what is 1,000,000,000 divided by -1,000

To find the maxima and minima of the function, we need to calculate the derivative of the function. Note, before the denominator is a perfect square trinomial, so the function can be simplified as

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f(x) = \frac{x^2 - x - 2}{(x - 3)^2}} \end{gathered}$}[/tex]

So the derivative is:

  [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f'(x) = \frac{(2x - 1)(x - 3)^2 - 2(x - 3)(x^2 - x - 2)}{(x - 3)^4} } \end{gathered}$}[/tex]

Simplifying the numerator, we get:

                 [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f'(x) = \frac{(x - 3)(-5x + 7)}{(x - 3)^4} = \frac{-5x + 7}{(x - 3)^3} } \end{gathered}$}[/tex]

The function will have a maximum or minimum when f'(x) = 0, that is,

                  [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f'(x) = \frac{-5x + 7}{(x - 3)^3} = 0 } \end{gathered}$}[/tex]

which is true if -5x + 7 = 0. Then x = 7/5.

To determine whether x = 7/5 is a maximum, we can use the second derivative test or the first derivative test. In this case, it is easier to use the first derivative test to avoid calculating the second derivative. For this, we evaluate f'(x) at a point to the left of x = 7/5 and at a point to the right of it (as long as it is not greater than 3). Since 1 is to the left of 7/5, we evaluate:

                    [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f(1) = \frac{-5 + 7}{(1 - 3)^3} = \frac{2}{-8} < 0} \end{gathered}$}[/tex]

Likewise, since 2 is to the right of 7/5, then we evaluate:

                                   [tex]\large\displaystyle\text{$\begin{gathered}\sf \displaystyle \bf{\frac{-10 + 7}{(2 - 3)^3} = \frac{-3}{-1} > 0} \end{gathered}$}[/tex]

Note that to the left of 7/5 the derivative is negative (the function decreases) and to the right of 7/5 the derivative is positive (the function increases).

The value of f(x) at 7/5 is:

                               [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f\left(\tfrac{7}{5}\right) = \frac{\tfrac{49}{25} - \tfrac{7}{5} - 2}{\tfrac{49}{25} - 6 \cdot \tfrac{7}{5} + 9} = -\frac{9}{16} } \end{gathered}$}[/tex]

This means that [tex]\bf{\left( \frac{7}{5}, -\frac{9}{16} \right)}[/tex] is a minimum (and the only extreme value of f(x)).

[tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

Answer:

[tex]\text{Minimum at }\left(\dfrac{7}{5},-\dfrac{9}{16}\right)[/tex]

Step-by-step explanation:

The local maximum and minimum points of a function are stationary points (turning points).  Stationary points occur when the gradient of the function is zero.  Differentiation is an algebraic process that finds the gradient of a curve.

To find the stationary points of a function:

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $y=\dfrac{u}{v}$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=\dfrac{v \dfrac{\text{d}u}{\text{d}x}-u\dfrac{\text{d}v}{\text{d}x}}{v^2}$\\\end{minipage}}[/tex]

[tex]\text{Given function}: \quad \text{f}(x)=\dfrac{x^2-x-2}{x^2-6x+9}[/tex]

Differentiate the function using the Quotient Rule:

[tex]\text{Let }u=x^2-x-2 \implies \dfrac{\text{d}u}{\text{d}x}=2x-1[/tex]

[tex]\text{Let }v=x^2-6x+9 \implies \dfrac{\text{d}v}{\text{d}x}=2x-6[/tex]

[tex]\begin{aligned}\implies \dfrac{\text{d}y}{\text{d}x} & =\dfrac{(x^2-6x+9)(2x-1)-(x^2-x-2)(2x-6)}{(x^2-6x+9)^2}\\\\& =\dfrac{(2x^3-13x^2+24x-9)-(2x^3-8x^2+2x+12)}{(x^2-6x+9)^2}\\\\\implies \text{f}\:'(x)& =\dfrac{-5x^2+22x-21}{(x^2-6x+9)^2}\\\\\end{aligned}[/tex]

Set the differentiated function to zero and solve for x:

[tex]\begin{aligned}\implies \text{f}\:'(x)& =0\\\\\implies \dfrac{-5x^2+22x-21}{(x^2-6x+9)^2} & = 0\\\\-5x^2+22x-21 & = 0\\\\-(5x-7)(x-3) & = 0\\\\\implies 5x-7 & = 0 \implies x=\dfrac{7}{5}\\\\\implies x-3 & = 0 \implies x=3\end{aligned}[/tex]

Put the x-values back into the original equation to find the y-values:

[tex]\implies \text{f}\left(\frac{7}{5}\right)=\dfrac{\left(\frac{7}{5}\right)^2-\left(\frac{7}{5}\right)-2}{\left(\frac{7}{5}\right)^2-6\left(\frac{7}{5}\right)+9}=-\dfrac{9}{16}[/tex]

[tex]\implies \text{f}(3)=\dfrac{\left(3\right)^2-\left(3\right)-2}{\left(3\right)^2-6\left(3\right)+9}=\dfrac{4}{0} \implies \text{unde}\text{fined}[/tex]

Therefore, there is a stationary point at:

[tex]\left(\dfrac{7}{5},-\dfrac{9}{16}\right)\:\text{only}[/tex]

To determine if it's a minimum or a maximum, find the second derivative of the function then input the x-value of the stationary point.

Differentiate f'(x) using the Quotient Rule:

Simplify f'(x) before differentiating:

[tex]\begin{aligned}\text{f}\:'(x) & =\dfrac{-5x^2+22x-21}{(x^2-6x+9)^2}\\\\& = \dfrac{-(5x-7)(x-3)}{\left((x-3)^2\right)^2}\\\\& = \dfrac{-(5x-7)(x-3)}{(x-3)^4}\\\\& = -\dfrac{(5x-7)}{(x-3)^3}\\\\\end{aligned}[/tex]

[tex]\text{Let }u=-(5x-7) \implies \dfrac{\text{d}u}{\text{d}x}=-5[/tex]

[tex]\text{Let }v=(x-3)^3 \implies \dfrac{\text{d}v}{\text{d}x}=3(x-3)^2[/tex]

[tex]\begin{aligned}\implies \dfrac{\text{d}^2y}{\text{d}x^2} & =\dfrac{-5(x-3)^3+3(5x-7)(x-3)^2}{(x-3)^6}\\\\& =\dfrac{-5(x-3)+3(5x-7)}{(x-3)^4}\\\\\implies \text{f}\:''(x)& =\dfrac{10x-6}{(x-3)^4}\end{aligned}[/tex]

Therefore:

[tex]\text{f}\:''\left(\dfrac{7}{5}\right)=\dfrac{625}{512} > 0 \implies \text{minimum}[/tex]

The ordered pair of the equation 3x +2y = 6 will be ( 0,3) and ( 2 , 0).

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.

We have an equation 3x + 2y = 6 now the ordered pair of the equation will be found by the graph will be ( 0,3) and ( 2, 0). The graph is also attached with the answer below.

Therefore the ordered pair of the equation 3x +2y = 6 will be ( 0,3) and ( 2 , 0).

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Answer:

24 ft.

Step-by-step explanation:

Radius = 4 ft

Central angle = 6°

Arc length = radius × central angle

= 4 × 6°

= 24 ft.

Please, make sure you understand the solution:

We can notice that x + (x - 28) = 90

2x - 28 = 90
2x = 118
x = 59

Now for y:

We can notice that y + 90 + x = 180

y + 90 + 59 = 180
y + 149 = 180
y = 180 - 149

y = 31

Answer:

A wave period is the measure of the time it takes for the wave cycle to complete.

The period of the wave is 2 seconds.

The angles are p=67°, q=15°, x=82°, y=81°, s=28° and m=72.5°.

For the given figures we need to find the unknown angles.

In the first figure to find angle p first apply the angle sum property to the triangle.

That is, 82°+31°+p=180° (∵ Sum of interior angles of a triangle is 180°)

⇒p=67°.

p=67° is a vertically opposite angle to the other triangle.

To find q:

67°+98°+q=180°

⇒q=15°.

In the second figure to find angles x and y apply the angle sum property to the triangle.

That is, 28°+(53°+x)+17°=180°

⇒98°+x=180°

⇒x=82°.

To find y:

x+y+17°=180°

⇒82°+y+17°=180°

⇒y=81°

In the third figure to find angles x and y apply the angle sum property to the triangle.

That is, 100-x+30+4x+7x=180°

⇒10x=80°⇒x=10°.

Now the angles of the triangle are 100-10=90°, 30+4x=70°

y=90°+70°=160° (∵Exterior angle is equal to the sum of two opposite interior angles).

In the 4th figure, to find angle 's' use the isosceles triangle concept.

That is, s+76°+76°=180° (∵In isosceles triangle base angles are equal)

⇒s=28°

In the 5th figure, to find angle 'm' use the isosceles triangle concept.

That is, 35°+m+m=180° (∵In isosceles triangle base angles are equal)

⇒2m=145°

⇒m=72.5°

Hence, the angles are p=67°, q=15°, x=82°, y=81°, s=28° and m=72.5°.

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Answer:

Tara can make 60 bracelets.

Step-by-step explanation:

908 / 15 = 60.5

Answer:

The square root of 36/196 is 3/7.

The square root of 36/169 is 6/13.

Answer:

The angles are 72° and 108°

Step-by-step explanation:

Supplementary angles add up to 180°

Ratio of supplementary angles = 2 : 3

The angles are 2x , 3x

2x + 3x = 180

        5x = 180

          x = 180 ÷ 5

         x = 36°

2x = 2*36 = 72°

3x = 3*36 = 108°

Answer:

[tex]C=23\pi[/tex] inches

or as a decimal

72.26 inches

Step-by-step explanation:

Formula for circumference: [tex]C=2\pi r[/tex]

Radius = [tex]\frac{d}{2}[/tex]

Altogether we get: [tex]C=2*\pi*\frac{d}{2}[/tex]

Which simplifies to: [tex]C=\pi d[/tex]

So now we can plug in 23 for [tex]d[/tex].

[tex]C=\pi*23[/tex]

Our final answer is:

[tex]C=23\pi[/tex] inches

or as a decimal

72.26 inches

The value of FY in the triangle will be 30.11

From the information given, the value of BE will be:

= [tex]\sqrt{64.2}[/tex]² - [tex]\sqrt{51.2}[/tex]²

= 38.7

From the triangle, DY will be

= [tex]\sqrt{64.22}[/tex]² - [tex]\sqrt{61.7}[/tex]²

= 17.7

AY will be:

= [tex]\sqrt{61.7}[/tex]² + [tex]\sqrt{17.7}[/tex]²

= 64.2

FY will now be:

= [tex]\sqrt{64.2 - 56.7}[/tex]²

= 30.11

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Answer:

1936

Step-by-step explanation:

We can start by removing the center tile, because all four diagonals over lap on that tile. We'll add it back later. 88/4=22. which means there are 22 tiles per half, 44+1(the center tile) total tiles per side, which means there are a total of 1936 tiles.

AOPS ANSWER:

Suppose that we have a square with dimensions [tex]$e \times e$[/tex]. The diagonals each have [tex]$e$\\[/tex] tiles. If [tex]$e$\\[/tex] is even, the number of yellow tiles is [tex]$2e$[/tex], because the [tex]2[/tex] diagonals don't intersect. If [tex]$e$[/tex] is odd, then the number of yellow tiles is [tex]$e+e-1=2e-1$[/tex]. (We have to subtract [tex]1[/tex] because the center tile is counted [tex]2[/tex] times). We know that there are [tex]89[/tex] yellow tiles, which is an odd number, so [tex]$89=2e-1$[/tex]. This implies that [tex]$e = 45$[/tex]. So the dimensions of the floor are [tex]$45 \times 45$[/tex], or [tex]2025\\[/tex] square units. Since all of the other tiles are gray, there are [tex]$2025-89=\boxed{1936}$[/tex] gray tiles.

Answer:

83.80 = 69 + 4x
x = 3.7
Sarah can use up to 3.7 gigabytes per month to stay within her budget

Step-by-step explanation:

83.80 = 69 + 4x
14.8 = 4x
x = 3.7

The number of gigabytes of data Sarah can use while staying within her budget is 3.7 gigabyte.

Given that, Sarah pays a flat cost of $69 per month and $4 per gigabyte.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of gigabyte be g.

69+4g=83.80

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Now, 4g=83.80-69

⇒ 4g=14.8

⇒ g=14.8/4

⇒ g=3.7 gigabyte

Therefore, the number of gigabytes of data Sarah can use while staying within her budget is 3.7 gigabyte.

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Answer:

ASA

Step-by-step explanation:

by ASA congruence theorem

The distance from the wall defined by the y-axis will be 8 feet. Then the correct option is B.

The equation of line is given as

y = mx + c

Where m is the slope and c is the y-intercept.

The table is given below.

Then the equation of the line will be

(y – 8) = [(8 – 6) / (0 – 20)](x – 0)

       y = -0.1x + 8

If the drain is at the minimum point.

Then the distance from the wall defined by the y-axis will be 8 feet.

Then the correct option is B.

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The algebraic expression that represents the number of new accounts that he will add in m months is x ≥ 7m.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Every month, a salesperson adds 7 new accounts.

Let m be the number of the month and x be the number of the accounts.

Then the inequality equation will be

x ≥ 7m

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Answer:

C [tex]\sqrt{5}[/tex]

Step-by-step explanation:

Use pythagorean theorem.

[tex]x^{2}[/tex] +[tex]\sqrt{7} ^{2}[/tex] = (2[tex]\sqrt{3}) ^{2}[/tex]    

[tex]x^{2}[/tex] + 7 = 12   Subtract 7 from both sides

[tex]x^{2}[/tex] = 5           Take the square root of both sides to solve

x = [tex]\sqrt{5}[/tex]

The remainder represented by synthetic division is -5.

Synthetic division can be defined as a simplified way of dividing a polynomial with another polynomial equation of degree 1.

Given

A vertical line and a horizontal line combine to make an L shape.

There are two rows of entries within the shape.

Row 1 has entries 2, 10, 1, 5.

Row 2 has entries blank, -10, 0, -5.

Entry -5 is on the outside to the left of the shape. The entry represents the zero of the divisor. This entry to the variable (assume the variable is x) is;

x + 5 = 0

x = -5

Hence, the divisor of the synthetic division is -5.

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Answer:

its a) -5

Step-by-step explanation:

Answer:

2.4 × 10⁶

Step-by-step explanation:

Given:

To calculate the value of R, substitute the given values into the given formula:

[tex]\begin{aligned}\sf R & = \sf \dfrac{x^2}{y}\\\\ \implies \sf R& = \sf \dfrac{(3.8 \times 10^5)^2}{5.9 \times 10^4}\\\\& = \sf \dfrac{3.8^2 \times (10^5)^2}{5.9 \times 10^4}\\\\& = \sf \dfrac{14.44 \times 10^{10}}{5.9 \times 10^4}\\\\& = \sf \dfrac{14.44}{5.9} \times \dfrac{10^{10}}{10^4}\\\\& = \sf 2.4474... \times 10^{(10-4)}\\\\& = \sf 2.4474... \times 10^6\\\\\end{aligned}[/tex]

Therefore, the value of R to 1 decimal place is 2.4 × 10⁶

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

Exponent Rules used

[tex](a^b)^c=a^{bc}[/tex]

[tex]{a^b}{a^c}=a^{b-c}[/tex]

[tex]R = \frac{ {x}^{2} }{ y} \\ \\ R = \frac{ {(3.8 \times {10}^{5})}^{2} }{5.9 \times {10}^{4} } \\ \\ R = \frac{ ({3.8})^{2} \times ( { {10}^{5} )}^{2} }{5.9 \times {10}^{4} } \\ \\ R = \frac{14.44 \times {10}^{10} }{5.9 \times {10}^{4} } \\ \\ R = \frac{14.44 \times {10}^{10 - 4} }{5.9} \\ \\ R = 2.45 \times {10}^{6} [/tex]

The correct answer is option D which is the probability is 1.

The complete question is given below:-

Jamaal knows that it is certain that he will win the election because he is the only person who is running for class treasurer. Which value represents the probability that he will win the election?

0

1/4

3/4

1

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

The probability of Event E is given by,

P = favourable outcomes / Total outcomes

Jamaal is the only candidate running in the class treasurer election.

There for Total No. of outcomes = 1

Here Event E is Jamaal winning the Election.

So, No. of favorable outcome = 1

P(E) = 1 / 1

P(E) = 1

This type of event is called a SURE EVENT Because the probability of a sure event is always 1.

The Probability of Jamaal winning the election is 1. So, Option D is correct.

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The probability that he will win the election will be 1. Then the correct option is D.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

The value of the probability of an event will be varying from zero to one.

Jamaal knows that it is certain that he will win the election because he is the only person who is running for class treasurer.

Then the probability that he will win the election will be

If the event will certainly happen, then the probability will be one.

P = 1

Then the correct option is D.

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Answer:

184.73

Step-by-step explanation:

1 yard = 0.91m

203 yard=?

(203x0.91)/1=184.73.

+1(415) 450-6164

Answer:

113 degrees

Step-by-step explanation:

Two angles are called supplementary when they add up to 180 degrees

[tex]180 = x + y \\ 180 = 67 + y \\ y = 180 - 67 \\ y = 113 \\ therefore \: mB \: = 113[/tex]

Answer:

48

Step-by-step explanation:

The mean of a number is the sum of all the numbers divided by how many numbers there are. We can set up this formula: [tex]mean = \frac{sum}{amountnumbers}[/tex].

When we plug our values into this equation, we get: [tex]6 = \frac{sum}{8}[/tex]. Solving this equation gets us sum = 6 * 8 = 48

The green-colored area of the graph attached below shows the solution set to 3eˣ>(-1/2)x.

Inequality is the relationship between two expressions showing the relationships like greater than, lesser than, lesser than equals to, and greater than equals to.

Here assume f is a function which is given by f(x)=3eˣ

and g be another function which is given by g(x)= (-1/2)x

Here we have to find the solution graph showing the relationship

f(x) > g(x)

Let at point (a,b) the f(x) and g(x) meet each other.

After that intersection point, g(x) will decrease as g(x) is a decreasing function. and f(x) will increase.

So in the solution set will contain the area where g(x) is larger than f(x).

Therefore the solution graph of this inequality is the green-colored area as shown below,

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Answer: 40/21

Step-by-step explanation:

[tex]3 \times 105=315\\\\6 \times 10^{2}=600\\\\\implies \frac{6 \times 10^{2}}{3 \times 105}=\frac{600}{305}=\boxed{\frac{40}{21}}[/tex]

Answer:

C

Step-by-step explanation:

The horizontal line, y=2, is solid and shaded above, so it represents

[tex]y \geqslant 2[/tex]

The slanted line, y=x is dashed and shaded below, so it represents y<x.

The number of matchsticks that each side of the biggest triangle contains is; 137 matchsticks

We know that for a diagram to be a triangle, then two smallest sides must not be greater than the third side.

Now, if there are 273 matchsticks, then the greatest side of the triangle must not be less than 273/2 = 136.5 ≈ 137

Thus, the largest side will have at least 137 matchsticks

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The solution is 1756.69

A number system is defined as a system of writing to express numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner.

We have to find the 18.5% of 2155.45.

So,

2155.45 * 0.185 = 398.75825

Now, subtract

21.55.45 - 398.75825

= 1756.69175

Hence, the value is 1756.69

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Hey there!

2(2y - 12) = 0
2(2y) + 2(-12) = 0

4y - 24 = 0

ADD 24 to BOTH SIDES

4y - 24 + 24 = 0 + 24

SIMPLIFY IT!

4y = 0 + 24

4y = 24

4y/4 = 24/4

SIMPLIFY IT!

y = 24/4

y = 6

Therefore, your answer should be:

y = 06 (Option B.)

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

y=6 (06) should be your answer

Step-by-step explanation:

4y-24=0

After you simply the first equation in the parenthesis, you then move the 24 to the 0,

4y=24

The answer becomes positive 24 because when you move things across the equal sign you switch the sign

y=6

Then divide 24 by 4 to isolate y, which then gives you the answer 6.