Plot all ordered pairs for the values in the domain.

If the congruence statement ABCA = AFGA is true, then the following must also be true:

B = G, since corresponding angles are congruent

AB = FG, since corresponding sides are congruent

C = F, since corresponding angles are congruent

Thus, the complete congruence statement is ABCA = AFGA, where B = G, AB = FG, and C = F.

Product ab has a value of 18 and is shaped like a regular hexagon.

The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The area is the region defined by an object's form. The area of a form is the space covered by a figure or any two-dimensional geometric shape in a plane.

Here,

Let the side of the hexagon be 2.

so the radius of the circle is sqrt(3),

area of hexagon=sqrt(3) * 2 * 3

= 6 sqrt(3)

area of circle is pi (sqrt(3))^2 = 3 pi

3 pi / 6 sqrt(3) = sqrt(3)/ 6

3 * 6 = 18

The value of product ab is 18 which is in the shape of a regular hexagon.

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Answer:

Answer. it is -111 because it is greater than 112 and in positive form it is smaller and in negative it is bigger .

Based on the provide system of linear equations, the solution is that there is no solution.

A system of linear equations refers to a collection of one or more linear equations involving the same variables. The solution to a system of linear equations refer to the point at which the lines representing the linear equations intersect. If the lines are parallel, they will never intersect hence, the system has no solution.

According to the provided information, the percentage of smokers in Russia is given by the equation 36x+100y=346 and the percentage of smokers in Poland is given by the equation 18x+50y=176. In order to determine the solution of the system of linear equations, multiply the Poland equation by 2 and subtract it from the Russian equation. Hence,

2*(18x+50y=176)

36x + 100y = 352

-(36x+100y=346)

0 = 6

It means the original equations are parallel. As both the variables are eliminated, the system has no solution.

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Answer:

215

Step-by-step explanation:

218+212/2

The overall price considering the percentages is decreased.

Percentage is defined as "out of 100." Similar to fractions and decimals, percentages are used in mathematics to represent subsets of a whole. When expressing a sum as a percentage, 100 equal components are regarded to make up the whole. A percentage can be shown by the symbol % or, less frequently, by the abbreviation 'pct'.

In stores, online, in commercials, and in the media, you can see percentages practically anywhere. Understanding what percentages signify is a crucial skill that could help you save time and money and raise your employability.

Let us suppose mary bought that antique clock for 100$.

So now in the first year its value is increased by 30% which is 100+30 = 130$ after the 1 st year.

Now the clock price is 130$

So now in the second year its value is decrease by 30% which is 130- 39 = 91 $

So the overall clock price has been decreased by $9 since mary bought it.

The overall price considering the percentages is decreased.

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Answer:[tex]x+8\geq 40[/tex]

Step-by-step explanation:

[tex]x+8\geq 40[/tex]

subtract 8 from both sides  to isolate x

[tex]x\geq 32[/tex]

You must spend 32 more dollars to receive three free songs.

The area of the triangular dock is 19.5 square feet and the area of the rectangular box is 10 feet. The box will fit under the dock.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle. The space occupied by the triangle in a two-dimensional plane is called the area of the triangle.

Calculate the area of the triangle first,

Area = 1 / 2 x B x H

Area = 1/2 x 12 x 3.25

Area = 19.5 square feet

Calculate the area of the rectangle,

Area = L x W

Area = 2 x 5

Area = 10 square feet

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The airplane pilot should include and follow the relation y > [D][x] for his fuel estimates.

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is that an airplane pilot is planning a flight to Hawaii. In his flight plan, he will include fuel estimates for the trip.

Assume that the distance of Hawaii from the initial location of pilot is [D] miles. If the amount of fuel burnt per miles is [x] liters/miles. Let the total amount of fuel needed to reach Hawaii is [y] liters. Than, his estimates should include and follow the given relation as -

y > [D][x]

Therefore, the airplane pilot should include and follow the relation y > [D][x] for his fuel estimates.

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the Central Limit Theorem, which states that as the sample size increases, the sampling distribution of the sample mean tends to become more normal.

The Central Limit Theorem states that as the sample size increases, the sampling distribution of the sample mean tends to become more normal. This means that the mean of the sample will be closer to the mean of the population, and the variability of the sample will be smaller. Since the sample proportion is just the mean of the sample, as the sample size increases, the distribution of the sample proportion will also become more normal. The larger the sample size, the more likely it is that the sample will accurately represent the population, and the more normal the distribution of the sample proportion will be. In other words, the sample proportion will be closer to the true population proportion, and the variability of the sample proportion will be smaller.

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Step-by-step explanation:

It takes 73 pounds of seed to completely plant an 11 -acre field. How many pounds of seed are needed per acre?

73 / 11 = 6.6363636 pounds per acre

rounded to two decimal places: 6.64 pounds per acre

To find the percentage of girls in class A, we need to divide the number of girls by the total number of students and then multiply by 100. This gives us:

14 / 20 * 100 = 70%

To find the percentage of girls in class B, we need to divide the number of girls by the total number of students and then multiply by 100. This gives us:

15 / 25 * 100 = 60%

Thus, the percentage of girls in class A is 70%, and the percentage of girls in class B is 60%.

The angles that satisfy the trigonometric equation 4 · cos 2x + cos x - 3 = - 5 · cos x - 8 are described below:

In this problem we find a trigonometric equation involving both cos 2x and cos x, we need to simplify the expression such that only cos x is present. This can be done by means of trigonometric formulas. First, write the entire expression:

4 · cos 2x + cos x - 3 = - 5 · cos x - 8

Second, use trigonometric formulas to eliminate cos 2x:

4 · (2 · cos² x - 1) + cos x - 3 = - 5 · cos x - 8

8 · cos² x  - 4 + cos x - 3 = - 5 · cos x - 8

8 · cos² x + 6 · cos x + 1 = 0

Third, use the quadratic formula to find all possible roots:

cos x₁ ≈ - 1 / 4, cos x₂ ≈ - 1 / 2

Fourth, use inverse trigonometric functions to determine all possible angles between 0° and 360°:

Case 1: - 1 / 4

x₁₁ ≈ 104.5°, x₁₂ ≈ 255.5°

Case 2: - 1 / 2

x₂₁ = 120°, x₂₂ ≈ 240°

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The gradient value of the line 2x + y = 4 is 2. This can be found by rearranging the equation into slope-intercept form, which is y = -2x + 4. The coefficient of the x term, -2, is the slope of the line.

The person who mows the lawn in less time is given as follows:

Daniel.

To obtain who mows the lawn in less time, we calculate the hourly rates for each person, applying the proportion, which is the division of the amount of area mowed by the time needed.

Daniel can mow 15,000 ft³ in 3/4 = 0.75 hours, hence his hourly rate is calculated as follows:

Daniel hourly rate = 15000/0.75 = 15000 x 4/3 = 20,000 ft² per hour.

Bronwyn can mow 12,000 ft² in hour, hence her rate is of:

12,000 ft² per hour.

20,000 > 12,000, hence Daniel can mow the law in less time, as he has a higher rate.

The missing sentence is of:

"Bronwyn can mow 12,000 ft² in hour".

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Answer:

39.95m

Step-by-step explanation:

To find the side length of a regular 36-gon with a given area and apothem, we need to use the formula for the area of a regular polygon and the formula for the apothem of a regular polygon.

The formula for the area of a regular polygon is given by:

A = (1/2) * a * p

where A is the area of the polygon, a is the apothem of the polygon, and p is the perimeter of the polygon.

The formula for the apothem of a regular polygon is given by:

a = r * cos(180/n)

where a is the apothem of the polygon, r is the radius of the polygon, and n is the number of sides of the polygon.

In this case, we are given that the area of the 36-gon is 164,592 square meters, the apothem of the 36-gon is 228.6 m, and the number of sides of the 36-gon is 36.

We can use these values to solve for the side length of the 36-gon. First, we can use the formula for the area of a regular polygon to solve for the perimeter of the 36-gon:

A = (1/2) * a * p

164,592 = (1/2) * 228.6 * p

164,592 = 114.3 * p

p = 1438.3

Next, we can use the formula for the apothem of a regular polygon to solve for the radius of the 36-gon:

a = r * cos(180/n)

228.6 = r * cos(180/36)

r = 561.8

Finally, we can use the formula for the perimeter of a regular polygon to solve for the side length of the 36-gon:

p = n * s

1438.3 = 36 * s

s = 39.95

Therefore, the side length of the 36-gon is 39.95 meters.

Answer: k=±`12

Step-by-step explanation:

[tex]ax^2-bx+c=0\\\\9x^2-kx+4=0\\\\D=b^2-4ac\\\\a=9\ \ \ \ b=-k\ \ \ \ c=4\\\\D=0\\\\Hence,\\\\D=(-k)^ 2-4(9)(4)=0\\\\k^2-144=0\\\\k^2=144\\\\k^2=12^2[/tex]

Extract the square root of both parts of the equation:

[tex]k=б\sqrt{12^2} \\\\k=б12[/tex]

Answer:

---------------------------------------------

A perfect square trinomial is:

Given trinomial:

Show this as:

Compare and find possible values of k:

Answer:

C. The graph of the function does not form a straight line

Answer:

Graph B

Step-by-step explanation:

First, simplify by subtracting 1 on both sides.

|x| + 1 - 1 < 3 - 1

|x| < 2

Using the absolute value definition, we know the inequalities are:

x < 2

-x < 2

Divide both sides by -1.

x < -2

If you multiply or divide both sides of an inequality by a negative number, you must flip the sign.

x > -2

x<2, x>-2

Graph B

Answer:

Graph A

Step-by-step explanation:

if x ≥ 0

x + 1 < 3

x < 3 - 1

x < 2

0≤ x < 2

if x < 0

-x + 1 < 3

-x < 3 - 1

-x < 2

x > -2

-2 < x < 0

Final solution

-2 < x < 2

Answer:

To find the new price after a discount, you can use the formula: new price = original price * (1 - discount rate). In this case, the new price would be $28 * (1 - 0.25) = $28 * 0.75 = $<<28*0.75=21>>21. So the new price, rounded to the nearest cent, would be $21.

Step-by-step explanation:

P(n) = 1³ +2³ +···+n³ = (n(n+1)/2)²

P(1) = 1³ = 1

According to statement P(n) = (n(n+1)/2)²

Checking for n = 1,

(n(n+1)/ 2)² = (1(1+1)/ 2)²

P(1) = (1 × 2/ 2)²

P(1) = 1² = 1

P(1) = 1³ = 1

So P(n) holds for n = 1.

The inductive hypothesis is that the statement holds for P(n). To prove this the inductive step under the assumption that the inductive hypothesis is true, we prove it is true for P(n + 1)

Let us assume P(n) = 1³ + 2³ + ... + n³ = (n(n+1)/ 2)²

Then P(n + 1) = 1³ + 2³ + ... + n³ + (n + 1)³ = (n(n+1)/ 2)² + (n + 1)³

P(n + 1) = (n(n+1)/ 2)² + n³ + 3n² + 3n + 1

P(n + 1) = ((n + 1)((n + 1) + 1)/ 2)²

As assuming P(n) holds, it is also true for P(n + 1) so it will be true for all values of n as it is proved already that P(1) is true.

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Answer:

y=1/3(x)+1/3

Step-by-step explanation:

x=3y-1

x+1=3y

(x+1)/3=(3y)/3

y=1/3x+1/3

Based on the relation between two numbers considering their difference and multiple, the numbers are 50 and 250.

Let the one number be x. So, the other number, according to the information in question, will be 5x. Now representing the equation depending on the stated details -

5x - x = 200

Performing subtraction on Left Hand Side of the equation

4x = 200

Writing the equation again to find the value of x

x = 200/4

Performing division on Right Hand Side of the equation

x = 50

First number = 50

Another number = 50×5

Performing multiplication on Right Hand Side of the equation

Second number = 250

The two numbers according to multiple and difference are 50 and 250.

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[tex]x^{2} + y^{2} = t^{2}[/tex] represent the correct graph which is the first figure graph.

Equations with Parameters If x and y are continuous functions of t on an interval I, the equations x = x(t) and y = y(t) are referred to as parametric equations, and t is also known as the parameter. The graph of the parametric equations is the set of points (x, y) obtained as t varies over the interval I.

Since x = tsint

And z= tcost

We have a circle in the x-z plane a

[tex]x^{2} + z^{2} = t^{2}[/tex]

Now, as y = t

The graph will be a helix with movement along the y-axis. Furthermore, the circle made on the x-z plane will have a variable radius since the radius is equal to t which by itself is changing.

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The simple interest is $2160 and the amount after 30 years is $6160.

Given that, principal =$4000, rate of interest =1.8%, and time period =30 years.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.

a) Now, S.I =(4000×1.8×30)/100

= 40×1.8×30

= $2160

b) Amount = Principal + Interest

= 4000 + 2160

= $6160

Therefore, the simple interest is $2160 and the amount after 30 years is $6160.

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Answer:

b

Step-by-step explanation:

Infer from domain and range

Answer:

----------------------------------------

Simplify the expression in below steps:

Answer:

[tex]32-60i[/tex]

Step-by-step explanation:

Given expression:

[tex](2+\sqrt{-4})(3 +5i)(-4-i)[/tex]

[tex]\textsf{Rewrite $\sqrt{-4}$ as $\sqrt{4 \cdot -1}$}:[/tex]

[tex]\implies (2+\sqrt{4 \cdot -1})(3 +5i)(-4-i)[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies (2+\sqrt{4}\sqrt{-1})(3 +5i)(-4-i)[/tex]

[tex]\implies (2+2\sqrt{-1})(3 +5i)(-4-i)[/tex]

[tex]\textsf{Apply imaginary number rule} \quad \sqrt{-1}=i:[/tex]

[tex]\implies (2+2i)(3 +5i)(-4-i)[/tex]

Multiply:

[tex]\implies (6+16i+10i^2)(-4-i)[/tex]

[tex]\implies -24-6i-64i-16i^2-40i^2-10i^3[/tex]

[tex]\implies -24-70i-56i^2-10i^3[/tex]

[tex]\textsf{Apply imaginary number rule} \quad i^2=-1:[/tex]

[tex]\implies -24-70i-56(-1)-10(-1)i[/tex]

Simplify:

[tex]\implies -24-70i+56+10i[/tex]

[tex]\implies 32-60i[/tex]

The radius of the sector of area 135π is 15.

A sector is a geometric figure bounded by two radii and the included arc of a circle.

To calculate the radius of the sector, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the radius of the sector is 15.

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The weighted mean of the mixture of recyclables would be (4 x $1 + 2 x $2) / 6 = $1.33.

To calculate the weighted mean of the mixture of recyclables, first identify the number of each material and their respective values. In this case, there are 4 items worth $1 each and 2 items worth $2 each. To calculate the weighted mean, multiply each item's value by the number of items and then divide by the total number of items

In this case,

4 x $1 + 2 x $2 = $6

and 6 items total, so the weighted mean is

$6 / 6 = $1.33.

This means that if compost is now worth twice as much, the weighted mean would be

(4 x $1 + 2 x $2) / 6 = $1.33.

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