8. Convert from exponential to logarithmic form (or vise versa).
a. 20 = ex+3
b. ex + 4 = 24
c. In(x+1) = 11
d. 2ln(x-3) = 12

Given a rectangle with the length of x+2 and width of 3x - 1. The area of a rectangle is given by the product of the length and width.

Thus, the area of this rectangle can be found as follows:Area = (x+2)(3x-1

Area = 3x^2 - x + 6x - 2

Area = 3x^2 + 5x - 2

Hence, we can express the area of the given rectangle in terms of the variable x as 3x^2 + 5x - 2. Therefore, the correct option is none of the provided options.

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Answer:

4. 1 units

Step-by-step explanation:

A diameter of a circle is equal to 2 of its radiuses. Just simply divide the diameter by 2.

Answer:

4<x<8                         interval notation is (4,8)

Step-by-step explanation:

hope this helps

Answer: d.[4,8]

Step-by-step explanation:got it right

If the system of equation be 9x - 7y - 3  = 0 then the coordinate exists (0.3, -0.4).

A straight line on the coordinate plane is represented by a linear function. A system of equations, usually referred to as an equation system or a set of simultaneous equations, is a finite set of equations for which common solutions are sought.

The X and Y intercepts and the Slope exists comprehended the line properties.

Let the equation be 9x - 7y - 3  = 0

When x = 0 the value of y is 3/-7 so this line "cuts" the y axis at y = -0.428

y-intercept = 3/-7  = -0.42857

When y = 0 the value of x is 1/3 so this line "cuts" the x axis at x = 0.33333

x-intercept = 3/9 = 1/3  =  0.33333

The change in y divided by the change in x is referred to as the slope. We observe that the value of y is -0.429 for x = 0 and 2.143 for x = 2.000.

Therefore, we get a change of 2.143 - (-0.429) = 2.571 in y for a change of 2.000 in x (the change in x is frequently referred to as "RUN").

Slope     =  2.571/2.000 =  1.286

Slope = 2.571/2.000 = 1.286

x-intercept = 3/9 = 1/3 = 0.33333

y-intercept = 3/-7 = -0.42857.

Therefore, the coordinate exists (0.3, -0.4).

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Answer:

C

Step-by-step explanation:

C is not true

For incompressible flow in a horizontal pipe of constant diameter and without fittings or valves, the pressure is a linear function of pipe length.

Linear function:A linear function can be defined as a function that shows a constant rate of change between input values (x) and output values (y). When we plot the graph of a linear function, it shows a straight line. The standard form of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Pressure:Pressure is defined as the force exerted per unit area. Pressure is a scalar quantity. It can be measured in units such as pascals, bars, pounds per square inch, etc.

Now let's consider the given statement for incompressible flow in a horizontal pipe of constant diameter and without fittings or valves to prove that pressure is a linear function of pipe length.

In a horizontal pipe of constant diameter, the following assumptions are made:No valves and fittings are presentFluid is incompressibleFriction is negligibleThe fluid flow is steady-state and laminarAt two points P1 and P2 along the horizontal pipe, let us assume that the fluid pressure and velocity are P1, V1 and P2, V2, respectively.

The pressure drop between the two points is given byΔP = P1 - P2The flow rate of the fluid through the pipe is given by the equation,Q = (A1V1) = (A2V2)

where, A is the cross-sectional area of the pipe.

Substituting V1 = Q/A1 and V2 = Q/A2 in ΔP = P1 - P2, we getΔP = P1 - P2 = 32μQL / πd4,

where μ is the viscosity of the fluid, L is the length of the pipe, d is the diameter of the pipe.

The above equation is called the Hagen-Poiseuille equation. It shows that pressure drop (ΔP) is proportional to the length of the pipe (L) when the other parameters such as flow rate (Q), viscosity (μ), and diameter (d) of the pipe are constant.

Thus, it can be concluded that the pressure is a linear function of pipe length.

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Answer:

The numbers are 36 and 68.

Step-by-step explanation:

Let the smaller number be x.

"The larger number is four less than two times the smaller

number."

The larger number is

2x - 4

The sum of the numbers is x + 2x - 4, or 3x - 4.

"The sum of the numbers is 104."

3x - 4 = 104

3x = 108

x = 36

The smaller number is 36.

The larger number is 2x - 4, or

2x - 4 = 2(36) - 4 = 72 - 4 = 68

The larger number is 68.

Answer: The numbers are 36 and 68.

Answer:

The diver will hit the water at 1.5 seconds

Step-by-step explanation:

Given

\(h= -16(t-1.5)(t+1)\)

Required (Missing from the question)

When will the diver hit the water?

To do this, we simply solve for t

When the diver hits the water, the height is 0 (at that point)

So, substitute 0 for h in \(h= -16(t-1.5)(t+1)\)

\(0= -16(t-1.5)(t+1)\)

Divide both sides by -16

\(\frac{0}{-16} =\frac{-16(t-1.5)(t+1)}{-16}\)

\(\frac{0}{-16} =(t-1.5)(t+1)\)

\(0 =(t-1.5)(t+1)\)

\((t-1.5)(t+1)=0\)

Split

\(t - 1.5 = 0\) or \(t + 1 = 0\)

Solve for t

\(t = 1.5\) or \(t = -1\)

But time (t) can not be negative.

So:

\(t = 1.5\)

Hence, the diver will hit the water at 1.5 seconds

The volume of the triangular prism is 15.75 cubic cm after using the formula for the volume of the triangular prism.

When a triangle is, stretch it out to produce a stack of triangles, one on top of the other. A triangular prism is the name given to this novel 3D object.

It is given that:

The prism is shown in the picture with dimensions.

As we know the volume of the triangular prism can be fins using the formula:

V = (1/2)bhl

Here b is the base length

h is the height of the triangular prism

l is the length of the triangular prism.

V = (1/2)4.5×3.5×2

V = (1/2)31.5

V = 15.75 cubic cm

Thus, the volume of the triangular prism is 15.75 cubic cm after using the formula for the volume of the triangular prism.

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The maximum monthly profit Mt. Nittany is  $23,100 and, for Happy Valley Rentals,  monthly profits will be approximately $23,100.

(a) To find the number of apartments Mt. Nittany should rent out each month to maximize profits, we need to find the vertex of the quadratic function P(x) = -7x^2 + 980x - 10900.

The x-coordinate of the vertex is given by -b/2a, where a = -7 and b = 980. So, x = -b/2a = -980/(2*(-7)) ≈ 70.

The maximum monthly profit is obtained by plugging this value of x into P(x), giving P(70) = -7(70)^2 + 980(70) - 10900 ≈ $23,100.

(b) Similarly, for Happy Valley Rentals, we need to find the vertex of the quadratic function P(x) = -7x^2 + 980x - 10900 when they manage 50 apartments.

The x-coordinate of the vertex is again given by

b/2a, where a = -7 and b = 980, but now we have x = -b/2a = -980/(2*(-7)) ≈ 70.

The maximum monthly profit is obtained by plugging this value of x into P(x), giving P(70) = -7(70)^2 + 980(70) - 10900 ≈ $23,100.

Therefore, both companies should rent out 70 apartments each month to maximize their profits, and their maximum monthly profits will be approximately $23,100.

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Answer:

Ethan has 8 cups of bread flour, and it takes 2/3 cup of Graham flour to make one loaf of bread. So, he can make:8 / (2/3) = 12 loaves of Graham bread.

Step-by-step explanation:

Answer: -15

Step-by-step explanation: 2r+8-r=-7

1r +8 = -7

1/1       -15/1

Answer: r = -15

Step-by-step explanation:

2r - r = -7 -8

r = -15

Answer:The right answer is B

Step-by-step explanation:

If it's negative then it should be on the other side with one side down on the graph and one side on the left.(hope this helped you) :)

A system of linear equations has one solution when the graphs intersect at a point.

A system of linear equations has no solution when the graphs are parallel.

A system of linear equations has infinite solutions when the graphs are on the exact same line.

The graphs attached below show the linear equations that have one solution, multiple solutions, and no solutions.

A linear equation in two variables of the form axe + by + c = 0, where a, b, c R, a 0, and b 0. By comparing the coefficients of the equations while taking the system of linear equations into consideration, we may determine how many solutions there are. Additionally, we can use a graphical way to determine whether the equation system has a single solution or an infinite number of solutions.

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Answer:

False, 82 inches is not greater than 5 feet and 10 inches

Step-by-step explanation:

1 feet = 12 inches

5x12=60+10=70

82 is greater than 70.

Answer: 0 = 23

Almost positiveee :))

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

If you substitute each x value from the input boxes into the equations, you can find your answer.

The first input value is 1, and the output value is 12, so plug those into the first equation in the answer options.

y = 4x + 8

(12) = 4(1) + 8

12 = 4 + 8

12 = 12

Because the simplified equation ended in a true equality statement, that pair works with the equation.

The next x value is 3 and the y value is 20:

y = 4x + 8

(20) = 4(3) + 8

20 = 12 + 8

20 = 20

Again, it ends in  true equality statement, so it also works with the equation.

(28) = 4(5) + 8 = 28 so that one works as well.

Then check the second equation with the second set of input and output values.

(2) = -7(-1) - 5 = 2

The first x and y values of that system work.

(9) = -7(-2) - 5 = 9

The second one works as well.

(16) = -7(-3) - 5 = 16

The last one is equal as well.

So the equations in A, or the first option, work with all of the inputs and outputs.

Answer: (3/6) then (2/6)

Step-by-step explanation:

FRACTIONS: YOU TIMES IT SO THE DENOMINATOR IS THE SAME APPLY THE NUMBER YOU TIMED BY THE NUMERATOR.

The maximum mass of the water bug to avoid sinking is approximately 0.079 grams.

To determine the maximum mass of the water bug that avoids sinking, we need to consider the buoyant force acting on it. The buoyant force is equal to the weight of the water displaced by the bug.

Calculate the volume of water displaced:

The bug's weight is balanced by the buoyant force, so the volume of water displaced is equal to the volume of the bug.

Each leg has a length of 5 mm, which means the total height of the bug is 5 mm. Assuming the cross-sectional area of the bug is constant along its height, we can use the formula for the volume of a cylinder to calculate the volume:

Volume = π * radius^2 * height

Since each leg is cylindrical, the radius would be half the leg's diameter, which is 5 mm (or 0.005 m).

Therefore, the volume of water displaced by the bug is:

Volume = π * (0.005 m)^2 * 0.005 m

Calculate the weight of the water displaced:

The weight of the water displaced is equal to the buoyant force acting on the bug.

Weight of water displaced = density of water * volume of water displaced * acceleration due to gravity

The density of water is approximately 1000 kg/m³, and the acceleration due to gravity is approximately 9.8 m/s².

So, the weight of the water displaced is:

Weight of water displaced = 1000 kg/m³ * Volume * 9.8 m/s²

Calculate the maximum mass of the bug:

The maximum mass of the bug is the mass at which its weight equals the weight of the water displaced:

Maximum mass = Weight of water displaced / acceleration due to gravity

Maximum mass = (1000 kg/m³ * Volume * 9.8 m/s²) / 9.8 m/s²

Now, let's plug in the values and calculate the maximum mass of the bug:

python

import math

radius = 0.005  # in meters (5 mm)

height = 0.005  # in meters (5 mm)

density_water = 1000  # in kg/m³

acceleration_due_to_gravity = 9.8  # in m/s²

volume = math.pi * radius**2 * height

weight_of_water_displaced = density_water * volume * acceleration_due_to_gravity

maximum_mass = weight_of_water_displaced / acceleration_due_to_gravity

maximum_mass_grams = maximum_mass * 1000  # converting to grams

print("Maximum mass of the bug to avoid sinking:", maximum_mass_grams, "grams")

Using the above calculations, the maximum mass of the water bug to avoid sinking is approximately 0.079 grams.

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Answer: 39 hot dogs

M= 3 + half of C , E= 2 × M , C= 12

Step-by-step explanation:

M= 3 + (half of C=12÷2) 6= 9

E=2×9=18

total= 12 + 9 + 18= 39

Answer:

0.875

Step-by-step explanation:

you just divide 7 by 8, and you would get 0.875

7/8=0.875

The annual profits of the company Eve works for will increase by 25% every year. The annual profits in 3 years will be approximately $709,555.52.

The annual profits of the company Eve works for will increase by 25% every year. If the company makes $363,200 this year, we can calculate the annual profits in 3 years by applying the 25% growth rate.

To find the annual profits in 3 years, we need to multiply the current year's profits by \((1 + \text{growth rate})^{\text {number of years}\).

In this case, the growth rate is 25% or 0.25, and the number of years is 3.

So, the calculation would be:

Annual profits in 3 years = $363,200 * (1 + 0.25)³

To simplify the calculation, let's break it down step by step:

Step 1: Calculate the growth rate by adding 1 to the percentage growth rate: 1 + 0.25 = 1.25

Step 2: Raise the growth rate to the power of the number of years: 1.25³ ≈ 1.9531

Step 3: Multiply the current year's profits by the result of step 2: $363,200 * 1.9531 ≈ $709,555.52

Therefore, the annual profits in 3 years will be approximately $709,555.52.

Please note that rounding the answer to the nearest cent gives $709,555.52.

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Answer:

21x - 28

You would multiply 7 times 3x which is 21 x and then you would multiply 7 times -4 which is -28.

Answer:

erase when you make mistakes; cross it out so that you can still see ... 3. Width 5 15 inches. Length

Step-by-step explanation:

erase when you make mistakes; cross it out so that you can still see ... 3. Width 5 15 inches. Length

Power series representation for the function:

\(f(x)=x^8\tan (x^3)\)

\(f(x)=\Sigma_{n=0}^\infty(8n+2(n+1)xn+3)(x3)n=(\Sigma_{n=0}^\infty8n+2(n+1)x3n)xn+3\)

It can be written in the following form:

\(f(x)=\Sigma_{n=0}^\infty anxn\) Where, \(an=8n+2(n+1)x3n\)

Therefore, the power series representation for the given function is:

\(f(x)=x^8\tan⁡(x^3)=\Sigma_{n=0}^\infty(8n+2(n+1)xn+3)(x3)n\)

Given function,\(f(x)=19+x^2\\f(x)=\Sigma_{n=0}^\infty(19n+2(-2)nxn)\)

The power series representation of the function is:\(\Sigma_{n=0}^\infty anxn\) Where, \(an=19n+2(−2)n\)

Let's simplify it: \(an=19n+2(−2)n=19n+2×(−1)nn!2n!\)

Taking the absolute value of we get,\(|an|=19n+2n!2n!\)

If \(\lim_{n \to \infty} |an+1an|=L\), then the radius of convergence is:

R=1

\(\lim_{n \to \infty} |an+1an|= \lim_{n \to \infty} |21(n+1)(n+3)|=0\)

The radius of convergence is R=0, which implies that the series converges at x=0 only.

Now, let's calculate the interval of convergence:

In the given series, an is always positive, therefore, the series is an increasing function for positive x.

Therefore, the interval of convergence is [0,0].

Radius of convergence, R=0

Interval of convergence, [0,0]

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Answer:

x=8

Step-by-step explanation:

x^2 - 48 = 2x    

x^2 - 2x - 48=0

(x+6)(x-8)=0

x+6=0     x-8=0

x= - 6         x=8

can not be negative so the answer is x=8

Answer:

hi long time no talk we need to talk on padle* i left msgs

Step-by-step explanation:

Answer:

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

Make x the subject in steps below:

                                                                                                                                                                                                                                                                          I understand that you may be struggling with understanding how to evaluate a square root expression with a negative number under the square root. Let me explain it further:

A square root is a mathematical operation that returns the value of a number that, when multiplied by itself, equals the original number. For example, √4 = 2 because 2*2 = 4. However, when you try to take the square root of a negative number, it is not possible to get a real number. Therefore, the square root of a negative number is represented by the imaginary number "i" which is defined as the square root of -1. So, √(-98x5) = √(98x5)i

Please let me know if there's anything else I can help you with.

im tired right now but i can tell you a way to find the answer

the number you need the equation to equate to is 41

run 6×x-19, replacing 'x' with various numbers until it equates to 41

hope this helps

The representation which is most appropriate for showing the change in the average hourly wage is: A. scatter plot with the title average hourly wage and the x axis labeled years since 2016 and the y axis labeled hourly wage in dollars, with points at 0 comma 9, 1 comma 9 and a half, 2 comma 10, 3 comma 11, 4 comma 12, 5 comma 13, and 6 comma 14.

In this scenario, the years would be plotted on the x-axis (x-coordinate) of the scatter plot while the hourly wage would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the years and hourly wage, an equation for the line of best fit is given by:

y = 0.8571x + 8.6429

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The required amount of sugar is given as 40 grams.

Given that,
A new soft drink has 20% less sugar than before. The drink had 50 grams of sugar originally, how much less sugar it has now is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
According to the question,
The final amount of sugar = [1 - 0.02][50]
                                  = 40 grams

Thus, the required amount of sugar is given as 40 grams.

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