You start at the origin (0,0). Complete the following transformations and determine the final point.
• translate 2 units right and 3 units down
• reflect over the x-axis
• rotate 180° about the origin
• translate (x,y) → (x + 6,9 + 7)

Answer:

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

Find the differences in the sequence  -11, -7, -3, 1, ...

The difference is common, so the sequence is an AP.

The nth term is:

Find the 52nd term:

Find the 52nd term using the given formula:

Find the previous term:

Find the common difference:

Answer:

\(\begin{aligned}\textsf{34)} \quad d&=4\\a_n&=4n-15\\a_{52}&=193\end{aligned}\)

\(\begin{aligned}\textsf{35)} \quad d&=-4\\a_{52}&=-238\end{aligned}\)

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Given sequence:

To determine if the given sequence is arithmetic, calculate the differences between consecutive terms.

\(a_4-a_3=1-(-3)=4\)

\(a_3-a_2=-3-(-7)=4\)

\(a_2-a_1=-7-(-11)=4\)

As the differences are constant, the sequence is arithmetic, with common difference, d = 4.

The explicit formula for an arithmetic sequence is:

\(\boxed{a_n=a+(n-1)d}\)

where:

To find the explicit formula for the given sequence, substitute a = -11 and d = 4 into the formula:

\(\begin{aligned}a_n&=-11+(n-1)4\\&=-11+4n-4\\&=4n-15\end{aligned}\)

To find the 52nd term, simply substitute n = 52 into the formula:

\(\begin{aligned}a_{52}&=4(52)-15\\&=208-15\\&=193\end{aligned}\)

Therefore, the 52nd term is a₅₂ = 193.

\(\hrulefill\)

Given explicit formula for an arithmetic sequence:

\(a_n=-30-4n\)

To find the common difference, we need to compare it with the explicit formula for the nth term:

\(\begin{aligned}a_n&=a+(n-1)d\\&=a+dn-d\\&=a-d+dn\end{aligned}\)

The coefficient of the n-term is -4, therefore, the common difference is d = -4.

To find the 52nd term, simply substitute n = 52 into the formula:

\(\begin{aligned}a_{52}&=-30-4(52)\\&=-30-208\\&=-238\end{aligned}\)

Therefore, the 52nd term is a₅₂ = -238.

Answer:

Add 16.20+ 40+8

Step-by-step explanation: 16+20+40+8= 84

Answer:

A ans - 50/6 process I an sending

There will be 4,723,920 insects present after 10 days.

Given that a colony of insects triples every day, to determine, if the colony has 80 insects today, how many will be present in 10 days, the following calculation must be made:

Therefore, there will be 4,723,920 insects present after 10 days.

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Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.

Heron of Alexandria (c. 62 ce) is credited with developing the Heron's formula, which determines the area of a triangle in regards of the lengths of its sides. If the side lengths are represented by the symbols a, b, and c: √s(s - a)(s - b)(s - c)

where s = half the perimeter,

s = (a + b + c)/2.

given data:

In ΔHIJ,

semi -perimeter s = (i + j + h) / 2

s = (33 + 61 + 39) / 2

s = 66.5

Now,

s - h = 66.5 - 33 = 33.5

s - i = 66.5 - 61 = 5.5

s - j = 66.5 - 39 = 27.5

area of ΔHIJ = √s(s - h)(s - i)(s - j)

area of ΔHIJ = √66.5*33.5*5.5*27.5

area of ΔHIJ = √336947.1875

area of ΔHIJ = 580.47

Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.

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There is a Weak positive association between the amount of goals scored and the number of wins a hockey team has. Most of the data points fall between 4 goals scored and 5  number of wins. Causation cannot be established because their relationship was not in a controlled setting.

When if a relationship between two variables is said to be  negative, it is one that does not just necessarily mean that the association is weak. Although though both variables tend to increase in reaction to one another, a weak positive correlation depicts that the relationship is not very strong.

Therefore, even though  the data tells us that there is a weak positive relationship that exist between the two variables, it is vital to know that that correlation does not equal causation.

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The highest height for the daily rainfall were for 5 and 6 inches

Dot plots are used to present data in the form of points or small circles. It is similar to a simplified histogram or bar graph in that the height of the bar made up of points represents the numerical value of each variable. Dot plots are used to represent small amounts of data.

From the given dot plot, we see the number of times for each height of rainfall.

Thus, we see that the highest number of times of rainfall height was from that of 5 and 6 inches.

Thus, we conclude those were the highest heights for the daily rainfall.

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Answer:

The correct answer is D. The hybrid car got 43.37 miles pero gallon.  

Step-by-step explanation:

To determine the number of miles traveled for each gallon of gasoline consumed by the car, the number of miles traveled must be divided by the number of gallons consumed.

Thus, if 442.4 miles were traveled and 10.2 gallons of gasoline were consumed, the following calculation should be performed:

442.4 / 10.2 = X

43.37 = X

Therefore, for every gallon consumed 43.37 miles were traveled.

Answer

The answer is C

Step-by-step explanation:

Answer:

If you look at the different triangles in the star they give you two angles....

all of the points in a triangle would be equal and you just subtract  24 from 105

x is 24 and y is 81

Step-by-step explanation:

Answer:

I think 21 is it right ...

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

Explanation:

We can replace y in the first equation with -x+12 due to the second equation.

x+4y = 21

x+4( y ) = 21

x + 4(-x+12) = 21

x-4x+48 = 21

-3x = 21-48

-3x = -27

x = -27/(-3)

x = 9

which leads to,

y = -x+12

y = -9+12

y = 3

Therefore, the solution as an ordered pair is (x,y) = (9, 3)

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

Check:

x+4y = 21

9+4(3) = 21

9+12 = 21

21 = 21 .... the first equation works

and,

y = -x+12

3 = -9+12

3 = 3 ... so does the second equation

Both equations are true for those x and y values. The answer is fully confirmed.

The corresponding part of PQ is WX

The congruent statement is given as:

polygon WXYZ ≅ polygon PQRS.

This means that the corresponding points are:

W and P, X and Q, Y and R, Z and S

When two points Q and P are joined together, we have:

polygon WX ≅ polygon PQ

Hence, the corresponding part of PQ is WX

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We have two equations, since both of them are linear in x and y we conclude that this is are lines. To find their slope we need to write them in the slope-intercept form:

Line x-y=2

Let's write the equation in slope intercept form:

Comparing the last line with the slope intercept form we conclude that the slope of this line is 1.

Now, to find the values of y given a value of x we just need to plug the value of x we want and find its corresponding value of y with the equation; for example, if x=0, then we have:

Following this procedure we have that:

To graph the line we plot this points on the plane and join them with a straight line:

Line 3x-4y=9

Following the same procedure as with the previous line we have that this line can be written as:

Hence the slope of this line is 3/4.

The table we get in this case is:

Plotting this points and joining with a straight line we get the graph of the equation:

Graphical solution.

To find the solution of the system graphically we need to graph both lines in the same plane; the solution of the system is the point where the lines intersect. Let's do that:

From the graph we notice that the intersection happens at the point (-1,-3).

Therefore, the solution of the system is the point (-1,-3) which means that x=-1 and y=-3

Algebraic solution.

To find the solution of the system:

we solve the first equation for y:

and plug this in the second equation:

once we have the value of x we plug it in the expression of y:

Therefore, we have that x=-1 and y=-3 just like we gound graphically

The height of a triangle with a hypotenuse of 23 and angle between base and hypotenuse of 75° is h= 23sin(75)

An equation is an expression that shows the relationship between two or more variables and numbers.

Trigonometric ratio shows the relationship between the sides and angles of a right angle triangle.

Let us assume that the right triangle has a altitude h, hypotenuse of 23 and angle between base and hypotenuse is 75°, hence:

sin(75) = h/23

h= 23sin(75)

The height of a triangle with a hypotenuse of 23 and angle between base and hypotenuse of 75° is h= 23sin(75)

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1a. The percentage total return is -19.56%

1b. The dividend yield is 2.42%.

1c. The capital gains yield is -21.98%.

2a. The arithmetic average annual return on large-company stocks in nominal terms is 14.5%.

2b. The arithmetic average annual return on large-company stocks in real terms is 9.67%.

3a. The real return on long-term government bonds is 3.195%

3b. The real return on long-term corporate bonds is 3.291%

In Financial accounting, the percentage total return (P) can be calculated by using this formula;

P = [(Ending price - Initial price) + Dividend] ÷ Initial price

P = [(71 - 91) + 2.20] ÷ 91

P = -0.1956 or -19.56%

1b. For the dividend yield, we have:

Dividend yield = Dividend ÷ Initial price

Dividend yield = 2.20 ÷ 91

Dividend yield = 0.0242 or 2.42%

1c. For capital gains yield, we have:

Capital gains yield = (Ending price - Initial price) ÷ Initial price

Capital gains yield = (71 - 91) ÷ 91

Capital gains yield = -0.2198 or -21.98%.

Part 2.

a. The arithmetic average of annual return on large-company stocks in nominal terms is equal to 14.5%.

b. For arithmetic average annual return in real terms, we have:

(1 + 0.145) = (1 + r)(1 + 0.044)

r = (1.145/1.044) - 1

r = 9.67%

Part 3.

a. For real return on the long-term government bonds, we would apply Fisher equation:

(1 + i) = (1 + r)(1 + h)

Where:

(1 + 0.066) = (1 + r)(1 + 0.033)

1 + r = 1.066/1.033

r = 3.195%

b. For real return on long-term corporate bonds:

(1 + 0.067) = (1 + r)(1 + 0.033)

1 + r = 1.067/1.033

r = 3.291%

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The total number of students who graduated from the Cincinnati universities and colleges are 15382.

We are given that 6.76 % of Cincinnati college and university graduates majored in Registered Nursing.

The number of the Cincinnati college and university graduates who majored in Registered Nursing = 1026.

We need to find the total number of students that graduated from the Cincinnati universities and colleges altogether in 2016.

Let the total number of students be x.

ATQ:

6.67 % x = 1026

6.67 x = 102600

667 x = 10260000

x = 10260000 / 667

x = 15382.309

Rounding off to the nearest whole number is:

x = 15382.

Therefore, we get that the total number of students who graduated from the Cincinnati universities and colleges are 15382.

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In fraction form, the answer is 1/4, which represents the simplified probability of the given event occurring.

To find the probability of picking a prime number and then picking another prime number, we first need to determine the total number of possible outcomes and the number of favorable outcomes.

Given the four numbers: 5, 6, 7, and 8, we can see that there are two prime numbers (5 and 7) and two non-prime numbers (6 and 8).

The total number of possible outcomes is 4 since there are four cards to choose from.

Now, let's consider the favorable outcomes, which are picking a prime number and then picking another prime number.

The probability of picking a prime number on the first draw is 2/4, as there are two prime numbers out of the four total cards.

Since we replace the card before the second draw, the probability of picking a prime number on the second draw is also 2/4.

To find the probability of both events occurring, we multiply the individual probabilities:

(2/4) * (2/4) = 4/16 = 1/4

Therefore, the probability of picking a prime number and then picking another prime number is 1/4.

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Answer:

Correct choice is B

The statement that is true about the number of rooms that can be painted using inequality is; D.

The hotel can repaint 2 rooms, but this number is neither the maximum nor the minimum.

We are given;

Budget of hotel to repaint the lobby and some hotel rooms; $63750

Amount spent on painting the lobby = $26700

Cost to paint each room = $4250

Thus, the inequality to represent the given situation is;

26,700 + 4,250n ≤ $63,750

where;

n is number of rooms the hotel can repaint

Subtract 26700 from both sides of the inequality to get;

4250n ≤ 37050

n ≤ 37050/4250

n ≤ 8.717

Since we can't paint only a portion, we leave it as a maximum of 8 rooms

Looking at the given options, the only correct one is option D.

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Answer: 84 seconds

Step-by-step explanation:

The image coordinates of K′ if the preimage is reflected across y = −7 is (-4, -8)

Based on the given question, we have certain variables that can be utilized for our calculations.

K = (-4, -6)

First, find the equation of the reflection line

The reflection line is y = -7.

This can be expressed as

y = a = -7

The image of the reflection is then calculated as

K' = (x, -(y + 2|a|))

Replace the given or established values in the equation mentioned earlier, resulting in the following expression

K' = (-4, -(-6 + 2 * 7))

Evaluate

K' = (-4, -8)

Hence, the image coordinates of K′ are (-4, -8).

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Answer:

4

Step-by-step explanation:

To find the number you have to reverse the equation

Let us call the number "x"

x + 9 = 13

So to find x we flip the equation

13 - 9 = x

Solve it

4 = x

So the missing number is 4

It depends on the number of variables, if the inequality has one variable, then it is graphed on a number line.

The type of diagram that we need to use depends on the number of variables that we have.

That is the main reason, for example:

x > 2

Is graphed on a number line.

y > 3x + 4

is graphed on a coordinate plane.

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The angle measure that belongs in the green box is given as follows:

70.67º.

We consider a triangle with side lengths and angles related as follows, as is the case for this problem:

Then the lengths and the sines of the angles are related as follows:

sin(A)/a = sin(B)/b = sin(C)/c.

The relation for this problem is given as follows:

sin(x)/12  = sin(76º)/12.34

Applying cross multiplication, the missing angle measure is given as follows:

sin(x) = 12 x sine of 76 degrees/12.34

sin(x) = 0.9436.

x = arcsin(0.9436)

x = 70.67º.

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Based on the information, we can infer that the gumball machine had 530 blue gumballs, 106 red gumballs, 848 green gumballs, 424 pink gumballs, 212 yellow gumballs.

To find the amount of gum of each color that was in the machine we must perform rules of three as shown below:

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Answer:

3 for $8

Step-by-step explanation:

Firstly, 3 for $8 is much better than 5 for $8. Same for 12 for $24 being better than 14 for $24, because it's the same price for a different amount. Now we multiply 3 for $8 by 3, to get 9 for $24, which is better than 12 for $24, so the answer is 3 for $8

The third quartile  if the distribution is $22.08.

To find the third quartile, we need to find the value of the stock that separates the top 25% of days from the bottom 75%.

Since the distribution is uniform, we can find the third quartile by taking 75% of the range and adding it to the minimum value.

The range of the stock is:

$26.17 - $9.82 = $16.35

75% of the range is:

0.75 x $16.35 = $12.26

Adding this to the minimum value gives us the third quartile:

$9.82 + $12.26 = $22.08

So the third quartile is $22.08.

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Answer:

21°

Step-by-step explanation:

In an sosceles trapezoid, the lower base and upper base angles are congurent

⇒ ∠HGF = ∠EFG

⇒ 9y + 3 = 8y + 5

⇒ 9y - 8y = 5 - 3

⇒ y = 2

⇒ ∠HGF = 9(2) + 3

= 18 + 3

= 21

The measure of angle HGF in the given isosceles trapezoid EFGH is calculated to be 21 degrees.

This problem deals with the properties of an isosceles trapezoid, which is a type of quadrilateral. In an isosceles trapezoid, opposite angles are equal. In this case, angle EFG and angle HGF would be equal to each other given the shape is an isosceles trapezoid. So, their measures should be equal.

Here, the measure of angle HGF is given as (9y + 3)°, and the measure of angle EFG is (8y + 5)°. Setting these equal to each other to find the value of y, we get 9y + 3 = 8y + 5. By simplifying, we get the value of y is 2. Substituting the found value of y in angle HGF we get, 9*2+3 = 21 degrees.

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Answer:

x = -1

Step-by-step explanation:

3(x - 6) - 8x = -2 + 5(2x + 1)

3x - 18 - 8x = -2 + 10x + 5

-5x - 18 = 10x + 3

-15x = 15

x = -1

Answer:

\(x=-\cfrac{7}{5}\)

Or

\(x=-1.4\)

Step-by-step explanation:

\(3(x-6)-8x=-2 + 5(2x+1)\)

\(3(x-6)-8x \:\bold{Expand}\)

\(-2+5\left(2x+1\right)\:\bold{Expand}\)

\(-5x-18=10x+3\)

\(-5x-18+18=10x+3+18\:\bold{Add\:18\:to\:both\:sides}\)

\(-5x=10x+21\)

\(-5x-18+18=10x+3+18\:\bold{Subtract\:10x \:from\:both\:sides}\)

\(-15x=21\)

\(\cfrac{-15x}{-15}=\cfrac{21}{-15}\:\bold{Divide \: both\: sides\: by\: 15}\)

\(x=-\cfrac{7}{5}\)

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