what is the exponential form for 7^√x^3

The simplified form of the function is 3/2 [\(x^{5} - 1/x^{5}\)] .

Given,

f(x) = 3sinh(5lnx)

Now,

sinhx = \(e^{x} - e^{-x} / 2\)

Substituting the values,

= 3sinh(5lnx)

= 3[ \(e^{5lnx} - e^{-5lnx}/2\) ]

Further simplifying,

=3 \([e^{lnx^5} - e^{lnx^{-5} } ]/ 2\)

= 3[\(x^{5} - x^{-5}/2\)]

= 3/2[\(x^{5} - x^{-5}\)]

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

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Complete question :

f(x) = 3sinh(5lnx)

The quadratic expression 10x² + 17x + 3 when divided by (5x + 1) gives 2x + 3.

Given quadratic expression is,

10x² + 17x + 3

We have to divide the polynomial with 5x + 1.

First let us factorize the given quadratic expression.

10x² + 17x + 3

Discriminant = 17² - (4 × 10 × 3) = 169

x = (-17 ± √169) / 20

x = (-17 ± 13) / 20

x = -4/20 and x = -30/20

x = -1/5 and x = -3/2

This can be factored as,

(x + 1/5) (x + 3/2)

(5x + 1) (2x + 3)

Hence the quotient is 2x + 3.

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Answer:

-12

Step-by-step explanation:

The slope formula is y2-y1 divided by x2-x1

I plugged it in and got

-12

The least number of arc measures needed to determine the measures of each angle in the inscribed quadrilateral is 2.

To determine the measures of each angle in the quadrilateral, we need to find the central angles of the arcs that intersect the quadrilateral's vertices. Since the quadrilateral is not a rectangle, it is not a cyclic quadrilateral, which means that its opposite angles do not add up to 180 degrees.

Therefore, we need to use the fact that the sum of the measures of the opposite angles in an inscribed quadrilateral is 360 degrees. Let the angles of the quadrilateral be A, B, C, and D, with opposite angles A and C, and B and D. We can find the measure of arc AC by drawing a chord connecting the endpoints of AC and finding the central angle that intercepts it. Similarly, we can find the measure of arc BD.

Now, we can use the fact that the sum of the central angles that intercept arcs AC and BD is equal to 360 degrees. Let these angles be x and y, respectively. Then, we have:

x + y = 360

We can solve for one of the variables, say y, in terms of the other:

y = 360 - x

Substituting this into the equation for arc BD, we have:

2x + 2(360 - x) = arc BD

Simplifying this equation, we get:

arc BD = 720 - 2x

Now, we can use the fact that the sum of the measures of angles A and C is equal to the measure of arc AC, and the sum of the measures of angles B and D is equal to the measure of arc BD. Therefore, we have:

A + C = arc AC
B + D = arc BD = 720 - 2x

We need to find the least number of arc measures needed to determine the measures of A, B, C, and D. Since we have two equations and two variables (x and A), we can solve for both variables. Then, we can use the equations for B and D to find their measures.

Solving for A in terms of x, we have:

A = arc AC - C
A = 360 - x - C

Substituting this into the equation for B + D, we have:

(360 - x - C) + B + D = 720 - 2x

Simplifying this equation, we get:

B + D = 360 + x - C

Now, we have three equations and three variables (x, A, and C). We can solve for each variable in terms of x, and then use the equation for B + D to find their measures.

Therefore, the least number of arc measures needed to determine the measures of each angle in the quadrilateral is two: arc AC and arc BD.

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Answer:

To find the solutions to this system of equations, we need to set f(x) equal to each other and solve for x.

x² - 2x - 15 = -x - 9

Simplifying and solving for x, we get:

x² - x - 6 = 0

Factoring the left side, we get:

(x - 3)(x + 2) = 0

So, the solutions are x = 3 and x = -2.

To find the corresponding y values, we can plug these x values back into either of the original equations. Using f(x) = x² - 2x - 15, we get:

f(3) = 3² - 2(3) - 15 = -3

f(-2) = (-2)² - 2(-2) - 15 = -9

Therefore, the ordered pair solutions for the system of equations are (3, -3) and (-2, -9).

Substituting this value into the exponential equation, we can represent the growth for Ingrid's business. k = ln(25) / 3.

Our current growth rate is k. When this quantity is substituted into the exponential equation,

We may use the standard exponential equation to illustrate Ingrid's company's exponential growth:

P(t) = P₀ *\(e^{(kt)\),

, where P(t) is the population or the number of employees at time t, P0 is the starting population or the number of employees, e is the natural logarithm's base (about 2.71828), k is the growth rate, and t is the amount of time in years.

Ingrid had 2 employees when she began her business in 2000 (t = 0), and she had 50 employees in 2003 (t = 3), therefore we can enter these numbers into the equation to determine the growth rate, k.

Using P0 = 2 and P(3) = 50, we have

50 = 2 * \(e^{(3k)\).

Dividing both sides by 2:

25 = \(e^{(3k).\)

Taking the natural logarithm (ln) of both sides to isolate the exponent:

ln(25) = 3k.

At last, we find k: k = ln(25) / 3.

Our current growth rate is k. This amount can be used to indicate the growth of Ingrid's company in the exponential equation.

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Answer:C

Step-by-step explanation:45

Answer:

Step-by-step explanation:

The slopes of both those lines are the same so there is no solution. Use slope triangles to find out the slope. They are both 1/4.

A. No solution

y = 1/4x+5

x - 4y = 4

You can simplify the second equation into y = 1/4x - 1

Since these equations both have the same slope, they are parallel. When two lines are parallel, they have no solutions.

The constraint(s) to ensure that the ratio of 3 bedroom rentals to 2 bedroom rentals is no more than 4 to 1 is:

3X3 <= 4X2

This constraint states that the number of 3 bedroom rentals (X3) must be less than or equal to four times the number of 2 bedroom rentals (X2). This ensures that the ratio of 3 bedroom rentals to 2 bedroom rentals does not exceed 4 to 1.

For example, if there are 10 2 bedroom rentals (X2), the constraint would be:

3X3 <= 4(10)
3X3 <= 40

This means that the number of 3 bedroom rentals (X3) cannot exceed 40.

The constraint to ensure the ratio of 3 bedroom rentals to 2 bedroom rentals is no more than 4 to 1 is 3X3 <= 4X2.

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Approximate length of the diameter, d is 14 inches with circle circumference of approximately 44 inches. So, correct answer is option(b).

It is defined as the total length of the arc of circle. It is also known as perimeter i.e the boundary distance. Formula for it is equals to C = 2πr

We have , Circumference of circle , C = 44 inches

we have to calculate the length of its diameter , d . Let "r inches" be radius of circle with diameter length "d inches" . As we know, diameter is longest chord of circle and it's length is 2 times of radius of Circle i.e d = 2r --(*)

Now, the circumference of circle, C = 2πr

where r --> radius of circle

π---> special constant or π = 3.14

=> 44 inches = 2 πr

=> 44 = 2×3.14×r

=> 44 = 6.28 × r

=> r = 44/6.28 = 7.001 ~ 7

from equation (1) , d = 2×7 = 14 inches

Hence, the diameter of circle is 14 inches.

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Answer:

42/55

Step-by-step explanation:

4/11+2/5  LCD=55

20/55+22/55

42/55

Answer:

B

Step-by-step explanation:

calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (2, - 1) and (x₂, y₂ ) = (- 4, 11) ← 2 ordered pairs from the table

m = \(\frac{11-(-1)}{-4-2}\) = \(\frac{11+1}{-6}\) = \(\frac{12}{-6}\) = - 2

The area of triangle ABC is equal to the area of parallelogram GHJK.  (option c).

To begin with, we need to understand the formula for finding the area of a triangle and a parallelogram. The area of a triangle is given by the formula:

Area of triangle = 1/2 × base × height

where the base and height are perpendicular to each other. The area of a parallelogram is given by the formula:

Area of parallelogram = base × height

where the base and height are perpendicular to each other.

Now, let's look at the problem. We are given four answer choices, and we need to choose the correct one based on our understanding of the area formulas.

Option (c) states that the area of triangle ABC is equal to the area of parallelogram GHJK. This is also possible if the base and height of the triangle are equal to the base and height of the parallelogram, respectively. In this case, the area of the triangle would be half the area of the parallelogram. So, option (c) could also be correct.

Therefore, we need more information to determined that (c) is correct.

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Complete Question:

How does the area of triangle ABC compare to the area of parallelogram GHJK?

a) The area of △ABC is 2 square units greater than the area of parallelogram GHJK.

b) The area of △ABC is 1 square unit greater than the area of parallelogram GHJK.

c) The area of △ABC is equal to the area of parallelogram GHJK.

d) The area of △ABC is 1 square unit less than the area of parallelogram GHJK.

The conditional distribution of X given that the first two tosses both land Heads is:

P(X = 0 | HH) = 1

P(X = 1 | HH) = 2

P(X = 2 | HH) = 0

Given that the first two tosses both land Heads, the sample space is reduced to {HH, HT}. Therefore, X can take values 0, 1, or 2, with respective probabilities P(X = 0 | HH) = P(X = 0, HH) / P(HH), P(X = 1 | HH) = P(X = 1, HH) / P(HH), and P(X = 2 | HH) = P(X = 2, HH) / P(HH).

We have:

Probability of getting two heads in a row = P(HH) = 1/2 × 1/2 = 1/4

Probability of getting one head and one tail = P(HT) = 1/2 × 1/2 = 1/4

Now, if the first two tosses are both Heads, then we can only get the following: HH. Thus, the distribution of X is:

X = 0:

- Only one way, P(X = 0, HH) = 1/4

- Hence P(X = 0 | HH) = (1/4) / (1/4) = 1

X = 1:

- Only one way, P(X = 1, HH) = 2/4 = 1/2

- Hence P(X = 1 | HH) = (1/2) / (1/4) = 2

X = 2:

- No way, P(X = 2, HH) = 0

- Hence P(X = 2 | HH) = 0

Thus, the conditional distribution of X given that the first two tosses both land Heads is:

P(X = 0 | HH) = 1

P(X = 1 | HH) = 2

P(X = 2 | HH) = 0

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Answer:

148

Step-by-step explanation:

(12×12)+7-3

144+7-3

151-3

148

Answer:

Step-by-step explanation:

First do the operation inside the parenthesis

(12*12) + 7 - 3 = 144 + 7 - 3

                     = 151 - 3

                     = 148

Answer: 144 ft

Step-by-step explanation:

352/22=16 16*9=144=length 16*2=32=width

Answer:

144 feet

Step-by-step explanation:

The ratio is 9:2 so if you add the ratio and multiply it by two because there are four sides NOT two so then you get twenty-two. Divide 352 by 22 and you get 16 now multiply nine by sixteen because you are trying to find the length.

Answer:

16.64911

Step-by-step explanation:

Answer:

area of the regular pyramid is =T.S.A=12pl+B is the formula for this question

If a measurement was not sensitive, and resulted in everyone scoring high, then this is called a ceiling effect

Given,

Ceiling effect;-

When a large percentage of study participants get the highest scores on the observable variable, it is said that a ceiling effect has occurred. Discrimination between subjects at the top end of the scale is therefore impossible. For instance, a test could result in, say, 50% of the students receiving a perfect score.

Here,

To be able to measure participant differences, variables must be measured with sufficient sensitivity. However, if a test was insensitive and everyone received good scores, this is known as ceiling effect

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Answer:

Step-by-step explanation:

The next step in the construction is Aaron should Use the compass to find the perpendicular bisector for side.

What is the bisector about?

A bisector is known to be a kind of straight line that cut or divide an angle or a line segment.

Note that The next step in the construction is Aaron should Use the compass to find the perpendicular bisector for side as it is the right step to take.

The correct answer to this question is letter b.There are only three steps in constructing a circle circumscribed by a triangle. He is done with the first step.  Use the compass to find the perpendicular bisector for side DF. I hope I have helped you.

The correct answer is option b. 1/36 is the expected value (Lesson 8.3: Unbiased Point Estimation. If X1, of the sample variance S2.

In unbiased point estimation, the expected value of the sample variance S2 is a crucial idea. When a sample is drawn from a population repeatedly, an average value of S2 is what is anticipated.

The population variance divided by the sample size represents the expected value of S2. It is, in other words, the population variance divided by n-1, where n is the sample size.

As a result, the expected value of the sample variance S2 for a sample size of 6 is equal to 1/36.

As a result, when a sample is drawn from a population repeatedly, the average value of S2 will be equal to 1/36 of the variance in the population.

Complete Question:

What is the expected value (Lesson 8.3: Unbiased Point Estimation. If X1, of the sample variance S2?

a. 1/6

b. 1/36

c. 6

d. 36

e.60

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Answer:

False

Step-by-step explanation:

The hypotenuse is not either of the two legs but is opposite of the right angle.

The air pressure at the peak of Mount Marcy is approximately 164.17 pascals.

Air pressure, also known as atmospheric pressure, is the force exerted by the weight of the Earth's atmosphere on any given surface. It is the weight of the column of air that extends from the Earth's surface up to the top of the atmosphere.

The Pascal (symbol: Pa) is the SI (International System of Units) unit of pressure, named after the French mathematician and physicist Blaise Pascal. One pascal is defined as the pressure exerted by the force of one Newton on an area of one square meter. In other words, 1 Pa = 1 N/m².

We are given the formula that relates the altitude (a) and the atmospheric air pressure (P):

a = 15,500 (5 - log₁0 P)

We are also given that the altitude at the peak of Mount Marcy is 1629 meters. We can use this information to find the atmospheric air pressure at the peak of Mount Marcy by plugging in a = 1629 and solving for P:

1629 = 15,500 (5 - log₁0 P)

Dividing both sides by 15,500, we get:

(5 - log₁0 P) = 1629 / 15,500

Subtracting 5 from both sides, we get:

-log₁0 P = (1629 / 15,500) - 5

Simplifying the right-hand side, we get:

-log₁0 P = -1.5454

Taking the inverse logarithm (base 10) of both sides, we get:

P = 10⁻¹.⁵⁴⁵⁴

Using a calculator, we can evaluate this expression to get:

P ≈ 164.17 pascals

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Answer:

B

Step-by-step explanation:

If we reorder the equation in a certain way then it will look like this:

y-4=1/2(x-6)

y-4=1/2x-3

y-1=1/2x

y=1/2x+1

therefore B is correct since we reduced the equation to y=1/2x+1.

It may be hard to understand but the question is basically asking which one of these answers is equal to y.

Hope this helped you and let me know if i messed up or if im correct so i can imporve from my mistakes

Answer:

11/20

Step-by-step explanation:

do BEDMAS

The reason why plant roots would take in water after a plant converts 1, 000 Sucrose molecules to 2, 000 glucose molecules.

Sucrose is turned into glucose by plants because glucose is more useful to plant processes than glucose.

The equation for this is:
sucrose + water → glucose + fructose

This means that if a plant should turn 1, 000 Sucrose molecules to 2, 000 glucose molecules, it would have used water to do this. This water needs to be replenished so the plant roots will take in more water.

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Using translation concepts, the series of transformations that shows that pentagon A is congruent to pentagon B is:

B. Rotate pentagon A 90° clockwise about the point (1, 1), reflect it over the x-axis, and translate it 3 units to the left.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

In this problem, we have that the Pentagons have different orientations, meaning that it was rotated, eliminating options A and D.

For the vertices to reach the position they reached in Pentagon B, there had to be a shift left, and before the shift left, the Pentagon must have been entirely at the fourth quadrant, meaning that it was reflected about the point (1,1), and option B is correct.

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Answer:

The equation for a circle is ( x - h )^2 + ( y - k )^2 = r^2, where h, k, is the center and r is the radius.

So, in this case: the center is (-1, 5) and the radius is 2.

Let me know if this helps!

we have that

if a function has vertical asymptotes

then

The function is not continuous

Example

f(x)=1/x

The function has a vertical asymptote at x=0

The domain is the interval (-infinite,0) U (0, infinite)

The value of x=0 is not included in the domain

therefore

The function is not continuous

The linear equation for the line passing through the points (0, 9) and (13, 61) can be found using the slope-intercept form, which is y = 4x + 9, where 4 represents the slope and 6 represents the y-intercept.

To find the slope of the line, we use the formula:

m = (y2 - y1) / (x2 - x1)

Using the coordinates of the given points, we have:

m = (61 - 9) / (13 - 0) = 52 / 13 = 4

Now that we have the slope, we can determine the y-intercept, b, by substituting the values of one of the points into the slope-intercept form and solving for b. Let's use the point (0, 9):

9 = 4(0) + b

b = 9

Therefore, the linear equation for the line passing through the points (0, 9) and (13, 61) is:

y = 4x + 9

This equation represents a straight line where the y-coordinate is equal to four times the x-coordinate plus nine.

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