Which expression is equivalent to 5x +10y-15?
A. 5(x-2y-3
B. 5(x5y-10
C. 5(x+2y-3
D. 5(x2y-15

The values of a and c for which f(x) = {ax^2 + sin x, x ≤ π; 2x - c, x > π} is differentiable at x = π are a = 3π/2 and c = 2/π.

For the piecewise function f(x) to be differentiable at the point x = pi, the left-hand limit and right-hand limit of the derivative of f(x) must be equal. Therefore, we need to find the derivative of f(x) separately for x ≤ π and x > π and then evaluate the limits of these derivatives at x = π.

For x ≤ π:

f'(x) = 2ax + cos(x)

For x > π:

f'(x) = 2

To ensure that f(x) is differentiable at x = π, we need the left-hand and right-hand limits of f'(x) to be equal:

lim f'(x) = lim (2ax + cos(x)) = 2a - 1

x → π- x → π+

lim f'(x) = lim 2 = 2

x → π+ x → π+

Therefore, we need to have 2a - 1 = 2, which gives a = 3/2.

Now we need to check which of the given values of c satisfies the condition that f(x) is differentiable at x = π.

a) a = 3π/2 and c = π/2:

For x ≤ π:

f'(x) = 3πx + cos(x)

For x > π:

f'(x) = 2

Therefore, f(x) is not differentiable at x = π because the left-hand and right-hand limits of f'(x) are not equal.

b) a = 3/2π and c = 7π/2:

For x ≤ π:

f'(x) = (3/2π)x + cos(x)

For x > π:

f'(x) = 2 - 3c/2π = -7/2

Therefore, f(x) is not differentiable at x = π because the left-hand and right-hand limits of f'(x) are not equal.

c) a = 3/2π and c = -π/2:

For x ≤ π:

f'(x) = (3/2π)x + cos(x)

For x > π:

f'(x) = 2 - 3c/2π = 5/2

Therefore, f(x) is not differentiable at x = π because the left-hand and right-hand limits of f'(x) are not equal.

d) a = 3/2π and c = π/2:

For x ≤ π:

f'(x) = (3/2π)x + cos(x)

For x > π:

f'(x) = 2 - 3c/2π = -1/2

Therefore, f(x) is not differentiable at x = π because the left-hand and right-hand limits of f'(x) are not equal.

e) a = 3π/2 and c = 2/π:

For x ≤ π:

f'(x) = 3πx + cos(x)

For x > π:

f'(x) = 2 - 3c/2π = -1/π

Therefore, f(x) is differentiable at x = π because the left-hand and right-hand limits of f'(x) are equal.

Therefore, the values of a and c for which f(x) = {ax^2 + sin x, x ≤ π; 2x - c, x > π} is differentiable at x = π are a = 3π/2 and c = 2/π.

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Answer:

2x + 24

Step-by-step explanation:

The product of 2 and a number is: 2x

because product means multiply. 2 and a number means 2 times an unspecified number represented as x. 24 more than that product just means to add 24 to the product of 2x.

Answer:2x + 24

Sorry I was gonna do it when it was posted but I was grounded that time sorry. Have a great day!

Answer:

m∠I = 50 degrees

Step-by-step explanation:

Mathematically, the base angles of an isosceles triangle are equal

So in this case, since H is a vertex;

m∠I + m∠H + m∠G = 180

m∠I = m∠G = x

2x + 80 = 180

2x = 180-80

2x = 100

x = 100/2

x = 50

Answer:

d is the answer on edge 2022

Step-by-step explanation:

Answer:

it is C.60.24. You are right

The system of equations 3x + 2y = –2 and 6x + 4y = 15 can be classified as inconsistent systems.

To classify the given system of equations, we will analyze the coefficients of the variables and constants to determine if the equations are dependent, independent, or inconsistent. The system is:

1) 3x + 2y = -2
2) 6x + 4y = 15

First, let's check if the equations are multiples of each other. If we multiply the first equation by 2, we get:

1') 6x + 4y = -4

Comparing equation 1' with equation 2, we can see that the left-hand sides are equal, but the right-hand sides are different (-4 ≠ 15). Therefore, the equations are not multiples of each other.

Next, we'll examine the coefficients of x and y. In both equations, the ratio of the coefficients of x to y is the same (3/2 and 6/4). This means the lines represented by these equations are parallel.

Since the lines are parallel and not multiples of each other, they do not intersect, meaning there is no common solution for this system of equations. Therefore, we can classify this system as inconsistent system.

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The probability that a homebuilder takes 200 days or less to complete a house is approximately 0.8238, or 82.38%.

Explanation :

To answer this question, we can use the concept of the z-score. The z-score tells us how many standard deviations a data point is from the mean.

Let's calculate the z-score for a completion time of 200 days:
z = (x - μ) / σ
where x is the completion time, μ is the mean, and σ is the standard deviation.
Plugging in the values, we get:
z = (200 - 176.7) / 24.8 = 0.93

To find the probability associated with this z-score, we can use a z-table or a calculator. In this case, the probability is 0.8238.

This means that there is an 82.38% chance that the completion time of a house will be 200 days or less, given that the completion time follows a normal distribution with a mean of 176.7 days and a standard deviation of 24.8 days.

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Answer:

Divide both sides by V

Step-by-step explanation:

The equation is not well written.

Mariko needs to solve the equation below for D. Here is the equation:

M = DV

For Mariko to get D, he needs to make D the subject of the formula by dividing both sides of the equation by the coefficient of D i.e V as shown;

Divide both sides by V

M/V = DV/V

V at the denominator will cancel out the V at the numerator to have:

M/V = D

Rearrange

D = M/V

Therefore, the statement which correctly describes the step he should take is:

Divide both sides by V. Option B is correct.

Answer:

the third one

Step-by-step explanation:

the conjugation is and

Answer:

Roberto walked home alone and thought about his day.

In the derivation of the Quadratic Formula is shown by completing the square and applying square roots. The missing step is D. x^2 + b/a + c/a = 0.

The quadratic formula derivation requires the initial equation of ax^2 + bx + c = 0, where a, b and c are constants; it is also necessary that a cannot be zero.

the step simplifies the division of a:

0 divided by anything is still zero, so you can remove the a denominator

a/a = 1, and is therefore irrelevant, so ax^2 / a = x^2

The correct option is D

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Answer:

21

Step-by-step explanation:

Using inequality to solve this question, we say

Let the total number of newspapers sold be x

Let the total number of magazines sold by y

x + y = 68

Suppose 1x = $2 and 1y = $5, then

2x + 5y = $199

Solving both as a simultaneous equation, we get that

2(68 - y) + 5y = $199

136 - 2y + 5y = $199

136 + 3y = $199

3y = 199 - 136

3y = 63

y = 63/3

y = 21

Then solving for x, we have

x + 21 = 68

x = 68 - 21

x = 47

Therefore, a total of 21 magazines were sold that day

Answer: 280

Step-by-step explanation:

                                                  (-11 - 17) (2 - 12) = 280/1 = 280

Subtract: -11 - 17 = -28

Subtract: 2 - 12 = -10

Multiple: the result of step No. 1 * the result of step No. 2 = -28 * (-10) = 280

Answer:

A. a net

Step-by-step explanation:

I did the test

Answer: r = 30 / 4.5

Step-by-step explanation:

From the question, we are informed that a football player can run 30 yards in 4.5 seconds.

The equation that is used to find r the number of yards he can run in a second will be calculated as:

r = 30 / 4.5

Solving further will be:

r = 30 / 4.5

r = 6.67 yards per seconds.

Answer:

Both are true.

Step-by-step explanation:

A absolute always has a positive answer no matter what.

Answer:

Both of the answers are true!

Absolute value always has a positive answer.

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God bless :)

Answer:

Step-by-step explanation:

It has one solution

Answer:

24 packages

Step-by-step explanation:

We solve this question using the Least Common Multiple Method

We have :

Hot dogs are sold in packages of 8 and buns in packages of 12

We find the multiplea of 8 and 12

Multiples of 8:

8, 16, 24, 32, 40

Multiples of 12:

12, 24, 36, 48

Therefore,

LCM(8, 12) = 24

The least number of packages of hot dogs and hot dog buns that Norma can buy to have an equal number of hot dogs and buns is 24 packages

let the no of sweets be 7x, 3x, and 1x

Colin gets 7x

Sara gets 3x

gordon gets 1x

7x = 1x+54  (given)

7x - 1x= 54

6x= 54

x=9

hece sara gets 3x= 3*9

                               =27

Answer:

If you mean x2+y, then the answer would be 11.

The optimal solution is (19, 25.3)

The optimal objective function value is 202.5

From the question, we have the following parameters that can be used in our computation:

Objective function, Max: 4X₁ + 5X₂

Subject to

2X₁ + 3X₂ ≤ 114

4X₁ + 3X₂ ≤ 152

X₁ + X₂ ≤ 85

X₁, X₂ ≥ 0

Next, we plot the graph (see attachment)

The coordinates of the feasible region is (19, 25.3)

Substitute these coordinates in the above equation, so, we have the following representation

Max = 4 * (19) + 5 * (25.3)

Max = 202.5

The maximum value above is 202.5 at (19, 25.3)

Hence, the maximum value of the objective function is 202.5

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The price elasticity of demand for x is -1.25.

Price elasticity of demand (PED) is a measure of how responsive quantity demanded is to changes in price. It is calculated as follows:

```

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

```

In this case, the price of x increases by 12% and the quantity demanded decreases by 15%. Therefore, the PED is -1.25.

A PED of -1.25 means that the quantity demanded is relatively inelastic. This means that a change in price will have a relatively small effect on quantity demanded.

The demand for x is a normal good. This means that as the price of x increases, the quantity of value demanded of x will decrease.

The demand for x is relatively inelastic. This is because the PED is -1.25, which is less than -1. A PED of -1 or less indicates that the demand is inelastic.

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One strategy that may help Emilio write more fluently is practicing speed writing or shorthand techniques.

Practicing speed writing or shorthand techniques can help Emilio increase his writing speed without sacrificing legibility. Speed writing involves using abbreviations, symbols, and shortcuts to represent words or phrases, allowing for faster transcription of thoughts onto paper.

Shorthand systems, such as Gregg shorthand or Pitman shorthand, provide structured methods for condensing words and phrases into simplified symbols.

By learning and practicing speed writing or shorthand techniques, Emilio can improve his writing efficiency and reduce the time it takes to write a few sentences. This strategy allows him to maintain neatness while increasing his writing speed, enabling him to express his thoughts more fluently.

With regular practice and familiarity, Emilio will become more comfortable with the shorthand system and experience a significant improvement in his writing speed and fluency.

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Step-by-step explanation:

slope is the rise over run

rise= X

run= Y

X/Y = slope

Answer:

Fractional Expression for how much each person pays = (64.04/4)

Each person pays $16.01.

Step-by-step explanation:

Complete Question

Write an expression using fractions to show how to determine the amount that each person will pay. Then calculate each person's contributions showing all steps in long division.

The total of the bill is $64.04 and there are 4 people splitting the bill.

Solution

Total amount to be shared equally by 4 persons = $64.04

Fractional Expression for how much each person pays = (64.04/4)

Long division method to do this division.

     16.01  

4 | 64.04

      4  

    24

    24

      00

    0

    04

      4

    0

Each person pays $16.01.

Hope this Helps!!!

The Maclaurin series for g(x) is ln(1+2x)\(.^{2}\) = -8\(x^2\) - 128ln(2)\(.^{2}\)\(x^{4}\)

To find the Maclaurin series for a function f(x) using the definition of Maclaurin series, we need to express f(x) as a power series centered at x=0, which is given by:

f(x) = Σ[ n=0 to infinity ] (\(n^{2}\)(0)/n!) * \(x^{n}\)

where \(f^n\)(0) is the nth derivative of f(x) evaluated at x=0.

Using the definition of Maclaurin series, we can find the Maclaurin series for f(x) and g(x) as follows:

f(x) = ln(1+2x)

First, we find the derivatives of f(x) with respect to x:

f'(x) = 2 / (1+2x)

f''(x) = -4 / (1+2x)

f'''(x) = 16 / (1+2x)

f''''(x) = -64 / (1+2x)

Next,

We evaluate the derivatives at x=0 to find the coefficients of the Maclaurin series:

f(0) = ln(1) = 0

f'(0) = 2

f''(0) = -4

f'''(0) = 16

f''''(0) = -64

Substituting these coefficients into the formula for the Maclaurin series, we get:

f(x) = 2x - 2x + (8/3)x - (32/3)x + ...

Therefore, the Maclaurin series for f(x) is:

ln(1+2x) = 2x - 2x + (8/3) - (32/3) + ...

g(x) = ln(1+2x)

Using the chain rule, we can find the derivatives of g(x) as:

g'(x) = 4ln(1+2x) / (1+2x)

g''(x) = -8[ln(1+2x) + 1] / (1+2x)

g'''(x) = 32[ln(1+2x) + 2] / (1+2x)

g''''(x) = -128[ln(1+2x) + 3] / (1+2x)

Evaluating these derivatives at x=0, we get:

g(0) = ln(1)\(.^{2}\) = 0

g'(0) = 0

g''(0) = -8

g'''(0) = 0

g''''(0) = -128*ln(2)\(.^{2}\)

Therefore, the Maclaurin series for g(x) is:

ln(1+2x)\(.^{2}\) = -8\(x^2\) - 128ln(2)\(.^{2}\)\(x^{4}\)

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The winner received 570 votes.

Let the winner candidate be c1

Let the  second-place candidate be c2

Let the  third-place candidate be c3

\(c2=c1-155\\\).........equation 1

\(c2=c3+200\\\)

\(c3=c2-200 \\\)

\(c3=c1-155-200\\\).........by equation 1

\(c3=c1-355\)........equation 2

Now we know,

\(c1+c2+c3=1200\)

\(c1+(c1-155)+(c1-355)=1200\) .....by equations 1 and 2

\(3c1-510=1200\)

\(3c1=1200+510\\3c1=170\\c1=570\)

Hence, The winner received 570 votes.

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The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.

In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.

Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.

Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.

Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.

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Answer:

C. 31 \(\frac{1}{6}\)

Step-by-step explanation:

1. Convert mixed numbers into improper fractions:

\(\frac{29}{4}\) · 2² + ( \(\frac{17}{2}\) - 2) ÷ 3

2. Calculate within the parenthesis:

\(\frac{29}{4}\) · 2² + \(\frac{13}{2}\) ÷ 3

3. Calculate the exponent:

\(\frac{29}{4}\) · 4 + \(\frac{13}{2}\) ÷ 3

4. Multiply and divide (left to right):

29 + \(\frac{13}{2}\) ÷ 3

29 + \(\frac{13}{6}\)

5. Add:

\(\frac{187}{6}\)

6. Convert the improper fraction to a mixed number:

= 31 \(\frac{1}{6}\)

hope this helps!

Answer:

450 meters

Step-by-step explanation:

4 minutes = 240 seconds

\(\frac{x}{240} =\frac{25}{13.7}\)

solve for x

x = 438m

Answer:

15

Step-by-step explanation:

hope this helps