find the time t when the line tangent to the path of the particle is vertical. is the direction of motion of the particle up or down at that moment? give a reason for your answer.

The table is completed using the function f(x) = 3ˣ and g(x) = 3x as shown below

x    f(x)    g(x)

0     1       0

1      3      3

2     9      6

f(x) has a greater rate of change between 1 and 2

f(x) has a greater rate of change between 0 and 2

The table is completed by substituting the values of x into the functions of f(x) and g(x)

The rate of change between 1 and 2

f(x)

= change in y / change in x

= (9 - 3) / (2 - 1)

= 6

g(x)

= change in y / change in x

= (6 - 3) / (2 - 1)

= 3

The rate of change between 0 and 2

f(x)

= change in y / change in x

= (9 - 1) / (2 - 0)

= 4

g(x)

= change in y / change in x

= (6 - 0) / (2 - 0)

= 3

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The coordinates of B is (-2, -6)

The formula to determine the midpoint of a straight line using the coordinates of its endpoints is known as the midpoint formula in coordinate geometry.

The formula is of the form

X= (x₂ + x₁)/2

Y = (y₂ + y₁)/2

From the formula the coordinates of B is solved knowing that midpoint is

M (3,-1) and A is (8,4) and say B (x₁, y₁)

3 = (8 + x₁)/2

6 = 8 + x₁

x₁ = -2

-1 = (4 + y₁)/2

-2 = 4 + y₁

y₁ = -6

hence B is (-2, -6)

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The equation which gives solutions, x=0 and y=-6.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

y=-x-6............................(1)

x+3y=-18.........................(2)

now, solving both equation we get

x+3y=-18

x + 3(-x-6) = -18

x - 3x - 18 = -18

-2x = 0

x= 0

and, y= -0 -6 = -6

Hence, the solution is x=0 and y=-6.

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Answer: sinθ=-12/13

Step-by-step explanation:

[tex]\displaystyle\\Given:\ cot\theta=\frac{5}{12} \ \ \ \ \pi < \theta < \frac{3\pi }{2} \ \ \ \ Find:\ sin\theta\\\\\frac{cos\theta}{sin\theta} =\frac{5}{12}[/tex]

 Multiply both parts of the equation by 12sinθ:

[tex]12cos\theta=5sin\theta[/tex]

Squared both parts of the equation:

[tex](12cos\theta)^2=(5sin\theta)^2\\\\144cos^2\theta=25sin^2\theta\ \ \ \ (1)\\[/tex]

[tex]Find\ sin\theta[/tex]

Add 144sin²θ to both parts of the equation (1):

[tex]144cos^2\theta+144sin^2\theta=25sin^2\theta+144sin^2\theta\\\\144(sin^2\theta+cos^2\theta)=169sin^2\theta\\\\144(1)=169sin^2\theta\\\\144=169sin^2\theta\\\\Thus,\ 169sin^2\theta=144[/tex]

Divide both parts of the equation by 169:

[tex]\displaystyle\\sin^2\theta=\frac{144}{169} \\\\sin\theta=б\sqrt{\frac{144}{169} } \\\\sin\theta=б\sqrt{\frac{12^2}{13^2} } \\\\sin\theta=б\sqrt{(\frac{12}{13})^2 } \\\\sin\theta=б\frac{12}{13}[/tex]

[tex]\displaystyle\\As, \ \pi < \theta < \frac{3\pi }{2} \ \ \ \ \Rightarrow\ \ \ \angle\theta\ is \ in\ the\ 3rd\ quadrant\\\\ So \ sin\theta\ takes \ negative \ values\\\\sin\theta=-\frac{12}{13}[/tex]

If the sidewalk A , B ,C are horizontal to each other and D is connecting them, then we can say that the the sidewalk D is perpendicular to them .

We say that two lines are perpendicular if they form the angle of 90 degree between them. Thus , we can say that the sidewalk D are having a perpendicular relationship whit the other 3 sidewalks.

Horizontal means something which has a parallel relationship with the horizon . The opposite of horizontal is vertical which is also known as the portrait mode. A horizontal line is any line normal to a vertical line. Horizontal lines do not cross each other similarly the vertical lines do not cross each other.

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The horizontal line test is a method used to determine if a given function is one-to-one, which means that for every unique x-value, there is a unique y-value. A function that is one-to-one can be inverted, meaning that it has an inverse function.

The inverse function of a one-to-one function is a function that undoes the original function.

The horizontal line test is used to determine if a given function is one-to-one by drawing a horizontal line through the graph of the function and seeing if the line intersects the graph at most once.

If the function is one-to-one, it has an inverse function and it can be found by switching the x and y values and solving for y.

For example, if the original function is f(x) = 2x + 1, its inverse function is f^-1(x) = (x-1)/2. This inverse function undoes the original function and it can be used to solve equations, find derivatives, and study geometric transformations.

It's important to note that the horizontal line test is only a sufficient condition, meaning that a function that passes the horizontal line test is one-to-one, but not all one-to-one function pass the horizontal line test.

In conclusion, the horizontal line test is a method used to determine if a given function is one-to-one, which is important because one-to-one functions can be inverted.

The inverse function undoes the original function, and it can be found by switching the x and y values and solving for y. The test is simple and easy to apply, but only a sufficient condition.

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Answer:

(5,4)

Step-by-step explanation:

first, if you have a calculator you can put the equation into y = and just find the maximum point there

to find the x value of the maximum point you do -B/2A

-80/2(8) = 5 so the x value would be 5

then to find y just plug in 5 for x and you should get 4

Answer:

Maximum value of
[tex]f(x) = - 8x^2 + 80x - 196[/tex]

is

[tex]\boxed{f(x) = 4}[/tex]

Step-by-step explanation:

The maximum or minimum value of a function f(x) occurs when the first derivative equals zero

The first derivative of
[tex]f(x) = - 8x^2 + 80x - 196[/tex]

[tex]f'(x) = \dfrac{d}{dx}\left(-8x^2+80x-196\right)[/tex]

[tex]=-\dfrac{d}{dx}\left(8x^2\right)+\dfrac{d}{dx}\left(80x\right)-\dfrac{d}{dx}\left(196\right)[/tex]

[tex]\dfrac{d}{dx}\left(8x^2\right) = 16x\\\\=- \dfrac{d}{dx}\left(8x^2\right) = -16x\\\\\\\dfrac{d}{dx}\left(80x\right)=80\\\\\dfrac{d}{dx}\left(196\right)=0[/tex]

[tex]\dfrac{d}{dx}\left(-8x^2+80x-196\right) \\\\\\ =-16x + 80 + 0\\\\= -16x + 80\\\\[/tex]

Set this expression equal to 0 and solve for x to find the x value which maximizes or minimizes the function

[tex]-16x + 80 = 0\\\\\implies -16x = -80\\\\x = -80/-16\\\\x = 5\\\\[/tex]

Plug this value of x into the original function to get the maximum or minimum value.

[tex]f(5) = -8(5^2) + 80(5) - 196\\\\= -8 (25) +400 -196\\\\= -200 + 400 - 196\\\\= 4\\\\[/tex]

So the maximum value of [tex]\boxed{f(x) = 4}[/tex] ANS

and occurs at [tex]x = 5[/tex]  

(Strictly speaking to find if this is a maximum or minimum, we have to find the second derivative and see if it is negative or positive. If negative, it is a maximum, if positive it is a minimum

But since the question does not ask for this, I am skipping it. In case you are interested, the second derivative of f(x) is the derivative of f'(x) which will work out to -16 so it is a maximum)

The pole was at a depth of 2 feet  = - 2

What is height and distance ?

height can be defined as the the measurement in vertical direction where as the distance can be defined as the measurement in horizontal direction.

Given :

Casey was at the surface of a swimming pool and recorded the following two measurements,

in feet, on a number line: −8, which represents the depth of water in the swimming pool +7,

which represents the height of the slide at the pool  

To Find, What does 0 represent in this situation?  

Describe the height of the slide in relation to 0 in the situation

Casey held a pole in the swimming pool. The bottom of the pole was at a depth of 2 feet. How should Casey mark the level of the bottom of the pole on the number line

0 represent in this situation  - Top surface of Swimming pool  - Surface matching with ground

height of the slide in relation to 0 in the situation  = 7 feet

pole was at a depth of 2 feet = - 2

Hence, The pole was at a depth of 2 feet  = - 2

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The measure of the angle ∠B of the triangle ABC will be 27°.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

In ∆ABC, if m∠A is seven more than four times m∠B and m∠C is eleven more than m∠B. Then the equations are given as,

∠A = 4∠B + 7                                ...1

∠C = ∠B + 11                                ...2

∠A + ∠B + ∠C = 180°                   ...3

From equations 1, 2, and 3, then we have

4∠B + 7° + ∠B + ∠B + 11° = 180°

6∠B = 162°

∠B = 27°

The measure of the angle ∠B of the triangle ABC will be 27°.

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Knowing a circle's circumference can be used to calculate its radius, which is given by the formula r = c / (2 * π ). If you know the diameter, D, you may calculate the radius, R, which is equal to D divided by 2.

For Example

Circumference c = 26.8in

Area A = 57.156

Diameter = 8.5307

Radius of the circle Radius r = 4.26535.

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Tom has to put up an additional $2,437.5 in collateral in order to borrow enough money to take his vacation as planned.

This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.

We typically utilize this technique for math calculations.

This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.

According to our question-

automobile is priced at $3,500.

Tom needs more collateral, so P

=P + 3500 Total Collateral Value

His bank is able to lend up to 80% of the value of the collateral.

=> loan = (80/100)(P + 3500)

=> loan = 0.8P + 2800

Loan amount needed: 4,750.

0.8P + 2800 = 4,750.

=> 0.8P = 1950

=> P = 2,437.5

Tom has to put up an additional $2,437.5 in collateral in order to borrow enough money to take his vacation as planned.

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Calculating the pixel ratio of a website involves measuring the width and height of each element on the page and then dividing the width by the height.

Ratio is a comparison of two numbers or values expressed as a fraction or proportion. Ratios are used to compare different measures, such as costs, efficiency, productivity, or profitability, and to evaluate the relative importance of different elements. Ratios are also used to compare different items to each other, such as the ratio of sales to expenses. Ratios can be used to compare different time periods, and to assess the performance of a company over time.

The result is the pixel ratio, which can be used to determine how much of an element is visible on the page and how much is hidden. To calculate the pixel ratio, you can use a variety of tools, such as online tools, browser extensions, or specialized software. It is also important to note that the pixel ratio will vary depending on the device used to view the website, so it is important to test the website on multiple devices. Once the pixel ratio is calculated, it can be used to optimize the website for different devices.

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By evaluating the formula for the sequence, we will get the terms:

Here we want to find the second, fourth, and eleventh terms in the sequence:

A(n) = -9 + (n - 1)*3

n defines the "number" of the term in the sequence.

So to get the second term, we need to use n = 2, we will get.

A(2) = -9 + (2 - 1)*3

A(2) = -9 + 3 = -6

The fourth term is what we get if we evaluate in n = 4, then:

A(4) = -9 + (4 - 1)*3

A(4) = -9 + 9 = 0

And the eleventh term is what we get when we use n = 11, we will get:

A(11) = -9 + (11 - 1)*3

A(11) = -9 + 30 = 21

These are the 3 terms of the sequence that we wanted to find.

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The solution for the equation 5t - 3 = 3t - 5 is when value of t is equal to -1.

Therefore the answer is A. -1.

To find the solution, you can start by isolating the variable t on one side of the equation by adding 3 to both sides and subtracting 3t from both sides:

5t - 3 + 3 = 3t - 5 + 3

5t = 3t - 2

Then subtract 3t from both sides:

5t - 3t = 3t -2 - 3t

2t = -2

Finally, divide both sides by 2 to solve for t:

t = -2/2

t = -1

So, the value of t that satisfies the equation 5t - 3 = 3t - 5 is -1.

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The angle of refraction is 32 degrees. The result is obtained by using the formula from the Snell's Law.

The Snell's Law is a formula to describe the relationship between the angles of incidence and refraction when a light passes through two medias. It can be expressed as

n₁ / n₂ = sin θ₂ / sin θ₁

Where

We have:

Find the angle of refraction!

Using the formula of Snell's Law, we'll get the refracted angle.

n₁ / n₂ = sin θ₂ / sin θ₁

1.5 / 2.0 = sin θ₂ / sin 45°

3 / 4 = sin θ₂ / (½√2)

sin θ₂ = 3(½√2)/4

sin θ₂ = 3/8 √2

sin θ₂ = 0.53

θ₂ = arc sin 0.53

θ₂ = 32°

Hence, the refracted angle is 32 degrees.

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Answer: $3

Step-by-step explanation:

Since the company charges $180 for an hour of service, we can say that it charges $180 for 60 minutes of service.

Let the cost of service per minute be C

The equation would be

60C = 180

Simplify, and you'll get

C = 3

And there's your answer.

The quotient rule essentially asserts that we may divide two powers by subtracting the exponents as long as the base is the same. This is a quick way to simplify exponents.

The quotient rule essentially asserts that we may divide two powers by subtracting the exponents as long as the base is the same. This is a quick way to simplify exponents. A power series is an infinite series in mathematics in which a represents the coefficient of the nth term and c is a constant. Power series may be found in mathematical analysis as Taylor series of indefinitely differentiable functions. The power of a number indicates how many times the number may be multiplied. Exponents and Indices are other names for powers. For example, 8^2 might be labeled "8 to the power 2" or "8 to the second power", or simply "8 squared".

Here,

The quotient rule essentially asserts that as long as the base is the same, we may divide two powers by subtracting the exponents. This is a shortcut for simplifying exponents.

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The problem states that a can of tomato sauce contains 8 oz of sauce and a case contains 12 cans. We are trying to find out how many cases of tomato sauce Chef Hugo orders and we know that he gets a total of 480 oz of sauce.

What in mathematics is a linear equation?

According to Wolfram MathWorld A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

We can use the formula 12(8)x = 480 to find out the number of cases of tomato sauce that Chef Hugo orders.

Here's the calculation:

12(8)x = 480

96x = 480

x = 5

Therefore, Chef Hugo orders 5 cases of tomato sauce.

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The function that represents the data in the table is 3x²+2. The correct answer is B.

The quadratic function is shown in the data table.

We must ascertain the function's equation.

The quadratic equation's generic form is

Let's replace the general form with the three coordinates (1,5, (2,14), and (3,29).

We therefore have;

a+b+c =5——— (1)

4a+2b+c= 14——— (2)

9a+3b+C =29------(3)

When (2) is subtracted from (1), we have;

9= 3a+b(4)

Subtracting (3) from (2) gives us;

15= 5a +b(5)

Subtracting (5) from (4) gives us;

6= 2a

3= a

As a result, the value of an is 3. When we replace this value in equation (4), we obtain;

3(3)+b= 9

b= 0

When a = 3 and b = 0 are substituted in equation (1), we obtain;

a+b+c =5

3+0+c=5

c=2

As a result, c has a value of 2.

As a result, when we substitute a = 3, b = 0, and c = 2 in the quadratic equation's general form y =ax²+bx+c, we obtain;

3x²+2

Consequently, the function that symbolizes the information in the table is 3x²+2

As a result, Option B is the right response.

Your question is incomplete but maybe your full question attached below

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Answer:

Step-by-step explanation:

y = kx

proportionality constant = k = y/x

A.  k = y/x = 7/2 = 3.5   (you can plug in any x,y pair from the table and will get the same answer, 3.5)

B. k = y/x = 12/3 = 4   (you can choose any point on the line)

C.  k = y/x = 2.75   (same as the slope of the line)

D.  k = y/x = earnings/games = 65/5 = 13

E.  k = y/x = 12/3 = 4   (you can plug in any x,y pair from the table and will get the same answer, 4)

Answer:

A. The domain should be all reals.

B. The range is y≤1 if the function is |x-2|+1.

C. It's a function.

If you get this wrong then my bad

The value of b is 2. Therefore (2, 1) is the midpoint of the line segment with endpoints (-4, 2) and (8, 0)

An equation is an expression that shows the relationship between numbers and variables.

If a point O(x, y) divides line segment AB with endpoints A(x₁, y₁) and B(x₂, y₂) in the ratio of 1:1 (midpoint). The coordinates of O is:

x = (x₁ + x₂)/2

y = (y₁ + y₂)/2

Given that (2, 1) is the midpoint of the line segment (-4, b) and (8, 0). Therefore:

1 = (0 + b)/2

b/2 = 1

b = 2

The value of b is 2.

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Customer questions had no impact on changes in discounts or customer behavior, according to those two variables.

A non-binding request for a quote or sales information from a customer to a business. The request may mention particular goods or services, terms, and, if required, delivery deadlines.

For the stated question-

Since, customer inquiries did not alter in response to changes in discount, we can conclude that discounts had no influence on them.

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The correct question is attached.

The formula for finding the hypotenuse of an isosceles right triangle when given the area is A = (1/2)bh, where A is the area, b is the base, and h is the height.

To calculate the hypotenuse, first solve for h, which is h = 2A/b. Then, use Pythagorean theorem to solve for the hypotenuse c, which is c = sqrt((b^2)+(2A/b)^2). To illustrate the formula, consider a triangle with an area of 20 and a base of 10. First, solve for h, which is h = 2(20)/(10) = 4. Then, solve for c, which is c = sqrt((10^2)+(4^2)) = sqrt(196) = 14. Therefore, the hypotenuse of the isosceles right triangle with an area of 20 and a base of 10 is 14.

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Answer:

When adding the fractions 2/7 and 3/7 you'll get 5/

Step-by-step explanation:

pls mark as brainliest

Answer:

A.

Step-by-step explanation:

looking at the scatter plot, we can sort of determine a line of best fit, so if we imagine a linear line passing through the middle of the plots, the slope of the line would be positive :)

Answer:

144%

Step-by-step explanation:

I hope this helps you