[tex]\lim_{x \to 0 (\frac{x(x-2)}{2-2e^2x} )[/tex]
Help evaluting this limit

Answer:

x=70, y=55

Step-by-step explanation:

Since the angle "y" and 2x-15 form a straight line, that means the sum of the angles, must be 180 degrees.

So using this we can derive the equation: [tex]y+2x-15=180[/tex]

The next thing you need to know is that the sum of interior angles of a triangle is 180 degrees, so if we add all the angles, we should get 180.

So using these we can derive the equation: [tex]x+2y=180[/tex]

So, in this case we simply have a systems of equations. We can solve this by solving for x in the second equation (sum of interior angles), and plug that into the first equation.

Original Equation:

[tex]x+2y = 180[/tex]

Subtract 2y from both sides

[tex]x = 180-2y[/tex]

Now let's plug this into the first equation

[tex]y+2x-15=180[/tex]

Plug in 180-2y as x

[tex]y+2(180-2y)-15=180[/tex]

Distribute the 2

[tex]y+360-4y-15=180[/tex]

Combine like terms

[tex]-3y + 345 = 180[/tex]

Subtract 345 from both sides

[tex]-3y = -165[/tex]

Divide both sides by -3

[tex]y=55[/tex]

So we can plug this into either equation to solve for x

[tex]x+2y=180[/tex]

Substitute in 55 as y

[tex]x+2(55)=180[/tex]

[tex]x+110=180[/tex]

Subtract 110 from both sides

[tex]x=70[/tex]

Answer:

  x = 70°

  y = 55°

Step-by-step explanation:

The angle sum theorem and the definition of a linear pair can be used to write two equations in the two unknowns. Those can be solved for the angle values.

  x + y + y = 180° . . . . . . angle sum theorem

  y + (2x -15) = 180° . . . . definition of linear pair

We can use the first equation to write an expression for x that can be substituted into the second equation:

  x = 180 -2y

  y +(2(180 -2y) -15) = 180 . . . . substitute for x

  345 -3y = 180 . . . . . . . . . . . collect terms

  115 -y = 60 . . . . . . . . . . . . .divide by 3

  y = 55 . . . . . . . . . . . . . . add (y-60)

  x = 180 -2(55) = 70

The values of the variables are ...

  x = 70°

  y = 55°

  exterior angle = 125°

4. Compute the derivative.

[tex]y = 2x^2 - x - 1 \implies \dfrac{dy}{dx} = 4x - 1[/tex]

Find when the gradient is 7.

[tex]4x - 1 = 7 \implies 4x = 8 \implies x = 2[/tex]

Evaluate [tex]y[/tex] at this point.

[tex]y = 2\cdot2^2-2-1 = 5[/tex]

The point we want is then (2, 5).

5. The curve crosses the [tex]x[/tex]-axis when [tex]y=0[/tex]. We have

[tex]y = \dfrac{x - 4}x = 1 - \dfrac4x = 0 \implies \dfrac4x = 1 \implies x = 4[/tex]

Compute the derivative.

[tex]y = 1 - \dfrac4x \implies \dfrac{dy}{dx} = -\dfrac4{x^2}[/tex]

At the point we want, the gradient is

[tex]\dfrac{dy}{dx}\bigg|_{x=4} = -\dfrac4{4^2} = \boxed{-\dfrac14}[/tex]

6. The curve crosses the [tex]y[/tex]-axis when [tex]x=0[/tex]. Compute the derivative.

[tex]\dfrac{dy}{dx} = 3x^2 - 4x + 5[/tex]

When [tex]x=0[/tex], the gradient is

[tex]\dfrac{dy}{dx}\bigg|_{x=0} = 3\cdot0^2 - 4\cdot0 + 5 = \boxed{5}[/tex]

7. Set [tex]y=5[/tex] and solve for [tex]x[/tex]. The curve and line meet when

[tex]5 = 2x^2 + 7x - 4 \implies 2x^2 + 7x - 9 = (x - 1)(2x+9) = 0 \implies x=1 \text{ or } x = -\dfrac92[/tex]

Compute the derivative (for the curve) and evaluate it at these [tex]x[/tex] values.

[tex]\dfrac{dy}{dx} = 4x + 7[/tex]

[tex]\dfrac{dy}{dx}\bigg|_{x=1} = 4\cdot1+7 = \boxed{11}[/tex]

[tex]\dfrac{dy}{dx}\bigg|_{x=-9/2} = 4\cdot\left(-\dfrac92\right)+7=\boxed{-11}[/tex]

8. Compute the derivative.

[tex]y = ax^2 + bx \implies \dfrac{dy}{dx} = 2ax + b[/tex]

The gradient is 8 when [tex]x=2[/tex], so

[tex]2a\cdot2 + b = 8 \implies 4a + b = 8[/tex]

and the gradient is -10 when [tex]x=-1[/tex], so

[tex]2a\cdot(-1) + b = -10 \implies -2a + b = -10[/tex]

Solve for [tex]a[/tex] and [tex]b[/tex]. Eliminating [tex]b[/tex], we have

[tex](4a + b) - (-2a + b) = 8 - (-10) \implies 6a = 18 \implies \boxed{a=3}[/tex]

so that

[tex]4\cdot3+b = 8 \implies 12 + b = 8 \implies \boxed{b = -4}[/tex].

Answer:

10 ≤ f(x) < 52

Step-by-step explanation:

the range is the values of f(x) given by the domain - 2 ≤ x < 5

substitute the end points of the interval into f(x)

f(- 2) = 2(- 2)² + 2 = 2(4) + 2 = 8 + 2 = 10

f(5) = 2(5)² + 2 = 2(25) + 2 = 50 + 2 = 52

then range is 10 ≤ f(x) < 52

Answer:

Step-by-step explanation:

To do conversion change miles into feet and hour into second.

One foot is 5280 feet

And an hour is 3600sec

70 miles / Hour

70 * 5280feet / 3600 second

369600 feet / 3600seconds

Then simplify

102. 66 feet / Second

Speed given

1 mi=5280ft

1h=3600s

So convert

need help I don't know the answer

The domain of the relation shown in the graph is -4 <= x <= 4

The relation on the graph is an ellipse function.

The domain is the set of x values the function can take

From the graph, we have the following x values

This means that the domain of x in the graph is -4 <= x <= 4

Hence, the domain of the relation shown in the graph is -4 <= x <= 4

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Answer:

13/3 or 4.333

Step-by-step explanation:

Let the number be x

the sum of x and 7 is 6 less than 4x, giving the equation: x+7+6 = 4x

Solve:

x+7+6 = 4x

x+13 = 4x

13 = 3x

x = 13/3

A total of 204 textbooks were sold with 153 math textbooks and 51 psychology textbooks being sold, as the number of math textbooks was three times the number of psychology textbooks.

Given that,

The combined total of math and psychology textbooks sold in a week is 204.

The number of math textbooks sold is three times the number of psychology textbooks sold.

To solve this problem,

Assign variables to represent the number of math and psychology textbooks sold.

Let's say "M" represents the number of math textbooks and "P" represents the number of psychology textbooks.

We know that the combined total of math and psychology textbooks sold is 204,

So the equation be:

M + P = 204  .....(i)

We are also given that the number of math textbooks sold was three times the number of psychology textbooks sold.

In equation form, this can be expressed as:

M = 3P

Now, we can substitute the value of M in terms of P into the equation (i):

3P + P = 204

Combining like terms, we get:

4P = 204

Dividing both sides by 4, we find:

P = 51

So, the number of psychology textbooks sold is 51.

To find the number of math textbooks sold,

Substitute this value back into the equation:

M = 3P

M = 3(51)

M = 153

Therefore, the number of math textbooks sold is 153.

Hence,

153 math textbooks and 51 psychology textbooks were sold.

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Using it's concept, the percentage of employees with 8 or more years at the company reported that email is their preferred method of communication is:

D. 44.79%.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

P = a/b x 100%

In this problem, there are 96 employees with 8 or more years of experience, of which 43 prefer email, hence the percentage is:

P = 43/96 x 100% = 44.79%.

Hence option D is correct.

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The linear inequality that is graphed in the xy plane is: C. 2x + 3y ≤ 4.

Values in the shaded part are the solution of a a linear inequality. Thus, a dotted or dashed line is used on the graph when the inequality sign is either "<" or ">". On the other hand, when a line that is not dotted or dashed is used when the inequality sign is either "≤" or "≥". These lines, dotted or not are the boundary lines.

Also, when the shaded area is above the boundary line, the sign "≥" or ">" is used. When the shaded part is beneath the boundary line, "≤" or "<" is used in the linear inequality.

The graph given has a boundary line that is not dashed or dotted, and also, the shaded part is beneath the boundary line. Therefore, the inequality sign to use is "≤".

Find the slope:

Slope (m) = rise/run = -4/3 / 2 = -4/6

m = -2/3

y-intercept (b) = 4/3.

Substitute m = -2/3 and b = 4/3 into y ≤ mx + b:

y ≤ -2/3x + 4/3

Rewrite

3y ≤ -2x + 4

2x + 3y ≤ 4

The answer is: C. 2x + 3y ≤ 4.

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Answer:

(x-7)/9

Step-by-step explanation:

F(c) = 9x + 7

y = 9x + 7  Now switch the y and the x and solve for y

x = 9y + 7  Subtract 7 from both sides

x - 7 = 9y  Divide both sides by 9

(x-7)/9

Answer:

  (a)  π + (-π) = 0

Step-by-step explanation:

You want a counterexample for the statement that irrationals are closed under addition.

A set is closed under addition if adding members of the set always results in a member of the set.

This shows that adding members of the set can result in a rational number. This is the counterexample you're looking for.

Irrelevant. 1/2 is rational, so is not a member of the set of irrationals.

An example of a sum that is an element of the set. This is not a counterexample.

Irrelevant. 1/2 is rational, so is not a member of the set of irrationals.

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Answer:

(11,0)

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

8-15 = -7 but since it's an absolute value, it is 7 and then you add the negative sign in front since it is not in the absolute value.

The next three numbers here would be 0, 10, 1011, 1031, 102113, 10311213, 10411223, 1031221314, 1041222314.

The term number sequence is used to refer to the list of numbers that have the relationship of having a linked rule. The number that follows in the sequence has to be worked out from the previous numbers in that particular sequence. You have to follow the particular rule to be able to work out the number that has to follow in the sequence.

For example we have these numbers 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34 etc. We would have to understand the pattern of numbers that are in the sequence. We can see that there is a difference of 3 between the number that succeeds the previous one in the sequence.

The first value here is given to be 0

Next we have the 1 0 = 10

The next that we have is 1 0 and 1 1 written as 1011

Next is 1 zero and three one = 1031

We continue to follow the pattern till we arrive at 1041222314. This is where the sequence would then have to stop.

Hence we have to conclude that the next numbers are 10411223, 1031221314, 1041222314.

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The  statement that is not true for​ goodness-of-fit tests is: A. Expected frequencies must be whole numbers.

Goodness-of-fit tests can be defined as the test conducted to help find out whether the observe value work hand in hand with expected value or the observe value is different from the expected value.

The statement is not true because it is not must for expected frequencies  to be whole number  despite the fact that expected  frequencies are whole numbers.

Therefore the  statement that is not true for​ goodness-of-fit tests is: A. Expected frequencies must be whole numbers.

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The lower-priced speaker docks and higher-priced speaker docks is 9 and 36 respectively.

Higher-priced speaker = 170 × x

= 170x

Lower-priced speaker = 80 × 4x

= 320x

Total sales = $4,410

170x + 320x = 4,410

490x = 4,410

divide both sides by 490

x = 4,410 / 490

x = 9

So,

Number of lower-priced speaker = 4x

= 4 × 9

= 36

Number of higher-priced speaker = x

= 9

Therefore, the lower-priced speaker docks and higher-priced speaker docks is 9 and 36 respectively.

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Answer:

(4,8)

Step-by-step explanation:

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Answer:

The function would be odd

The answer is neither.

Let's take an odd number and substitute.

Now, let's take an even number.

Since both even and odd numbers are possible, it is neither.

Answer: its the 3rd one if im wrong im sorry

:3

What is ordinary number?

1 : a number designating the place (such as first, second, or third) occupied by an item in an ordered sequence — see Table of Numbers. 2 : a number assigned to an ordered set that designates both the order of its elements and its cardinal number.

The given statement that's true about the function is g(-13) = 20 is true for g.

From the information given, the function, g, has a domain of -20 < x < -5 < g(x) <45 and that g(0)= -2 and g(-9)= 6.

Let's analyze the options that are given in the scenario. g(7) = -1. It should be noted that 7 isn't in our domain. Therefore, this isn't possible.

g(-13) = 29

x = 13 is in our domain and 20 is also is in our range. Therefore, this is true for g.

g(0) = 2.

This isn't true because it is given that g(0) = 2

In conclusion, the given statement that's true about the function is g(-13) = 20 is true for g.

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Seven less than the product of thirteen times a number, and two squared is as follows;

(13x × 2²) - 7

The expression says  seven less than the product of thirteen times a number, and two squared.

Let

the number  = x

Hence, the product of thirteen times a number, and two squared is as follows:

13(x)(2²)

Therefore,  seven less than the product of thirteen times a number, and two squared is as follows;

(13x × 2²) - 7

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[tex]l = sec {}^{2} x - 1 \\ l = \frac{1}{cos {}^{2} x} - \frac{cos {}^{2} x}{cos {}^{2} x} \\ l = \frac{1 - cos {}^{2} x}{cos {}^{2}x } \\ l = \frac{sin {}^{2} x}{cos {}^{2} x} = ( \frac{sinx}{cosx} ) {}^{2} = tan {}^{2} x[/tex]

The maximum area of a rectangular piece of metal with perimeter of 27.75 in² has length of 6.9375 in and width of 6.9375 in.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the length and y represent the width. hence:

Perimeter = 2(x + y)

27.75 = 2(x + y)

y = 13.875 - x

Area (A) = xy

A = x(13.875 - x)

A = 13.875x - x²

Maximum area is at A' = 0, hence:

A' = 13.875 - 2x

13.875 - 2x = 0

x = 6.9375

y = 6.9375

The maximum area of a rectangular piece of metal with perimeter of 27.75 in² has length of 6.9375 in and width of 6.9375 in.

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Answer:

A

Step-by-step explanation:

x - 4 / (x + 5)(x - 1)

let's expand:

x - 4 / x² + 4x - 5

4 - 4 / 16 + 16 - 5 = 0 so answer is 4

Answer:

Step-by-step explanation: