A linear equation has a slope of 2 and goes through points (3,5). Write an
equation for this line in slope intercept form.

Answer:

\(\displaystyle \int^x_0\sin(3t^2)\,dt\approx x^3-\frac{27}{42}x^7\)

Step-by-step explanation:

Recall the MacLaurin series for sin(x)

\(\displaystyle \sin(x)=x-\frac{x^3}{3!}+\frac{x^5}{5!}-...\)

Substitute 3t²

\(\displaystyle \displaystyle \sin(3t^2)=3t^2-\frac{(3t^2)^3}{3!}+\frac{(3t^2)^5}{5!}-...=3t^2-\frac{3^3t^6}{3!}+\frac{3^5t^{10}}{5!}-...\)

Use FTC Part 1 to find degree 7 for F(x)

\(\displaystyle \int^x_0\sin(3t^2)\,dt\approx\frac{3x^3}{3}-\frac{3^3x^7}{7\cdot3!}\\\\\int^x_0\sin(3t^2)\,dt\approx x^3-\frac{27}{42}x^7\)

Hopefully you remember to integrate each term and see how you get the solution!

360 odd-digit numbers can be formed using the given set of digits, with each digit being used only once.

To determine the number of odd numbers that can be formed using a given set of digits, where each digit can only be used once, we need to consider a few conditions:

The last digit: The last digit of an odd number must be one of the odd digits (1, 3, 5, 7, or 9). So there are five choices for the last digit.

The first digit: The first digit cannot be zero since it would make the number less than the desired number of digits. Therefore, the first digit has nine options (excluding zero and the odd digit already chosen for the last digit).

The remaining digits: For every other digit in the number, we have eight remaining options (since we have used two digits already - one for the first digit and one for the last digit).

Considering the above conditions, the total number of odd-digit numbers that can be formed is obtained by multiplying the number of choices for each digit:

Total number of odd-digit numbers = Number of choices for last digit × Number of choices for first digit × Number of choices for remaining digits

Total number of odd-digit numbers = 5 × 9 × 8

Total number of odd-digit numbers = 360

Therefore, 360 odd-digit numbers can be formed using the given set of digits, with each digit being used only once.

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Answer:

\(\\\sf7x^3 - 2x^2 - 5\)

Step-by-step explanation:

\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)

Remove parenthesis.

6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3

Rearrange:

6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3

Combine like terms to get:

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

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Answer:

7x³ - 2x² - 5

Step-by-step explanation:

(6x³ + 3x² - 2) + (x³ - 5x² - 3)

Remove the round brackets.

= 6x³ + 3x² - 2 + x³ - 5x² - 3

Put like terms together.

= 6x³ + x³ + 3x² - 5x² - 2 - 3

Do the operations.

= 7x³ - 2x² - 5

____________

hope this helps!

Given:

Fixed fee = $40

Additional fee = $15 per hour

To find:

The equation to represent Bob's cost to repair his refrigerator.

Solution:

Let y be the total cost for x hours.

Additional fee for one hour = $15

Additional fee for x hour = $15x

Total cost = Fixed fee + Additional fee

\(y=40+15x\)

Therefore, the required equation is \(y=40+15x\).

Lakisha's total job benefits per year are (D) $58,196.

To find  Lakisha's total job benefits:

If Lakisha's employer pays $2,150 in health insurance and $86 in life insurance per year, and she also gets $3,520 in paid time off per year, then Lakisha's total job benefits per year are equal to:

Total Benefits = Health Insurance + Life Insurance + Paid Time Off + Annual Gross Pay

Therefore,  Lakisha's total job benefits per year are (D) $58,196.

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Answer The answer is D

Step-by-step explanation:

I got it correct on edg

To calculate the amount Briana saved by purchasing a backpack with a sales promotion, we need to find the difference in prices between the two backpacks after applying the respective discounts.

For the first backpack that originally costs $45 with a sales promotion of 20% off:

Discounted price = $45 - (20% * $45) = $45 - $9 = $36

For the second backpack that originally costs $42 with a sales promotion of 10% off:

Discounted price = $42 - (10% * $42) = $42 - $4.2 = $37.8

Now we can calculate the savings:

Amount saved = Original price - Discounted price

Amount saved = $42 - $37.8 = $4.2

Therefore, Briana saved $4.2 by purchasing the backpack that cost $45 with a 20% off promotion instead of the backpack that cost $42 with a 10% off promotion.

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The x-component of the total electric field due to the two charges at a point on the x-axis a distance 3d from the origin, at the point (x = 3d, y = 0) is 3.962 N/C.

The electric field at point P which is located on the x-axis a distance 3d from the origin due to two charges Q1 and Q2 is a vector sum of the individual electric fields created by the two charges.

Electric field due to point charge Q at a distance r from the point charge Q can be calculated using Coulomb's law as:

                                     E = k Q / r^2where k = 9 x 10^9 Nm^2/C^2 is the Coulomb's constant

Now, the electric field created by Q1 at point P isE1 = k Q1 / r^2where r is the distance between Q1 and P.

Here, Q1 is at a distance d from P on the y-axis and the distance between Q1 and P is given as:

                                             r1 = sqrt[(3d)^2 + d^2] = sqrt(10) * d

We know that, Q1 = 6.80 x 10^-9 CE1 = 9 x 10^9 * 6.80 x 10^-9 / [sqrt(10) d]^2= 4.628 N/C

Again, the electric field created by Q2 at point P isE2 = k Q2 / r^2where r is the distance between Q2 and P.

Here, Q2 is at a distance d from P on the y-axis and the distance between Q2 and P is given as:

                                                  r2 = sqrt[(3d)^2 + d^2] = sqrt(10) * d

We know that, Q2 = 6.20 x 10^-9 CE2 = 9 x 10^9 * 6.20 x 10^-9 / [sqrt(10) d]^2= 4.208 N/C

The x-component of the electric field E1 along the x-axis will be zero, since it is perpendicular to the x-axis.

The x-component of the electric field E2 is directed towards the origin and is given as:

                              Ex2 = E2 cos θ = E2 (x / r2) = E2 [3d / sqrt(10) d]= 0.9407 * E2

Therefore, the x-component of the total electric field at point P due to the two charges is:

                                       Ex = Ex1 + Ex2= 0 + 0.9407 * E2= 3.962 N/C (approx.)

Hence, the x-component of the total electric field due to the two charges at a point on the x-axis a distance 3d from the origin, at the point (x = 3d, y = 0) is 3.962 N/C.

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Given the equation:

You need to remember that Newton's method to approximate a root of the equation provides this formula:

In this case:

Then, you need to derivate it, in order to find:

Use these Derivative Rules:

Where "k" is a constant.

You get:

• Knowing that:

You can set up that:

Substitute the given value of "x" and evaluate, in order to find the second approximation:

• Now you can set up that:

Then, substituting the corresponding x-value and evaluating, you get:

Hence, the answers are:

• Second approximation:

• Third approximation:

Answer:

the real part is part of -12i is 0

Answer:

118085.765 hope this helps have a nice day please give me brainliest:)

Step-by-step explanation:

Step-by-step explanation:

-5x+2y= 4         <==== Multiply entire equation by -3 to get:

15x-6y = -12  

2x+3y= 6          <====  Multiply entire equation by 2 to get :

4x+6y = 12    Add the two underlined equations to eliminate 'y'

19x = 0     so x = 0

sub in x = 0 into any of the equations to find:  y = 2

(0,2)

Assuming that the order of the cities matters, the number of possible routes is 11! (11 factorial), which is 39916800.

The number of possible routes for an overnight express company that includes eleven cities on its route is 39916800. This is because when the order of the cities matters, the number of possible routes can be calculated by finding 11 factorial, which is:

This calculation results in 39916800, which means that there are 39916800 potential routes for an overnight express company with eleven cities on its route.

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Answer:

The temperature six minutes after being turned on is 125°.

T(t)= 65° + t * 10°

Step-by-step explanation:

Linear Equations

Ellie sets the temperature of the oven to 65°. The oven will increase the temperature at 10° per minute after being turned on.

After the first minute, the temperature of the oven is

65° + 10° = 75°

After the second minute, the temperature is:

65° + 2*10° = 65° + 20° = 85°

The same pattern goes on after minute 6, where the temperature is:

65° + 6*10° = 65° + 60° = 125°

The temperature six minutes after being turned on is 125°.

The general formula can be deducted for any time t as:

T(t)= 65° + t * 10°

Answer:

165 centimeters

Step-by-step explanation:

An example of calculating BMI using the formula: Height = 165 cm (1.65 m), Weight = 68 kg One centimeter is equal to 0.01 meter: 1cm = 0.01m. You are 65 inches tall. 65 * (2.54) = 165.1 cm.

Answer:

165 cm

Step-by-step explanation:

1.65 meters = 1.65 × 100 = 165 centimeters

Answer:

The probability when rolling a regular six-sided dice that the score is an odd number is three-sixths or three out of six. Both three and six are divisible by three. Therefore, this fraction could be simplified to one-half. Three divided by three is equal to one

Answer:

The 2 figures have the same shape and the corresponding points are "lined up" so I would say that this is a translation.

Answer:

translation

see below

Step-by-step explanation:

translation because it didn't change direction of the figure

translation is sliding down or up rotation is moving in circle

The general solution to the differential equation is y = [-(1/4)x^2 - (1/3)x + (C/4)]^(1/3).

To solve 2yy' + x^2 + y^2 + x = 0 using an appropriate substitution, we can substitute u = y^2. Taking the derivative of u with respect to x, we get du/dx = 2yy'. We can then rewrite the original equation as 2(u^(1/2))(du/dx) + x^2 + u + x = 0.

This is now a separable differential equation, where we can move the u term to the right side and the x terms to the left side: 2(u^(1/2))du/u = -(x^2 + x)dx. Integrating both sides, we get 4/3u^(3/2) = -(1/3)x^3 - 1/2x^2 + C, where C is the constant of integration.

Substituting back u = y^2, we get 4/3y^3 = -(1/3)x^3 - 1/2x^2 + C.

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The area of a rectangle that is inscribed with its base on the x-axis and its upper corners on the parabola   \(y=c-x^2\)   is   \(4(\frac{c}{3})^\frac{3}{2}\).

A rectangle has a width  \(2x\) ⇒ w= \(2x\)

height of the rectangle is   \(c-x^2\) ⇒    \(y=c-x^2\)

Area=width multiplied by the height

                                       ⇒\(area=width*height\)

we maximize Area by setting   \(\frac{dA}{dx} =0\) .

                                     \(\frac{d(2c-2x^3)}{dx} =0\\\\2c-6x^2=0\\\\x^2=\frac{1}{3}c\\ \\x=\sqrt{\frac{c}{3} }\)

substituting back the value of x in the formula of the area we get  

                                  \(area=2\sqrt{\frac{c}{3} } *2\frac{c}{3} \\\\area=4(\frac{c}{3})^\frac{3}{2}\)

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Answer:

13.5 and 2.76

Step-by-step explanation:

Answer:

9/7

Step-by-step explanation:

-24/35 ÷ -8/15

=-24/35 × -15/8

=9/7

Answer:

9/7

Step-by-step explanation:

when dividing with a fraction, the -8/15 reciprocates to 15/-8. Then, -8 cancels out -24 remaining with 3 since they are both negative while 15 and 35 have a common of 5 giving them a remainder of 3 and 7 respectively. you then multiply what you have which is 3/7 * 3/1 giving you 9/7.

Check the picture below.

The rectangular form of n = (2.80∠–29.9°) is n = 2.45 – 1.38j.

To convert the polar form of n = (2.80∠–29.9°) to rectangular form, we can use the following equations:

a = r*cos(θ)
b = r*sin(θ)

where r is the magnitude of the complex number and θ is its angle in polar form.

Using the given values, we have:

r = 2.80
θ = –29.9°

Converting θ to radians:

θ = –29.9° * π/180 = –0.522 radians

Substituting the values in the equations, we get:

a = 2.80*cos(–0.522) = 2.45
b = 2.80*sin(–0.522) = –1.38

Therefore, the rectangular form of n = (2.80∠–29.9°) is:

n = 2.45 – 1.38j

So,  The rectangular form of n = (2.80∠–29.9°) is n = 2.45 – 1.38j.

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(1) Using the Black/Scholes Option Pricing Model, the value of the call option is $7.70.

(2) The intrinsic value of the call is the difference between the stock price and the strike price of the option. Therefore, it is $4.

(3) The stock price required to break-even is the sum of the strike price and the option premium. Therefore, it is $74.

(4) If volatility were to decrease, the value of the call would decrease.

(5) If the exercise price would increase, the value of the call would decrease.

(6) If the time to maturity were 3-months, the value of the call would decrease.

(7) If the stock price were $62, the value of the call would be zero.

(8) The maximum value that a call option can take is unlimited.

In the Black/Scholes option pricing model, the value of a call option can be calculated using the formula:

C = S*N(d1) - X*e^(-rT)*N(d2)

where S is the stock price, X is the exercise price, r is the risk-free rate, T is the time to maturity, and σ2 is the variance of the stock's return.

Using the given values, we can calculate d1 and d2:

d1 = [ln(S/X) + (r + σ2/2)T]/(σ2T^(1/2))

   = [ln(74/70) + (0.10 + 0.50/2)*0.5]/(0.50*0.5^(1/2))

   = 0.9827

d2 = d1 - σ2T^(1/2) = 0.7327

Using these values, we can calculate the value of the call option:

C = S*N(d1) - X*e^(-rT)*N(d2)

= 74*N(0.9827) - 70*e^(-0.10*0.5)*N(0.7327)

= $7.70

The intrinsic value of the call is the difference between the stock price and the strike price of the option. Therefore, it is $4.

The stock price required to break-even is the sum of the strike price and the option premium. Therefore, it is $74.If volatility were to decrease, the value of the call would decrease. This is because the option's value is directly proportional to the volatility of the stock.

If the exercise price would increase, the value of the call would decrease. This is because the option's value is inversely proportional to the exercise price of the option.

If the time to maturity were 3-months, the value of the call would decrease. This is because the option's value is inversely proportional to the time to maturity of the option.If the stock price were $62, the value of the call would be zero. This is because the intrinsic value of the call is zero when the stock price is less than the strike price.

The maximum value that a call option can take is unlimited. This is because the value of a call option is directly proportional to the stock price. As the stock price increases, the value of the call option also increases.

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A sequence of transformation that would move ΔABC onto ΔDEF is: D. a dilation by a scale factor of 1/2, centered at the origin, followed by a 90° clockwise rotation about the origin.

In Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.

In this scenario an exercise, we would dilate the coordinates of the pre-image by applying a scale factor of 1/2 that is centered at the origin as follows:

Ordered pair B (-4, 2) → Ordered pair B' (-4 × 1/2, 2 × 1/2) = Ordered pair B' (-2, 1).

In Mathematics and Geometry, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction;

(x, y)                               →            (y, -x)

Ordered pair B' (-2, 1)   →          E (1, 2)

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Answer:

the scale factor is 4

Step-by-step explanation:

Step 1: Multiply both sides by 9. (This will cancel out the denominator in -u/9.)

-59 × 9 = -531
and \(\frac{-u}{9}\) × 9 = -u

Step 2: Whenever both sides of an algebraic equation are negative, you can remove the negative signs and re-write the equation:

Final Answer: u = 531

Answer:

p ^ q is  true

Step-by-step explanation:

25>20 so p is true

25 is  divisible by 5 so q is true

p ^ q is  true

The solution for x is x ≤ -3/4.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

To solve for x in the inequalities:

5x - 4 ≥ 12 and 12x + 5 ≤ -4

We'll solve each inequality separately:

5x - 4 ≥ 12

Adding 4 to both sides, we get:

5x ≥ 16

x ≥ 16/5

So the first inequality is solved for x as x ≥ 16/5.

Now, 12x + 5 ≤ -4

Subtracting 5 from both sides, we get:

12x ≤ -9

x≤ -9/12

x≤ -3/4

The only values of x that satisfy both inequalities are those that are less than or equal to -3/4.

Therefore, the solution for x is x ≤ -3/4.

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The final equation for the tangent plane to the graph of f at the point (a, b) is z = 2e^a(x - a) - y + 2e^a - 2b. This equation represents the plane that is tangent to the graph of f at the specified point (a, b).

To find the equation for the tangent plane to the graph of the function f(x, y) = 2e^x - y at a given point (x0, y0), we need to calculate the partial derivatives of f with respect to x and y at that point.

The partial derivative of f with respect to x, denoted as ∂f/∂x or fₓ, represents the rate of change of f with respect to x while keeping y constant. Similarly, the partial derivative of f with respect to y, denoted as ∂f/∂y or fᵧ, represents the rate of change of f with respect to y while keeping x constant.

Let's calculate these partial derivatives:

fₓ = d/dx(2e^x - y) = 2e^x

fᵧ = d/dy(2e^x - y) = -1

Now, we have the partial derivatives evaluated at the point (x0, y0). Let's assume our point of interest is (a, b), where a = x0 and b = y0.

At the point (a, b), the equation for the tangent plane is given by:

z - f(a, b) = fₓ(a, b)(x - a) + fᵧ(a, b)(y - b)

Substituting fₓ(a, b) = 2e^a and fᵧ(a, b) = -1, we have:

z - f(a, b) = 2e^a(x - a) - (y - b)

Now, let's substitute f(a, b) = 2e^a - b:

z - (2e^a - b) = 2e^a(x - a) - (y - b)

Rearranging and simplifying:

z = 2e^a(x - a) - (y - b) + 2e^a - b

The final equation for the tangent plane to the graph of f at the point (a, b) is z = 2e^a(x - a) - y + 2e^a - 2b.

This equation represents the plane that is tangent to the graph of f at the specified point (a, b).

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