find the coordinates of the centroid of DEF with vertices (0,4) (6,6) (2,2)

Prolific will bike 2 miles to get to the mechanic at the 6th gas station if the pattern continues.

Assuming the rate remains constant, we can use the equation d = rt, where d is the distance, r is the rate, and t is the time. In this case, we want to find the equation to determine the distance of the Nth gas station.

Let's analyze the given information:

The first gas station is 1.5 miles away.

From the second gas station onwards, each gas station is located at a distance 0.1 miles greater than the previous one.

Based on this pattern, we can write the equation for the distance of the Nth gas station as follows:

d = 1.5 + 0.1(N - 1)

B. To find the distance Prolific will bike to get to the 6th gas station, we can substitute N = 6 into the equation from part A:

d = 1.5 + 0.1(6 - 1)

= 1.5 + 0.1(5)

= 1.5 + 0.5

= 2 miles

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The equation that can be used to find the value, y, of the limited-edition poster after x years is: a.  \(y = 18(1.15)^x\).

We know that the initial value of the poster is $18. After 1 year, with an increase of 15% per year, the value becomes $20.70.

To find the equation for the value, y, after x years, we can use the formula for compound interest:

\(y = P(1 + r)^x\)

Where:

P is the initial value ($18)

r is the growth rate (15% or 0.15)

x is the number of years

Plugging in the values, we have:

\(y = 18(1 + 0.15)^x\)

Simplifying:

\(y = 18(1.15)^x\)

The given equation helps determine the worth, represented by y, of the limited-edition poster after a certain number of years, denoted as \(y = 18(1.15)^x\).

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Complete Question:

A limited-edition poster increases in value each year with an initial value of $18. After 1 year and an increase of 15% per year, the poster is worth $20.70. Which equation can be used to find the value, y, after x years? (Round money values to the nearest penny.)

a. y = 18(1.15)^x

b. y = 18(0.15)^x

c. y = 20.7(1.15)^x

d. y = 20.7(0.15)^x

The sum of the radii of the two circles C₁ and C₂ is 4 units

Given data

Two circles C₁ and C₂ have their centres at the point (3,4)

The centre of C3 is at the point (0,0) and its radius is 2

And C1 and C2 is touching C3

Since the two circles have same centre and touch a third circle at same point, The two circles have equal radius r

The distance, d from the origin using point x and y given is solved for as follows:

d^2 = x^2 + y^2

d^2 = 3^2 + 4^2

d^2 = 9 + 16

d^2 = 25

d = √25

d = 5

Radius if the two circles is 5 - 3 = 2

One of the radius is 2 hence sum of the two radii

= 2 + 2

= 4 units

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Answer:

.25

Step-by-step explanation:

hundredth's is the second place over so you look the the 3rd number. 4 or less it stays the same 5 or more you add one

The value 12 is the minimum price of the bill independent of the consumption of minutes of Janelle.

The constant in the expression is 12.

Given

The expression represents the cost of Janelle’s cell phone bill.

Where m represents the number of minutes of use. 0.05m + 12.

The linear equation is as follows;

\(\rm y=mx+c\)

Where m is the slope and c is the constant.

The constant of the expression is the value that is independent of the number of minutes Janelle uses.

The given equation is;

y = 0.05m + 12.

On comparing with the standard equation the constant value is 12.

The value 12 is the minimum price of the bill independent of the consumption of minutes of Janelle.

She will always be charged this value.

Hence, The constant in the expression is 12.

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The probability that you will be satisfied with 3 or more of the purchased products is 0.916

Given that,

The chance of being pleased with an internet purchase is 0.555. if you purchase 8 items online

Solution -

let  X denote the no of success of

Purchased product online

X ~ B(n,p)

n = 8

P= 0. 555

a = 1 - 0 .555 = 0.445

P ( X = x) = \(nc_{x} b^{x} a^{n-x}\)

P ( X = x)= \(8c_{x} (0.555^{x} )(0.445)^{8-x\)

P ( X>=3)= \(\lim_{3 \to 8} 8c_{x} (0.555^{x} )(0.445)^{8-x\)

P ( X>=3)) = 0.91614

                 =0.916

Therefore we can conclude the probability that you will be satisfied with 3 or more of the purchased products is 0.916

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Answer:

The 1st option

Step-by-step explanation:

The base of a logarithm is always the base of an exponent. The log of part would always be the final powered form of the exponent. So, 2 would be the base, 16 would be logged, and 4 would be your answer.

Answer:

x = - 20, x = - 3

Step-by-step explanation:

To find the zeros, let h(x) = 0, that is

x² + 23x + 60 = 0

Consider the factors of the constant term (+ 60) which sum to give the coefficient of the x- term (+ 23)

The factors are + 20 and + 3, since

20 × 3 = 60 and 20 + 3 = 23, thus

(x + 20)(x + 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 20 = 0 ⇒ x = - 20

x + 3 = 0 ⇒ x = - 3

Answer:

\(\frac{27y^6}{8x^{12}}\)

Step-by-step explanation:

1) Use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3x^{-5+2}{y^3}}{2z^0yx}) ^3\)

2) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3\times\frac{1}{x^3} y^3}{2x^0yx} )^3\)

3) Use Rule of Zero: \(x^0=1\).

\((\frac{\frac{3y^3}{x^3} }{2\times1\times yx} )^3\)

4) use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3y^3}{2x^{3+1}y} )^3\)

5) Use Quotient Rule: \(\frac{x^a}{x^b} =x^{a-b}\).

\((\frac{3y^{3-1}x^{-4}}{2} )^3\)

6) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3y^2\times\frac{1}{x^4} }{2} )^3\)

7) Use Division Distributive Property: \((\frac{x}{y} )^a=\frac{x^a}{y^a}\).

\(\frac{(3y^2)^3}{2x^4}\)

8) Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{(3^3(y^2)^3}{(2x^4)^3}\)

9) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{(2x^4)^3}\)

10)  Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{26y^6}{(2^3)(x^4)^3}\)

11) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{8x^12}\)

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Answer:

\(\displaystyle \frac{27y^{6}}{8x^{12}}\)

Step-by-step explanation:

\(\displaystyle \biggr(\frac{3x^{-5}y^3x^2}{2z^0yx}\biggr)^3\\\\=\biggr(\frac{3x^{-5}y^2x}{2}\biggr)^3\\\\=\frac{(3x^{-5}y^2x)^3}{2^3}\\\\=\frac{3^3x^{-5*3}y^{2*3}x^3}{8}\\\\=\frac{27x^{-15}y^{6}x^3}{8}\\\\=\frac{27y^{6}x^3}{8x^{15}}\\\\=\frac{27y^{6}}{8x^{12}}\)

Notes:

1) Make sure when raising a variable with an exponent to an exponent that the exponents get multiplied

2) Variables with negative exponents in the numerator become positive and go in the denominator (like with \(x^{-15}\))

3) When raising a fraction to an exponent, it applies to BOTH the numerator and denominator

Hope this helped!

Answer:

A. 1.4x and C. 1/2x

Step-by-step explanation:

Relationship A is 4/2x which is 2x. So everything lower than y=2x would be the answer.

Answer:

y=1.4x

y=1/2x

Step-by-step explanation:

the correct answer

Answer:

3/8

Step-by-step explanation:

So, Leena eats 1/8 of the bread first.

Now, she gave 1/6 of the bread to EACH of her 3 friends.

So you will need to do 1/6*3, which is 3/6=1/2.

Now you want to do 1/8+1/2 = 1/8+4/8 = 5/8.

This means 5/8 of the bread is gone.

Now you will need to do 1-5/8 = 8/8-5/8=3/8.

Therefore, 3/8 of the bread is left.

I hope this helps!

The price elasticity of demand for both Shakib and Sunny at P = 5 is 0.

To find the aggregate demand of oranges, we need to sum up the individual demands of Shakib and Sunny.

a) Aggregate demand:

Shakib's demand:

P = 50 - 5Q

Sunny's demand:

P = 200 - 100

To find the aggregate demand, we need to find the quantity demanded (Q) at each price (P) for both Shakib and Sunny.

For Shakib:

P = 50 - 5Q

5Q = 50 - P

Q = (50 - P) / 5

For Sunny:

P = 200 - 100

P = 100

Now, we can substitute P = 100 into Shakib's demand equation to find the quantity demanded by Shakib at this price:

Q = (50 - 100) / 5

Q = -50 / 5

Q = -10

The quantity demanded by Shakib at P = 100 is -10 (we assume the quantity demanded cannot be negative, so we consider it as 0).

Therefore, the aggregate demand is the sum of the quantities demanded by Shakib and Sunny:

Aggregate demand = Q(Shakib) + Q(Sunny)

= 0 + Q(Sunny)

= Q(Sunny)

b) Price elasticity of demand:

The price elasticity of demand measures the responsiveness of the quantity demanded to a change in price. It can be calculated using the formula:

Elasticity = (% change in quantity demanded) / (% change in price)

To find the price elasticity of demand for both Shakib and Sunny at P = 5, we need to calculate the percentage changes in quantity demanded and price.

For Shakib:

P = 50 - 5Q

5Q = 50 - P

Q = (50 - P) / 5

At P = 5:

Q(Shakib) = (50 - 5) / 5

= 45 / 5

= 9

For Sunny:

P = 200 - 100

P = 100

At P = 5:

Q(Sunny) = (200 - 100) / 5

= 100 / 5

= 20

Now, let's calculate the percentage changes in quantity demanded and price for both Shakib and Sunny:

Percentage change in quantity demanded:

ΔQ / Q = (Q2 - Q1) / Q1

For Shakib:

ΔQ(Shakib) / Q(Shakib) = (9 - 0) / 0

Since Q(Shakib) = 0 at P = 100, the percentage change in quantity demanded for Shakib is undefined.

For Sunny:

ΔQ(Sunny) / Q(Sunny) = (20 - 0) / 0

Since Q(Sunny) = 0 at P = 100, the percentage change in quantity demanded for Sunny is undefined.

Percentage change in price:

ΔP / P = (P2 - P1) / P1

For both Shakib and Sunny, P1 = 100 and P2 = 5. Therefore:

ΔP / P = (5 - 100) / 100

= -95 / 100

= -0.95

Now, we can calculate the price elasticity of demand:

Elasticity(Shakib) = (∆Q / Q) / (∆P / P)

= (0 / 0) / (-0.95)

= 0 / (-0.95)

= 0

Elasticity(Sunny) = (∆Q / Q) / (∆P / P)

= (0 / 0) / (-0.95)

= 0 / (-0.95)

= 0

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Answer:

x > 9/5

Step-by-step explanation:

180

First, let's state what we are given:

Then we convert the decimal to standard form and solve:

(2x10^6) x (0.00009)​ = 180

The results of the expressions involving logarithms are listed below:

Case 1: 1 / 2

Case 2:

Subcase a: 0

Subcase b: 11 / 2

Subcase c: - 11 / 2

In this problem we have a case of an expression involving logarithms that must be simplified and three cases of expressions involving logarithms that must be evaluated. Each case can be solved by means of the following logarithm properties:

㏒ₐ (b · c) = ㏒ₐ b + ㏒ₐ c

㏒ₐ (b / c) = ㏒ₐ b - ㏒ₐ c

㏒ₐ cᵇ = b · ㏒ₐ c

Now we proceed to determine the result of each case:

Case 1

㏒ ∛8 / ㏒ 4

(1 / 3) · ㏒ 8 / ㏒ 2²

(1 / 3) · ㏒ 2³ / (2 · ㏒ 2)

㏒ 2 / (2 · ㏒ 2)

1 / 2

Case 2:

Subcase a

㏒ [b / (100 · a · c)]

㏒ b - ㏒ (100 · a · c)

㏒ b - ㏒ 100 - ㏒ a - ㏒ c

3 - 2 - 2 + 1

0

Subcase b

㏒√[(a³ · b) / c²]

(1 / 2) · ㏒ [(a³ · b) / c²]

(1 / 2) · ㏒ (a³ · b) - (1 / 2) · ㏒ c²

(1 / 2) · ㏒ a³ + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · ㏒ a + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · 2 + (1 / 2) · 3 + 1

3 + 3 / 2 + 1

11 / 2

Subcase c

㏒ [(2 · a · √b) / (5 · c)]⁻¹

- ㏒ [(2 · a · √b) / (5 · c)]

- ㏒ (2 · a · √b) + ㏒ (5 · c)

- ㏒ 2 - ㏒ a - ㏒ √b + ㏒ 5 + ㏒ c

- ㏒ (2 · 5) - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- ㏒ 10 - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- 1 - 2 - (1 / 2) · 3 - 1

- 4 - 3 / 2

- 11 / 2

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Answer:

true

Step-by-step explanation:

because there's less humidity

The ROI per unit for Jaymes Corporation's rotors is $200.

To calculate the ROI per unit, we need to divide the total return on investment by the number of units produced. In this case, the company has invested $6,000,000 to produce 30,000 rotors.

ROI per unit = Total ROI / Number of units produced

Total ROI = $6,000,000

Number of units produced = 30,000

ROI per unit = $6,000,000 / 30,000 = $200

Therefore, the ROI per unit for Jaymes Corporation's rotors is $200. This means that for every rotor produced, the company expects to generate a return of $200.

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Answer:

???????????????????????

Step-by-step explanation:

sorry di ko po alam yung sagot pasensiya na po

Given :

Parallel lines are

x – 2y = 3 and 2x – 4y = 12

Step-by-step explanation:

Lets write the given lines in slope intercept form y=mx+b

\(x -2y = 3 \\-2y=-x+3\\Divide \; both \; sides \; by -2\\y=\frac{x}{2} -\frac{3}{2}\)

From the above equation , y intercept of first line is \(\frac{-3}{2}\)

Solve the second equation for y and find out y intercept

\(2x-4y=12\\-4y=-2x+12\\Divide \; by \; -4\\y=\frac{1}{2} x-3\)

y intercept of second line is -3

To find the distance between parallel lines, we subtract the y intercepts

\(\frac{-3}{2} -(-3)=\frac{-3}{2} +\frac{6}{2} =\frac{3}{2} =1.5\)

Answer:

The distance between the parallel lines = 1.5

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The final temperature of the mixture, assuming no heat loss to the surroundings, is 312.47 K.

To calculate the final temperature of the mixture, we can use the principle of energy conservation, assuming no heat loss to the surroundings. The equation used is:

\(m_{1}\)\(c_{1}\)(\(T_{f}\)  - \(T_{1}\) ) = \(m_{2}\)\(c_{2}\) (\(T_{2}\) - \(T_{f}\) )

Where:

\(m_{1}\) = mass of the first sample (31.0 g)

\(c_{1}\) = specific heat capacity of water (4.18 J/g·K)

\(T_{1}\) = initial temperature of the first sample (285 K)

\(T_{f}\) = final temperature of the mixture (unknown)

\(m_{2}\) = mass of the second sample (47.0 g)

\(c_{2}\) = specific heat capacity of water (4.18 J/g·K)

\(T_{2}\) = initial temperature of the second sample (340 K)

Plugging in the values:

31.0* 4.18* (\(T_{f}\) - 285) = 47.0*4.18*(340 - \(T_{f}\) )

Now we can solve this equation for \(T_{f}\) :

31.0 * 4.18 * \(T_{f}\) - 31.0 * 4.18 * 285 = 47.0 * 4.18 * 340 - 47.0 * 4.18 * \(T_{f}\)

125.98 * \(T_{f}\) - 35793 = 65231.6 - 197.26 * \(T_{f}\)

323.24 * \(T_{f}\)  = 101024.6

\(T_{f}\)  = 312.47 K

Therefore, the final temperature of the mixture, assuming no heat loss to the surroundings, is approximately 312.47 K.

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Answer:

1/16 ia answer

Step-by-step explanation:

1/8 ×1/2 =1/16

may be this helpful!

Answer: y = 0.5x - 10

Step-by-step explanation:

2x + y = -4

y = -2x - 4

perpendicular, so slope = 1/2

y + 6 = (1/2)(x - 8)

y = (1/2)x - 10

Answer:

The asnwer in the bottom right corner is correct. When multiplying exponents with the same base all you do is add the exponent for example: For 9 to the 6 power times 9 to the 4 power the answer is 9 to the 10 since we just add 4 and 6

Step-by-step explanation:

Answer:

-26!!!! :))))

Step-by-step explanation:

The correct statement regarding the maximum values of the quadratic functions is given as follows:

Function 1 has the larger maximum at (4, 1).

The standard definition of a quadratic function is given as follows:

y = ax² + bx + c.

The x-coordinate of the vertex of a quadratic function is given as follows:

x = -b/2a.

Hence, for each function, the x-coordinate of the vertex is given as follows:

Each function has a negative leading coefficient, hence the vertex represents a maximum value, and the y-coordinate is given as follows:

1 > -14, hence the correct statement is given as follows:

Function 1 has the larger maximum at (4, 1).

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The coin makes approximately 16.53 turns when rolled on its edge for 1.34 m.

The circumference of the coin can be calculated as follows to determine the number of turns it makes:

C = πd

where C is the circumference, d is the diameter, and π is the mathematical constant pi (approximately equal to 3.14159).

So, for the given $2 coin with a diameter of 25.75 mm, the circumference is:

C = πd = 3.14159 x 25.75 mm ≈ 80.926 mm

Divide the distance traveled by the coin's circumference to determine the number of turns it makes when rolled on its edge for 1.34 meter:

Number of turns = distance traveled / circumference of the coin

Number of turns = 1.34 m / 0.080926 m

Number of turns ≈ 16.53

Therefore, the coin makes approximately 16.53 turns when rolled on its edge for 1.34 m.

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Given that C3 = C2C1, we can use the quaternion multiplication formula to relate the quaternions of C1, C2, and C3.

(μ3, ∈3) = (μ2η1 + μ1η2 + ρ2σ1 - ρ1σ2)i+  (μ2ρ1 - μ1ρ2 + η2σ1 + η1σ2)j + (μ2σ1 + μ1σ2 - η2ρ1 + η1ρ2)k

Let q1, q2, and q3 be the quaternions corresponding to C1, C2, and C3, respectively.

Then we have:

q3 = q2q1

Expanding this using the quaternion multiplication formula, we get:

q3 = (μ2 + η2i + ρ2j + σ2k)(μ1 + η1i + ρ1j + σ1k)

= μ2μ1 - η2η1 - ρ2ρ1 - σ2σ1+ (μ2η1 + μ1η2 + ρ2σ1 - ρ1σ2)i + (μ2ρ1 - μ1ρ2 + η2σ1 + η1σ2)j + (μ2σ1 + μ1σ2 - η2ρ1 + η1ρ2)k

where μ1, η1, ρ1, and σ1 are the scalar and imaginary parts of the quaternion corresponding to C1, and similarly for C2 and C3.

Comparing this with the quaternion representation of C3, which is (μ3, ∈3), we can see that:

μ3 = μ2μ1 - η2η1 - ρ2ρ1 - σ2σ1

and

(μ3, ∈3) = (μ2η1 + μ1η2 + ρ2σ1 - ρ1σ2)i + (μ2ρ1 - μ1ρ2 + η2σ1 + η1σ2)j + (μ2σ1 + μ1σ2 - η2ρ1 + η1ρ2)k

So we have:

∈3 = η2η1 + ρ2ρ1 + σ2σ1 + μ2η1 - μ1η2 - ρ2σ1 + ρ1σ2 + μ2ρ1 + μ1ρ2 - η2σ1 - η1σ2 - μ2σ1 - μ1σ2 + η2ρ1 - η1ρ2

Therefore, we can express (μ3, ∈3) in terms of (μ2,∈2) and (μ1,∈1) as shown above. Note that the quaternion multiplication formula involves both scalar and vector quantities, so the calculation can be a bit involved. However, the steps are straightforward and can be carried out using standard algebraic techniques.

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something you should keep in mind is that all three angles in a triangle always add up to 180 degrees.

so, here, since you know the two other angles, you can find the third.

180 - 106 - 42 will give you the measure of that third angle.

your answer will be 32.

hope i helped, good luck!

Answer:

32

Step-by-step explanation:

as you triangle angle add up to 180 so you add 106 by 42 which gives you 148 then

you take 180 -148 which it will give you =32