let o be the point of intersection for the diagnols of quadrilateral abcd prove that abcd could be a trapezoid (that is if it has one sides parallel) is Aaod = Aboc

The slope-intercept form is

    y = - x + 1

Given points are  (2, - 1)

          and  y = x + 4

The product of slopes of perpendicular lines is  - 1

   so ,  m = - 1/1  =  -1

     ∴ y = -1 (x) + b

       y  = - x + 1

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In the given circle, the values of required angles are as follow:

a = 51°, b = 28° , c = 31°, and d = 70°.

As given in the question,

In the given circle,

As we know by theorem , angles formed in the same arc are congruent.

Angle a° and angle 51° is formed in the same arc XY .

⇒ Value of a = 51°

Angle b° and angle 28° is formed in the same arc ZY .

⇒ Value of b = 28°

Angle c° and angle 31° is formed in the same arc WX .

⇒ Value of c = 31°

Angle d° and angle 70° is formed in the same arc WZ .

⇒ Value of d = 70°

Therefore, in the given circle the values of required angles are as follow:  a = 51°, b = 28° , c = 31°, and d = 70°.

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According to the solving the probability will be 0.159.

The area of mathematics known as probability deals with numerical assessments of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. In addition to being expressed in percentages ranging from 0% to 100%, probabilities can also be expressed as proportions between 0 and 1.

The incidence rate is = 0.2%  or 0.002

The false negative rate is = 8%  or 0.008

The false positive rate is = 1%  or 0.001

The probability is

0.01*(1-0.002) + 0.95*0.002

= 0.00998 + 0.0019 = 0.01188

Probability that a person who tests positive actually has the disease would be represented as:

Let the probability be represented by = p

p * 0.01188 = 0.95 * 0.002

p = 0.0019/0.01188

p = 0.159

Hence, probability is 0.159

According to the solving the probability will be 0.159.

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equation and graph attached

Answer:

$10,000 invested at 5%

$20,000 invested at 8%

Step-by-step explanation:

1. Let x = the amount of money invested at 5%, and y = the amount of money invested at 8%.

   x + y = 30,000 (the total amount invested)

   0.05x + 0.08y = 2,100 (the total interest earned)

2. Solve the system by whatever method you choose.

Answer:

1.5x = 30 - 1.5

Step-by-step explanation:

30 grams minus the weight of the bag 1.5

1.5x x is the number of marbles and the bag so take 1 out and you have an answer which is 28.5 19 marbles

Answer:

[tex]d=7[/tex]

[tex]a_9=59[/tex]

Step-by-step explanation:

If the first term of a sequence is [tex]3[/tex] and the second term is [tex]10[/tex], then each successive term in the sequence is [tex]7[/tex] more than the previous term. The common difference is [tex]7[/tex] ( [tex]d=7[/tex] ).

The formula representing the arithmetic sequence is:

[tex]a_n=7n-4[/tex]

Therefore, the ninth term in the sequence is:

[tex]a_9=7(9)-4[/tex]

[tex]a_9=63-4[/tex]

[tex]a_9=59[/tex]

The value of (2/3) ÷ (1/4) is 8/3 and the value of 7 ÷ (2/3) is 21/2.

This is a question from the division of fractions.

We know the property of fractions is given by:-

(m/n) ÷ (a/b) = (m/n)*(b/a) = mb/na

Hence, we can write,

(2/3) ÷ (1/4) = (2/3) * (4/1) = 2*4/3*1 = 8/3

7 ÷ (2/3) = (7/1)*(3/2) = 7*3/ 1*2 = 21/2

Fractions

A fraction represents a part of a whole or, more generally, any number of equal parts. Numerators and denominators are also used in fractions that are not common, including compound fractions, complex fractions, and mixed numerals.

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Therefore the required polynomial is [tex]f(x) = a(x^5+13x^4+53x^3+83x^2+52x+70)[/tex]

What is an leading coefficient?

The numbers placed in front of the variable with the biggest exponent are known as leading coefficients. They can be whole numbers, fractions, or decimals, as well as positive, negative, real, or imaginary, just like conventional coefficients.

According to fundamental theorem of algebra , if a + bi be a zero of a polynomial with real coefficients then a-bi is also a zero

Now given that f(x) be a polynomial with degree 5 and with zeros -7,-i,-3+i

and f(x) be a polynomial with real coefficients.

therefore by fundamental theorem of algebra

+i and -3-i are also zeros of f(x)

so zeros of f(x) are 7, -i, -3 + i, i, -3 -i

Degree is 5, so there is at most 5 zeros therefore the required polynomial will be

f(x) = a(x + 7)(x + i )(x - i)(x +3- i)(x +3 +i)

= a[(x +7)(x² + 1)(x² +6x + 10)]

[tex]= a\left[x^5+ 13x^4 + 53x^3 +83x^2 + 52x + 70]\right[/tex]

[tex]f(x) = a(x^5+13x^4+53x^3+83x^2+52x+70)[/tex]

Therefore the required polynomial is [tex]f(x) = a(x^5+13x^4+53x^3+83x^2+52x+70)[/tex]

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The mode will not change.

Given data,

58,60,53,54,60,35,58,60

Outlier is the value in a set of data that much higher or lower than other values in data.

from given data, outlier is 35.

Mode is the value in a set of data that occurs more frequently in set of data.

from given data, 60 occurs more frequently.

Hence, 60 is the mode of data.

If outlier is removed from the data set then it will not affect the mode of the data

Thus, the mode will not change.

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R₀, 270° is the rule that describes the transformation

Rotation simply means turning. In a cartesian plane, if a point P, whose position vector is (x,y), is rotated through θ° about the origin, the position of the image P' is

a. (-y, x) for θ = 90°

b. (-x, -y) for θ = 180°

c. (y, -x) for θ = 270°

Given the: Triangle RST with vertices R(2, 0), S(4, 0), and T(1, -3). And the image of triangle RST after a rotation has vertices R'(0, -2). S'(0, -4), and T(-3, -1)

From the given vertices it is obvious that the relation between preimage and image is defined as

(x, y) => (y, -x)

Therefore, the rule that describes the transformation is (y, -x) for θ = 270° (i.e. when the figure rotates 270° counterclockwise). So the third option (R₀, 270° ) is the answer.

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Two plants will never be of the same height.

Given, the height of an experimental plant after x days can be

represented by the formula 3(4x + 2).

The height of a second plant can be represented by the formula 6(2x + 2).

We have to state that will the two plants ever be of the same height,

Let assume that, the height of two plants be same,

So, 3(4x + 2) = 6(2x + 12)

On simplifying, we get

12x + 6 = 12x + 72

On subtracting 12x from both the sides, we get

12x + 6 - 12x = 12x + 72 - 12x

6 ≠ 72

It is an absurd condition, so we do not have any solution for x.

So, the two plants will never be of the same height.

Hence, two plants will never be of the same height.

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The required net income of the companies is given as 49,000.

Given that,
Accounts receivable of 88000 and accounts payable of 39000 and have revenues of 121000 and expenses of 83000 what is the company's net income is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
Total income = 88000 + 121000 = 209000
Total outflow = 39000 + 83000 = 122000
Net income = 209000 - 122000 = 49000

Thus, the required net income of the companies is given as 49,000.

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The Required Factors   (x + 1) (x - 3 ) (x + 2) (x - 2).

Given equation.
x^4 - 2x^3 - 7x^2+8x+12 = 0

Factors : factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.

polynomial : an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable

Now, factorize the polynomial of degree 4 as follows.

= (x + 1) (x - 3) (x^2 - 4)

Then, again factorize polynomial of degree 2.

Therefore  (x + 1) (x - 3 ) (x + 2) (x - 2)

This is the required factors.

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The fraction that represents the percentage of 57% is presented as follows:

57/100.

A fraction is represented by the division of a term x by a term y, according to the equation presented as follows:

Fraction = x/y.

The terms are know as numerator and denominator, respectively, as follows:

For a percentage of a%, the equivalent fraction is obtained as follows:

Hence, for a percentage of 57%, as is the case in this problem:

Hence the fraction is:

57/100.

The problem asks to represent the percentage as a fraction.

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The scale factor of the drawing that Desmond is illustrating is is 1/125.

A scale factor is the ratio between rte scale of a particular object and the new object.

In this case, Desmond made a scale drawing of a house, the garage is 4 centimeters wide in the drawing and the actual garage is 5 meters wide.

100 centimeters = 1 meters

5 meters = 500 centimeters

Therefore, the scale will be:

= 4 / 500

= 1 / 125

= 1:125

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The graph with the y-intercept of 1 and a slope of -2/3 is added as an attachment

Linear equations are equations whose slopes are constant average rates of change.

The given parameters are

A linear equation is represented as

y = slope * x + y-intercept i.e. y = mx + c

Substitute the known values in the above equation

So, we have the following equation

y = -2/3x + 1

Hence. the linear equation is y = -2/3x + 1

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Answer:

$370.62

Step-by-step explanation:

Ken spends $344.76 before tax at a hardware store. If the sales tax rate in his city is 7.5%, what is the total cost of his purchase? Round to the nearest cent if necessary.

7.5% = 0.075

0.075 * $344.76  = $25.857 in tax so:

cost + tax

$344.76 + $25.857 = $370.617

rounded:  $370.62

Answer: daniel and sarah will deposit the same amount

The height of the statue that exactly with the bottom of a building is approximately 9.3926 feet tall.

height of the office window , a = 45 feet

the bottom of a building that is horizontal  from the office, b = 600 feet

let x represent the angle

tan(x) = a/b

tan(x) = 45/600

x = tan⁻¹(0.75)

x = 4.28 degree

the height of the statue, h  = ?

the statue is from the building, c = 125 feet

tan(45/600) = h/125

h = tan(0.075) x 125

h = 9.3926 feet

The height of the statue that exactly with the bottom of a building is approximately 9.3926 feet tall.

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Answer:

Step-by-step explanation:

You have tickets that sell for $25 and $15, and you sold 55 tickets for $1025. You want to know the number of each sold.

Let 'a' represent the number of advance tickets sold. Then 55-a is the number of same-day tickets sold. The total revenue is ...

  25a +15(55 -a) = 1025

  10a + 825 = 1025 . . . . . simplify

  10a = 200 . . . . . . . . . . subtract 825

  a = 20 . . . . . . . . . . . divide by 10; the number of advance tickets

  55 -20 = 35 . . . . the number of same-day tickets

20 advance tickets and 35 same-day tickets were sold.

Answer: Yes

Step-by-step explanation:It can because math works like that.

The zeros of the polynomial x⁴ - 6x³ - 21x² - 150x - 100  are 0.6511 and 8.262 respectively

Zeros of polynomial are the points where the polynomial equals zero on the whole. In simple words, we can say that zeros of polynomial are values of the variable such that the polynomial equals 0 at that point. Zeros of a polynomial are also referred to as the roots of the equation and are often designated as α, β, γ respectively.

The zeros of a polynomial f(x) are the values of x which satisfy the equation f(x) = 0. Here f(x) is a function of x, and the zeros of the polynomial are the values of x for which the f(x) value is equal to zero. The number of zeros of a polynomial depends on the degree of the equation f(x) = 0. All such domain values of the function, for which the range is equal to zero, are called the zeros of the polynomial.

To find the zeros of this polynomial function, we have to write the function appropriately.

x⁴ - 6x³ - 21x² = 150x - 100

x⁴ - 6x³ - 21x² - 150x - 100 = 0

The roots of this function is 0.6511 and 8.262 respectively

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The stack of paper will have the height of 1048576 papers

The first cut will produce 2 papers, the second cut will produce 4 papers, the third cut will produce 8 papers and the fourth cut will produce 16 papers.

If you examine the stages of cut and the number of papers, the relationship between them is:

1st cut: number of papers = 2¹ = 2  

2nd cut: number of papers = 2² = 4

3rd cut: number of papers = 2³  = 8

4th cut: number of papers = 2⁴  = 16

nth cut: number of papers = 2ⁿ

So if the  process is repeated 20 times, the number of papers will be:

Number of paper = 2²⁰ = 1048576

Therefore, the stack of paper will be as high as 1048576 papers

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The equation of the line  in slope-intercept form is y = -x/12 + 23/4

Given that: the line is perpendicular to the line y= 12x−2 and it contains the (−3,6).

The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system

The slope-intercept form of a straight line is:

y = mx + c,

where m is the slope and c is the y-intercept

When the two lines are perpendicular, the product of their slope is -1 i.e.

m₁ x m₂ = -1

where m₁ and m₂ represent the slope of the lines

Let the slope of the given line be m₁ and the slope of the unknown line be m₂

Line1(given):

y = 12x−2   and m₁ x m₂ = 12

m₁ x m₂ = -1

12 x m₂ = -1

m₂= -1/12

Line 2(unknown) with the point (−3,6):

y = mx + c

6 = -1/12 (-3) + c

6 = 1/4 + c

c = 6 -1/4 = 23/4

y = -x/12 + 23/4

Therefore, the slope-intercept form of the equation of the line is y = -x/12 + 23/4

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The area of a square with a side length √8 represents a rational number, which is equal to 8 square units.

Rational numbers are real numbers of the form m / n, where m and n are integers, where n ≠ 0. The rest of real numbers are irrational (i.e. π, √5, ∛7, e) Besides, the area of the square is determined by the following formula:

A = l²

Where l is the side length of the square.

First, substitute the side length of the square in the area formula:

A = (√8)²

Second, use algebraic properties to simplify the expression and find the corresponding result:

A = ([tex]8^{\frac{1}{2} }[/tex])²

A = 8

This number represents a rational number as 8 is equivalent to the rational number 8 / 1.

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The solution of the absolute value equation |3x - 6| = 12 is x= 6 and x = -2

The absolute value equation is

|3x - 6| = 12

We can write the absolute value equation in two ways

3x - 6 = 12

-(3x - 6) = 12

We have to solve each equation

The first equation is 3x - 6 = 12

3x - 6 = 12

3x = 12+6

3x = 18

x = 18/3

x = 6

The second equation is -(3x - 6) = 12

Apply the distributive property

-3x + 6 = 12

-3x = 12 - 6

-3x = 6

x = 6/-3

x = -2

Hence, the solution of the absolute value equation |3x - 6| = 12 is x= 6 and x = -2

The complete question is:

Solve the absolute value equation |3x - 6| = 12 .

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Answer:

-2/3 or -0.6666

Step-by-step explanation:

-3x + 6 = 4 -6x

Let's move the x to one side

-3x +6x=4-6

Combine like terms

3x = -2

Divide both sides by 3

-2/3=x

or -0.666666