Solve for x ... x/6 = 2

Answer:

with wind velocity = 3156/4 = 789 mph

against wind velocity = 2836/4 = 709 mph

(789/709) / 2 = 40 mph

wind velocity = 40 mph

plane velocity = 789 - 40 = 749 mph

Step-by-step explanation:

Answer:

The third term of the expansion [tex](a+b)^n[/tex] is [tex]C(n,2)\cdot a^{n-2}\cdot b^{2}[/tex].

Step-by-step explanation:

According to the binomial expansion,

[tex](a+b)^n=C(n,0)a^{n}+C(n,1)a^{n-1}b+...+C(n,n)b^n[/tex]

So, the rth term of this expansion is

[tex]C(n,r-1)a^{n-r+1}b^{(r-1)}[/tex]

We have to find the third term of the expansion [tex](a+b)^n[/tex] is

[tex]C(n,3-1)a^{n-3+1}b^{(3-1)}[/tex]

[tex]C(n,2)\cdot a^{n-2}\cdot b^{2}[/tex]

Therefore the third term of the expansion [tex](a+b)^n[/tex] is [tex]C(n,2)\cdot a^{n-2}\cdot b^{2}[/tex].

Answer:

2

Step-by-step explanation:

An inverse of a function is a reflection across the y=x line. This results in each (x,y) point becoming (y,x).

x         f(x)

-6          1

-3          2

2           5

5           3

8           0

So the inverse becomes:

x         Inverse

1            -6

2           -3

5            2

3            5

0            8

g(2) = -3 and f(-3) = 2.

Answer:

44%

Why? Because there is only 4 of each and you have so many more chances to pull a different card.

Answer:

a) The increasing intervals would be from negative infinity to -6 and 3 to infinity. The decreasing interval would just be from -6 to 3

b) The local maximum comes at x = -6. The local minimum would be x = 3

c) The inflection point is x= -3/2

Step-by-step explanation:

To find the intervals of increasing and decreasing, we can start by finding the answers to part b, which is to find the local maximums and minimums. We do this by taking the derivatives of the equation.

f(x) = 4x^3 + 18x^2 - 216x + 3

f'(x) = 12x^2 + 36x -216

Now we take the derivative and solve for zero to find the local max and mins.

f'(x) = 12x^2 + 36x - 216

0 = 12(x^2 + 3x - 18)

0 = 12(x + 6)(x - 3)

x = -6 OR x = 3

Given the shape of a positive quartic function, we know that the first would be a maximum and the second would be a minimum.

As for the increasing, we know that a third power, positive function starts down and increases to the local maximum. It also increases after the local min. The rest of the time it would be decreasing.

In order to find the inflection point, we take a derivative of the derivative and then solve for zero.

f'(x) = 12(x^2 + 3x - 18)

f''(x) = 2x + 3

0 = 2x + 3

-3 = 2x

-3/2 = x

For analyzing the given function, find the first and second derivatives, and solve for critical points. Use these points to determine your intervals where the function is increasing, decreasing, concave up, or concave down. Also, find local minima, maxima, and inflection points.

The subject of this question is Calculus, a branch of mathematics. We are asked to analyze the function f(x) = 4x3 + 18x2 − 216x + 3. To determine intervals where this function is increasing or decreasing, we'd differentiate the function to find its derivative, f'(x). We then set f'(x) equal to zero and solve for x. These solutions define the intervals. Similarly, for finding local minima, maxima and inflection points, we'd need to determine f''(x), the second derivative.

Given the nature of this question, specific calculations have been omitted. However, carrying out the steps of finding the first and second derivatives of the function, solving for critical points, and then using these points to define your intervals, will yield your final results.

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Answer: a loss of 4 cents

Step-by-step explanation:

The probability of rolling a sum of 2, 3, 4, 5, or 6 is [tex]\dfrac{15}{36}[/tex] which earns $2.00

The probability of rolling a sum of 28, 9, 10, 11, or 12 is [tex]\dfrac{15}{36}[/tex] which loses $2.00

The probability of rolling a sum of 7 is [tex]\dfrac{6}{36}[/tex] which loses $0.25

[tex]\bigg(\dfrac{15}{36}\times \$2.00\bigg)+\bigg(\dfrac{15}{36}\times -\$2.00\bigg)+\bigg(\dfrac{6}{36}\times -\$0.25\bigg)=\boxed{-\$0.04}[/tex]

The expected value of playing the game once is -$0.62, indicating an expected average loss of 62 cents per game.

The expected value of playing the game once is -$0.62, rounded to the nearest cent. This means that if you play the game repeatedly over a long string of games, you would expect to lose 62 cents per game, on average. The expected value indicates an expected average loss, so it is not recommended to play this game to win money.

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Answer:

y = 4x - 23

Step-by-step explanation:

To write the slope intercept form, convert the point slope form using the distributive property and inverse operations.

y + 3 = 4(x - 5)         Distributive Property

y + 3 = 4x - 20         Subtract 3 from both sides

y = 4x - 23

Answer:

y=4x-23

Step-by-step explanation:

its correct i just did the assignment on linear functions.

The formula for finding the circumference of a circle is [tex]c=\pi *d[/tex] (where d is the diameter). So, simply plugging in 622 mm for d and 3.14 for pi, we find that c = 622 * 3.14 = 1953.08 mm.

Answer:

2160 BTU

Step-by-step explanation:

Ben looks at his plan and realizes that his building can be viewed as a triangular prism sitting on a cube.

Calculating the volume of a cube is easy… Length x Width x Height (LWH)… so 12 x 10 x 8 = 120 x 8 = 960 cubic feet for the cube part.

For the prism, it’s almost the same… but divided by 2 : (LWH)/2, so… (12 x 10 x 2) / 2 = (120 x 2) / 2 = 240 / 2 = 120 cubic feet for the prism part.

Total for the building : 960 + 120 = 1080 cubic feet

Since 2 BTU per cubic foot, the power of the unit needs to be at least  1080 x 2 = 2160 BTU.

Answer:

Step-by-step explanation:

Use the cosine law:

[tex]AB^2=CB^2+CA^2-(CB)(CA)\cos(\angle C)[/tex]

We have:

[tex]AB=6,\ CB=6.5,\ CA=7.5[/tex]

Substitute:

[tex]6^2=6.5^2+7.5^2-2(6.5)(7.5)\cos(\angle C)[/tex]

[tex]36=42.25+56.25-97.5\cos(\angle C)[/tex]

[tex]36=98.5-97.5\cos(\angle C)[/tex]           subtract 98.5 from both sides

[tex]-62.5=-97.5\cos(\angle C)[/tex]           divide both sides by (-97.5)

[tex]\cos(\angle C)\approx0.641\to m\angle C\approx50^o[/tex]

your fraction would be 3 12/15

[tex]n\cdot1\cdot\dfrac12\cdot\dfrac13\cdot\dfrac14\cdot\dfrac15=\dfrac n{5!}[/tex]

[tex]\dfrac12\cdot\dfrac14\cdot\dfrac16\cdot\dfrac18\cdot\dfrac1{10}=\dfrac{3\cdot5\cdot7\cdot9}{10!}[/tex]

So we have

[tex]\dfrac n{5!}=\dfrac{3\cdot5\cdot7\cdot9}{10!}[/tex]

[tex]n=\dfrac{3\cdot5\cdot7\cdot9}{6\cdot7\cdot8\cdot9\cdot10}[/tex]

[tex]n=\dfrac{3\cdot5}{6\cdot8\cdot10}[/tex]

[tex]n=\dfrac1{2\cdot8\cdot2}[/tex]

[tex]n=\dfrac1{32}[/tex]

Answer:

3

Step-by-step explanation:

trust me , it worked

Answer:

Option 1 - [tex]x\approx 1.58[/tex]

Step-by-step explanation:

Given : Exponential equation [tex]17^x=89[/tex]

To find : Solve exponential equation by using properties of common logarithms?

Solution :

Step 1 - Write the exponential equation,

[tex]17^x=89[/tex]

Step 2 - Take logarithm both side,

[tex]\log 17^x=\log 89[/tex]

Step 3 - Apply logarithmic property, [tex]\log a^x=x\log a[/tex]

[tex]x\log 17=\log 89[/tex]

Step 4 - Divide both side by log 17,

[tex]x=\frac{\log 89}{\log 17}[/tex]

Step 5 - Solve,

[tex]x=1.584[/tex]

[tex]x\approx 1.58[/tex]

Therefore, Option 1 is correct.

Answer:

vertical intercepts: (7, pi/2) and (-7, pi/2)

horizontal intercepts: (10,0) and (-4,0)

Step-by-step explanation:

The horizontal and vertical intercepts are respectively; [(10,0) and (-4,0)] and [(7, π/2) and (-7, π/2)]

We are given the parametric equation;

r = 7 + 3 cos θ

Now, the vertical intercept will be when cos θ = 0 and that is at θ = π/2

Thus;

At θ = π/2, we have;

r = 7 + (3 * 0)

r = 7

But this will also give the same value of θ when r = -7

Thus; vertical intercepts are; (7, π/2) and (-7, π/2)

Horizontal intercept will occur when cos θ = 1. Thus;

At θ = 0, we have;

r = 7 + (3 * 1)

r = 10

Also, the lower interval will be when cos θ = -1. Which is 0 on the negative side. Thus

r = 7 + (3 * -1)

r = 4

Thus; horizontal intercepts are; (10,0) and (-4,0)

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Answer:

C

Step-by-step explanation:

a^2 + b^2 = c^2 so 6^2 + 9^2 = 36 + 81 = square root of 117

The length of the hypotenuse of right triangle ΔDEF is 10.82 units

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

Here we have ,

to find hypotenuse of a right triangle:

The hypotenuse side can be found using Pythagoras theorem,

Therefore,

c² = a² + b²

where

c = hypotenuse

a and b are the other legs.

Therefore,

a^2 + b^2 = c^2

so 6^2 + 9^2

= 36 + 81

= square root of 117

=10.82

learn more on Pythagoras theorem here:

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Answer:

The equation after translation is x² + y² + 16x - 8y + 73 = 0 ⇒ answer (a)

Step-by-step explanation:

* Lets study the type of the equation:

∵ Ax² + Bxy + Cy² + Dx + Ey + F = 0 ⇒ general form of conic equation

- If D and E = zero

∴ The center of the graph is the origin point (0 , 0)

- If B = 0

∴ The equation is that of a circle

* Lets study our equation:

 x² + y² = 7 ⇒ x² + y² - 7 =0

∵ B = 0 , D = 0 , E = 0

∴ It is the equation of a circle with center origin

- The equation of the circle with center origin in standard form is:

  x² + y² = r²

∴ x² + y² = 7 is the equation of a circle withe center (0 , 0)

  and its radius = √7

* We have two translation one horizontally and the other vertically

- Horizontal: x-coordinate moves right (+ve value) or left (-ve value)

- Vertical: y-coordinate moves up (+ve value) down (-ve value)

∵ The point of translation is (-8 , 4)

∵ x = -8 (-ve value) , y = 4 (+ve value)

∴ The circle moves 8 units to the left and 4 units up

* now lets change the x- coordinate and the y-coordinate

  of the center (0 , 0)

∴ x-coordinate of the center will be -8

∵ y-coordinate of the center will be 4

* That means the center of the circle will be at point (-8 , 4)

- the standard form of the equation of the circle with center (h , k) is

 (x - h)² + (y - k)² = r²

∵ h = -8 and y = 4

∴ The equation is: (x - -8)² + (y - 4)² = 7

∴ (x + 8)² + (y - 4)² = 7

* lets change the equation to the general form by open the brackets

∴ x² + 16x + 64 + y² - 8y + 16 - 7 = 0

* Lets collect the like terms

∴ x² + y² + 16x - 8y + 73 = 0

∴ The equation after translation is x² + y² + 16x - 8y + 73 = 0

* Look at the graph the blue circle is after translation

Answer:

1/6

Or in decimal form,

0.16

ANSWER

[tex]b = \frac{1}{3} [/tex]

[tex]x = \frac{1}{2} \: or \: x = - \frac{1}{7} [/tex]

EXPLANATION

The given expression is

[tex](b - 5) {x}^{2} - (b - 2)x + b = 0[/tex]

If

[tex]x = \frac{1}{2} [/tex]

is a root, then it must satisfy the given equation.

[tex](b - 5) {( \frac{1}{2} )}^{2} - (b - 2)( \frac{1}{2} )+ b = 0[/tex]

[tex](b - 5) {( \frac{1}{4} )} - (b - 2)( \frac{1}{2} )+ b = 0[/tex]

Multiply through by 4,

[tex](b - 5)- 2(b - 2)+4 b = 0[/tex]

Expand:

[tex]b - 5- 2b + 4+4 b = 0[/tex]

Group similar terms;

[tex]b - 2b + 4b = 5 - 4[/tex]

[tex]3b = 1[/tex]

[tex]b = \frac{1}{3} [/tex]

Our equation then becomes:

[tex]( \frac{1}{3} - 5) {x}^{2} - ( \frac{1}{3} - 2)x + \frac{1}{3} = 0[/tex]

[tex]( - \frac{14}{3} ) {x}^{2} - ( - \frac{5}{3} )x + \frac{1}{3} = 0[/tex]

[tex] - 14{x}^{2} + 5x + 1= 0[/tex]

Factor:

[tex](2x - 1)(7x + 1) = 0[/tex]

[tex]x = \frac{1}{2} \: or \: x = - \frac{1}{7} [/tex]

find prime factors to get the inbetween numbers for product, and choose the one that has a difference of 20, and it should be 5 and 25, both requirements are met.

Answer:

Solution 1: The numbers are 25 and 5

Solution 2: The numbers are -5 and -25

Step-by-step explanation:

We have 2 unknown numbers, then we can define them as:

x: Unknown number 1  

y: Unknown number 2

The problem states that "the difference of two numbers is 20". We can translate this to x - y = 20

We also know that "their product is 125". We can translate this to x . y = 125

Putting both equations together, we get the following system of equations

[tex]\left \{ {{x - y = 20} \atop {x y=125}} \right.[/tex]

Now, to solve this system of equations we can use the Substitution Method.

We can solve 1st equation for x, by adding y to both sides

x - y + y = 20 + y

x = 20 + y

We can substitute x by 20 + y on the 2nd equation

(20 + y) . y = 125

Applying distributive property on the left side

20y + y² = 125

Substracting 125 to both sides and rearranging the terms, we get

20y + y² - 125 = 125 -125

y² + 20y - 125 = 0

We can apply the quadratic equation attached to solve this (with a = 1, b = 20, c = -125).

( -20 ± √(20² - 4 . 1 . -125) ) / ( 2. 1 ) =

( -20 ± √(400 + 500) ) / ( 2) =

( -20 ± √900 ) / ( 2) =

( -20 ± 30 ) / ( 2) =

We get 2 results:

For each of these values of y, we can find the corresponding value of x:

Answer:

-10/3, 10/3

Step-by-step explanation:

(In this answer I will use y' to denote the derivative of y with respect to t. You shouldn't normally do this because y' normally means the derivative of y with respect to x but I'll be a bit messy for this case)

First calculate the derivatives:

[tex]y=\cos(kt) \Rightarrow y'=-k\sin(kt) \Rightarrow y'' = -k^2\cos(kt)[/tex].

Then plug the derivtes y'' and y into the equation:

[tex]-9k^2\cos(kt) = -100\cos(kt)[/tex]

Solve the equation for k:

[tex]100\cos(kt) - 9k^2\cos(kt) = 0 \\\\\Rightarrow \cos(kt)(100-9k^2) = 0[/tex]

So then we have that [tex]y=\cos(kt)[/tex] satisfies the differential equation when [tex]\cos(kt) = 0[/tex] or when [tex]100-9k^2=0[/tex] (or both). The solutions to these equations are:

[tex]\left \{ {{\cos(kt)=0 \Rightarrow k=\frac{n\pi}{2t}} \atop {100-9k^2 = 0 \Rightarrow k= \pm \sqrt{\frac{100}{9}}=\pm \frac{10}{3}}} \right.[/tex]

I understand that looks a bit complicated and I doubt you would have to give your answers in terms of t so if it asks for a separated list of answers I would go for:

k = -10/3, 10/3.

The values are [tex]k = \pm \frac{10}{3}[/tex].

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

The function is:

[tex]y = \cos{kt}[/tex]

The derivatives are:

[tex]y^{\prime}(t) = -k\sin{kt}[/tex]

[tex]y^{\prime\prime}(t) = -k^2\cos{kt}[/tex]

The equation is:

[tex]9y^{\prime\prime} = -100y[/tex]

Replacing:

[tex]-9k^2\cos{kt} = -100\cos{kt}[/tex]

[tex]9k^2 = 100[/tex]

[tex]k^2 = \frac{100}{9}[/tex]

[tex]k = \pm \sqrt{\frac{100}{9}}[/tex]

[tex]k = \pm \frac{10}{3}[/tex]

Those are the values.

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Answer:

(-a, 0).

Step-by-step explanation:

The long diagonal corresponds to the y-axis. S is the same distance from the y-axis as Q.

Answer:

Option d

Step-by-step explanation:

If the ball landed 3 feet east of where it was thrown, then it moved 3 units horizontally along the x-axis.

If you moved 4 units to the north then we can say that 4 units were moved on the y axis

Therefore, the original matrix [tex]\left[\begin{array}{cc}x\\y\end{array}\right][/tex] is transformed in the matrix [tex]\left[\begin{array}{cc}x+3\\y+4\end{array}\right][/tex]

Therefore, the answer is [tex]\left[\begin{array}{cc}x+3\\y+4\end{array}\right][/tex]

Answer:

d

Step-by-step explanation:

fr ong

Answer:

Dan eat [tex]2\frac{2}{3}[/tex] pizzas

Step-by-step explanation:

Let

x-----> amount of pizza Jay ate

y-----> amount of pizza Dan ate

we know that

[tex]x=\frac{2}{3}[/tex] ----> equation A

[tex]y=4x[/tex] -----> equation B

substitute equation A in the equation B and solve for y

[tex]y=4(\frac{2}{3})=\frac{8}{3}[/tex]

Convert to mixed number

[tex]\frac{8}{3}=\frac{6}{3}+\frac{2}{3}=2\frac{2}{3}[/tex]

To find the amount Dan ate, we multiply the amount Jay ate (2/3) by 4, giving us 8/3, which is also known as 2 2/3 pizzas.

Jay ate 2/3 of a pizza. Dan ate 4 times the amount that Jay ate. To find out how much Dan ate, we need to multiply the fraction of the pizza that Jay ate by 4.

So, Dan ate 4 x (2/3) = 8/3 pizzas. Since 8/3 is greater than the whole, it can also be represented as 2 2/3 pizzas.

Answer:

x = 1 and x = 2

x = 4 and x = -4

Step-by-step explanation:

Vertical asymptotes appear where the function does not have a value. This is most commonly when the denominator of a rational function is 0. Find the asymptotes by factoring the denominator and setting it equal to 0. Then solve for x.

First equation

x² - 3x + 2 factors into (x-1)(x-2)

When x-1 = 0, x = 1. When x-2=0, x = 2. The V.A. are at x = 1 and x = 2.

Second equation

x²  - 16 factors into (x+4)(x-4)

When x+4= 0, x = -4. When x-4 = 0, then x = 4. The V.A. are at x = -4 and x = 4.

Final answer:

The function f(x) = 3x/(x² - 16) is defined for x = -16, x = 0, and x = 16, but undefined for x = -4 and x = 4, where it has vertical asymptotes.

Explanation:

The question requires evaluating the function f(x) = 3x/ x²-16 for different values of x. When we evaluate this function, we must pay attention to the values at which the function is undefined, which is when the denominator x^2 - 16 equals zero. This occurs when x = -4 or x = 4, as these values make the denominator (x + 4)(x - 4) equal to zero.

Options (b) and (d) correspond to the values at which the function has vertical asymptotes, as the denominator becomes zero and the function value approaches infinity.

Answer:

[tex]30-3d\leq 20[/tex]

Step by step explanation:

Let d represent the rate of temperature decrease in degrees Celsius per day from Monday to Thursday.  

As temperature decreased at a constant rate in the next 3 days, so the rate of temperature will decrease 3d degree Celsius in 3 days.  

We are told that the pool was open on Monday. The high temperature was [tex]30^{\circ}{\text{C}[/tex] on Monday. So the decrease in temperature from Monday to Thursday will be [tex]30-3d[/tex].

We have been given that the swimming pool is open when the high temperature is higher than [tex]20^{\circ}{\text{C}[/tex].

As the pool was closed on Thursday. This means that temperature on Thursday was less than or equal to 20 degree Celsius. We can represent this information in an inequality as:

[tex]30-3d\leq 20[/tex]

Therefore, the inequality [tex]30-3d\leq 20[/tex] can be used to determine the rate of temperature decrease in degrees Celsius per day, d, from Monday to Thursday.

Answer:

30-3d=20

Step-by-step explanation:

Trust me i got it correct

The local bank charges 2%.

When the balance is $600, the local bank would charge: 600 x 0.02 = $12

This means if the balance is higher the $600, the local bank would charge more than $12.

The answer would be the second choice: The fee at the local bank will be more than the fee at the local credit union only when the account balance is more than $600.

Answer: Option A.

Step-by-step explanation:

By definition, the equation of the line in slope-intercept form is:

[tex]y=mx+b[/tex]

Where m is the slope of the line and b is the y-intercept.

Let's solve for y from the equation A, as following:

[tex]5x-y=7\\-y=-5x+7\\(-1)(-y)=(-5x+7)(-1)\\y=5x-7[/tex]

As you can see in the equation:

[tex]m=5\\b=7[/tex]

Therefore, the option A is the answer.

In Mathematics, the slope of a line is represented by 'm' in the equation y=mx+b. By comparing the provided options with this format, we find option A has the equation of a line with a slope of 5.

In the subject of

Mathematics

, particularly

Algebra

, the equation of a line in the form y=mx+b represents a straight line on the xy-plane, where 'm' is the slope and 'b' is the y-intercept. With this in mind, we analyze the given options.

Therefore, option A has a line with a slope of 5.

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Answer:

[tex]\large\boxed{A=112x\ m^2}[/tex]

Step-by-step explanation:

The formula of an area of a trapezoid:

[tex]A=\dfrac{b_1+b_2}{2}\cdot h[/tex]

b₁, b₂ - bases

h - height

We have

b₁ = 17x m , b₂ = 11x m, h = 8 m.

Substitute:

[tex]A=\dfrac{17x+11x}{2}\cdot8=\dfrac{28x}{2}\cdot 8=14x\cdot 8=112x[/tex]

Answer:

the cost of each charm

Step-by-step explanation:

Since x is the number of charms and it is multiplied by 25, 25 is the cost of each charm