "cX" depends on the values of the scalar "c" and the constant X.

Gamma (Γ) is a mathematical constant that is used in various areas of mathematics, including probability theory, statistics, and engineering.

The symbol "c" is a constant that represents a scalar multiplier in mathematics. This means that when you multiply a value by "c", you are multiplying it by a constant number. In this case, when we say "cX", we are multiplying the value of X (which is gamma) by the constant "c".

So, in mathematical terms, the expression "cX" can be defined as a function that takes a scalar value (c) and a constant value (X = gamma) as inputs, and returns a scalar result. This function can be used to determine the value of "cX" for a given value of "c".

It is important to note that the value of "cX" depends on the value of the scalar "c". For example, if "c" is equal to 2, then "cX" would be equal to 2 times the value of gamma.

On the other hand, if "c" is equal to 0.5, then "cX" would be equal to 0.5 times the value of gamma.

Complete Question:

Show that if X is gamma distributed and c(> 0) is a constant, then cX is gamma distributed. In particular, if X is chi-squared distributed, then cX is gamma distributed.

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The elements 7 and 8 are not in the set B. So every element of A is not an element of B. So the Statement is false.

The elements of set A and set B are:

A = {5, 6, 7, 8, 9, 10}

B = {5, 6, 9, 10}

Total elements in set A is 6 and set B is 4.

We have to check every element of A is also an element of B. To check we have see that every elements of set A is in the set B.

The elements of set A 5, 6, 9, 10 are in the set B but the elements 7 and 8 are not in the set B.

So the given statement is False.

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The complete question is:

Determine if the following statement is true or false regarding sets A and B.

A = {5, 6, 7, 8, 9, 10}

B = {5, 6, 9, 10}

Every element of A is also an element of B. Choose the correct answer below.

1. False

2. True

The answer to the equation is x = 6 or x = 6.

To solve the equation x^2 - 12x + 18 = 0 by completing the square, follow these steps:

Rewrite the equation in the form (x - a)^2 = b, where a and b are constants. In this case, a = 6 and b = 0.

Add (a^2 - b) to both sides of the equation to complete the square.

x^2 - 12x + 36 = 18

Factor the left side of the equation as a perfect square trinomial.

(x - 6)^2 = 0

Take the square root of both sides of the equation.

x - 6 = 0 or x - 6 = 0

Solve for x by adding or subtracting a to both sides of the equation.

x = 6 or x = 6.

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This is simple question , answer is 4 ways

The proportion of the class with a midterm grade less than 75 is approximately 0.3085, or 30.85%. This means that 30.85% of the class is expected to have a midterm grade lower than 75.

We can use the cumulative distribution function (CDF) of the normal distribution to find the proportion of the class with a midterm grade less than 75.

The CDF of a normal distribution with mean μ and standard deviation σ evaluated at a point x is given by the formula:

CDF(x) = 0.5 * [1 + erf((x - μ) / (σ * √2))]

where erf is the error function.

For this problem, μ = 78 and σ = 6, and x = 75, so the CDF can be calculated as follows:

CDF(75) = 0.5 * [1 + erf((75 - 78) / (6 * √2))]

= 0.5 * [1 + erf(-0.3536)]

The value of erf(-0.3536) can be looked up in a table or calculated using a software package. The result is approximately -0.383.

CDF(75) = 0.5 * [1 + -0.383] = 0.5 * [0.617] = 0.3085

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The missing angles and side of the triangle are;

m∠FXD = 44°

EG = 14

m∠FZG = 32°

We are told that the angle bisectors of ΔXYZ are XG, YG and ZG

The parameters are;

∠DYE = 94°

∠FXG = 22°

Thus;

m∠FXD = 2* 22°

m∠FXD = 44°

The sum of angles in a triangle is 180 degrees. Thus;

m∠FZE + 94 + 22 = 180

m∠FZE = 180 - (94 + 22)

m∠FZE = 64°

Thus;

m∠FZG = 64°/2

m∠FZG = 32°

The incenter of a triangle lies at equal distances from the three line segments forming the sides of the triangle, and also from the three lines containing those segments. Thus;

DG = EG = FG = 14

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The answer is that the triangle should be here in the image.

Any shape that is 180 degrees turn from (x, y) to (-x, -y).

So pretend a point is on (2, 3), do a 180 degree rotation it will be (-2, -3).

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Answer:

you

Step-by-step explanation:

130 jwphbsmhisjs

zjoshsksn

112.34375%

215.7 is 112.34400% of 192

The table using this function rule y = 3x+2 is as follows:

x      y

1       5

2      8

7      23

8      26

What is function rule?

The relationship between the input or domain and the output or range is represented by the function rule. A relation is a function if and only if each domain value has one value in the range.

An output is produced by a function machine using an input and a set of rules. Connecting a function described by a verbal rule with corresponding values in a table is the goal of this task (one of six connections to be made between the four ways to represent a function, the other two being through its graph and through an expression).

Although this broad application is not meant to be evaluated, it encourages students to think more broadly about functions as relating objects other than numbers.

Given that, y = 3x+2

Below is the completed table,

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Answer:

The slope of the function y = -2x - 3 is -2. This is calculated by taking the coefficient of the x-term and making it the numerator of a fraction, and making the constant term the denominator.

Step-by-step explanation:

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The dimensions of the largest complete enlargement are

[tex]8\frac{1}{2} and10\frac{5}{8} inches[/tex].

A scale factor is defined as a number by which the size of any geometrical figure or shape can be changed with respect to its original size.

we know that

If two figures are similar, then the scale factor is the ratio of their corresponding sides

first, we have to divide 8 1/2 by 4

8 1/2=8*2+1/4=17/2

so

17/2=2.125 inches.

Now divide 11 by 5.

11/5=2.2.

The final step is to find the largest complete enlargement and the scale factor is the smaller of the two previous values

The scale factor=2.125

The dimensions are

4*2.125=8.5=8 1/2

5*2.125=10.625=10 5/8

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The following formula can be used to get the coordinates of P such that P divides segment AB into parts having a part-to-whole ratio of 1 to 5 with A(-9, 3) and B(1, 8). P = (1 - t)A + TB.

where A and B are the coordinates of the segment's two endpoints, P's position on the segment AB is represented by the scalar value t, and

The part-to-whole ratio in this situation is 1:5, thus t equals 1/6.

In order to change the values of A, B, and t in the formula, we do as follows:

P = (1 - 1/6)A + (1/6)B

P = (5/6)A + (1/6)B

P = (-95/6, 35/6) + (1/6, 8/6)

P = (-15/2, 5/2) + (1/6, 4/3)

P = (-15/2 + 1/6, 5/2 + 4/3)

P = (-30/3, 23/6)

The positioning of P is (-10,3.83)

Regarding the second issue,

Using the same procedure as before, we can determine P's coordinates such that P divides segment AB in three equal halves if A(7, -4) and

B(-5, 4).

P = (1 - t)A + TB

The part-to-whole ratio in this situation is 3:1, therefore t equals 3/4.

In order to change the values of A, B, and t in the formula, we do as follows:

P = (1 - 3/4)A + (3/4)B

P = (1/4)A + (3/4)B

P = (7/4, -4/4) + (-53/4, 43/4)

P = (7/4 + -15/4, -4/4 + 3)

P = (-8/4, -1/4)

The positioning of P is (-2,-0.25)

Point P in the first issue is hence (-10,3.83), while Point P in the second issue is (-2,-0.25)

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It is a proportionate relationship if the ratio remains not constant constant.

As an illustration of a proportionate relationship in real life, let's look at the following: There is a correlation between the number of gallons of gas we put in our car and the price we will have to pay when we fill up the tank. That is to say, the more gas we use, the more we will have to pay.

When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. The "constant of proportionality" is a term used to describe this constant.

Examining the ratios between the two variables will help you determine whether a relationship is proportional. It is a proportionate relationship if the ratio remains constant.

11     $24  

36    $39

66     $79

85     $98

It is a proportionate relationship if the ratio remains not constant constant.

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Answer: A) The equation can be written as y = mx + b, where m is the slope and b is the y-intercept. The slope represents the cost per person and the y-intercept represents the fixed cost. Using the two given points, we can find the slope and y-intercept:

(15, 120) and (25, 200)

m = (200 - 120) / (25 - 15) = 80 / 10 = 8

b = 120 - 8 * 15 = 120 - 120 = 0

So the equation is y = 8x.

B) In the equation y = 8x, x represents the number of people attending the party and y represents the cost of having the party catered.

C) To predict the cost of having a party of 40 people catered, we plug in x = 40 into the equation:

y = 8x

y = 8 * 40

y = 320

So it will cost $320 to have a party of 40 people catered.

Step-by-step explanation:

The required quotient of the given expression -2 1/2 / [3/4] is given as -2.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
= -2 1 / 2 [3/4]
= -3/2 × 4 / 3
= -2

Thus, the required quotient of the given expression -2 1/2 / [3/4] is given as -2.

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The value of the equation x + 17 = 0 is x = -17

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

x - ( -7 ) = - 10   be equation (1)

On simplifying the equation , we get

x + 7 = -10

Adding 10 on both sides of the equation , we get

x + 17 = 0

Now , subtracting 17 on both sides of the equation , we get

x = -17

Hence , the value of equation is x = -17

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it takes approximately 14 hours to produce 10,000 amoebas, rounded to the nearest tenth of an hour.

The formula T = [tex]log^2[/tex] N can be used to determine the number of hours, T, it takes to produce a certain number of amoebas, N.

We can use this formula to find the number of hours it takes to produce 10,000 amoebas, given that the scientist starts with one amoeba:

T = [tex]log^2[/tex] N = l[tex]log^2[/tex] 10,000 = 14.000

So it takes approximately 14 hours to produce 10,000 amoebas, rounded to the nearest tenth of an hour.

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Completed the first step in dividing the fraction 45 ÷ 63 = 45/63 = 7/10.

What is fraction ?

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Divide 45 by 63 to get the first digit of the quotient:

45 ÷ 63 = 7/10

Multiply 63 by 7/10 to get 45:

7/10 × 63 = 45

Subtract this result from 45:

45 - 45 = 0

Bring down the next digit (i.e., 43) to the next decimal place:

7/10

Repeat the above steps to find the next digit in the decimal expansion of the quotient.

Completed the first step in dividing the fraction 45 ÷ 63 = 45/63 = 7/10.

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The value of h for which b is in the plane spanned by a1 and a2 is -17

If the plane is spanned by a1 and a2 and if y is in the plane, then y is a linear combination of a1 and a2.

y = x(a1) +  y(a2), where x and y are constants.

[4, 1, h] = x[1, 4, -2] + y[-2, -3, 7]

[4, 1, h] = [x - 2y, 4x -3y, -2x+ 7y] .

Vectors are equal if their corresponding components are equal:

So, x - 2y = 4, 4x - 3y = 1 and -2x + 7y = h

We can solve for x and y from the first two equations to find h:

                                                 x = -2

                                                 y = -3

                                                 h = -17

The question is incomplete, the complete question is

"For what value(s) of h is b in the plane spanned by a1 and a2?

a1 = [1, 4, -2] a2 = [-2, -3, 7] b = [4, 1, h]"

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After 13 hours, there are 17,582 people living there, to the nearest whole number.

Divide the amount by the cost of capital, the length of time, and other factors to arrive at simple interest. Simple gain = initial + return + hours is the marketing formula. This system makes it easiest to calculating interest. The most conventional technique to figure out interest is as a portion of the principal sum. He will indeed pay his share of the 100percent annual interest, for example, if he borrows $100 from a partner and commits to pay it back with 5% concern. $100 (0.05) = $5. When you borrow money, you must pay interest, and when you give it out, you must charge interest. Interest is often determined as an extra component of the loan total. The interest on the loan is this percentage.

given

initially populous,

Increased Rate, r = 2

Time-doubling, d=5 Hours

Population after t hours is P(t).

After 13 hours, we want to know how many bacteria are present.

e.g., at t=13 hours

After 13 hours, there are 17,582 people living there, to the nearest whole number.

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Answer:

√3 is not rational

Step-by-step explanation:

• A rational number is that number that can be expressed as a fraction provided its denominator is not equal to zero.

Forexample;

Answer:

The answer is $297

Answer: The price of the PC is now $693.

Step-by-step explanation:

1. Find 30% of $990.

30% of $990 = $297

2. subtract.

$990 - $297 = $693

The money could Marshall have saved if he would have conserved in those ways [tex]T=298N+10[/tex]

Marshall would like to get an idea of his monthly electricity expenses.

So, he compiles a list of the last several months' electricity bill amounts

Marshall finds that if he spent at least $145 in a given month on electricity,

Have saved $10 in that month

We are given the following:

A = 145N + 10

B = 153N

We are required to determine the total amount (P) saved using both plans combined.

This can be achieved thus:

[tex]T=A+B[/tex]

[tex]T = 145N+10+153N[/tex]

[tex]T =298N+10[/tex]

Therefore,

The money could Marshall have saved if he would have conserved in those ways [tex]T=298N+10[/tex]

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The equation is given as y = 2t + 9  and Connor would pay $13 if he left his car for 2 hours

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

The standard form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

Let y represent the total money paid for parking for t hours.

There is an automatic fee of $9 just to enter the parking lot, and when he leaves the lot, he will have to pay an additional $2 for every hour. Hence:

y = 2t + 9

To park for 2 hours, t = 2:

y = 2(2) + 9 = $13

The equation is given as y = 2t + 9

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The six functions that are incresing on their domain are : identity, cubing, square root, exponential, natural log and logistic function.

Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

The set of integers x for which a function has a valid definition is known as its domain. A closed interval is referred to as a function's domain if it is specified across the interval a≤ x ≤b.

The logistic function is a function that simulates the exponential expansion of a population while also taking into account variables like the carrying capacity of land and other considerations.

The inverse of an exponential function, the natural log is the logarithm to the base of the integer e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues. The basis of logarithms and natural logs are exponential functions and logarithmic functions.

The six functions that are incresing on their domain are :

identity, cubing, square root, exponential, natural log and logistic.

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