the vertices of a polygon are (1,2) (1,6) (7,6) (7,2) (5,0) (3,0) graph the polygon then find its area

Answer: 3, 5, and 7

Step-by-step explanation:

Vertical angles, corresponding angles, and alt. ext. angles

The value of the fractions will be:

a. 1/3 + 1/4 = 7/12

b. 1/3 + 2/7 = 13/21

c. 1/2 + 2/9 = 13/18

d. 3/4 + 1/5 = 19/20

e. 1/3 + 4/9 = 7/9

f. 1/6 + 3/4 = 11/12

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

The value of the fractions will be:

a. 1/3 + 1/4

= 4/12 + 3/12

= 7/12

b. 1/3 + 2/7

= 7/21 + 6/21

= 13/21

c. 1/2 + 2/9

= 9/18 + 4/18

= 13/18

d. 3/4 + 1/5

= 15/20 + 4/20

= 19/20

e. 1/3 + 4/9 = 7/9

f. 1/6 + 3/4 = 11/12

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Answer:

-2

Step-by-step explanation:

[tex]m=\frac{4-(-8)}{-4-2} \\m=\frac{4+(+8)}{-4-2} \\m=\frac{12}{-6} \\m=\frac{2}{-1} \\m=-2[/tex]

Check the picture below.

Answer:

please give brainliest

Step-by-step explanation:

P(x)=(x+5)(x−4)(x−5)

is the lowest order of all polynomials with given zeroes.

The trinomial [tex]x^(2)+7x-18[/tex] factors into (x+9)(x-2), and the trinomial [tex]x^(2)-7x-18[/tex] factors into (x-9)(x+2). The signs in each binomial are opposite.

In the first trinomial, the signs are positive and negative, while in the second trinomial, the signs are negative and positive. This is because the signs in the binomials are determined by the signs of the constant term and the coefficient of the linear term in the trinomial.

For the first trinomial, the constant term is -18 and the coefficient of the linear term is 7. To factor this trinomial, we need to find two numbers that multiply to -18 and add to 7. The numbers 9 and -2 satisfy this condition, so the trinomial factors into (x+9)(x-2).

For the second trinomial, the constant term is -18 and the coefficient of the linear term is -7. To factor this trinomial, we need to find two numbers that multiply to -18 and add to -7. The numbers -9 and 2 satisfy this condition, so the trinomial factors into (x-9)(x+2).

In both cases, the signs in the binomials are opposite because one of the numbers is positive and the other is negative.

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The answer of the given question based on the histogram of Investment Account Values the correct option is c) 63%.

Investment refers to act of allocating resources, like  money or time, with  expectation of generating income or profit in  future. In other words, it involves sacrificing something of a value in  present, in hope of obtaining something of the greater value in  future

Investments can be taken  in many forms, including stocks, bonds, mutual funds, real estate, and commodities, among others. The choice of investment depends on variety of factors, including investor's risk tolerance, financial goals, and the investment time horizon.

Based on the histogram of Investment Account Values provided, it appears that approximately 63% of investments have a value of $150 or less. This can be determined by adding up the percentage of investments in each bar up to and including the $150 bar.

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The revised mean is thus 20.8, which is consistent with choice (B).

How can you calculate the mean?

Simply dividing the total number of values in a data collection by the aggregate of all of the values yields it. The computation can be performed on unprocessed data or data that has been combined into a frequency chart.

We must first compute the average of the dataset such as the new number, then split by the overall number of data points in order to determine the innovative mean within a week of adding a count to the dataset.

Let's call the four original numbers in the dataset A, B, C, and D. We know that their mean is 19, so we can write:

(A + B + C + D)/4 = 19

Multiplying both sides by 4 gives us:

A + B + C + D = 76

Now, if we add the number 28 to the dataset, we get a new sum:

A + B + C + D + 28

To find the new mean, we need to divide this sum by the total number of values in the dataset, which is 5 now:

(A + B + C + D + 28)/5

Substituting in our earlier expression for A + B + C + D, we get:

(76 + 28)/5 = 104/5 = 20.8

Therefore, the new mean is 20.8, which corresponds to option (B).

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In response to the aforementioned query, we may say that As a result, expressions the response is A. A quotient of two sums is this.

Mathematical operations include doubling, dividing, adding, and subtracting. A phrase is constructed as follows: Expression, monetary value, and mathematical operation Numbers, parameters, and functions make up a mathematical expression. It is possible to use words and terms in contrast. Every mathematical statement including variables, numbers, and a mathematical operation between them is called an expression, sometimes referred to as an algebraic expression. For example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.

It is better to refer to the phrase (8+5)/(y+6) as "a quotient of two sums" since it divides the sum of 8 and 5 by the sum of y and 6.

As a result, the response is A. A quotient of two sums is this.

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Answer:

5.30

Step-by-step explanation:

One hundredth is 0.01. 5.31-0.01=5.30.

sorry for answering late!

Answer:

Step-by-step explanation:

A$AP BEAN$: Khan Academy can help you. Do your work and stop cheating!!!!!

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The required four values of θ that satisfy the equation tan θ = -√3 are:

θ = 4π/3 radians (or 240 degrees)
θ = 7π/3 radians (or 420 degrees)
θ = π/3 radians (or 60 degrees)
θ = 2π/3 radians (or 120 degrees)

These are the equation that contains trigonometric operators such as sin, cos.. etc. In algebraic operations.

Here,
Since the tangent function has a period of π, we can find the angles θ that satisfy the equation tan θ = -√3 by adding or subtracting multiples of π until we find all possible solutions in the desired range.

For θ < 0,

Therefore, one solution for θ in the fourth quadrant is:

θ = π + π/3 = 4π/3 radians (or 240 degrees)

To find another solution, we can add one full period of π to 4π/3 to get:

θ = 4π/3 + π = 7π/3 radians (or 420 degrees)

For θ > 2,

One solution for θ in the first quadrant is,

θ = π/3 radians (or 60 degrees)

One solution for θ in the fifth quadrant is:

θ = 2π - π/3 = 5π/3 radians (or 300 degrees)

To find another solution in the fifth quadrant, we can subtract one full period of π from 5π/3 to get:

θ = 5π/3 - π = 2π/3 radians (or 120 degrees)

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Answer: Without knowing the specifics of the spinner, it's not possible to list all the possible outcomes.

However, we can determine the total number of possible outcomes by multiplying the number of outcomes for each event. For example, if the coin has two possible outcomes (heads or tails) and the spinner has six possible outcomes, then the total number of possible outcomes would be:

2 (outcomes for the coin) x 6 (outcomes for the spinner) = 12 possible outcomes

If you provide me with the specific details of the spinner (such as the number of sections and what each section represents), I could list all the possible outcomes.

Step-by-step explanation:

Answer:

$6236.56

Step-by-step explanation:

Compound Formula

[tex]A = P (1+\frac{r}{n} )^n^t\\[/tex]

I plugged in the numbers of P, r, and t.

n means the number of times the interest is applied per period. It is compounded monthly, and the time is given 3 years.

This means 12 months x 3 years = 36 months.

[tex]A = $5700(1+.03/36)^3^6^(^3^)[/tex]

[tex]A=6236.559672[/tex]

[tex]A=6236.56[/tex]

The area of the parallelogram with base of 8cm and height of 9cm is 72cm²

It is important to note the following properties of a parallelogram;

From the information given, we have that;

Area = bh

Given that;

Now, substitute the values

Area = 8(9)

Area = 72cm²

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The solution to the system of equations: x = 1 and y = 3

We have that the equations are;

y = −x^2 + 4     (1)

y = 2x + 1         (2)

Now, equate the two equations, we get;

-x² + 4 = 2x + 1

collect the like terms

-x² - 2x + 4 - 1

subtract the values

-x² - 2x + 3

Make into standard form

x² + 2x - 3 = 0

Solve the quadratic equation

Find the pair factors of -3 that sums up to 2, we have;

x² +3x - x - 3 = 0

factor the terms

x(x + 3) - 1(x + 3) = 0

(x - 1) = 0

Make 'x' the subject

x = 1

x + 3 = 0

x = -3

Then, y = 2(1) + 1 = 3

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The system of equations according to the given instructions are x + (1/2)y = -5; 2y - 12 = x

The sum of one number and half another is negative five. Twelve less than twice the second number yields the first number.

Let x represent the first number and y represent the second number.

System:

x + (1/2)y = -5
2y - 12 = x

The system of equations that represents this situation is:
x + (1/2)y = -5
2y - 12 = x

Where x represents the first number and y represents the second number.

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Solving a quadratic equation we can see that the 3 consecutive numbers are:

4, 5, and 6.

First, we can write 3 consecutive integers as:

x, (x + 1), and (x +2 )

The square of the first increased by the last is 22, then we can write:

x^2 + (x + 2) = 22

x^2 + x + 2 - 22 = 0

x^2 +x  - 20 = 0

Using the quadratic formula we will get the solutions:

[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*1*-20} }{2} \\\\x = \frac{-1 \pm 9}{2}[/tex]

We know that x is positive, then the solution is:

x = (-1 + 9)/2 = 4

The 3 consecutive numbers are:

4, 5, and 6.

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Answer:8

Step-by-step explanation: I got 8 because when you multiply 4/5 and 10 together you put 10 over one then multiply across.

After that you will get 40/5 and that is 8.

The measure of width of the computer is 75.89 inches.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

The ratio of a and b is denoted as a : b.

Given that,

Ratio of diagonal to length of a rectangular computer = 13 : 7

This means that,

If diagonal = 13k and length = 7k for some constant k.

Given Actual length = 18 inches.

3k = 18

k = 18/3 = 6

So Diagonal length = 13 × 6 = 78 inches

We know that, the length, width and diagonal of a rectangle form a right angled triangle.

Let width of the rectangular computer be x.

Using Pythagorean Theorem,

(Length)² + (Width)² = (Diagonal)²

18² + x² = 78²

x² = 78² - 18²

x² = 5760

x = 75.89 inches.

Hence the measure of width is 75.89 inches.

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Answer:

Step-by-step explanation:

slope of line = 7/3

y-intercept is = 7

By answering the above question, we may infer that Ling will thus require equation 42 feet of wallpaper border to install at the top of the three walls.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

Three walls, each 14 feet long and 12 feet tall, are being wallpapered by Ling. Just the top of the wall will be covered by the border. As a result, each wall requires a 14-foot-long wallpaper border.

The length of the border on each of the three walls must be added together to determine the overall length of wallpaper border required. So:

Whole wallpaper border length is one wall's border length times the number of walls.

Overall wallpaper border length is 14 feet multiplied by 3 walls.

42 feet is the total length of the wallpaper border.

Ling will thus require 42 feet of wallpaper border to install at the top of the three walls.

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Number of years = 4

Hi there! To answer your question, Doug needs to deposit $2226.19 into a savings account that earns 2.9% interest compounded continuously. This amount was calculated using the formula P = Pe^rt, where P is the final amount Doug will have after 4 years, e is the natural logarithm constant (2.71828), r is the interest rate (2.9%), and t is the number of years (4).

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The inequality for the number of sales Ken needs to make this week in dollars is: 4x + 55 > 115. Where x is the number of sales.

Inequalities are the mathematical term for the relationship between two values that are not equal. Not all people are created equal. We typically use the "not equal symbol ()" when two values are not equal. However, various inequalities are utilized to compare the values, whether they are less than or greater than.

To solve for x, we first need to isolate it on one side of the inequality. We can start by subtracting 55 from both sides:

4x > 60

Then, we can divide both sides by 4:

x > 15

Therefore, Ken needs to make more than 15 sales this week to earn more than $115.

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No, the expression w^(2)+64 is not a difference of squares.

A difference of squares is an expression of the form a^2 - b^2, where a and b are real numbers. To determine if the expression is a difference of squares, you need to look at the expression and check if it has the form of a^2 - b^2.

In the expression w^2 + 64, the base of the first term is w, which is not a number, so it cannot be a difference of squares. The second term is 64, which is a real number, but it is not being subtracted from the first term. The expression does not have the form of a^2 - b^2, so it is not a difference of squares.

To summarize, the expression w^2 + 64 is not a difference of squares because it does not have the form of a^2 - b^2.

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Mmaximum number of apples produced per year is 98000 when 70 apple trees are planted in the farm.

To find the maximum number of apples per year, we need to find the vertex of the quadratic equation y=-20x^(2)+2800x. The x-coordinate of the vertex can be found using the formula x=-b/(2a), where a=-20 and b=2800.

Plugging in the values for a and b, we get:
x=-2800/(2*-20)
x=-2800/(-40)
x=70

So, the maximum number of apples per year will be produced when 70 apple trees are planted in the farm. We can find the y-coordinate of the vertex by plugging x=70 back into the equation:

y=-20(70)^(2)+2800(70)
y=-20(4900)+196000
y=-98000+196000
y=98000

Therefore, the maximum number of apples produced per year is 98000 when 70 apple trees are planted in the farm.

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The point of maximum growth rate is approximately (1.76, f'(1.76)) or (5.54, f'(5.54)) so the answer is (C) (5.54, 9).

What is the rate?

In mathematics, the rate is a measure of the change in one quantity with respect to another quantity. It is typically expressed as a ratio between the two quantities.

To find the point of maximum growth rate, we need to find the maximum value of the derivative of the function f(x).

First, we need to find the derivative of f(x):

[tex]f'(x) = (20 * 27e^{(-3x)}) / (1 + 9e^{(-3x)})^2[/tex]

To find the maximum value of f'(x), we set f''(x) = 0, where f''(x) is the second derivative of f(x):

[tex]f''(x) = (20 * 81e^{(-6x)} * (81e^{(-6x)} - 18e^{(-3x)} + 1)) / (1 + 9e^{(-3x)})^3[/tex]

Solving f''(x) = 0, we get:

[tex]81e^{(-6x)} - 18e^{(-3x)} + 1 = 0[/tex]

Letting [tex]y = e^{(-3x)}[/tex], we can rewrite the equation as:

81y² - 18y + 1 = 0

Using the quadratic formula, we get:

y = (18 ± √(18² - 4 * 81)) / (2 * 81) = 0.069 or 0.012

So,  [tex]y = e^{(-3x)}[/tex] = 0.069 or 0.012

Solving for x, we get:

x = ln(0.069) / (-3) ≈ 1.76 or x = ln(0.012) / (-3) ≈ 5.54

Therefore, the point of maximum growth rate is approximately (1.76, f'(1.76)) or (5.54, f'(5.54)).

Now we need to calculate f'(1.76) and f'(5.54) to find the answer.

[tex]f'(1.76) = (20 * 27e^{(-5.28)}) / (1 + 9e^{(-5.28)})^2 = 9.62[/tex]

[tex]f'(5.54) = (20 * 27e^{(-16.62)}) / (1 + 9e^{(-16.62)})^2 = 1.01[/tex]

Rounding these values to the nearest hundredth, we get:

(1.76, 9.62) and (5.54, 1.01)

Therefore, the point of maximum growth rate is approximately (1.76, f'(1.76)) or (5.54, f'(5.54)) so the answer is (C) (5.54, 9).

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Ans - The pilot is 1868.08 mi from her starting position, To find the distance the pilot is from her starting position, we can use the law of cosines. The law of cosines states that for any triangle with sides a, b, and c, and angle C opposite side c:

[tex]c^2 = a^2 + b^2 - 2ab*cos(C)[/tex]

In this case, the pilot's original path is one side of the triangle (a), her new path after the course correction is another side of the triangle (b), and the distance she is from her starting position is the third side of the triangle (c). The angle between the two paths is 20 degrees (C).

First, we need to find the length of sides a and b. The pilot flew for 1.5 hrs at a speed of 685 mi/h on her original path, so:

a = 1.5 hrs * 685 mi/h = 1027.5 mi

She then flew for 2 hrs at the same speed on her new path, so:

b = 2 hrs * 685 mi/h = 1370 mi

Now we can plug these values into the law of cosines to find the distance the pilot is from her starting position (c):

[tex]c^2 = 1027.5^2 + 1370^2 - 2*1027.5*1370*cos(20)[/tex]
[tex]c^2 = 3,488,806.25[/tex]
[tex]c = sqrt(3,488,806.25)[/tex]
[tex]c = 1868.08 mi[/tex]

Therefore, the pilot is 1868.08 mi from her starting position.

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