HELP SUMMER ALGEBRA 2! the rest of the answer d is numerator and denominator of both fractions
​

Therefore, the derivative of e^(sin(x)) * \(e^{x}\) is \(e^{x}\) * \(e^{sinx}\)* (cos(x) + 1), which we have found from first principles using the product rule.

In mathematics, a derivative is a measure of how a function changes as its input changes. It is the rate at which the function is changing at a particular point.

More specifically, the derivative of a function f(x) at a point x0 is defined as the limit of the difference quotient (f(x) - f(x0)) / (x - x0) as x approaches x0, provided this limit exists. This limit is denoted by f'(x0), which is read as "f prime of x0".

Geometrically, the derivative of a function at a point represents the slope of the tangent line to the graph of the function at that point.

The concept of derivatives is essential in calculus and is used in many fields of science, engineering, economics, and finance. They are used to find rates of change, optimize functions, and model physical phenomena.

We can use the product rule of differentiation to find the derivative of \(e^{sinx}\) * \(e^{x}\):

Let f(x) = \(e^{sinx}\) and g(x) = \(e^{x}\)then the product rule states that:

(f(x) * g(x))' = f(x)' * g(x) + f(x) * g(x)'

Now we find the derivatives of f(x) and g(x):

f(x) = \(e^{sinx}\), so, f'(x) = cos(x) * e^(sin(x))

g(x) =\(e^{x}\), so, g'(x) = \(e^{x}\)

Therefore, the derivative of \(e^{sinx}\) * \(e^{x}\)is:

(f(x) * g(x))' = \(e^{sinx}\) * \(e^{x}\))'

= f'(x) * g(x) + f(x) * g'(x)

= cos(x) * \(e^{sinx}\) * \(e^{x}\) + \(e^{sinx}\) * \(e^{x}\)

Simplifying this expression gives:

(\(e^{sinx}\)) * \(e^{x}\))' = \(e^{x}\) * \(e^{sinx}\)* (cos(x) + 1)

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The value of x is 6.

What is system of linear equations?

A collection of one or more linear equations involving the same variables is known as a system of linear equations in mathematics. For instance, the system of three equations 3x + 2y - z = 1, 2x - 2y + 4z = -2, -x + y - z = 0 has the three variables x, y, and z.

A collection of one or more linear equations involving the same variables is known as a system of linear equations (or linear system) in mathematics.

Graphically, a system of linear equations that has no solution indicates two parallel lines-that is, two lines that have the same slope but different y-intercepts.

To have the same slope, the x-and y-coefficient must be the same.

To get from -2/3 to -8 you multiply by 12, so multiply  -1/2x by 12 as well to yield 6x.

Because the other x-coefficient is a, it must be that a = 6  and (D) is correct.

Note that, even though it is more work, you could also write each equation in slope-intercept form and set the slopes equal to each other to solve for a.

Hence, the value of x is 6.

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Answer:

5.78571428571

Step-by-step explanation:

9/7 = 1.28571428571

9/2 = 4.5

And if you add it you get 5.78571428571

hopes this helps..

The last expression finally simplifies to cot β + tan α using quotient identity in trigonometric identities.

We want to verify the trigonometric  identity;

cos (α - β)/(cos α sin β) = cot β + tan α

Now, according to trigonometric identities in mathematics, we know that;

cos (α - β) = (cos α cos β) + (sin α sin β)

Thus, plugging that back into our left hand side of the main question gives;

[(cos α cos β) + (sin α sin β)]/(cos α sin β)

Rewriting this expression by separating the denominator gives;

[(cos α cos β)/(cos α sin β)] + [(sin α sin β)]/(cos α sin β)

Using quotient identities, this can be simplified to;

cot β + tan α

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Answer:

See Explanation

Step-by-step explanation:

The question has mission options; However, the question is still solvable.

Given

\(A = \{a,b,c\}\)

\(B = \{3,4,5,6\}\)

Required

Determine possible ordered pairs of A to B

A function is of the form (x,y)

Let A be the range of the function and B, the domain

Let (x,y) be a function of A to B, where x represents any of the values in A sets and y represents any of the values in B

A ordered pair can only be regarded as a function if and only if it has unique y-values

Hence, a possible ordered pair is:

\((A,B) = \{(a,3),(b,4),(c,5)\}\)

Another possible ordered pair is

\((A,B) = \{(a,4),(b,5),(c,6)\}\)

Note that there as as many as possible ordered pair as long as the y-values are unique

There are many possible ordered pair as long as the y-values are unique.

           Given that, A = {a, b, c} and B = {3, 4, 5, 6}

           Order pair may be,

               \((a,3),(b,4),(c,5)\)

    May be,   \((a,6),(b,5),(c,4)\)

There are many possible ordered pair as long as the y-values are unique.

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\( \sf \longrightarrow \: 5 \bigg( \: n - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{n}{1} - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10 \times n - 1 \times 1}{1 \times 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10n - 1}{ 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: \frac{50n - 5}{ 10} = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =1(10) \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =10 \\ \)

\( \sf \longrightarrow \: \: 100n - 10=10 \\ \)

\( \sf \longrightarrow \: \: 100n =10 + 10\\ \)

\( \sf \longrightarrow \: \: 100n =20\\ \)

\( \sf \longrightarrow \: \:n = \frac{2 \cancel{0}}{10 \cancel{0}} \\ \)

\( \sf \longrightarrow \: \:n = \frac{1}{5} \\ \)

Answer:-

To solve the equation \(\sf 5(n - \frac{1}{10}) = \frac{1}{2} \\\) for \(\sf n \\\), we can follow these steps:

Step 1: Distribute the 5 on the left side:

\(\sf 5n - \frac{1}{2} = \frac{1}{2} \\\)

Step 2: Add \(\sf \frac{1}{2} \\\) to both sides of the equation:

\(\sf 5n = \frac{1}{2} + \frac{1}{2} \\\)

\(\sf 5n = 1 \\\)

Step 3: Divide both sides of the equation by 5 to isolate \(\sf n \\\):

\(\sf \frac{5n}{5} = \frac{1}{5} \\\)

\(\sf n = \frac{1}{5} \\\)

Therefore, the solution to the equation \(\sf 5(n - \frac{1}{10})\ = \frac{1}{2} \\\) is \(\sf n = \frac{1}{5} \\\), which corresponds to option (d).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

Step-by-step explanation:

$100x0.5x1=$5

Answer:

y ≥ 2/15

HOPE THIS HELPS :)

ANSWERS TO THE WHOLE QUIZ:

1. 13.23

2. 1/2

3. 0.25

4. 31.16

5. 76.50

Your Welcome and have a great day!

( I had to fail the quiz to give the answers)

Answer:

Use distributive property and divide each term as follows:

Answer:

? = 77°

Step-by-step explanation:

the 3 angles in a triangle sum to 180° , that is

? + 35° + 68° = 180°

? + 103° = 180° ( subtract 103° from both sides )

? = 77°

Answer:77

Step-by-step explanation:

180-103=77

The function of the sequence -4,-6,-9,-27/2,-81/2 is f(n) = -4(3/2)^(n - 1)

from the question, we have the following parameters that can be used in our computation:

-4,-6,-9,-27/2,-81/2

The above sequence is a geometric sequence

This is because it has a common ratio calculated as

r = -6/-4

So, we have

r = 3/2

The sequence is then represented as

f(n) = ar^n-1

So, we have

f(n) = -4(3/2)^(n - 1)

Hence, the function is f(n) = -4(3/2)^(n - 1)

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Answer:

A. There are 8 seventh grade students

B. There are 14 total questions on the test

Step-by-step explanation:

To show that the angle bisector of an equilateral triangle is perpendicular to the base​, we can assume an equilateral triangle with sides ABC. Next, we can get an angle bisector in the middle represented by BD which becomes perpendicular to the base BC.  

After getting the angle bisector, we would see that the line segment BD, divides angle BAC into two equal angles, each measuring 30 degrees. Now, we can draw a perpendicular line from point D to the base BC.

We could also draw a line E, which is the perpendicular line that intersects the base BC. We want to show that BD is perpendicular to BC, which means we need to show that angle BDE is a right angle.

Since the sum of angles BDA and ADE is 90 degrees (they form a right angle), and the sum of angles BAD, ABD, and BDA is 180 degrees, it follows that angle BDE must be a right angle.

Therefore, we have shown that the angle bisector of an equilateral triangle is perpendicular to the base.

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Answer:

the 2nd option is correct.

Step-by-step explanation:

Hope you have a great day!

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Answer:

It is B

Step-by-step explanation:

All it is asking is what times itself equals 64, 8*8 equals 64 and -8*-8 equals 64 so therefore it is line B, if you want to learn this better by yourself just look at the numbers and ignore the letters, it makes it less scary. Please mark brainlest.

Answer:

Step-by-step explanation:

The events are not independentd) The events are not mutually exclusiveStep-by-step explanation:Hi!Lets call: Gar = {homes with garage}Pool

y = -x - 2

To check if an ordered pair is a solution to the equation, we have to replace the value of one variable and compute the other variable, as follows:

x = 1

y = -1 - 2

y = -3

Then, (1, -3) is a solution to the equation

x = -2

y = -(-2) - 2

y = 2 - 2

y = 0

Then, (-2, 0) is a solution to the equation

x = 4

y = -4 - 2

y = -6

Then, (4, -1) is not a solution to the equation

x = 0

y = -0 - 2

y = -2

Then, (0, 2) is not a solution to the equation, and (0, -2) is a solution to the equation

Given:

The sixth term of an arithmetic sequence is

The twelfth term is

To find:

The common difference

Explanation:

The nth term formula of an arithmetic sequence is,

So, the sixth and twelfth terms become,

Subtract (1) from (2),

Thus, the common difference is,

Final answer:

The common difference is,

To calculate the monthly lease payment, we need to use the formula:

Monthly Payment = Depreciation + Finance Charge

The depreciation represents the portion of the car's value that is lost during the lease period, while the finance charge is the interest charged on the lease.

First, let's calculate the depreciation:

MSRP = $51,500

Residual Value = 49% of MSRP = 0.49 x $51,500 = $25,235

Depreciation = (Negotiated Price - Residual Value - Down Payment) / Lease Term

Depreciation = ($49,000 - $25,235 - $4,000) / 36 = $541.53

Next, let's calculate the finance charge:

Lease Balance = (Negotiated Price - Down Payment) - Residual Value

Lease Balance = ($49,000 - $4,000) - $25,235 = $19,765

Money Factor = Annual Interest Rate / 2400

Money Factor = 7.8% / 2400 = 0.00325

Finance Charge = Lease Balance x Money Factor

Finance Charge = $19,765 x 0.00325 = $64.26

Finally, we can calculate the monthly payment:

Monthly Payment = Depreciation + Finance Charge

Monthly Payment = $541.53 + $64.26 = $605.79

Therefore, the monthly lease payment is $605.79.

Answer:

the solution to the system of equations is (x, y) = (3, -2).

Step-by-step explanation:

y = -2x + 4 (Equation 1)

y = x - 5 (Equation 2)

To solve for x, we can equate the right sides of the equations:

-2x + 4 = x - 5

Now, we can solve for x:

-2x - x = -5 - 4

-3x = -9

x = (-9) / (-3)

x = 3

Substituting the value of x back into Equation 2, we can solve for y:

y = 3 - 5

y = -2

Answer:

$166.75

Step-by-step explanation:

look at the photo.

Hope this helps. Please mark me brainliest!

Answer:

I took the time to graph the image onto the image that you had used, I hope this helps! <3

Step-by-step explanation:

Dilating by 1/2, is a contraction, it makes the pre-image smaller than the image.

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Step-by-step explanation:

31 + 6x + x + 16 = 180

7x + 47 = 180

7x = 180 - 47

x = 133/7

x = 19

Answer:

B. The limits Lim x-->7 (x²-9x+14)/x-7  and  lim x--> 7 (x-2) equals the same number when evaluated using direct substitution. The limit of both functions is 5

Step-by-step explanation:

Find the complete question in the attachment.

Given the limit of the functions

Lim x-->7 (x²-9x+14)/x-7

To solve this, we will need to factorize the quadratic function at the numerator first.

x²-9x+14

= x²-2x-7x+14

= x(x-2)-7(x-2)

= (x-7)(x-2)

The expression therefore becomes:

= lim x-->7 (x-7)(x-2)/x-7

= lim x-->7 (x-2)

Now substitute the value of x into the simplified function

lim x-->7 (x-2) = 7-2

lim x-->7 (x-2) = 5

Hence Lim x-->7 (x²-9x+14)/x-7 = 5

From the calculation above, it can be seen that Lim x-->7 (x²-9x+14)/x-7 = lim x--> 7 (x-2) = 5

Hence the correct answer based on the explanation above is B.

The limits Lim x-->7 (x²-9x+14)/x-7  and  lim x--> 7 (x-2) equals the same number when evaluated using direct substitution.

Answer:

A, .54

Step-by-step explanation:

The number line ranges from .542 up until .611, giving you three options below. For .6, it can be translated into .600 which is in bounds of the number line. Next for .604, it is still in bounds of the number line. For .54 it would be translated to .540 which is not in bounds, being before .542.

Answer:

27

Step-by-step explanation:

322415154551

Answer:

Step-by-step explanation:

Just simply add 57 to 35.

57+35=92