Find the equations of the tangents to the curve y = x²-x-12 at each of the points where the curve crosses the x-axis.​

this qeustion cannot be solved! never seen it before andusally there is a number instead of a y

The answer is ,  the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

The Taylor series expansion is a way to represent a function as an infinite sum of terms that depend on the function's derivatives.

The Taylor series of a function f(x) centered at c is given by the formula:

\(\large f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(c)}{n!}(x-c)^n\)

Using the definition of Taylor series to find the Taylor series (centered at c=0) for the function f(x) = e^(4x), we have:

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{e^{4(0)}}{n!}(x-0)^n\)

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n\)

Therefore, the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

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The Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

To find the Taylor series for the function f(x) = e^(4x) centered at c = 0, we can use the definition of the Taylor series. The general formula for the Taylor series expansion of a function f(x) centered at c is given by:

f(x) = f(c) + f'(c)(x - c) + f''(c)(x - c)^2/2! + f'''(c)(x - c)^3/3! + ...

First, let's find the derivatives of f(x) = e^(4x):

f'(x) = d/dx(e^(4x)) = 4e^(4x)

f''(x) = d^2/dx^2(e^(4x)) = 16e^(4x)

f'''(x) = d^3/dx^3(e^(4x)) = 64e^(4x)

Now, let's evaluate these derivatives at x = c = 0:

f(0) = e^(4*0) = e^0 = 1

f'(0) = 4e^(4*0) = 4e^0 = 4

f''(0) = 16e^(4*0) = 16e^0 = 16

f'''(0) = 64e^(4*0) = 64e^0 = 64

Now we can write the Taylor series expansion:

f(x) = f(0) + f'(0)(x - 0) + f''(0)(x - 0)^2/2! + f'''(0)(x - 0)^3/3! + ...

Substituting the values we found:

f(x) = 1 + 4x + 16x^2/2! + 64x^3/3! + ...

Simplifying the terms:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

Therefore, the Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

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Answer: 6x

Step-by-step explanation:

so consider x as the number,

twice of x= 2x

2x tripled= 2x*3

               = (2*3)x

               = 6x

Answer:

9506

Example:

Multiply the 7 and 8 to get 56.

Since 56 is greater than 9, you'll have to carry the 5.

       5

       9 7

x 9 8

___________

               6

Multiply the 9 and 8 to get 72.

And, add the carried 5 to get 77.

77 is greater than 9, but there are no more digits to carry over, so just write the 7 down in front.

   7  5

       9 7

x 9 8

___________

       7    7   6

Multiply the 7 and 9 to get 63.

Since 63 is greater than 9, you'll have to carry the 6.

       6

       9 7

x 9 8

___________

       7    7   6

             3   0

_____________

Multiply the 9 and 9 to get 81.

And, add the carried 6 to get 87.

87 is greater than 9, but there are no more digits to carry over, so just write the 8 down in front.

   8  6

       9    7

x 9    8

___________

       7    7   6

  8   7    3   0

_____________

Then add 776 + 8730 to get your answer which is 9506! :)

  1    1

      7   7  6

+  8  7  3  0

_________

    9  5  0  6

The prime factors that the numbers 24 and 36 have in common are found out to be; 2 × 2 × 3

A prime factor of a number is simply factor of that number that is a prime number. This means that any of the prime numbers that can be multiplied to give the original number.

Now, we have;

Prime factors of 36; 2 × 2 × 3 × 3

Prime factors of 24; 2 × 2 × 2 × 3

The prime factors that they have in common will be; 2 × 2 × 3

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Answer:

ans:88.18cm

Step-by-step explanation:

The score needed on the final exam to achieve a C grade is 79.33, rounded to 2 decimal places.

Homework is worth 30% of the grade, which is also a significant portion. The average homework score is 90, which means the average of all homework scores is 90.

Test reviews are only worth 5% of the grade, so they have the smallest impact on the overall average. The average test review score is 72, which means the average of all test review scores is 72.

Finally, the final exam is worth 15% of the grade, and we need to find out what score is needed on the final exam to achieve a C grade, which is 72%.

To calculate the overall average, we can use the weighted average formula.

Overall Average = (Tests Average x 0.5) + (Homework Average x 0.3) + (Test Reviews Average x 0.05) + (Final Exam Score x 0.15)

Substituting the values we know, we get:

Overall Average = (59 x 0.5) + (90 x 0.3) + (72 x 0.05) + (Final Exam Score x 0.15)

Simplifying this equation, we get:

Overall Average = 29.5 + 27 + 3.6 + (Final Exam Score x 0.15)

Overall Average = 60.1 + (Final Exam Score x 0.15)

To get a C grade, the overall average needs to be 72%. So we can set up an equation and solve for the Final Exam Score:

72 = 60.1 + (Final Exam Score x 0.15)

Solving for Final Exam Score, we get:

Final Exam Score = (72 - 60.1) / 0.15

Final Exam Score = 79.33

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The result of diving 107 by 10⁻³ is (E) 107,000.

So, we know that 10⁻³ is 0.001.

Therefore, the result of diving 107 by 10⁻³ is (E) 107,000.

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The correct question is given below:

The result of dividing 107 by 10^-3 is?

a. 10-4.

b. 102.5.

c. 1010.

d. 104.

e. 107,000

The price of small sized print photo is $0.5 and large sized print photo is $1.25.

In the given question,

Andy and Alex both decided to order prints of their photos.

Andy ordered 40 small 4x6 inch prints and 10 large 8x10 inch prints.

Alex paid $20 for 20 small 4x6 inch prints and 8 large 8x10 inch prints.

We have to find how much do the small and large sized prints cost.

Let the cost of small 4x6 inch prints is x.

Let the cost of large 4x6 inch prints is y.

Since, Andy ordered 40 small 4x6 inch prints and 10 large 8x10 inch prints and paid total of $32.50 for his photos.

Now the equation should be

40x + 10y = 32.50...............(1)

Since Alex paid $20 for 20 small 4x6 inch prints and 8 large 8x10 inch prints.

Now the equation should be

20x + 8y = 20...............(2)

Multiply equation (2) by 2, we get

40x + 16y = 40...............(3)

Now subtract equation (3) by (1), we get

6y = 7.5

Divide by 6 on both side, we get

y = 1.25

Now putting the value of y in equation (1), we get

40x + 12.5 = 32.50

Subtract 12.5 on both side, we get

40x = 20

Divide by 40 on both side, we get

x = 0.5

Hence, the price of small sized print photo is $0.5 and large print photo is $1.25.

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The complete question is:

Andy and Alex both decided to order prints of their photos. Andy ordered 40 small 4x6 inch prints and 10 large 8x10 inch prints. He paid a total of $32.50 for his photos. Alex paid $20 for 20 small 4x6 inch prints and 8 large 8x10 inch prints. How much do the small and large-sized prints cost?

The speed of the proton is \(\rm 4.7 \times 10^7 \ meter \ per \ second\).

For the speed of a proton that has been accelerated from rest, we would apply the work-energy theorem:

A proton moves in a circular orbit with a radius of 65 cm that is perpendicular to a uniform magnetic field of magnitude 0.75 T.

The speed of the proton is given by the following formula;

\(\rm V=\dfrac{2\pi R}{T}\\\\V=\dfrac{2 \times 3.14 \times 0.65m }{87.4ns}\\\\V =4.7 \times 10^7 \ meter \ per \ second\)

Hence, the speed of the proton is \(\rm 4.7 \times 10^7 \ meter \ per \ second\).

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Answer:

He will earn $51 more

Step-by-step explanation:

Let us compare the amounts he will earn in both banks

Mathematically, simple interest is;

I = PRT/100

Where P represents principal, R represents rate and T represents time

For Citibank, we have

I = (500 * 4.75 * 12)/100 = $285

For National bank

I = (500 * 3.9 * 12)/100 = 234

The difference between the amount of money earned in both banks will be;

285-234 = 51

Answer:

x = -3    b no answer is 1/27000

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

Angle S and Angle T are consecutive interior angles. Therefore, we know that T + S = 180°.

First, we need to solve for T, and since angles S and T are consecutive interior angles, we know that T + S = 180°. If we reorganize the equation to include the things we know (S = 105°), then we get 180° - 105° = 75°. So T is 75°.

Now, we use T = 75° and the information given to us in the picture to set up an equation. 75 = 24x + 3. Now, we can find x by isolating it. Do this by:

1) Subtracting 3 from both sides to give you 72 = 24x. We do this to get rid of the 3 from the "x side", but we must also do it to the other to keep the equation true. This moves the 3 from the "x side" to the other since we're trying to isolate x.

2) Divide 24 by both sides to get 3 = x. We use the same logic as we did for 3, except this time we divide since that's the opposite of multiplying.

In conclusion, x = 3.

Answer:

14.4in so your radius is your third answer

Answer:

230-300= -70

All you have to do is subtract :)

The Probability that Robert randomly pulls out a black sock is 1/5  .

In the question ,

it is given that

Total number of socks in sock drawer = 30 socks

number of white socks in the drawer = 16 socks

number of black socks in the drawer = 6 socks

number of red socks in the drawer = 2 socks

number of yellow socks in the drawer = 6 socks

So , the probability that he randomly pulls out a black sock = (number of black socks in the drawer) / ( total number of socks in the drawer )

= 6 / 30

= 1/5

Therefore , The Probability that Robert randomly pulls out a black sock is 1/5  .

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The angle measures of each vertex will be 160°, 142°, 120°, 156°, 31°, and 111°.

The inclination is the separation seen between planes or vectors that meet.

Let 'n' be the number of sides of the polygon. Then the sum of the interior angles of the polygon is given as,

Sum of angles = (n - 2) × 180°

The number of sides of the polygon is 6. Then the sum of internal angles is given as,

Sum of angles = (6 - 2) × 180°

Sum of angles = 4 × 180°

Sum of angles = 720°

Then the equation is given as,

(7x - 8) + (4x + 46) + (5x) + (6x + 12) + (x + 7) + (5x - 9) = 720

28x + 48 = 720

28x = 672

x = 24

Then the measure of each angle is given as,

(7x - 8) = 7 × 24 - 8 = 160°

(4x + 46) = 4 × 24 + 46 = 142°

(5x) = 5 × 24 = 120°

(6x + 12) = 6 × 24 + 12 = 156°

(x + 7) = 24 + 7 = 31°

(5x - 9) = 5 × 24 - 9 = 111°

The angle measures of each vertex will be 160°, 142°, 120°, 156°, 31°, and 111°.

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"If the congruent sides in one isosceles triangle have the same measure as the congruent sides in another isosceles triangle, then the triangles are congruent."

The given statement true.

When two angles become congruent, their degree measures are the same. The reverse of something like the Isosceles Triangle Theorem asserts that the sides of a triangle opposing congruent angles are also congruent.

If two two triangles are congruent, then perhaps the sides opposite the congruent angles are equal, in accordance with the isosceles triangle theorem converse.

Mathematics is defined by theorems. A theorem is a proposition that has been proven true by a rigorous proof, which is a type of logical argument.

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The total cost for x number of tickets is expressed as: C(x) = 4.5x + 8.5

An algebraic word problem is defined as a problem that requires converting a sentence into an equation and solving that equation. Usually in real-life scenarios variables represent unknown quantities.

Now, the formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

We are given:

Base cost of carnival = $8.50

Cost of each additional ticket = $4.50

Thus, total cost for x number of tickets is expressed as:

C(x) = 4.5x + 8.5

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Scenario 1A:

Coinsurance amount is $90

Medicare payment is $360

Provider write-off is $290

Scenario 1B:

Remaining amount for Insurance and patient to pay is $350

Coinsurance amount is $70

Total paid by patient is $170

Medicare payment is $280

Provider write-off is $370

Scenario 1A:

Submitted charge: $650

Medicare participating physician fee schedule (PFS): $450

Coinsurance amount (20% paid by patient): $

Medicare payment (80% of the PFS): $

Provider write-off: $

To calculate the missing amounts, we can use the provided information:

Coinsurance amount (20% paid by patient):

Coinsurance amount = 20% of the Medicare participating physician fee schedule (PFS)

Coinsurance amount = 0.2 * $450 = $90

Medicare payment (80% of the PFS):

Medicare payment = 80% of the Medicare participating physician fee schedule (PFS)

Medicare payment = 0.8 * $450 = $360

Provider write-off:

Provider write-off = Submitted charge - Medicare payment

Provider write-off = $650 - $360 = $290

Scenario 1B:

Submitted charge: $650

Medicare participating physician fee schedule (PFS): $450

Patient pays $100 remaining on their deductible

Remaining amount for Insurance and patient to pay: $

Coinsurance amount (20% of remaining amount): $

Total paid by patient (deductible & 20% of remaining): $

Medicare payment (80% of the remaining amount): $

Provider write-off: $

To calculate the missing amounts, we can use the provided information:

Remaining amount for Insurance and patient to pay:

Remaining amount for Insurance and patient to pay = PFS - remaining deductible

Remaining amount for Insurance and patient to pay = $450 - $100 = $350

Coinsurance amount (20% of remaining amount):

Coinsurance amount = 20% of the remaining amount

Coinsurance amount = 0.2 * $350 = $70

Total paid by patient (deductible & 20% of remaining):

Total paid by patient = remaining deductible + coinsurance amount

Total paid by patient = $100 + $70 = $170

Medicare payment (80% of the remaining amount):

Medicare payment = 80% of the remaining amount

Medicare payment = 0.8 * $350 = $280

Provider write-off:

Provider write-off = Submitted charge - Medicare payment

Provider write-off = $650 - $280 = $370

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The Project Triangle is also known as the triple constraints model and consists of three elements: cost, time and scope.

The Project Triangle is also known as the Iron Triangle or Triple Constraints and is a graphical representation of the connection between project costs, schedule, and scope. It is one of the key principles of project management, and it is utilized to help organizations and project managers understand and handle trade-offs between different objectives of a project.

The three elements of the Project Triangle are:

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The area of the shaded face of the cylinder is 1,520 mm².

We can see that the shaded area of the cylinder is circular in shape.

This means that we can find the area of the shaded area by finding the area of the circle.

The radius of the circle is given as 22 mm.

The formula for finding the area of a circle is given as:

Area = πr²

= 3.14 × 22 × 22

= 1,519.76

≈ 1520 mm²

Therefore, we have found the area of the shaded face of the cylinder to be 1,520 mm².

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Disclaimer: The question was incomplete, the complete question is attached below.

Answer:

Step-by-step explanation:

Subtract 4x from both sides

4x-4x + 2y = -4x - 12

2y = - 4x - 12            

Divide by 2

2y/2 = -4x/2 - 12/2

y = -2x - 6

The y intercept happens when x = 0

y intercept is - 6

or 0,-6

Answer:

y intercept = -6

x intercept = -3

Step-by-step explanation:

Answer:

the answer is c, (-10,4) and the radius is 10

Step-by-step explanation:

Hope this helps!❆

Answer:

its 28

Step-by-step explanation:

hope this helps also u have to divide 70 divided by 48% in order to get 28

Answer:

43 plants per seed packet

Step-by-step explanation:

From this information, we can form an equation, y=3x+40. 40 is because of the y-intercept, and 3 is the slope of the line. If you plug in 1 as x to represent 1 seed packet, you get y as 43. Hope this helped!

Answer:

56 degrees

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

Opposite angles of two parallel lines formed by crossing by third line are equal

The forecasts for periods 11 through 15 are: F11 = 297.4, F12 = 296.7, F13 = 297.1, F14 = 296.9, F15 = 297.0

Given: Smoothing constant α = 0.45, Forecast for period 10 = 297

We need to calculate the forecasts for periods 11 through 15 using the essential smoothing forecast method.

The essential smoothing forecast is given by:Ft+1 = αAt + (1 - α)

Ft

Where,

At is the actual value for period t, and Ft is the forecasted value for period t.

We have the forecast for period 10, so we can start by calculating the forecast for period 11:F11 = 0.45(297) + (1 - 0.45)F10 = 162.35 + 0.45F10

F11 = 162.35 + 0.45(297) = 297.4

For period 12:F12 = 0.45(At) + (1 - 0.45)F11F12 = 0.45(297.4) + 0.55(297) = 296.7

For period 13:F13 = 0.45(At) + (1 - 0.45)F12F13 = 0.45(296.7) + 0.55(297.4) = 297.1

For period 14:F14 = 0.45(At) + (1 - 0.45)F13F14 = 0.45(297.1) + 0.55(296.7) = 296.9

For period 15:F15 = 0.45(At) + (1 - 0.45)F14F15 = 0.45(296.9) + 0.55(297.1) = 297.0

Therefore, the forecasts for periods 11 through 15 are: F11 = 297.4, F12 = 296.7, F13 = 297.1, F14 = 296.9, F15 = 297.0 (All values rounded to two decimal places)

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