Select the correct answer. Which equation, when solved, gives 8 for the value of x? OA. +3 = =+14 OB. 5-9=31-12 OC. 21-2=r-4 OD. 5.-7=*=+14

The derivative of the given expression ln(x)cos(x) can be written as (cos(x))/x - sin(x)ln(x).

What is derivative?

In mathematics, the derivative of a function of a real variable measures how sensitive the function's value (or output value) is to variations in its argument (input value). The derivative is the fundamental tool in calculus. A measure of how quickly an object's position changes over time is its velocity, which is the derivative of that object's position with respect to time.

We can solve this derivation using multiplication property of derivatives:

i.e. [tex]\frac{d}{dx}(uv) = u\frac{dv}{dx} + y \frac{du}{dx}[/tex]

In the given question, lets consider ln(x) as u and cos(x) as v

putting the values from question.

[tex]\frac{d}{dx}(ln(x)cos(x)) = ln(x)\frac{d(cos(x))}{dx} + cos(x) \frac{d(ln(x))}{dx}[/tex]

[tex]= ln(x)(-sin(x)) + cos(x)(\frac{1}{x})[/tex]

= (cos(x))/x - sin(x)ln(x)

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Answer:

Step-by-step explanation:

Linear functions are represented by the following equation:

The slope of a line is given as;

(-4,-8) and (-8,-13):

Use the slope-point form of a line, to find the slope-intercept form:

Determine the total cost for 3 order of fries and 2 drinks.

Determine the expression for f orders of fries and d drinks.

So cost of 3 order of fries and 2 drinks is $4.9.

The cost order for f orders of fries and d drinks is 0.94f + 1.04d.

To solve 12x÷4y, first, let's evaluate the products on both sides of the ÷ symbol, we know that x = -8, then we have:

We have -96 on the left side of the ÷ symbol.

We know that y = 3, then, on the right side, we have:

Then, we have 12 on the right side of the ÷ symbol, now the expression looks like this:

-96 ÷ 12. what we have to do is to divide -96 by 12, then we get:

Then, the answer is 8

If we find the point X on the plane we can see the following:

Notice that the point D and the point X are 10 units apart with respect the x-axis, therefore, the point that is 10 units away from X is point D

To solve the problem, we notice that both of the equations are written with the y solved then we can equate the expressions of x and solve the resulting equation of x:

Once we have the value of x we plug it on the first equation to find y:

Therefore, the solution of the system of equations is (6,-6)

We need to think of something that will cool down 10 degrees in 5 hours to be more realistic. You may say that this graph describes the temperature profile of a fermentation broth after it is heated to 82 degrees is left on the tank to cool down to room temperature.

The graph of the line y [tex]=[/tex] -3x + 4 is a line that shows the set of all solutions to the equation , the correct option is (c) .

In the question ,

it is given that

the equation of the line is y [tex]=[/tex] -3x + 4 ,

we have to plot the line in the coordinate plane .

we plot the line ,w e need at least two points .

for the first point ,

for x = 0 , we have

y = -3(0) + 4

y= 0 + 4

y = 4

the first point is (0,4)

for the second point

for y = 0 , we have

0 = -3x + 4

-3x = -4

x = 4/3

the second point is (4/3 , 0)

so , from the graph plotted below , we can see that the line y [tex]=[/tex] -3x+4 shows the set of all solutions to the equations .

Therefore , The graph of the line y [tex]=[/tex] -3x + 4 is a line that shows the set of all solutions to the equation .

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Answer:

The correct option is option a.

$18.08 for 9 bottles is the better buy.

Explanation:

The best buy is the item with the lesser price tag.

Let us chech which of the given items has the lesser price tag.

a. $18.08 for 9 bottles of juice

Let us find how much one bottle costs.

1 bottle = 18.08/9

= 2.01

1 bottle of juice costs $2.01 approximately

b. $22.23 for 11 bottles of juice

1 bottle = 22.23/11

= 2.03

1 bottle of juice costs $2.03 approximately.

Comparing these prices per bottle of juice, we realise that the one with $18.08 for 9 bottles is the better buy.

Determine whether is a solution for:

For, x=-8, y has to be 3:

(-8, 3) is not a solution for the equation.

For x=-4, y has to be -1:

(-4, -1) is a solution for the equation.

For x=6, y has to be -7:

(6, -7) is a solution for the equation.

For x=7, y has to be 2

(7, 2) is not a solution for the equation.

6 + m = 12

A. This IS equivalent

6 + m - m = 12 - m ==> 6 = 12 - m ==> 6 + m = 12

B. This IS NOT equivalent

6 + m - 6 = 12 - 12 ==> m = 0

C. This IS equivalent

6 + m + 2 = 12 + 2 ==> 6 + m = 12

D. This IS equivalent

6 + m - 6 = 12 - 6 ==> m = 6 ==> 6 + m = 12

Answer:

B is not equivalent

Examples:

1. Five increased by four times a number

where n is the number

2.The product of 4, and a number decreased by 7

The mode is the number that appears most or occurs most frequently. Therefore, the mode of the data set below can be calculated below

Let's rearrange the data

The mode will be

The statement

41 increased by 4

The word increase mean adding to the given number 41

Hence,

The statement can be expressed as

Simplifying the result gives

Therefore, the answer is

The given equation is:

x^4-8x^3+5x^2+14x​

In this question, we have to find the zeros algebraically. Hence, we need to find the values of x that satisfy the equation.

Note: The roots (values of x) are equal to the power of the equation. Therefore, the given equation will have 4 roots

Therefore,

x^4-8x^3+5x^2+14x​ = 0

or

x(x^3-8x^2+5x+14​) = 0

=> x = 0 and x^3-8x^2+5x+14​ = 0

Therefore, the first root is x = 0.

Now,

x^3-8x^2+5x+14​ = 0

To simplify that, try putting different values of x (starting from 1 and -1). The value that makes both sides equal to zero would be the solution.

Let's start with (1):

For x = 1

(1)^3 - 8(1)^2 + 5(1) + 14 = 0

1 -8(1) + 5 + 14 = 0

-1 -8 +5 + 14 = 0

- 9 + 19 = 0

10 = 0

It is false, therefore, x = 1 is not the solution.

For x = -1

(-1)^3 - 8(-1)^2 + 5(-1) + 14 = 0

-1 -8(1) - 5 + 14 = 0

-1 -8 -5 + 14 = 0

- 14 + 14 = 0

0 = 0

hence, x = -1 is the second solution.

If x = -1 is the solution, (x + 1) should be the factor of x^3-8x^2+5x+14. Therefore, the whole equation can be divided by factor

x^3-8x^2+5x+14 / (x+1). = x^2 - 9x + 14. (using division)

Now, let's find the roots of x^2 - 9x + 14

x^2 - 9x + 14 = 0

x^2 - 7x - 2x + 14 = 0

x(x - 7) - 2 (x - 7) = 0

(x - 7) (x - 2) = 0

or

x - 7 = 0. and x - 2 = 0

x = 7 and x = 2

Therefore, the zeros of the given equation are, 0, -1, 2 and 7.

Net worth is equal to total assets minus total liabilities (debt).

So,

Total Assets = 253000

Total Liabilities = 216345

Hence,

Net Worth = 253000 - 216345 = $36,655

If the perimeter of the quadrilateral MNOP is x

And a scale factor of a dilated image is

If the perimeter of M'N'O'P' = y

Then

Cross multiplying,

The perimeter of M'N'O'P' = 7/8 x units

Option A is correct

we have that

44/13=3.38

rounded to the nearest tenths

3.38=3.4

Answer:

k-19

Step-by-step explanation:

If Alan had k baseball card and gave 19 away then he would have 19 less then k

Answer:

K - 19= X

Step-by-step explanation:

I hope this helps!

Let's begin by listing out the given information:

Loan (p) = $3,800

Time (t) = 8 months = 8/12 year

Interest rate (r) = 5.5%

a)

We calculate it thus:

b)

The amount paid in total is:

the first x value, when the y-value of the equation is greater than the y value of equation one, is x=15

Because the y-value of equation 2 with x=15 is 32771, while the y-value of equation 1 is 16875

Solution

The diagram below will be of help

From the image above

We know that the sum of angle in a triangle is 180 degrees

That is

Now, to find x

We also know that the sum of angle in a straight line is 180 degrees

That is

We now solve for x

Therefore, the value of x = 149 degrees

Option B

The area of right triangle is [tex]\frac{1}{15}[/tex].

The given coordinates are [tex](-2,-1), (1, 1), (3,-2)[/tex].

We have to find the area of right triangle.

To find the area we first draw the graph using that coordinate.

The graph of the coordinate is

To find the area we use the formula

[tex]\angle ABC=\frac{1}{2}(|AB|)(|AC|)[/tex]

We first find the value of [tex](|AB|)[/tex] and [tex](|AC|)[/tex].

e coordinate of [tex]A[/tex] is [tex](-2,-1)[/tex] and [tex]B[/tex] is [tex](1,1)[/tex].

The slope of [tex](|AB|)=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

The slope of [tex](|AB|)=\frac{1-(-1)}{1-(-2)}[/tex]

The slope of [tex](|AB|)=\frac{1+1}{1+2}[/tex]

The slope of [tex](|AB|)=\frac{2}{3}[/tex]

The coordinate of [tex]A[/tex] is [tex](-2,-1)[/tex] and [tex]C[/tex] is [tex](3,-2)[/tex].

The slope of [tex](|AC|)=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

The slope of [tex](|AC|)=\frac{(-2)-(-1)}{3-(-2)}[/tex]

The slope of [tex](|AC|)=\frac{-2+1}{3+2}[/tex]

The slope of [tex](|AC|)=-\frac{1}{5}[/tex]

Now finding the area of right triangle by putting the values.

[tex]\angle ABC=\frac{1}{2}\times\frac{2}{3} \times(-\frac{1}{5})[/tex]

Area can't be negative so

[tex]\angle ABC=\frac{1}{2}\times\frac{2}{3} \times\frac{1}{5}\\\angle ABC=\frac{2}{30}\\\angle ABC=\frac{1}{15}[/tex]

Hence, the area of right triangle is [tex]\frac{1}{15}[/tex].

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Given:

The ratio of men to women = 5: 4

Total number of employees = 225

The total ratio is:

The number of women is the ratio of women to the total ratio times the number of employees

Answer:

100 women

there are 12 questions

I got 7 right

the easiest way to solve this is by using a rule of three

Step 1

Let

then

Step 2

do the relation and solver for x

so, you did the 58.33 %

Let's set d as the age of Davon and m as the age of Milan.

Devon is 30 years old than his son Milan, it is represented by the equation:

The sum of both ages is 56, the equation that represents the situation is:

To find Devon's age, in equation 1, solve for m in terms of d:

Now, replace in equation 2 and solve for d:

Devon is 43 years old.

We are given the following information:

Table sides = 36 inches & 18 inches

Diagonal of table = 43 inches

We are to find out if the table is "square" (that is if the table follows the Pythagoras theorem). We will check this below:

Therefore, the table is not "square" (it does not have right angles at the corners)

So,

The line:

Is a good fit of the data given.

To predict the number of bachelor's degrees in Mississippi, we replace x by 40.6 and operate:

The number of bachelor's degrees per 1000 people when x=40.6 median income, is predicted as 228.778.

the option D is the correct answer

the equation is

y = 35x +180

that means he started with 180 $ and his monthly subscription is 35 $.

The practical domain is 1 ≤ x ≤ 20 and the practical range is 13.61 ≤ C(x) ≤ 127.61

From the question, the given parameters are:

The domain is dependent on the number of windows washed

Using the maximum as a guide, the minimum number of windows could be

Minimum = 1

The domain is then represented as

Minimum ≤ x ≤ Maximum

So, we have

1 ≤ x ≤ 20

Using the given parameters in (a), we have

Total cost, C = Charges * Number of windows + Reservation

So, we have

C(x) = 7.61 + 6x

Where x is the number of windows

When x = 0, we have

C(1) = 7.61 + 6(1)

C(1) = 13.61

When x = 20, we have

C(20) = 7.61 + 6(20)

C(20) = 127.61

So, we have the range to be 13.61 ≤ C(x) ≤ 127.61

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