Use a graphing calculator to find the equation of an exponential function given the points on the curve. Round your answers to two decimal places. ( 3 , 71.88 ) and ( 10 , 1.79 )

According to the given information, the slope of line AB is  [tex]\frac{2}{3}[/tex].

What is the slope?

The slope of a line is a measure of how steep the line is. It tells us how much the y-coordinate of the line changes for each unit of change in the x-coordinate.

To visualize a slope, imagine a line on a coordinate plane. If the line is steep, it means that for each unit of increase in the x-coordinate, the y-coordinate changes by a larger amount. Conversely, if the line is less steep, it means that for each unit of increase in the x-coordinate, the y-coordinate changes by a smaller amount.

To find the slope of a line that passes through two given points, we use the slope formula:

[tex]slope = \frac{(change in y) }{(change in x)}[/tex]

In this case, we have points A(0, -2) and B(3, 0).

So the change in y is 0 - (-2) = 2, and the change in x is 3 - 0 = 3.

Therefore, the slope of line AB is:

[tex]slope = \frac{(change in y) }{(change in x)} = \frac{2}{3}[/tex]

Since the slope is positive, we know that the line slants upwards as we move from left to right on the coordinate plane.

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The required surface area of the prism is 378 square meters.

To find the surface area of the prism, we need to know the dimensions of the prism. Let's call the length, width, and height of the prism l, w, and h, respectively.

Since the prism has right angles between its faces, we know that it is a right rectangular prism.

The formula for the volume of a right rectangular prism is V = lwh, and we know that the volume of the prism is 490m^3. Therefore,

lwh = 490

We are not given any specific values for l, w, or h, so we need to use another piece of information to solve for one of these variables.

The surface area of a right rectangular prism is given by the formula

SA = 2lw + 2lh + 2wh

If we can find the value of one of these dimensions, we can use it to calculate the surface area of the prism

lwh = 490

Since we know that the prism has right angles between its faces, we can assume that its dimensions are integers. We can start by testing integer values for l and w, and see if we can find an integer value for h that satisfies the equation.

For example, if we let l = 7 and w = 10, we get

7 * 10 * h = 490

Simplifying, we get

70h = 490

Dividing both sides by 70, we get

h = 7

Therefore, the dimensions of the prism are l = 7, w = 10, and h = 7.

To find the surface area, we can substitute these values into the formula for SA:

SA = 2lw + 2lh + 2wh

= 2(7)(10) + 2(7)(7) + 2(10)(7)

= 140 + 98 + 140

= 378

Therefore, the surface area of the prism is 378 square meters.

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The system of linear equations 3y = x + 6 and 6y - 2x = 12 has infinitely many solutions.

Given the system of euqation in the question;

We can solve this system of linear equations using the substitution method:

From the first equation, we can rewrite x in terms of y as:

x = 3y - 6

Substituting this expression for x in the second equation, we get:

6y - 2(3y - 6) = 12

Simplifying this equation, we get:

6y - 6y + 12 = 12

The equation simplifies to 12 = 12.

This means that the two equations are equivalent and represent the same line in the xy-plane.

The system has infinitely many solutions, and all points on the line satisfy both equations.

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By answering the presented question, we may conclude that As a result, equation the real circumference of the triangle space is around 30 metres.

A math equation is a technique that links two assertions and denotes equivalence using the equals sign (=). In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For example, in the equation 3x + 5 = 14, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on either side of a letter. The logo and the programme are usually interchangeable. As an example, 2x - 4 equals 2.

Because the blueprint is designed on a scale of 12 centimetres Equals 1 metre, each 1 centimetre on the blueprint represents 0.0833 metres (1/12 of a metre).

Assume the triangle chamber on the blueprint has a perimeter of 30 cm. We may apply the following calculation to determine the real perimeter in metres:

Blueprint perimeter x Scale factor x 0.0833 = Real perimeter

Real circumference = 30 x 12 x 0.0833

Actual circumference = 29.988 metres

As a result, the real circumference of the triangle space is around 30 metres.

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Answer: The perimeter of a parallelogram is the sum of the lengths of all four sides. In this case, the perimeter is given as 69, so we can write:

EF + FG + GH + HE = 69

We know that opposite sides of a parallelogram are equal in length, so EF = GH and FG = HE. Substituting these into the equation above, we get:

2(EF) + 2(FG) = 69

2(GH) + 2(HE) = 69

Simplifying each equation:

2(2x+15) + 2(6x+4) = 69

4x + 30 + 12x + 8 = 69

16x + 38 = 69

16x = 31

x = 31/16

Substituting x into the equation for GH, we get:

GH = 2x+15

GH = 2(31/16) + 15

GH = 31/8 + 120/8

GH = 151/8

Therefore, the value of GH is 18.875 units.

Step-by-step explanation:

The measure of the angle M is 129 degrees

It is important to note that the properties of a parallelogram are;

Then, we have that;

m< M = m < K

substitute the values

12x - 39 = 8x + 17

collect the like terms, we have;

12x - 8x = 17 + 39

Add the collected like terms, we get;

4x = 56

divide both sides by the coefficient of 4, we get;

4x/4 = 56/4

Divide the values

14

Then, m < M = 12(14) -39 = 129 degrees

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The complete question:

In the parallelogram, Find mZN: K (8x + 17)9 (12x - 39)8 01;0 - Lx'An M Ax+8x +17 + iax -3 = 360 3ax-33 = H0 +3 42 20 22X 7 x=17.30

Therefore , the solution of the given problem of trigonometry comes out to be the length of the shadow at a 60° angle from the light is 2 to 3 inches.

It is thought that the interaction of the triangle different fields led to the development of astrophysics. With the aid of precise mathematical techniques, many metric issues can be resolved or the consequences of about there calculation can be established. The analysis of six fundamental trigonometric formulas is known as angle of trigonometry..

Here,

The length of the stick's shadow can be calculated using trigonometry when the sun is at a 30° or 60° angle with the earth.

Assume that the silhouette measures "x" inches in length.

The shadow and stick form a right triangle when the sun forms a 30° angle with the ground. The stick is 6 inches tall, and it is angled 30 degrees away from the shade. Therefore, we can use the tangent function to determine the shadow's length:

=> tan(30°) = 6/x

=>  x = 6/tan(30°)

=>  6/(1/√3)

=>  6√3

As a result, the shadow's length at a 30° angle from the light is 6 34 inches.

Consequently, we can use the tangent function once more to determine the length of shadow:

=>   tan(60°) = 6/x

=>  x = 6/tan(60°) = 6/√3 = 2√3

As a result, the length of the shadow at a 60° angle from the light is 2 to 3 inches.

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The complete question is " Ben made a sundial in his backyard by placing a stick with height 6 in. straight into the ground, and marking the hours in the grass. To test it, he checks the time each day when the sun makes an angle of 30° or 60° with the ground. Select all the possible lengths of the shadow when Ben checks the sundial.

A. 12 in.

B. 23√ in.

C. 8 in.

D. 63√ in.

E. 22√ in."

Answer:

y - 3 = [tex]\frac{3}{4}[/tex] (x + 8)

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

4x + 3y = - 24 ( subtract 4x from both sides )

3y = - 4x - 24 ( divide through by 3 )

y = - [tex]\frac{4}{3}[/tex] x - 8 ← in slope- intercept form

with slope m = - [tex]\frac{4}{3}[/tex]

given a line with slope m then the equation of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{4}{3} }[/tex] = [tex]\frac{3}{4}[/tex]

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

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = [tex]\frac{3}{4}[/tex] and (a, b ) = (- 8, 3 ) , then

y - 3 = [tex]\frac{3}{4}[/tex] (x - (- 8) ) , that is

y - 3 = [tex]\frac{3}{4}[/tex] (x + 8) ← equation of perpendicular line

Wayne's mistake is that he omitted the parentheses around the two factors of 2x² and 8.

Parentheses, also known as round brackets, are punctuation marks that are used to contain related information within a sentence. They are most commonly used to set off additional information, such as a clarification or an example. Parentheses can also be used to indicate a digression from the main point of a sentence, or to indicate that something is not essential to the foundation of a statement. In addition, they can be used to indicate an interruption in a sentence, or to separate items in a list. Parentheses are also used to indicate a pause or an aside in dialogue.

The step should have been written as: 4x (2x² + (8)(2x+3)). This properly shows that 8 is being multiplied by the expression 2x+3, rather than being added to it.

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Answer:

(3,-6)

Step-by-step explanation:

Coordinate for the point R is (3, -6)

A polygon with four sides and four vertices is called a quadrilateral. Quadrilateral literally means "four sides" because "quad" means four and "lateral" implies sides. Quadrilaterals come in a variety of sizes, forms, and angles, but they all have four sides in common.

If all of the matching sides and angles of two quadrilaterals are equal in size, they are said to be congruent.

Given that the quadrilateral PQRS congruent to the quadrilateral JKLM.

Find out the all sides and angles of given quadrilateral JKLM and quadrilateral PQRS,

according to the graph the points are:

for quadrilateral JKLM,

J (-6, 2)

K (-3, 5)

L (-5, 8)

M (-8, 4)

for quadrilateral PQRS,

P (9, -7)

Q (6, -4)

R  ( _, _ )

S (7, -9)

By the formula distance between any two points is:

[tex]d=\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2}[/tex]    

where, [tex]x_{1}, x_{2} , y_{1}, y_{2}[/tex] are the points of two sides of line.

using that formula we have to find out the points of R is (3, -6)

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Answer:

63.81 inches

Step-by-step explanation:

Answer:

the net asset value of Rae's antivirus software two years after her purchase was $570.84, which is not one of the given options.

Step-by-step explanation:

The software was used for 12 years, and Rae is selling it now. So, it has been used for 12 - 2 = 10 years.

Annual depreciation = (cost - salvage value) / useful life = (985 - 0) / 12 = 82.08

Depreciation for 10 years = 82.08 x 10 = $820.80

Net asset value after 2 years = cost - accumulated depreciation = 985 - 82.08 x 2 = $820.84

However, Rae is selling the software for $250, so her net asset value is $820.84 - $250 = $570.84

Therefore, the net asset value of Rae's antivirus software two years after her purchase was $570.84, which is not one of the given options.

The probability are given as follows:

15) P (point is on N.Q.) = 6 / 13

16) P (point is not on Q.R.) = 10 / 13

17) P (point is on N.Q. or RS) = 10/13

18) P  = 1/54

15)

To find the probability that the point is on line segment N.Q., we need to divide the length of N.Q. by the total length of the line segment NS. The length of NS is the sum of the lengths of N.Q., Q.R., and RS, which is 12 + 6 + 8 = 26. Therefore, the probability that the point is on line segment N.Q. is:

P(point is on N.Q.) = length of N.Q. / length of NS = 12 / 26 = 6 / 13

16)

To find the probability that the point is not on line segment Q.R., we need to subtract the length of Q.R. from the length of NS and divide by the length of NS. The length of Q.R. is 6, so the length of NS without Q.R is 12 + 8 = 20. Therefore, the probability that the point is not on line segment Q.R. is:

P (point is not on Q.R.) = (length of NS without Q.R.) / length of NS = 20 / 26 = 10 / 13

17)

To find the probability that the point is on line segment N.Q. or RS, we can add the probabilities of the point being on N.Q. and the point being on RS. We already calculated that the probability of the point being on N.Q. is 6/13. To find the probability of the point being on RS, we can use the same method as in part (15). The length of RS is 8, so the probability that the point is on RS is:

P(point is on RS) = length of RS / length of NS = 8 / 26 = 4 / 13

Therefore, the probability that the point is on N.Q. or RS is:

P(point is on N.Q. or RS) = P (point is on N.Q.) + P(point is on RS) = 6/13 + 4/13

= 10/13

18)

The bus stops at the lot every 18 minutes and stays for 2 minutes, so the shuttle is at the lot for a total of 20 minutes out of every 18 * 60 = 1080 minutes. Therefore, the probability that the bus is at the lot when you arrive is:

P (bus is at the lot) = time the shuttle is at the lot / total time = 20 / 1080

= 1/54

Note that this assumes that you arrive at a random time within the 1080 minutes and that the bus is equally likely to be at the lot at any time during its 20-minute stay.

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Answer:

Mary Ellen is MOST LIKELY going to use shears to cut the linen.

Answer:20$ per foot

Step-by-step explanation: just multiply the first cost(400) by the first foot amount(20) 400/20=20

The prime polynomial, considering it's concept, is given as follows:

x² + 6.

A polynomial is called a prime polynomial if cannot be factored into a product of two or more polynomials of lower degree with integer coefficients.

The most common way to factor a polynomial into polynomials of lower degree is according to the Factor Theorem, when the roots of polynomial are obtained, and then the linear factors generated from these roots are multiplied.

For this problem, the polynomial x² + 6 has no real roots, as x² = -6 means that the roots are complex, hence it is the prime polynomial in the context of the problem.

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Answer: B.

Step-by-step explanation:

trust me on that one lol.:p

Answer:

slimer 16 goofy butt fart gamer setup

Step-by-step explanation:

The equation for the trigonometric graph is y = 2sin4x

A trigonometric graph is the graph of a trigonometric function.

Since we desire to find the equation of the graph, we then want to use the equation for the general sine graph.

y = AsinBx where

Now, A = (maximum - minimum)/2

From the graph,

So, we now substitute the variables into the equation, thus

A = (maximum - minimum)/2

= [2 - (-2)]/2

= (2 + 2)/2

= 4/2

= 2

Also B = 2π/T

Now from the graph, T = π/2

So,  we substitute for B in the equation for B, thus

B = 2π/T

= 2π/(π/2)

= 2π × 2/π

= 4

We then substitute A and B into y, thus

y = AsinBx

= 2sin4x

So, y = 2sin4x

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The relationship that represent between x, the time in minutes and y, the shot made is y = 4x  .

Proportional relationships are relationships between two variables where their ratios are equivalent. A proportional relationship is one in which two quantities vary directly with each other.

Proportional relationships can be represented as follows;

y = kx

where

Hence, the equation that can be used to represent the relationship between x, the time in minutes and y, the shot made is as follows;

Therefore,

y = kx

where

Therefore,

12 = 3k

k = 12 / 3

k = 4

Therefore,

y = 4x  

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Step-by-step explanation:

To find the ordered pair, you can use the elimination method to solve for one variable in terms of the other, and then substitute into one of the equations to solve for the other variable. Here's how:

First, multiply the first equation by 2 to get:

6x - 4y = 8

Then, add the second equation to this one to eliminate y:

6x - 4y + (-6x + 4y) = 8 + 7

Simplifying and solving for x, we get:

0x + 0y = 15

0 = 15

This is a contradiction, which means the system of equations has no solution. In other words, there is no ordered pair of (x,y) that satisfies both equations simultaneously.

By conversion formulas, the measures of angles in degrees are, respectively:

In this problem we find thirty cases of angles in radians that must be converted in degrees, this can be done by following conversion formula:

θ' = (180 / π) × θ

Where:

Now we proceed to determine the angles, measured in degrees:

Case 1:

θ' = (29π / 36) × (180 / π)

θ' = 145°

Case 2:

θ' = (17π / 12) × (180 / π)

θ' = 255°

Case 3:

θ' = (8π / 9) × (180 / π)

θ' = 160°

Case 4:

θ' = (55π / 36) × (180 / π)

θ' = 275°

Case 5:

θ' = (5π / 18) × (180 / π)

θ' = 50°

Case 6:

θ' = (53π / 36) × (180 / π)

θ' = 265°

Case 7:

θ' = (2π / 9) × (180 / π)

θ' = 40°

Case 8:

θ' = (47π / 180) × (180 / π)

θ' = 47°

Case 9:

θ' = (π / 180) × (180 / π)

θ' = 1°

Case 10:

θ' = (17π / 45) × (180 / π)

θ' = 68°

Case 11:

θ' = (23π / 90) × (180 / π)

θ' = 46°

Case 12:

θ' = (77π / 30) × (180 / π)

θ' = 462°

Case 13:

θ' = (- 109π / 60) × (180 / π)

θ' = - 327°

Case 14:

θ' = (19π / 30) × (180 / π)

θ' = 114°

Case 15:

θ' = (- 233π / 60) × (180 / π)

θ' = 699°

Case 16:

θ' = (17π / 180) × (180 / π)

θ' = 17°

Case 17:

θ' = (131π / 36) × (180 / π)

θ' = 655°

Case 18:

θ' = (191π / 45) × (180 / π)

θ' = 764°

Case 19:

θ' = (- 71π / 90) × (180 / π)  

θ' = - 142°

Case 20:

θ' = (97π / 30) × (180 / π)

θ' = 582°

Case 21:

θ' = (- 179π / 36) × (180 / π)

θ' = 895°

Case 22:

θ' = (55π / 12) × (180 / π)  

θ' = 825°

Case 23:

θ' = (- 233π / 180) × (180 / π)

θ' = - 233°

Case 24:

θ' = (- 5π / 18) × (180 / π)

θ' = 50°

Case 25:

θ' = (299π / 180) × (180 / π)

θ' = 299°

Case 26:

θ' = (- 269π / 60) × (180 / π)

θ' = 807°

Case 27:

θ' = (- 89π / 30) × (180 / π)  

θ' = 534°

Case 28:

θ' = (47π / 45) × (180 / π)

θ' = 188°

Case 29:

θ' = (91π / 18) × (180 / π)  

θ' = 910°

Case 30:

θ' = (- 107π / 45) × (180 / π)

θ' = - 428°

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Answer:

see step by

Step-by-step explanation:

a) the polynomial must be fifth degree, so it must have a [tex]x^5[/tex] term, also need to have 2 additional terms (Lets add any, lets say [tex]x^2+8[/tex] (notice this is totally random, just need to be under 5th degree)

So a polynomial can be

[tex]x^5+x^2+8[/tex]
notice is in standard form since degrees drops from left to right.
Also notice there's an infinite amount of possible answers

b) p-q is the same as -q+p
For example, lets say

[tex]p=x+1[/tex]

[tex]q=3x^2-5[/tex]
[tex]p-q=x+1-(3x^2-5)=x+1-3x^2+5=-3x^2+x+6[/tex]

also

[tex]-q+p=-(3x^2-5)+x+1=-3x^2+5+x+1=-3x^2+x+6[/tex]

notice is the same expression.

Addressing issue hand, we state that As a result, the linear equation likelihood of obtaining a mean temperature of 98.2 or lower is 0.0030, or approximately 0.003. up to get together with.

In algebra, a linear equation refers to one with its form y=mx+b. B is the gradient, and m is the esta. The preceding clause is commonly referred to as a "linear function with two variables" so even though y and x are variables. Bivariate linear equations are linear equations with two variables. There are several linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation seems to have the structure y=mx+b, where m is the slope and b is the y-intercept, it is said to be linear. When a measurement seems to have the formula y=mx+b, both with m identifying its slope and b denoting the y-intercept, it is said to be linear.

z = (64 - 63.6) / (2.5 / sqrt(150)) = 1.7889

P(Z > 1.7889) = 1 - P(Z < 1.7889) = 1 - 0.9633 = 0.0367

As a result, the probability of selecting 150 women at random with a mean height greater than 64 inches is 0.0367, or approximately 0.037. As a result, the answer is (B) 0.0250.

(x - mu) / (sigma / sqrt(n)) = z

where x represents the sample mean, mu represents the population mean, sigma represents the population standard deviation, and n represents the sample size.

When we substitute the given values, we get:

z = (98.2 - 98.6) / (0.62 / sqrt(106)) = -2.7465

The probability of getting a z-score less than -2.7465 using a standard normal distribution table is 0.0030. As a result, the likelihood of obtaining a mean temperature of 98.2 or lower is 0.0030, or approximately 0.003. up to get together with.

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Using Boyle's law, which is mathematically expressed as P1V1 = P2V2, the new pressure is calculated as: ​​c. 1.5 atm

Boyle's law states that the product of the pressure and volume of a gas is constant, assuming that the temperature remains constant. Mathematically, it can be expressed as:

P1V1 = P2V2

where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.

Using the given values, we can set up the equation as follows:

1 atm × 750 mL = P2 × 500 mL

Simplifying this equation, we get:

750 atm·mL = 500 P2

Dividing both sides by 500 mL, we get:

P2 = 750 atm·mL / 500 mL

P2 = 1.5 atm

Therefore, the new pressure is 1.5 atm.

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Answer:

[tex] \frac{x - 9}{x - 8} [/tex]

Step-by-step explanation:

[tex] \frac{(x - 9)(x + 8)}{(x + 8)(x - 8)} [/tex]

[tex] \frac{x - 9}{x - 8} [/tex]

[tex]\cfrac{x^2-x-72}{x^2-64}\implies \cfrac{(x+8)(x-9)}{x^2-8^2}\implies \cfrac{(x-9)~~\begin{matrix} (x+8) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} (x+8) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(x-8)}\implies \cfrac{x-9}{x-8}[/tex]

Answer:

The profit function can be expressed as:

Profit = Revenue - Cost

Revenue = Price x Quantity

Price = p = 450,000 - 100x

Quantity = x

Cost = C = 500/x + 200x + x²

Substituting these values, we get:

Profit = (450,000 - 100x) x - (500/x + 200x + x²)

Simplifying this expression, we get:

Profit = -x² + 450,000x - 500 - 200x² - x³

To find the quantity that gives maximum profit, we need to differentiate the profit function with respect to x and set it equal to zero:

d(Profit)/dx = -3x² + 450,000 - 400x - 500/x²

Setting this derivative equal to zero and solving for x, we get:

3x³ - 450,000x² + 400x³ + 500 = 0

This equation can be solved numerically to obtain:

x ≈ 98.9

To confirm that this is a maximum, we can check the second derivative of the profit function:

d²(Profit)/dx² = -6x + 800/x³

At x = 98.9, this evaluates to:

d²(Profit)/dx² ≈ -2.71

Since the second derivative is negative, the profit function has a maximum at x ≈ 98.9.

The maximum profit can be found by substituting this value of x into the profit function:

Profit ≈ $20,007,710

To find the selling price that maximizes profit, we can use the demand function:

p = 450,000 - 100x

At x = 98.9, this evaluates to:

p ≈ $35,110

Therefore, the corporation should sell its product for $35,110 to maximize profit.