Find the measurement indicated in each parallelogram
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However, the recent 2022 Social Security Trustees report finds that in 2034, retirees will start receiving a reduced benefit if Congress doesn't fix funding issues for the social program. In other words, Social Security will exist after 2034, but retirees will only receive 77% of their full benefit starting then.

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a) The increasing line y = 2x is plotted on the graph given at the end of the answer.

b) The horizontal line y = 3 is plotted on the graph given at the end of the answer.

c) The point of intersection of the two graphs is given as follows: (1.5, 3).

The increasing line is given as follows:

y = 2x.

Hence we plot a few points of coordinate (x,y), from the numeric values of the function, and connect them through a line.

The numeric values of the function are given as follows:

The horizontal line is given as follows:

y = 3.

Meaning that a single horizontal line through y = 3 is traced, for which we are going to use the same domain as the increasing line.

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The point that satisfies this inequalities y > -(1/3)x - 2 and y > 2x + 6 is (2, 15)

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The slope intercept form of a linear equation is:

y = mx + b

Where m is the slope (rate of change) and b is the y intercept.

Given the linear inequalities:

y > -(1/3)x - 2    (1)

y > 2x + 6       (2)

Plotting both inequalities:

The point that satisfies this graph is (2, 15)

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Answer:

2 inches

Step-by-step explanation:

The radius is simply the distance from the edge if you were at the center, which is equal to half the diameter. So given the diameter is 4 inches, we divide that by two, [tex]\frac{4\text{ inches}}{2}=2\text{ inches}[/tex] and that's our radius!

The precise middle value of a data set when it is ordered is called the median.Consequently, 7 is the needed median for the specified data set.

The precise middle value of a data set when it is ordered is called the median.Separating the lowest 50% of data from the top 50% of values is a measure of central tendency.If you have an odd or even number of data points, the processes for calculating the median will be different.

The exact middle value in an ordered data set is known as the median.It is a metric of central tendency that separates the bottom and top half of the data.

Sort the provided data set into the following order: 1, 4, 5, 7, 8, 9, 15, and 16.

Eight terms total, all even.

The data set's median is equal to the nth term, the eighth term, and the fourth term. = 7

Consequently, 7 is the needed median for the specified data set.

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Answer:

B will get more $

Step-by-step explanation:

3000 annual rate 6% so half a year is 3%, compounding semiannually for 6 years =  12 times

so 3000*(1+3%)^12 =4277.28

$4000 invested for four years compounded quarterly at 2.7%. so every quater is 2.7%/4 =0.675%, compounding quarterly for 4 years =  16 times

so 4000*(1+0.675%)^16=4454.57

The required difference is equal to 25x/42

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.

Given here: Alton shoveled snow on 5/6 of his driveway before lunch. Then he shoveled 2/7 of it after lunch.

Let the total snow quantity be x then we have

Before lunch as = 5/6×x

                           =5x/6

After lunch = 5x/6 × 2/7

                   =5x/21

∴ Difference = 5x/6 - 5x/21

                     =35x-10x / 42

                     = 25x/42

Hence, The required difference is equal to 25x/42

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6. The measure of angle BEC is 48°

7. The measure of angle 1 is 41°

8. The value of x is 12

   The measure of angle UST is 36°

6. The angles AEB and BEC form a straight line whose angle measure is 180°.

So that,

∠AEB + ∠BEC = 180°

132° + ∠BEC = 180°

∠BEC = 180° - 132°

∠BEC = 48°

7. The angles 1 and 5 form a right angle whose measure is 90°.

So that,

∠5 + ∠1 = 90°

49° + ∠1 = 90°

∠1 = 90° - 49°

∠1 = 41°

8. The angles RSU and UST form a right angle whose measure is 90°.

∠RSU + ∠UST = 90°

(5x - 6)° + (2x + 12)° = 90°

(7x + 6)° = 90°

7x° = (90 - 6)°

7x° = 84°

x = 12

∠UST =  (2x + 12)°

∠UST =  (2(12) + 12)°

∠UST =  (24 + 12)°

∠UST = 36°

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The triangles are similar as follows:

ABC ~ DEF

The criteria is AA(angle angle)

Similar triangles are the triangles that have corresponding sides as a ratio of each other and corresponding angles congruent to each other.

Therefore, the corresponding angles of the triangles are suppose to be congruent and the corresponding sides in proportion for it to be similar.

Hence, If two triangles have two of their angles equal, the triangles are similar by AA(angle angle).

Therefore, the triangles are similar by AA.

Triangle ABC is similar to triangle DEF.

The criteria for the similarity is AA.

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Answer:

71

Step-by-step explanation:

the circle standard form is

(x - h)² + (y - k)² = r²

r being the radius, (h, k) being the coordinates of the center.

fully multiplied that is

x² - 2hx + h² + y² - 2ky + k² = r²

we have here

4x² + 12x + 4y² - 40y - B = 0

our first step is to bring this back to an excision in x² and y². so, we divide everything by 4.

x² + 3x + y² - 10y - B/4 = 0

by comparing this to the general equation we see

3 = -2h

h = -3/2 = -1.5

-10 = - 2k

k = 5

-B/4 = h² + k² - r² = 9/4 + 25 - (3×sqrt(5))² =

= 9/4 + 25 - 9×5 = 9/4 + 25 - 45 = 9/4 - 20

-B = 9 - 80 = -71

B = 71

The domain of the composite function f(g(x)) is equal to (x - 2)/(4 + 4x).

A function is composite when the co- domain of the first mapping is the domain of the second mapping

We shall evaluate the domain of the function f(g(x)) as follows:

f(g(x)) = 1 ÷ 12/[(x - 2) + 4]

f(g(x)) = 1 ÷ [12 + 4(x - 2)]/(x - 2) {simplify the denominator to a single fraction}

f(g(x)) = 1 ÷ (12 + 4x - 8)/(x - 2) {open bracket for 4(x - 2)}

f(g(x)) = 1 ÷ (4 + 4x)/(x - 2) {simply like terms}

f(g(x)) = 1 × (x - 2)/(4 + 4x) {changing division to multiplication}

f(g(x)) = (x - 2)/(4 + 4x)

Therefore, the result (x - 2)/(4 + 4x) is the domain of the composite function f(g(x)).

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The approximate area of the shaded region of the circle is 191 metres squared.

The radius of the circle below is given as 9 metres. The approximate area of the shaded region of the circle can be found as follows:

area of the shaded region = area of the circle - area of the sector uncoloured

Therefore,

area of the circle = πr²

where

Therefore,

area of the circle = π × 9²

area of the circle = 81π m²

Hence,

area of the sector uncoloured = ∅ / 360 × πr²

where

Therefore,

area of the sector uncoloured = 90 / 360 × π × 9²

area of the sector uncoloured = 1 / 4 × π × 81

area of the sector uncoloured = 81 / 4 π

Hence,

area of the shaded region = 81π  - 20.25π

area of the shaded region = 60.75π

area of the shaded region = 190.755

area of the shaded region = 191 m²

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Answer:

To find out how many years it would take to double an initial investment with a 1% annual interest rate, you can use the rule of 72. The rule of 72 states that you can divide 72 by the annual interest rate to find out how many years it would take to double an investment.

In this case, you would divide 72 by 1 to get 72 years. Therefore, it would take 72 years for an investment of $1,000 at a 1% annual interest rate to have a future value of $2,000.

Answer:

  x = 0 and x = 16

Step-by-step explanation:

You want the solution to √(2x+4) -√x = 2.

We eliminate the radicals by squaring until there aren't any. After the first squaring, we have to separate the radical term from the others.

  [tex]\sqrt{2x+4}-\sqrt{x}=2\\\\(2x+4)-2\sqrt{(2x+4)(x)}+(x)=4\qquad\text{square both sides}\\\\3x=2\sqrt{x(2x+4)}\qquad\text{add $\sqrt{x(2x+4)}-4$}\\\\9x^2=4(2x^2+4x)\qquad\text{square both sides}\\\\x^2-16x=0\qquad\text{subtract the right side from both sides}\\\\x(x -16) = 0\qquad\text{factor}[/tex]

The solutions to this are the values of x that make the factors zero. Those values are x=0 and x=16. Trying these in the original equation, we have ...

  √(2·0 +4) -√0 = 2 -0 = 2 . . . . . . x=0 is a solution

  √(2·16 +4) -√16 = 6 -4 = 2 . . . . . x=16 is a solution

The two solutions to the equation are x=0 and x=16.

Answer: The appropriate dosage of medicine for a 180 Ib person is 12 ounces.

Step-by-step explanation:

From the word problem, we know that:

Since we are given w (the amount the person weighs is 180 Ib), we can plug the value into the equation to solve for t.

t= 3 + 0.05 (180)

t = 3 + 9

t = 12

So the appropriate dosage of medicine for a 180 Ib person is 12 ounces.

To solve for x in the equation A = 6x + 5, we can first subtract 5 from both sides, giving us A - 5 = 6x. This simplifies to A = 6x + 5. Dividing both sides by 6 gives us x = (A-5)/6.

Similarly, we can solve for x in the equation B = 4x + 45. Subtracting 45 from both sides gives us B - 45 = 4x, and dividing by 4 gives us x = (B-45)/4.

To find the measure of A, we can substitute the value of x that we found into the equation for A.

A = 6x + 5

A = (6 * (B-45)/4) + 5

A = (3/2) * B - 45/2 + 5

A = (3/2) * B + 5/2

So the measure of A is (3/2) * B + 5/2.

Answer:

14

Step-by-step explanation:

Para simplificar esta expresión, debemos seguir el orden de las operaciones, también conocido como PEMDAS: paréntesis, exponentes, multiplicación y división (de izquierda a derecha), y suma y resta (de izquierda a derecha).

1. Comience por simplificar la expresión dentro de los paréntesis.

4-2[6-3+4(5-7)]

4-2[6-3+4(-2)]

4-2[6-3-8]

4-2[-5]

4+10 = 14

2. Ahora sustituya el valor simplificado dentro de los paréntesis en la expresión original:

-3+{14}+3

3. Ahora podemos sumar y restar de izquierda a derecha.

-3+14+3 = 14

Entonces, la expresión simplificada es 14.

The trigonometric identities equivalent to cos(2·x)/cos(x) are;

cos(x) - (sin(x))/(tan (x))

2·cos(x) - sec(x)

Trigonometric identities are equations of trigonometric functions that are correct for the values of the input and output variables in the equations.

The trigonometric identity for cos(2·x) is specified as follows;

cos(2·x) = cos²x - sin²x

Therefore;

cos(2·x)/(cos(x)) = (cos²x - sin²x)/(cos(x))

(cos²x)/(cos(x)) = cos(x)

sin²(x)/(cos(x) = sin(x) × sin(x)/(cos(x)) = sin(x)·tan(x)

(cos²x - sin²x)/(cos(x)) = (cos²x)/(cos(x)) - sin²(x)/(cos(x)

(cos²x)/(cos(x)) - sin²(x)/(cos(x) = cos(x) - sin(x)·tan(x)

cos(2·x) = 2·cos²x - 1

Therefore; cos(2·x)/cos(x) = (2·cos²x - 1)/cos(x)

(2·cos²x - 1)/cos(x) = 2·cos(x) - 1/cos(x)

2·cos(x) - 1/cos(x) = 2·cos(x) - sec(x)

cos(2·x) = 1 - 2·sin²x

cos(2·x)/cos(x) = (1 - 2·sin²x)/cos(x)

(1 - 2·sin²x)/cos(x) = sec(x) - 2·sin(x)

The expressions equivalent to cos(2·x)/cos(x) are therefore;

cos x - (sin x)·(tan x) and 2·cos x - sec x, which are I and III

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The people that have posted the meme after 8 days using the exponential equation y=t^3 will be 512.

What are Exponential Equations?

An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable. For example, 3^x = 81, 5^x - 3 = 625, 62^y - 7 = 121, etc are some examples of exponential equations. We may come across the use of exponential equations when we are solving the problems of algebra, compound interest, exponential growth, exponential decay, etc.

Now,

To find number of people who have re-posted

we need to make a exponential equation

Here, As cindy tags meme to 3 people in starting and they also tag 3 people in subsequent days, then equation will be y=t^3 where t=no of days.

No of people after 8 days,

y=8^3

y=512 (no of people after 8 days)

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This is an example of geometric growth, So after 8 days 6561 people will have re-posted the meme.

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Answer:

4 x [tex]10^{8}[/tex]

Step-by-step explanation:

Round the number to

400,000,000

4 x [tex]10^{8}[/tex]

We moved the decimal 8 places.

Answer:

4 x 10^8 (four times ten to the power of eight) is the best approximation of the number 399,867,231 written in scientific notation.

Step-by-step explanation:

Answer: There is no solution for these equations.

Explanation: This equation system is not solvable. Because we cannot eliminate x or y while holding one of them in the equation.

The border should be 6 inches wide.

The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.

Given that, A picture is to be put on a poster board that is 18 in. by 22 in. there is to be an even amount of poster board around the picture, the area of the picture is 192 in.²

Let the marginal space left is x in

Therefore,

(18-x)(22-x) = 192

396 -18x - 22x + x² = 192

x² - 40x + 204 = 0

Factorizing the expression, we get,

x = 34 or x = 6

(Note :- Neglecting 34 because 34 is grater than the dimensions given)

Therefore, the marginal space is 6 inches.

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Answer:

We can use the equation:

amount of a given nutrient / % of recommended daily amount = recommended daily amount

Here, we know that 69 grams of carbohydrates is 22% of the recommended daily amount, so we can plug in the given values and solve for the recommended daily amount:

69 / 0.22 = Recommended Daily Amount

Recommended Daily Amount = 69 / 0.22 = 313.64 grams (rounded to one decimal place)

So, the total recommended daily amount of carbohydrates in grams is 313.6 grams.

Answer:

The mass number of the other isotope is 10.01613 amu.

Step-by-step explanation:

Let the percentage abundance of the first isotope be: 10B5 = 19.80%

Then, the percentage abundance of the second isotope will be xB5 = 80.20%

Mass of one isotope = 10.012938 amu

(10*19.80 + x*80.20)/100 = 10.012938 

198 + x*80.20 = 1001.2938 

x*80.20 = 1001.2938 - 198

x*80.20 = 803.2938

x = 803.2938 / 80.20

x = 10.01613

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15ft

Step-by-step explanation:

bc I said so..............

Answer:

Step-by-step explanation:

The general form of the equation for the line described by the point-slope form y + 3 = −2/7 (x − 5) is y = -2/7x + 19/7.

Answer:

Step-by-step explanation:

To prove that OHAP is a square, we need to show that all four sides are congruent and all four angles are right angles.

Since AOB is a right isosceles triangle, we know that angle OAB and angle OBA are both congruent to 90 degrees, which means that they are both right angles. Since [OH] is the altitude relative to [AB], it bisects angle OAB, which means that angle AOH and angle HOA are both congruent to 45 degrees. Since P is the symmetric of H with respect to OA, we know that OA is congruent to OP, and we also know that OH is congruent to OP. Therefore, all four sides of OHAP are congruent, which means that OHAP is a square.

Using the provided conditions and values, This is solved with the concept of word problem, The answer is first, second and third aircrafts have 576,512 and 864 seats.

A word problem in mathematics is a problem that is written in natural language (i.e., words) rather than in mathematical notation. It presents a real-world scenario that requires the use of mathematical concepts and skills to solve. Word problems often involve finding unknown quantities based on given information, and they can be challenging because they require students to understand the problem and translate it into mathematical equations or formulas. They are often used in primary and secondary education to help students apply their math skills to real-world situations and develop critical thinking skills.

A mathematical expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that represents a mathematical statement or equation. Mathematical expressions can be evaluated to find a numerical value. They can also be simplified by applying the order of operations (PEMDAS) to combine like terms or to remove unnecessary parentheses. Additionally, mathematical expressions can also be used to represent the relationship between different variables.

Let x be the number of seats on the second aircraft. Then, the first aircraft has x+64 seats and the third aircraft has 2x-152 seats.

We know that the total number of seats for all three aircraft is 1900, so we can set up the following equation:

x + (x+64) + (2x-152) = 1900

Solving this equation gives us x = 512, which means the second aircraft has 512 seats. We can then use this information to find the number of seats for the other two aircraft:

First aircraft: 512 + 64 = 576 seats

Third aircraft: 2(512) - 152 = 864 seats.

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There are 720 possible gate codes your apartment complex have.

The subject matter of the math discipline of algebra is symbols and the arithmetic operations performed on them. Variable describes these symbols because they don't have any fixed values. We frequently notice values that are in constant flux in our day-to-day problems.

To represent these shifting values, however, is always necessary. These values are frequently represented in algebra with symbols like x, y, z, p, or q; these symbols are referred to as variables.

The gate code at your apartment complex is three numerical digits followed by # sign.



There are 10 digits (0 to 9).

Compute the number of possible gate codes if each code contains non-repeating digits as follows.

The first 3 place in the code must be filled by three non-repeating digits.

So, there are 10 possibilities for the first digit, 9 possibilities for the second digit and 8 possibilities for the third digit.

Hence, the three non-repeating digits can occur in 10×9×8 ways.

The three non-repeating digits are followed by "#" sign. The sign # can occur in only one way.

Combine the above results and obtain the number of possible gate codes as,

10×9×8×1=720

Thus, there are 720 possible gate codes.

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the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below.

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{0}}} \implies \cfrac{4 }{ 5 }\implies \cfrac{\$ 4}{5~apples}\implies \cfrac{0.8}{1}~\cfrac{\$}{apples}~\hfill \textit{80 cents per apple}[/tex]