A 90° rotation around the origin followed by a reflection across the line x = 3 maps △JKL, with coordinates J(–2, 2), K(–2, 6), and L(–8, 2), to △PQR. Find the area of △PQR.

If $4400 is placed in account at 8.25% for 22 years , then the final amount received after 22 years will be $26480.08  .  

We use the formula for compound interest to find the final amount  :

that is ⇒  A = P(1 + r)ˣ  ;

where:  A = the amount of money in the account after "x years"  ;

P(initial amount) = $4400 ;   r (interest rate) = 0.0825  ;

⇒ x(time) = 22 years

we get ;

⇒ A = 4400×(1 + 0.0825)²²  ;

⇒ A =  4400×(1.0825)²²  ;

⇒ A =  4400×6.018028  ;

⇒ A = 26480.08  ;

Therefore , the amount in the account after 22 years is $26480.08  .

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1) Note that the ratio of the Area of the Trapezoid to that of the Triangle is 3:1 (Option D)

2) No. Ivan is not correct. He multiplied the base by the length of the side of the parallelogram to get 99cm the correct answer, however, is 90cm.

1) To determine the ratio of the Trapezoid to that of the Triangle, we need to first find the Areas of both.

a) To find the area of a trapezium, we use the formula:

Area = (1/2) × (sum of the parallel sides) × (height)

In this case, the trapezium has bases of length 9 cm and 18 cm, and a height of 10 cm. So, we can substitute these values into the formula to get:

Area = (1/2) × (9 + 18) × 10

Area = (1/2) × 27 × 10

Area = 135 square cm

Therefore, the area of the trapezium is 135 square cm

b) To find the area of an isosceles triangle, we can use the formula:

Area = (1/2) × base × height

In this case, the base of the triangle is 9 cm and the height is 10 cm. So, we can substitute these values into the formula to get:

Area = (1/2) × 9 × 10

Area = 45 square cm

Therefore, the area of the isosceles triangle ACE is 45 square cm.

c) To find the ratio of the area of the trapezium to that of the isosceles triangle, we need to calculate the area of the isosceles triangle using the given dimensions and then divide the area of the trapezium by the area of the triangle.

The ratio of the area of the trapezium to the area of the triangle is:

Ratio = Area of trapezium / Area of triangle

Ratio = 135 / 45

Ratio = 3

Therefore, the ratio of the area of the trapezoid to that of the triangle is 3:1.

d) Note that the area of a parallelogram is given by the formula:

Area = base x height

In this case, the base of the parallelogram is 9 cm and the height is 10 cm. So, we can substitute these values into the formula to get:

Area = 9 cm x 10 cm

Area = 90 square cm

Therefore, the area of the parallelogram is 90 square cm, not 99cm as indicated by Ivan.

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1) The area of the first figure is 99 square units, 2) Total area = Area of rectangle + Area of triangle = 30 + 6 = 36 square units, 3) Total area = Area of rectangle + Area of triangle = 13.5 + 10.5 = 24 square units.

i) The first figure is a trapezium with height 9 units, bottom base 9 units and top base 13 units.
To find the area of the trapezium, we can use the formula:
Area of trapezium = h/2[a + b]
where h is the height, a and b are the lengths of the parallel sides.
Substituting the given values, we get:
Area = 9/2[13 + 9] = (9 x 22)/2 = 99 square units
Therefore, the area of the first figure is 99 square units.

ii) The second figure is composed of a rectangle with sides 6 and 5 units and a right-angled triangle with base 3 and height 4 units.
To find the area of the rectangle, we can use the formula:
Area of rectangle = length x breadth
Substituting the given values, we get:
Area of rectangle = 6 x 5 = 30 square units
To find the area of the right-angled triangle, we can use the formula:
Area of right-angled triangle = 1/2 x base x height
Substituting the given values, we get:
Area of right-angled triangle = 1/2 x 3 x 4 = 6 square units
Therefore, the total area of the second figure is:
Total area = Area of rectangle + Area of triangle
= 30 + 6 = 36 square units

iii) The third figure is made up of a rectangle with length 9 and breadth 1.5 units and a right-angled triangle with base 6 (9-3) and height 3.5 (5-1.5) units.
To find the area of the rectangle, we can use the formula:
Area of rectangle = length x breadth
Substituting the given values, we get:
Area of rectangle = 9 x 1.5 = 13.5 square units
To find the area of the right-angled triangle, we can use the formula:
Area of right-angled triangle = 1/2 x base x height
Substituting the given values, we get:
Area of right-angled triangle = 1/2 x 6 x 3.5 = 10.5 square units
Therefore, the total area of the third figure is:
Total area = Area of rectangle + Area of triangle
= 13.5 + 10.5 = 24 square units
Thus, the areas of all three figures have been determined.

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Complete question is in the image provided.

"Choose" means "select". Finding the number of possible methods to choose k items out of n items is done using the "n choose k formula."

C (n, k) represents "n select k" (or) [tex]_n C_k[/tex] (or) (n k) . A binomial coefficient is another name for it. It is used to determine how many different ways there are to choose k distinct items from n distinct items.

The combination formula is another name for the n select k formula (as we call a way of choosing things to be a combination). Factorials are used in this formula.

The n Choose k Formula is:

C (n , k) = n! / [ (n-k)! k! ]

"Choose" means "select". Finding the number of possible methods to choose k items out of n items is done using the "n choose k formula." We occasionally prefer choosing than ordering things.

When preparing for a trip, for instance, you decide to bring five of your ten brand-new clothes. There are several ways you can achieve this; it doesn't matter what sequence you choose them in, but it does matter which dresses you picked.

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Answer:

Step-by-step explanation:

the probability of drawing a face card=12/52

drawing the king of diamonds=1/52

Answer:

Probability of face is 12/52

The area of the sidewalk in terms of x would be 3 x ² + x + 2

The area of the sidewalk would be :

= Area of rectangular area - Area of rectangular garden

Area of rectangular area = 2 x ( 2x + 1 )

Area of rectangular garden = x ( x + 1 )

The area of the sidewalk in terms of x is therefore :

= ( 2 x ( 2x + 1 ) ) - ( x ( x + 1 ) )

= ( 4 x ² + 2 ) - ( x ² + x )

= 4 x ² + 2 -  x ² + x

= 4 x ² - x ² + x + 2

= 3 x ² + x + 2

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During assignment, the result of the calculation on the right side of an equals sign is assigned to a variable on the left of the equals sign. Where as, equality is a logical test that evaluates whether two values are equivalent.

In the given question, the first option is correct among the four.

An assignment operator assigns the result of the calculation on the right side of an equals sign to a variable on the left of the equals sign. It is indicated by ' = '.

Example: s = 4 + years, then the operator assigns the value of the sum of 4 and years to the variable s.

On the other hand, equality is a logical test that evaluates whether two values are equivalent or not. It is indicated by ' == '. The results obtained by this operator is either true or false.

Example: If f == s, it checks whether the value stored in f equals the value stored in s. If they are equal it returns output as true else false.

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The farmer needs to purchase 66 feet of fencing to enclose the rectangular region.

Let's call the length of the side of the rectangle that is parallel to the barn "2x" (since it is twice the length of the adjacent side), and let's call the length of the adjacent side "x". The length of the side opposite the barn is also "x", since it is opposite to the adjacent side.

We know that the area of the rectangle is 242 ft^2. The formula for the area of a rectangle is:

area = length * width

So we can write an equation for the area of the rectangle in terms of "x":

242 = 2x * x

Simplifying this equation, we get:

242 = 2x²

Dividing both sides by 2, we get:

121 = x²

Taking the square root of both sides, we get:

11 = x

So the adjacent side of the rectangle is 11 feet, and the side parallel to the barn is twice as long, or 22 feet.

To find the amount of fencing needed, we need to add up the lengths of all three sides that are not parallel to the barn. The formula for the perimeter of a rectangle is:

perimeter = 2 * length + 2 * width

Since one of the sides is the barn, we only need to add up the lengths of the two sides opposite the barn:

Perimeter = 2 * length + 2 * width

Therefore, the farmer needs to purchase 66 feet of fencing to enclose the rectangular region.

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Answer:

30%

Step-by-step explanation:

100-70=30

(i) The function that predicts your expected payroll for the day is,

For first person; y = $50 + $10.50x

For second person; y = $60 + $10.50x

Where, y is total amount and x is number of working hours.

(ii) In Wednesday; The amount expect to pay your employees is,

For first person;

⇒ y = $102.50

For second person;

⇒ y = $112.50

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The first employee scheduled to work next Wednesday makes $10.50 per hour and averages $50 per day for commission.

And, The other person that is scheduled earns $10.50 per hour and averages $60 per day for commission.

Let total amount earn = y

And, Number of working hours = x

Hence, We can formulate;

The function that predicts your expected payroll for the day is,

For first person;

⇒ y = $50 + $10.50x

For second person;

⇒ y = $60 + $10.50x

And, For 5 hours, the amount is,

For first person;

⇒ y = $50 + $10.50x

⇒ y = 50 + 10.50 × 5

⇒ y = 50 + 52.50

⇒ y = $102.50

For second person;

⇒ y = $60 + $10.50x

⇒ y = 60 + 10.50 × 5

⇒ y = 60 + 52.50

⇒ y = $112.50

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The expression is constant for b = -7.5, and the constant is 49.5.

A mathematical expression is a phrase that contains at least two terms or numbers and one action. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given that, The expression 3(5x - 1) + b(2x - 7) is constant

It means the expression doesn't consist of a variable. So, we need to find the 'b' such that the variable 'x' need to be eliminated.

The co-efficient of the 'x' should be '0'.

3(5x - 1) + b(2x - 7)

= 15x - 3 + 2bx - 7b

= (15 + 2b)x - 3 - 7b

Now, 15 + 2b = 0

2b = -15

b = -7.5

On substituting the value of 'b' in the expression,

= -3 - 7 * (-7.5)

= 52.5 - 3

= 49.5

Therefore, The expression is constant for b = -7.5, and the constant is 49.5

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The probability of spinning green and then rolling an even number is 1/36

Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

The probability of spinning green is 1/6 because there are 6 equally likely outcomes and 1 of them is green.

The probability of rolling an even number is 3/6 because there are 6 equally likely outcomes and 3 of them are even numbers (2, 4, and 6).

The probability of spinning green and then rolling an even number is the product of the probabilities of each event. To find this, we multiply the probability of spinning green (1/6) by the probability of rolling an even number (3/6):

(1/6) * (3/6) = 1/36

So, the probability of spinning green and then rolling an even number is 1/36.

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Answer:

Step-by-step explanation:

9 times

6,7,8,9 (4 times starting at 5)

Answer: 1.25

Step-by-step explanation:

you divide/combine 5 and 4 to get Ur anwser 1.25.  Yet it's the same thing as asking ,"How much is 5 divided by 4?" just think of it to yourself as how many times you can fit 4 into 5. One tip you can use is 4(x) = 5 and x will equal 1.25.

Maximum number of hours per day that first smokestack can operate 12.5 hours and for second smokestack is 7 hours.

According to the question a  factory has two smokestacks:

Let first smokestack take x  number of hours per day

and second smokestack take y number of hours per day

The rate of particle pollution produced is 12 kg/h for the first smokestack

and rate of particle pollution produced is 32 kg/h for the second.

A local pollution control board has ordered that the factory produce no more than 374 kg of particle pollution per day.

so, equation becomes 12x + 32y = 374

also the first smokestack operates 2 hours longer than 1. 5 times as long as the second.

so, x = 2 + 1.5y

putting value of x in other equation

12(2 + 1.5y) + 32y = 374

24 + 18y + 32y = 374

50y = 350

y = 7 hours

x = 2 + 1.5(7) = 12.5 hours

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well, if we use the vertex form of a parabola, we can pretty much see the parabolas all pretty much have a vertext at the origin, (0,0), now, let's take a look of a point they go by, Check the picture below.

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ \end{cases}\implies y=a(~~x-0~~)^2 + 0\hspace{4em}\textit{we also know that} \begin{cases} x=4\\ y=4 \end{cases} \\\\\\ 4=a(4-0)^2 + 0\implies 4=16a\implies \cfrac{4}{16}=a\implies \cfrac{1}{4}=a~\hfill \boxed{y=\cfrac{1}{4}x^2}[/tex]

now let's do D

[tex]\begin{cases} h=0\\ k=0\\ \end{cases}\implies y=a(~~x-0~~)^2 + 0\hspace{4em}\textit{we also know that} \begin{cases} x=-1\\ y=-3 \end{cases} \\\\\\ -3=a(-1-0)^2+0\implies -3=a\hspace{5em}\boxed{y=-3x^2}[/tex]

The kinetic energy of the 3 kg ball rolling at 2 m/s is 6 joules. The kinetic energy of an object is the energy it possesses due to its motion.

The kinetic energy of an object is the energy it possesses due to its motion. The formula for kinetic energy is given by:

Kinetic Energy = (1/2) * mass * velocity^2

In this case, the mass of the ball is 3 kg and its velocity is 2 m/s, so we can plug these values into the formula:

Kinetic Energy = [tex](1/2) * 3 kg * (2 m/s)^2[/tex]

Kinetic Energy = [tex](1/2) * 3 kg * 4 m^2/s^2[/tex]

Kinetic Energy = 6 J

So the kinetic energy of the 3 kg ball rolling at 2 m/s is 6 joules.

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Divide the students into the four class years (freshman, sophomore, junior, senior) and randomly select students from each year in proportion to the number of students in each year.

There are several ways to obtain a sample in research. The most common sampling methods in research are the following:

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a) Periodic Deposit = (A - P×(1 + r/n)ⁿᵗ) × (n / ((1 + r/n)ⁿᵗ - 1))

b) The amount of the financial goal that comes from deposits is $60305.24 and the amount that comes from interest is = $149694.76.

Compound interest is a method of calculating interest on a principal amount that includes not only the initial principal but also the accumulated interest from previous periods.

a. The formula for periodic deposits, assuming a fixed interest rate and the same amount of deposit made at the end of each period, is:

Periodic Deposit = (A - P×(1 + r/n)ⁿᵗ) × (n / ((1 + r/n)ⁿᵗ - 1))

Where:

A = Financial goal

P = Initial deposit (assumed to be 0 in this case)

r = Annual interest rate (as a decimal)

n = Number of compounding periods per year

t = Time (in years)

Substituting the given values, we have:

Periodic Deposit = (210000 - 0*(1 + 0.035/12[tex])^{(12\times 13)}[/tex] * (12 / ((1 + 0.035/12[tex])^{(12\times 13)}[/tex] - 1))

= $543.15 (rounded to the nearest cent)

Therefore, the periodic deposit needed to reach the financial goal of $210000, with a 3.5% annual interest rate compounded monthly over 13 years, is $543.15 at the end of each month.

b. To determine how much of the financial goal comes from deposits and how much comes from interest, we can use the following formula for the future value of an annuity:

FV = P * ((1 + r/n)ⁿᵗ - 1) / (r/n) + A * (1 + r/n)ⁿᵗ

Where:

FV = Future value of the annuity (i.e., the financial goal)

P = Initial deposit

A = Periodic deposit

r, n, t = Same as before

Substituting the given values and solving for P, we have:

P = (210000 - 543.15 * (1 + 0.035/12[tex])^{(12\times 13)}[/tex] ) * (0.035/12) / ((1 + 0.035/12[tex])^{(12\times 13)}[/tex] - 1)

= $60305.24 (rounded to the nearest cent)

Therefore, the amount of the financial goal that comes from deposits is $60305.24, and the amount that comes from interest is $210000 - $60305.24 = $149694.76.

Hence,

a) Periodic Deposit = (A - P*(1 + r/n)ⁿᵗ) * (n / ((1 + r/n)ⁿᵗ - 1))

b) The amount of the financial goal that comes from deposits is $60305.24 and the amount that comes from interest is = $149694.76.

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a) 0 kg of sugar is in the tank at the beginning., b) ds/dt = 0.08-(S/1120)*4, c) 0.32 kg of sugar is in the tank after 1 minute., d) 2.59 kg of sugar is in the tank after 84 minutes.

a) At the beginning, there is no sugar in the tank since it contains only pure water.

b) Let S(t) be the amount of sugar in the tank at time t (in minutes). The rate of change of S is given by the rate at which sugar enters the tank minus the rate at which it leaves. Since the solution enters at a rate of 4 L/min, and contains 0.08 kg of sugar per liter, the rate at which sugar enters is 0.08 kg/L * 4 L/min = 0.32 kg/min. Since the solution leaves at the same rate, the differential equation that models the situation is:

dS/dt = 0.32 - (S/1120) * 4

c) To find the amount of sugar after 1 minute, we need to solve the differential equation from part (b) with the initial condition S(0) = 0 (since the tank initially contains only water). One possible way to solve the differential equation is to use separation of variables:

dS/dt + (4/1120) S = 0.32

Multiplying both sides by dt and dividing by (0.32 - (4/1120) S), we get:

(1/S) dS = (4/0.32 - (1120/4)) dt

Integrating both sides from t = 0 to t = 1 and from S = 0 to S = S(1), we get:

ln(S(1)) - ln(0) = (1.25 - 280) * 1

S(1) = [tex]e^{0.25} * 1120[/tex] ≈ 300.92 kg

Therefore, after 1 minute, there is approximately 300.92 kg of sugar in the tank.

d) To find the amount of sugar after 84 minutes, we can solve the differential equation from part (b) numerically using an appropriate method such as Euler's method, or we can use an integrating factor to solve it analytically. One possible way to use an integrating factor is to multiply both sides of the differential equation by exp(4t/1120):

exp(4t/1120) dS/dt + (S/280) exp(4t/1120) = 0.32 exp(4t/1120)

This can be written as:

d/dt [S exp(4t/1120)] = 0.32 exp(4t/1120)

Integrating both sides from t = 0 to t = 84, we get:

[S(84) exp(4/1120 * 84)] - [S(0) exp(4/1120 * 0)] = ∫(0 to 84) 0.32 exp(4t/1120) dt

Since S(0) = 0 and exp(4/1120 * 84) is a constant, we can simplify this to:

S(84) = (1/exp(4/1120 * 84)) ∫(0 to 84) 0.32 exp(4t/1120) dt

Using integration by substitution with u = 4t/1120, we get:

S(84) = (1/exp(4/1120 * 84)) * (1120/4) * (0.32/4) * [exp(4/1120 * 84) - 1]

S(84) ≈ 301.53 kg

Therefore, after 84 minutes, there is approximately 301.53 kg of sugar in the tank.

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The complete question is:

A tank contains 1120 L of pure water. At a rate of 4 L/min, a solution that contains 0.08 kilogramme of sugar per litre enters the tank. At the same rate that it drains from the tank, the solution is mixed.

a) How much sugar is in the tank when it first starts?

b) With S representing the amount of sugar (in kg) at time t, write a differential equation which models the situation.

c) After 1 minute, calculate the sugar content (in kilogramme).

d) After 84 minutes, calculate the sugar content (in kg).

Answer: look at the image for the answer and solution

Step-by-step explanation:

Answer: x = 365

Step-by-step explanation:

find the angle bisector and divide and multiply it

Answer:

sin(35)

Step-by-step explanation:

Because of the co-function identity [tex]\cos(\theta)=\sin(90^\circ-\theta)[/tex], then [tex]\cos(55^\circ)=\sin(90^\circ-55^\circ)=\sin(35^\circ)[/tex].

Answer:

In 6 seconds: 180 m

20 m: in 2 seconds

Step-by-step explanation:

y = distance

x = time

y is proportional to x:

y = kx

y is proportional to the square of x:

y = kx²

We are given: (3, 45)

45 = k × 3²

45 = 9k

k = 5

The equation is:

y = 5x²

When x = 6,

y = 5(6²)

y = 180

180 m in 6 seconds

When y = 20,

20 = 5x²

x² = 4

x = 2

2 seconds for 20 m

Using the equation  [tex]C =a (1 - r)^{t}[/tex] , 179.75 grams will remain after 2 hours

What is Exponential Decay?

Exponential Decay is the process of reducing an amount by a consistent percentage rate over a period of time using the formula [tex]C = a(1-r)^{t}[/tex]

Where a = 480 grams

r = 15.1% = 0.151

t = 2 hours

C = 480(1 - 0.151)^2

C = 480(0.849)^2

C = 346 grams

Therefore, 346 grams will remain after 2 hours

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The method for addressing inequality 2v + 12 ≥ 16 is v ≥ 2. This indicates that any value of v larger than or equal to 2 will fulfil the inequality.

The idea of inequality—the state of not being equal, particularly in status, rights, and opportunities1—is one that is central to social justice theories. However, because it frequently has diverse meanings to different people, it can become confusing in public discourse.

The equation-like appearance of the phrase 5x 4 > 2x + 3 is altered by the arrowhead in place of the equals sign. It serves as an illustration of inequity. This shows that the section on the left, 5x 4, is bigger than the part on the right.

Subtract 12 from both sides of the inequality:

2v + 12 - 12 ≥ 16 - 12

Simplifying, we get:

2v ≥ 4

Divide both sides of the inequality by 2:

2v/2 ≥ 4/2

Simplifying, we get:

v ≥ 2.

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Answer:

258cm

it is the vertex's hieght as well as the length of the sides to multiply together and also divide since there is 5 sides

The correct weight of butter is 1/32 pounds. Olivia will use 1/32 pound of butter in each batch of muffins.

Olivia has 1/8 pound of butter that she needs to divide equally among 4 batches of muffins. To find out how much butter is used each batch of muffins, we can divide the total amount of butter by the number of batches. So, the amount of butter in each batch of muffins is: 1/8 ÷ 4 batches = 1/32 pound. So, Olivia will use 1/32 pound of butter in each batch of muffins. A pound (lb) is a unit of weight or mass commonly used in the United States and other countries that follow the customary system of measurement.

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The function that can be used to find the total height, h, of the building in feet, including the antenna is h = 6.8n + 13.5.

A builder is constructing an office building with n floors that will have an antenna 13.5 feet tall on its roof. Each floor of the building will be 6.8 feet high.

Therefore, the function that can be used to find the total height of the building in feet including the antenna can be calculated as follows:

Therefore,

n = numbers of floors in the building.

h = total height of the building

Hence, the function is as follows

h = 6.8n + 13.5

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Answer:

25.85 cubic feet

Step-by-step explanation:

Volume of a cylinder is

Base Area • height

The Base Area of a cylinder is a circle. The area of a circle is pi•r^2.

Vol = pi•r^2•h

They gave the diameter of the circle as 2.8, so the radius is half of that.

r = 1.4

The height was given

h = 4.2

Fill in radius and height and 3.14 for pi. Square the radius and then multiply everything.

see image.

Round to two decimal places.

hi i just did the test and the answer is 25.85 cubic feet

and it was correct btw other person deserves brainly have a nice day!

We can draw the conclusion that Sadio and Amir's methods for solving the equation are both valid.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.

As in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, and others.

Equation: A declaration that two expressions with variables or integers are equal.

In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

So, as we have the equation:

12x + 3 = 3(5x + 9)

Now, as we can see, Sadio took out 3 as common from LHS and RHS and solved the equation.

Which gave her the value of x as -8.

Amir, on the other hand, did not take out anything as common and directly multiply 3 with other terms in the brackets to solve the equation.

He also got -8 as the value of x.

Hence, we can conclude that yes both the ways of solving the equation is correct which is done by Sadio and Amir.

Therefore, we can draw the conclusion that Sadio and Amir's methods for solving the equation are both valid.

Know more about equations here:

https://brainly.com/question/2972832

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