Every person at a party of twenty eight people said hello to each of the other people at the party once. How many "hellos" were said at the party?

The graph that shows the new position of the rectangle after a translation is; Option C

When it comes to transformation in mathematics, there are different types such as reflection, dilation, rotation, translation.

Now, we are dealing with translation which is defined as a transformation of a shape in a plane that preserves the length, which tells us that the object is transformed without getting its dimensions affected.

In this case, we see the rectangle in the graph and we can conclude that the translation of the rectangle shows the correct translation would be the second option because it shows that the length is preserved without getting its dimensions or shape altered.

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Answer:

7

Step-by-step explanation:

:)

f(x) = a - x

y = a - x

y + x = a - x + x

y + x = a

y + x - y = a - y

x = a - y

f-¹(x) = a - x

The inverse of a function is the opposite of the function.

See below for the proof of: \(\mathbf{f(x) = f^{-1}(x)}\)

The function is given as:

\(\mathbf{f(x) = a - x}\)

Rewrite as:

\(\mathbf{y = a - x}\)

Swap x and y

\(\mathbf{x = a - y}\)

Make y the subject

\(\mathbf{y = a - x}\)

Rewrite as:

\(\mathbf{f^{-1}(x) = a - x}\)

Hence:

\(\mathbf{f(x) = f^{-1}(x) = a - x}\)

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Answer:

123

Step-by-step explanation:

492 divided by four equals 123

Answer:

Round it to the nearest hundredth

Step-by-step explanation:

Answer:

Step-by-step explanation:

This problem could keep you going for quite a while. My suggestion is that you go get a cup of coffee and sip it slowly as you read this.

Equation One

Sqrt(x - 1)^3 = 8

(x - 1)^(3/2) = 8

Square both sides to get rid of the 2.

(x - 1)^3 = 8^2  

(x - 1)^3 = 64

Now take the cube root of both sides to get rid of the 3 on the left

x - 1 = cuberoot(64)

x - 1 = 4                     Add 1 to both sides

x - 1+1 = 4 + 1

x  =  5

==============================

Second Equation

4th root (x - 3)^5 = 32

Take the 5th root of both sides.

4th root(x - 3) = 2

This can be written as (x - 3)^(1/4) = 2

Now take the 4th power of both sides.

(x - 3) = 2^4

x - 3 =  16

add 3 to both sides.

x = 16 + 3

x = 19

============================

Equation 3

(x - 4)^(3/2) = 125

Take the cube root of both sides

(x - 4)^(1/2) = 125^(1/3)     1/3 is the cube root of something

(x - 4)^(1/2) = 5    

square both sides to get rid of the 2    

(x - 4) = 5^2

x - 4 = 25

Add 4 to both sides.

x = 25 + 4

x = 29

============================

Fourth Equation

(x + 2)^(4/3) = 16        

take the 4th root of both sides

(x + 2) ^(1/3) = 16^(1/4)

(x + 2)^(1/3) = 2

Cube both sides

(x + 2) = 2^3

x + 2 = 8  

Subtract 2 from both sides

x + 2 - 2 = 8-2

x = 6

##########################

The first step is the most critical. You must look at what you are going to take the root of. When you do, for this question, it must come out even.

There must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

To prove the existence of a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can employ a contradiction argument. Assume that such a vertex u does not exist.

Since the number of vertices in T is odd, there must be at least one path from v to another vertex w such that the distance between v and w is greater than (n-1)/2.

Denote this path as P. Let x be the vertex on path P that is closest to v.

By assumption, the distance from x to v is greater than (n-1)/2. However, the remaining vertices on path P, excluding x, must have distances at least (n+1)/2 from v.

Therefore, the total number of vertices in T would be at least n + (n+1)/2 > n, which is a contradiction.

Hence, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

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\(\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x)= 2x^2 + x -3 \qquad \begin{cases} x_1=0\\ x_2=2 \end{cases}\implies \cfrac{f(2)-f(0)}{2 - 0} \\\\\\ \cfrac{[2(2)^2 + (2) -3]~~ - ~~[2(0)^2 +(0) -3]}{2}\implies \cfrac{7-(-3)}{2}\implies \cfrac{7+3}{2}\implies \text{\LARGE 5}\)

The rate of change for the interval between 0 and 2 for the quadratic equation will be 5. Then the correct option is C.

It is the average amount by which the function varied per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph depicting the function.

Average rate = [f(x₂) - f(x₁)] / [x₂ - x₁]

The function is given below.

f(x) = 2x² + x - 3

The rate of change of the function for the interval between 0 to 2 is calculated as,

Average rate = [f(2) - f(0)] / [2 - 0]

Average rate = [(2(2)² + 2 - 3) - (2(0)² + 0 - 3)] / 2

Average rate = 10 / 2

Average rate = 5

The rate of change for the interval between 0 and 2 for the quadratic equation will be 5. Then the correct option is C.

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The coordinates of polygon A'B'C'D' after the rotation of 180º are given as follows:

A'(0,0), B'(-5,-2), C'(-5,5), D'(0,3).

The five more known rotation rules are given as follows:

The original coordinates for this problem are given as follows:

A(0,0), B(5,2), C(5,-5), D(0,-3).

Exchanging the sign of each of the coordinates, the coordinates after the rotation are given as follows:

A'(0,0), B'(-5,-2), C'(-5,5), D'(0,3).

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The present value (PV) of the investment today is approximately $2,965.05.

To find the present value (PV) of the investment today, we need to calculate the present value of each individual contribution and then sum them up. We can use the formula for the present value of an annuity to do this calculation.

The formula for the present value of an annuity is given by:

PV = C * [(1 - (1 + r)^(-n)) / r]

Where:

PV = Present Value

C = Cash flow per period

r = Interest rate per period

n = Number of periods

In this case, the cash flow per period (C) is $500, the interest rate per period (r) is 10.5% (or 0.105), and the number of periods (n) is 20 years.

Let's plug in these values into the formula and calculate the present value (PV):

PV = $500 * [(1 - (1 + 0.105)^(-20)) / 0.105]

Using a calculator, we can evaluate the expression inside the brackets:

PV = $500 * [(1 - 0.376889) / 0.105]

Simplifying further:

PV = $500 * [0.623111 / 0.105]

PV = $500 * 5.930105

PV = $2,965.05

Therefore, the present value (PV) of the investment today is approximately $2,965.05.

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Step-by-step explanation:

The original function is f(m) = 5(1.07)^m, with the m as an exponent

part A) if the final length is 9.19, we can set f(m) = 9.19 and solve for m

plugging it into a calculator, I get m = ~8.99, so a bit less than 9. therefore, a reasonable domain might be all the m values 9 or below, or m ≤ 9

part B) the y-intercept of a function is the value of the independent variable when the dependent variable = 0. the two variables in your problem are height and number of months - which one do you think is the independent one, and which one is dependent? then re-interpret "value of the independent variable when the dependent variable = 0" in terms of the actual quantities that the variables represent

part C) average rate of change from m = 1 to m = 9

f(9)−f(1)9−1

evaluate, and think about what that represents in terms of height and number of months

The coordinate of JK is (-1.7, -0.3)

The coordinate of the points that divides the line segment in the given ratio is calculated as:

\((x, y) = (\frac{ax_1 +bx_2}{a+b} , \frac{ay_1 +by_2}{a + b} )\)

where;

a:b = 7:8

From the image;

(x₁, y₁) = (-6, 5) and,

(x₂, y₂) = (2, -5)

Substitute the given points in the equation above to calculate the coordinates of JK.

\((x, y) = (\frac{7(-6)+8(2)}{7+8} , \frac{7(5) +8(-5)}{7+8} )\\\\(x, y) = (\frac{-26}{15} , \frac{-5}{15} )\\\\(x,y) = (-1.7, -0.3)\)

Thus, the coordinate of JK = (-1.7, -0.3)

Check the image uploaded for the plot of point K

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Answer: D

Step-by-step explanation:

Hope it helps

The number of pizza expected to be eaten is equal to the number of persons that attends the party and this is equal to 0.8gp/s

From the problem it can be deduced that

number of people invited to the party = g

number of people attending

= 80% of people invited to the party

= 80% of g

and 80% = 80 / 100 = 0.8

therefore,

= 0.8g

You estimate that your guests will each eat p pieces of pizza

= 0.8g * p

= 0.8gp

and each pizza has s slices

the number of slices = s

the number of pizza to be taken is  0.8gp/s

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Answer:

C

Step-by-step explanation:

Easy man ..............

Explanation:

This is known as a cyclic quadrilateral since all four points are on the circle's edge, and the quadrilateral is entirely inside the circle (no parts of the quadrilateral spill outside the circle). Another term is "inscribed quadrilateral"

Since we have an inscribed quadrilateral, this means the opposite angles of the quadrilateral are supplementary.

B+D = 180

120+x = 180

x = 180-120

x = 60

Answer:

Zero Slope

Step-by-step explanation:

rise over run or y2 - y1 / x2 - x1

6-6/5-2 = 0/3

Answer:

49x^4-42x^2 y+9y^2

Step-by-step explanation:

Answer:

49x^4-42x^2 y+9y^2

Step-by-step explanation:

Answer:

He made a 75%.

Step-by-step explanation:

Divide 9 by 12 to get 75%.

I hope you do well in this assignment! :)

Answer:

x = -80538738812075974, y = 80435758145817515, and z = 12602123297335631.

Step-by-step explanation:

yes

Answer:

C

Step-by-step explanation:

:)

Answer: 4

Step-by-step explanation:

Angle 8 is = to 4, they are corresponding.

Answer:

the answer is x=3 for the question

Molina jumped the greatest distance at a long jump competition which is 9.601 feet

Decimal: A decimal is a number that consists of a whole and a fractional part. Decimal numbers lie between integers and represent numerical value for quantities that are whole plus some part of a whole.

Given in the question that, the distance each of four students jumped a long jump competition

Student Distance

Aleena  9.46 feet

Susan    9.068 feet

Molina   9.601 feet

Anna      9.04 feet

let us compare the feet jumped by the  students

write them in ascending order to get the highest feet based on decimal values

9.04, 9.068, 9.46, 9.601

by checking the order we can confirm that 9.601 feet is the highest

9.601 feet long jump was done by Molina

so we can conclude that Molina jumped the greatest distance

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Answer:

513.45

Step-by-step explanation:

use intelligence

The best estimate for the number of fish is that there are 82 yellow fish and 18 green fish, which you can calculate using the rule of three. This estimate is expected to be accurate.

This can be calculated using a rule of three as follows. Let's start with the yellow fish:

53 = 65

x    = 100

53 x 100 / 65 = 82 yellow fish

Green fish:

12 = 65

x = 100

12 x 100 / 65= 18 green fish

This estimate is expected to be accurate; however, there might be small differences in real life such as 80 yellow fish and 20 green fish.

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Answer:

3 - 9g = -8g + 4

-9g + 8g = 4 -3

g = -1

Answer:

sorry for that

Step-by-step explanation:

image is so unclear can't even read

Despite traditional economic theory suggesting that an increase in the minimum wage should lead to unemployment, the actual impact on employment has been more nuanced. Empirical evidence suggests that moderate increases in the minimum wage have not led to massive job losses, but rather have resulted in small increases in labor costs that are offset by increased productivity and reduced employee turnover. Additionally, higher wages can increase consumer spending, leading to an increase in demand for goods and services, which can ultimately create more jobs.

There are several reasons why the federal minimum wage in the US is lower than in other developed countries. One reason is the political climate in the US, where there is often resistance to government intervention in the labor market. Additionally, many US states have their own minimum wage laws, which can be higher than the federal minimum wage. Finally, the US has a large low-skilled immigrant workforce, which can put downward pressure on wages.

I am not okay with the real minimum wage falling over time with the rise of inflation. Inflation erodes the purchasing power of workers, making it difficult for them to make ends meet. This can lead to increased financial hardship, which can have negative effects on individuals and families. Furthermore, the minimum wage was originally designed to ensure that workers earn a living wage, which is a basic necessity for a decent standard of living. As such, it is important that the minimum wage keep pace with inflation.

According to the Bureau of Labor Statistics, in 2021, about 1.9 million workers in the US earned at or below the federal minimum wage of $7.25 per hour. However, many more workers earn slightly above the minimum wage, and an increase in the minimum wage could potentially raise wages for those workers as well. Additionally, many states have higher minimum wage rates than the federal minimum wage, which means that the number of workers affected by changes to the minimum wage will vary depending on the state.

~~~Harsha~~~