Find a quadratic equation which has solutions x=4/9 and x=9/2. Write the quadratic form in the simplest standard form x^2+bx+c

Answer:

Here is a Venn diagram that illustrates the information:

```

           ___________

          |           |

          |    N      |

          |_____  ____|

          |\    ||    /|

          | \   ||   / |

          |  \  ||  /  |

          |   \ || /   |

          |  C \||/ T  |

          |_____\v/____|

              A

```

In the diagram, N represents the set of students who read the novel, C represents the set of students who read the comics, and T represents the set of students who read the textbook. The region labeled A represents the set of students who read all three.

Using the Venn diagram, we can find the number of students who read:

a. comics and novel only: This corresponds to the region of the diagram that is exclusively shaded with the circles for comics and novel, but not for textbook. This region has 9 students.

b. textbook and novel only: This corresponds to the region of the diagram that is exclusively shaded with the circles for textbook and novel, but not for comics. This region has 1 student.

c. none of the 3: This corresponds to the region of the diagram that is outside of all three circles. This region has 13 students.

Therefore, the number of students who read a. comics and novel only is 9, b. textbook and novel only is 1, and c. none of the 3 is 13. Answer: a. 9, b. 1, c. 13.

Based on the graph, there is no association because the distribution of preferred transportation differs among the age groups. The Option C is correct.

The significant factors is accessibility and convenience because younger individuals may be more likely to use public transportation such as buses or trains because it is more affordable and convenient than owning a car.

But the older individuals may prefer to use personal cars because it provides more flexibility and control over their transportation needs. Another factor that influences is the cost of ownership, maintenance, and fuel.

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Answer:

The series ∑6n=1 3n is a sum of the first 6 terms of the sequence 3n, which starts with n = 1 and increases by 3 for each successive term. Therefore, the first 6 terms of the sequence are:

3(1), 3(2), 3(3), 3(4), 3(5), 3(6)

which simplify to:

3, 6, 9, 12, 15, 18

The sum of these terms is:

∑6n=1 3n = 3 + 6 + 9 + 12 + 15 + 18 = 63

Therefore, S6, the sum of the first 6 terms of the series, is 63.

The product between the complex numbers gives:

(-2 + 8i)*(-2 + 6i) = -44 - 28i

Here we have the product of two complex numbers.

It is (-2 + 8i)*(-2 + 6i)

Expanding that we will get:

(-2 + 8i)*(-2 + 6i) = (-2)*(-2) + (-2)*(6i) + (-2)*(8i) + (8i)*(6i)            

Remember that i² = -1, then we will get:

(-2)*(-2) + (-2)*(6i) + (-2)*(8i) + (8i)*(6i)  = 4 - 12i - 16i - 48

                                                            = -44 - 28i

Then the expression simplified is:

(-2 + 8i)*(-2 + 6i) = -44 - 28i

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Journal entries are a record of financial transactions in chronological order, showing the accounts and amounts debited and credited for each transaction. Below is the journal entries of the transactions:

Constitutes the journal entries :-

Below are the debit and credit entries for each transaction:

Dec. 1:

Debit: Cash (55,000)

Credit: Common Stock (55,000)

Debit: Equipment (9,000)

Credit: Cash (9,000)

Debit: Prepaid Insurance (1,500)

Credit: Cash (1,500)

Dec. 9:

Debit: Land (16,000)

Credit: Cash (16,000)

Dec. 10:

Debit: Office Supplies (2,000)

Credit: Accounts Payable (2,000)

Dec. 19:

Debit: Cash (12,000)

Credit: Notes Payable (12,000)

Dec. 22:

Debit: Advertising Expense (1,700)

Credit: Cash (1,700)

Dec. 26:

Debit: Accounts Payable (300)

Credit: Cash (300)

Dec. 28:

Debit: Utilities Expense (180)

Credit: Accounts Payable (180)

Dec. 31:

Debit: Cash (16,600)

Debit: Accounts Receivable (2,600)

Credit: Service Revenue (17,600)

Debit: Salary Expense (3,800)

Debit: Rent Expense (1,300)

Credit: Cash (5,100)

Debit: Unearned Revenue (1,400)

Credit: Cash (1,400)

Debit: Cash Dividends (4,000)

Credit: Cash (4,000)

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The mean of brothers and sisters = 3

From the attached data set of brothers and sisters we can write the data values (frequency) as:

1, 5, 4, 2

We need to find the mean of brothers and sisters,

We know that the formula for the mean of data.

mean([tex]\bar{x}[/tex]) = sum of all data values / total number of data values

First we find the sum of all data values.

1 + 5 + 4 + 2 = 12

and the total number of data values = 4

Using above formula of mean,

mean([tex]\bar{x}[/tex]) = sum of all data values / total number of data values

mean([tex]\bar{x}[/tex]) = 12 / 4

mean([tex]\bar{x}[/tex]) = 3

Therefore, the required mean is: 3

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Find the complete question below.

The result when 4x³ + 15x² + 17x + 6 is divide by 4x + 3 using long dividion method will be x² + 3x + 2.

Given that:

Dividend, 4x³ + 15x² + 17x + 6

Divisor, 4x + 3

The division of the polynomial is given below.

4x + 3 ) 4x³ + 15x² + 17x + 6 ( x² + 3x + 2

         - (4x³ + 3x²)

                    12x² + 17x

                 - (12x² + 9x)

                               8x + 6

                            - (8x + 6)

                                0    0    

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The calculated value of the area of the circle is 5544 square yards

From the question, we have the following parameters that can be used in our computation:

Radius, r = 42

Using the above as a guide, we have the following:

Area = π * r^2

Substitute the known values in the above equation, so, we have the following representation

Area = 22/7 * 42^2

Evaluate the products and exponents

Area = 5544

Approximate

Area = 5544

Hence, the value of the area is 5544 square yards

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Answer:

The given sequence is decreasing by a factor of 2 each time, so each term is half of the previous term.

We can write the nth term of the sequence as:

a_n = a_1 * (1/2)^(n-1)

where a_1 is the first term of the sequence (12 in this case) and n is the position of the term we want to find.

For example, to find the 4th term of the sequence, we would have:

a_4 = 12 * (1/2)^(4-1)

= 12 * (1/2)^3

= 12 * 1/8

= 1.5

Therefore, the formula for the nth term of the sequence 12, 6, 3, ... is:

a_n = 12 * (1/2)^(n-1)

Answer:1/4, 25%

Step-by-step explanation:

even number: 2,4,6

odd umber 1,3,5

even number probability when 1 dice is rolled: 3/6 = 1/2

2 dice is rolled: 1/2*1.2 = 1/4 = 25%

Using the expression 5x/12 = 20, the amount that A originally had was $48.

We have,

Let x be the amount of money that A originally had.

Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.

The amount received by B is 1/2 of the remaining amount,

which is (x - x/6)/2 = 5x/12.

We know that 5x/12 = 20,

Solving for x.

5x/12 = 20

5x = 240

x = 48

Therefore,

The amount that A originally had was $48.

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The question about a particular animal that could NOT be answered using only the data collected from the tracking collars would be do the movement patterns of the animal vary according to the weather? That is option C.

A tracking collars is a neck device that usually has a GPS device attached to it which is used by biologists to track the movement of animals that are under study.

The functions of the tracking collars include the following:

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Complete question:

Biologists often attach tracking collars to wild animals. For each animal, the following geolocation data is collected at frequent intervals.

The time

The date

The location of the animal

Which of the following questions about a particular animal could NOT be answered using only the data collected from the tracking collars?

A. Approximately how many miles did the animal travel in one week?

B. Does the animal travel in groups with other tracked animals?

C. Do the movement patterns of the animal vary according to the weather?

D. In what geographic locations does the animal typically travel?

C. Do the movement patterns of the animal vary according to the weather?

The solutions to the function y = -x^2 - 8x + 8 are (-8.9, 0) and (0.9, 0)

From the question, we have the following parameters that can be used in our computation:

y = -x^2 - 8x + 8

To solve using a graphing calculator, we enter the equation in a graph and write out the solution

Having said that we have

When y = -x^2 - 8x + 8 is plotted, the soluton is (-8.9, 0) and (0.9, 0)

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The number of students are as follows:

To find the number of students who read comics and novels only:

Let novel and textbook = x

Let textbook and comics = y

Let comic and novel = z

y + x = 11 --- (1)

y + z = 10 --- (2)

x + z = 13 --- (3)

Make y subject of the formula in (2)

y = 10 - z

substitute for y in (1)

10 - z + x = 11 --- (4)

solve (3) and (4) simultaneously by addition

10 - z + x + x + z = 11 + 13

2x = 24 - 10

x = 7

y = 11 - 7

y = 3

z  = 13 - 7

z = 4

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Using Tia's box method, the multiplication of the polynomials (x + 2)(x² -3x + 5) in the standard form is  x³ - x² - x + 10

Here, we need to multiply the polynomials (x + 2)(x² -3x + 5)

Tia's stargergy for multiplying polynomials is to make a box that fits the two factors.

Using Tia's box method,

          x²          -3x            +5

x         x³           -3x²          +5x

+2     +2x²         -6x           +10

Consider (x + 2)(x² -3x + 5)

= (x . x²) - (x . 3x) + (x . 5) + (2x²) -(2 × 3x) + (2 × 5)

= x³ - 3x² + 5x + 2x² - 6x + 10

= x³ - 3x² + 2x² + 5x - 6x + 10

= x³ - x² - x + 10

This is the required polynomial.

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Find the complete question below.

(i)  [tex]\lim_{x \to \frac{\pi^-}{2}}[/tex] h(x) = 3

(ii) [tex]\lim_{x \to \frac{\pi^+}{2}}[/tex] h(x) = -1

(iii) h(0) = 1/7

The value of λ must be 7, for h(x) to be continuous at x = 0.

The given function is,

h(x) = 1/7, when x = 0

      = 1 - 2 cos 2x, when x < π/2

      = 1 + 2 cos 2x, when x > π/2

      = x cos x/sin λx, when x < 0

Now,

(i) [tex]\lim_{x \to \frac{\pi^-}{2}}[/tex] h(x) = [tex]\lim_{x \to \frac{\pi^-}{2}}[/tex] (1 - 2 cos 2x) = 1 - 2 cos π = 1 + 2 = 3

(ii) [tex]\lim_{x \to \frac{\pi^+}{2}}[/tex] h(x) = [tex]\lim_{x \to \frac{\pi^+}{2}}[/tex] (1 + 2 cos 2x) = 1 + 2 cos π = 1 - 2 = -1

(iii) h(0) = 1/7

Since the function is continuous at x = 0, so

[tex]\lim_{x \to 0}[/tex] h(x) = h(0)

[tex]\lim_{x \to 0}[/tex] x cos x/sin λx = 1/7

[tex]\lim_{x \to 0}[/tex] cos x.[tex]\lim_{x \to 0}[/tex] 1/λ(sinλx/λx) = 1/7

1/λ = 1/7

λ = 7

Hence the value of λ must be 7.

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Answer:

she can divide the amount of cookies to friends

Step-by-step explanation:

120/5= 24

Answer:

Step-by-step explanation:

To answer this question, we need to know the dimensions of the rectangle and the triangle. Assuming that the triangle is right-angled and has one side coinciding with one side of the rectangle, we can use the formula for the area of a triangle: \ ( \frac {1} {2} \) × base × height1. The base and height of the triangle are the same as the length and width of the rectangle. The area of the rectangle is length × width. The probability that a point chosen randomly inside the rectangle is in the triangle is then the ratio of the area of the triangle to that of the rectangle, which is: \ ( \frac {\frac {1} {2} \times length \times width} {length \times width} \) = \ ( \frac {1} {2} \). So, the probability is 0.5 or 50% to the nearest hundredth2.

Answer:    C  .08

Step-by-step explanation:

Probability is the part out of the whole.  you first need to find the part, which is the triangle

In other words find out how much of the triangle is taking up the rectangle, which is done through area

A(triangle)=1/2 b h      where b=6   h=9

A(triangle)=1/2 (6)(9) = 27

A(rectangle)= Lw      where L=24    h=15

A(rectangle)= (24)(15) = 360

P(triangle in rectangle)= 27/360

=.075   rounded = .08

Answer:

The probability that the number chosen is not even = 4/8

The within-group sum of squares is 58250.44

The degrees of freedom are given as 355

The estimate of the within-groups variance is 164.0657

Variance, as a statistical measure, evaluates the level of variability or dispersion contained in a dataset by inspecting how distant each value in a set is from the mean of that same set.

If there is a higher variance, it signals that data points are more widely distributed and further removed from the mean, whereas if there is a lower variance, one can assume that they are primarily clustered more closely around the mean.

To obtain the variance value, one must determine an average signal-to-noise ratio for each squared difference derived from every respective value taken away from the arithmetic mean. It is no exaggeration to say that variance is progressively employed across diverse subject areas including finance, engineering, and science.

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The average rate of decrease of the area as the length goes from 13 cm to 16 cm is given as follows:

D) 11 and 1/3 cm² per cm.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function.

From the graph, the parameters are given as follows:

Hence the rate is approximated as follows:

r = (24 - 60)/(16 - 13)

r = -12 cm² per cm.

Which is closest to option D.

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I answered this on Khan Academy and my lawyer above me has the papers for the work.

See u in court...

The graph of this function will behave as (b) A graph of this function would slope downward, starting from a price of $100 dollars because the rate of change is less than 0 and the initial value is -10.

The demand function is given by d = 100 - 10p. This means that the quantity demanded (d) decreases as the price (p) increases.

The slope of the demand function is the rate of change of the quantity demanded with respect to the price. In this case, the slope is -10, which is negative. This indicates that as the price increases, the quantity demanded decreases.

The initial value of the demand function is 100, which represents the quantity demanded when the price is zero. This means that the demand function intersects the y-axis at (0, 100).

Therefore, the correct answer is (b) A graph of this function would slope downward, starting from a price of $100 dollars because the rate of change is less than 0 and the initial value is -10.

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Answer:

Step-by-step explanation:

Ronald's walking speed is 3 miles per hour, and he walks for 2 hours, so he covers 3 * 2 = 6 miles. In the next hour, he runs at a speed of 6 miles per hour, covering an additional 6 miles. Therefore, Ronald traveled a total of 6 + 6 = 12 miles.

Answer:

a

Step-by-step explanation:

The length of the rectangular prism is 18 cm.

The formula for the volume of a rectangular prism is given as:

Volume of a rectangular prism = (length x width x height) cubic units.

V = (l x w x h) cubic units

In a rectangular prism, the product of the length and the width is known as the base area. Therefore, we can also represent the volume of a rectangular prism formula as:

Volume of a rectangular prism = Base area x height

Now, We have :

The volume of a rectangle prism is 810 square centimeters .

Height = 15 cm

Width = 3 cm

To find the length of the rectangular prism

Now, Apply the formula of volume of rectangular prism

Volume of rectangular prism is(V) : (l x w x h) cubic units

Plug all the values in above formula:

810 = l x 3 x 15

810 = 45L

L = 810 / 45

L = 18cm

Hence, The length of the rectangular prism is 18 cm.

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Answer:

5

Step-by-step explanation:

300÷2=150 ⇒300 wiggles=10 wiggles⇒ 10÷2=5

The surface area of the prism for the given dimensions is equal to option B. 180 square centimeters.

Surface area of the prism

= Area of two right triangles + Area of rectangle 1 + Area of rectangle 2 + Area of the rectangle3

In a Triangle ,

Base = 12cm

height = 5cm

Area of the triangle = ( 1/2 ) × base × height

                                 = (1/2)× 12 × 5

                                 = 30 cm²

Length of rectangle 1 = 12cm

Width of rectangle 1 = 4cm

Area of rectangle 1 = 12 × 4

                                = 48 cm²

Length of rectangle2= 13cm

Width of rectangle 2 = 4cm

Area of rectangle 2= 13 × 4

                                = 52 cm²

Length of rectangle 3 = 5cm

Width of rectangle 3 = 4cm

Area of rectangle 3 = 5 × 4

                                = 20 cm²

Surface area of the prism

= Area of two right triangles + Area of rectangle 1 + Area of rectangle 2 + Area of the rectangle3

Substitute the values of the area we have,

⇒ Surface area of the prism  = 2(30 ) + 48 + 52 + 20

⇒ Surface area of the prism  =  180 square centimeters

Therefore, the surface area of the prism is equal to option B. 180 square centimeters.

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The calculated expression that represents the distance between point j and point k is |j - k|

From the question, we have the following parameters that can be used in our computation:

Point j and point k

The expression that represents the distance between point j and point k is the absolute difference of the points j and k

Using the above as a guide, we have the following:

Distance = |point j - point k|

So, we have

Distance = |j - k|

Hence, the expression that represents the distance between point j and point k is |j - k|

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The value of c for the parallelogram WXYZ is 5

Parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary and the opposite sides need to be parallel.

How to determine this

When WXYZ is a Parallelogram

ZX = 104

ZU = 11-2c

By using the law of parallelogram

ZU = UX

Therefore, ZX = ZU + UX

Where ZU = UX

So, 104 = 11c- 23 + (11c -3)

104 = 11c - 3 + 11c - 3

104 = 11c + 11c - 3 - 3

104 = 22c - 6

Collect like terms

104 + 6 = 22c

110 = 22c

Divides through by 22

110/22 = 22c/22

5 = c

Therefore, the value of c = 5

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