f(x)=1/x at x=1 find slope of tangent

Answer:

[tex]\rm slope: -\dfrac{7}{6}[/tex]

[tex]\rm Distance: 2\sqrt{85} \ units[/tex]

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y }{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

Here given points are: (6, -6), (-6, 8)

Insert the values:

[tex]\sf \rightarrow slope: \dfrac{8-(-6)}{-6-6}[/tex]

[tex]\sf \rightarrow slope: \dfrac{8+ 6}{-12}[/tex]

[tex]\sf \rightarrow slope: \dfrac{14}{-12}[/tex]

[tex]\sf \rightarrow slope: -\dfrac{7}{6}[/tex]

[tex]\sf Distance \ between \ points : \sf d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]

Using the formula,

[tex]\sf d = \sqrt{(-6 - 6)^2 + (8-(-6))^2}[/tex]

[tex]\sf d = \sqrt{(-12)^2 + (14)^2}[/tex]

[tex]\sf d = \sqrt{144 +196}[/tex]

[tex]\sf d = \sqrt{340}[/tex]

[tex]\sf d = \sqrt{85 \times 4}[/tex]

[tex]\sf d = 2\sqrt{85}[/tex]

Hence, the distance is 2√85 units.

Hii!

___________________________________________________________

[tex]\stackrel\bigstar{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer}\circ\leftharpoonup}}[/tex]

Slope =

Distance =

[tex]\stackrel\bigstar{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation}\circ\leftharpoonup}}[/tex]

[tex]\bullet[/tex] Let's work out the slope

[tex]\twoheadrightarrow\sf \cfrac{y2-y1}{x2-x1}[/tex]

[tex]\bullet[/tex] Stickin the values

[tex]\twoheadrightarrow\sf \cfrac{8-(-6)}{-6-6}[/tex]

[tex]\bullet[/tex] Simplify

[tex]\twoheadrightarrow\sf \cfrac{8+6}{-12}[/tex]

[tex]\bullet[/tex] Finish simplifying

[tex]\twoheadrightarrow\sf \cfrac{14}{-12}[/tex]

[tex]\bullet[/tex] Reduce the fraction

[tex]\twoheadrightarrow\sf \cfrac{7}{-6}[/tex]

[tex]\bullet[/tex] Work out the distance

[tex]\twoheadrightarrow\sf \sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

[tex]\bullet[/tex] Stick in the values

[tex]\twoheadrightarrow\sf \sqrt{(-6-6)^2+(8-(-6)^2}[/tex]

[tex]\bullet[/tex] Simplify the radical expression

[tex]\twoheadrightarrow\sf \sqrt{(-12)^2+14^2}\\\\\twoheadrightarrow\sf \sqrt{144+169} \\\\\twoheadrightarrow\sf \sqrt{340}\\\\\twoheadrightarrow\sf \sqrt{85\cdot4} \quad (simplifying\,the\,surd)[/tex]

[tex]\ddagger[/tex] [tex]\boldsymbol{DISTANCE=2\sqrt{85} \,Units}[/tex] [tex]\ddagger[/tex]

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Hope that this helped! Best wishes.

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Answer:

40.9 %

Step-by-step explanation:

8.8   is   .4 hours above the mean this is  .4/1.77 = .226 standard deviations above the mean

 Using z-score table this corresponds to ~ .5910    (59.10%)

    this percentage is LESS than 8.8 hours

      the percentage ABOVE this is 40.9%

(Not asked, but this is  40.9 (40 ) = ~ 16 of the 40 mechanics sampled)

Answer: Choice C

As [tex]\text{x} \to \infty[/tex] then [tex]\text{y} \to -\infty[/tex]

As [tex]\text{x} \to -\infty[/tex] then [tex]\text{y} \to \infty[/tex]

Check out the diagram below.

========================================================

Explanation:

The leading term is the term with the largest exponent. That would be the term of [tex]-\text{x}^3[/tex]. The leading term directly determines the end behavior. The other terms will not play a role.

What this means is that the end behavior of [tex]\text{y} = -\text{x}^3 - \text{ax} + 3[/tex] is the exact same as the end behavior of [tex]\text{y} = -\text{x}^3[/tex]

As x gets really big in the positive direction, we'll have [tex]-\text{x}^3[/tex] get really small in the negative direction. For instance, x = 10 leads to [tex]-\text{x}^3 = -10^3 = -1000[/tex] and x = 100 leads to [tex]-\text{x}^3 = -100^3 = -1,000,000[/tex]

Therefore, as [tex]\text{x} \to \infty[/tex] then [tex]\text{y} \to -\infty[/tex]

Visually the graph goes forever downward when we move to the right. We can consider this as "falls to the right".

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

The graph "rises to the left" because as [tex]\text{x} \to -\infty[/tex] then [tex]\text{y} \to \infty[/tex]

Here's a small table to give numeric examples:

[tex]\begin{array}{|c|c|} \cline{1-2}x & y\\\cline{1-2}-1 & 1\\\cline{1-2}-10 & 1000\\\cline{1-2}-100 & 1,000,000\\\cline{1-2}\end{array}[/tex]

As x gets more negative, y becomes more positive. We have this opposite nature going on similar to the previous section.

This graph goes uphill when moving to the left.

Check out the graph below. In the diagram I used a = 2, but you could use any value of 'a' you want to get the same end behavior.

Answer:

 1.5

Explanation:

Given that:

While solving this problem, the above following is not required to use.

[tex]\rightarrow \sf log_b ([b^3])^{1/2}[/tex]

apply log rule

[tex]\rightarrow \sf \dfrac{1}{2}\log _b\left(b^3\right)[/tex]

[tex]\boxed{\sf \log _b\left(b^3\right)=3}[/tex]

[tex]\rightarrow \sf \dfrac{1}{2}(3)[/tex]

distribute

[tex]\rightarrow \sf \dfrac{3}{2} \quad or \quad 1.5[/tex]

To find the point of intersection of two lines, we can use substitution to find the x and y coordinates.

We're given:

Use substitution to find x:

[tex]-2x + 2=x-4\\-2x=x-6\\-3x=-6\\x=2[/tex]

Use substitution to find y:

[tex]y=x-4\\y=2-4\\y=-2[/tex]

The point of intersection is (2,-2).

Answer:

5/8

Step-by-step explanation:

5/8=0.6.25

0.625> all the other numbers

The margin of error will be 20 and 10 respectively.

The margin of error for Robert will be:

= 1.96 × 50/✓25

= 1.96 × (50/5)

= 1.96 × 10

= 20 approximately

The margin of error for Val will be:

= 1.96 × 50/✓100

= 1.96 × 50/10

= 1.96 × 5

= 10 approximately

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Answer:

It's A. (2, 0) and (0, -4)

our system of inequalities is:

x + y ≤ 13.

x*$15 + y*$10 ≥ $180.

The graph can be seen at the end.

Here we have the variables:

We know that she can only work 13 hours per week, then we have:

x + y ≤ 13.

And she wants to earn at least $180 per week, then:

x*$15 + y*$10 ≥ $180.

So our system of inequalities is:

x + y ≤ 13.

x*$15 + y*$10 ≥ $180.

The graph of the system can be seen below. The solution set is defined by the zone where the two shaded regions intersect (where we also should add the restrictions x >0, y > 0).

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The answer is 40/10 because the total number of square units is 40 option second 40/10 is correct.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

The question is incomplete.

The complete question is:

Which expression is modeled by this arrangement of tiles? 40 positive tiles are broken up into 10 groups of 4 positive tiles.

Please refer to the attached picture.

We have a rectangular shape as shown in the picture.

Total number of square units = 40

Each row has 10 units cube.

Each cube = 40/10

Thus, the answer is 40/10 because the total number of square units is 40 option second 40/10 is correct.

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The quotient is x+1.

Long division is a method for dividing one large multi digit number into another large multi digit number.

Given:

f(x)=  x²+2x+1

g(x)= x+1

The steps to divide the polynomial is :

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The statement "the y-intercept of g is 4 units above the y-intercept of f'' is true option first is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have two functions:

f(x) = |2x - 1|   and

g(x) = |2x - 5|

After plotting on a coordinate plane.

The y-intercept of f(x) is 1

The y-intercept of g(X) is 5

Or plug x = 0 to find the y-intercept.

The y-intercept of g is 4 units above the y-intercept of f

Thus, the statement "the y-intercept of g is 4 units above the y-intercept of f'' is true option first is correct.

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Applying the negative exponent, it is found that the equivalent expression to [tex]3^{-3}[/tex] is [tex]\frac{1}{27}[/tex].

When we have a negative exponent, we use a fraction, with the term with the exponent going to the denominator, as follows:

[tex]a^{-b} = \frac{1}{a^b}[/tex]

Hence, in this problem, the equivalent expression is:

[tex]3^{-3} = \frac{1}{3^3} = \frac{1}{27}[/tex]

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The English phrase of the obtained equation is 12 times z subtracted by 3. The obtained equation after solving is 12z -23

Simplifying means making something easier to do or comprehend, as well as making something less difficult.

Given data;

z be the unknown number

Given conditions;

1. The difference between a number and −23.

2.−23 is equal to the product of the number and 13.

The mathematical form of the given phrase is;

⇒ z - (-23) = z × 13

⇒z+23 = 13z

⇒12z -23

The English phrase of the obtained equation is 12 times z subtracted by 3.

Hence the simplification of the given expressions is 12z -23.

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Answer:slope is 0.4

Step-by-step explanation:

y2-y1 divided by x2-x1

2-4/0-5=0.4

Answer:

y= 4x - 10

Step-by-step explanation:

y-6 = 4(x - 4)

y - 6 = 4x -16

+6. +6

y= 4x - 10

The descriptive answer of different part is described below.

An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent more than 1. The graph of a linear equation always forms a straight line.

Here, Studio A rents for $75 plus $75 an hour .

Studio B rents for $150 and $50 an hour.

Let t = the number of hours and c = cost.

Part A

Studio A: c = 75 +75·t

Studio B: c = 150 +50·t

Part B

We solve the system of equation using substitution method, where we substitute c in the first equation with 150 +50t.

150 +50·t = 75 +75·t, subtract 75 and 50t from both sides

  150 -75 = 75t -50t, combine likes terms

          75 = 25t, divide both sides by 25

            3 = t

Now we know that t = 3 so we find c by substituting t with 3 in the second equation.

c = 150 +50·t

c = 150 +50·3

c = 300

The solution of the system of equations is c = 300 and t = 3

Part C:

The solution of the system of equation tells us that if we rent either studio A or B for 3 hours will pay the same price $300.

The price will be different if we rent studio A then studio B if we rent it for a different amount of time than 3 hours.

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Answer:

The Equation of the line is y = [tex]\frac{-1}{3}[/tex]x + [tex]\frac{11}{3}[/tex]

Step-by-step explanation:

Multiplication of slope of two perpendicular lines is = -1

first line is  y= [tex]\frac{1}{3}[/tex]x +6

slope of this line is [tex]\frac{1}{3}[/tex]

So the slope of the second line is : [tex]\frac{-1}{3}[/tex]

Equation of line would be written by using :

(y - y1) = m(x - x1)

here the line passing through (-4,5)

put the values in equation

y -5 =[tex]\frac{-1}{3}[/tex][x - (-4)]

3y - 15 = -x -4

3y = -x +11

y = [tex]\frac{-1}{3}[/tex]x + [tex]\frac{11}{3}[/tex]

So The Equation of the line is y = [tex]\frac{-1}{3}[/tex]x + [tex]\frac{11}{3}[/tex]

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Answer:

if angle 2 is congruent to 6 them the slope of line o and q is equal

that is line o is parallel to q

Answer:792

Step-by-step explanation:

Answer:

Dilate circle A by a scale factor of 4.

Step-by-step explanation:

To show that two circles are similar, use transformations to map one to the other.

Step 1

Translate circle A so that its center is the same as circle B.

Translate circle A using the rule (x - 4, y - 3)

Step 2

Find the scale factor needed to dilate circle A to the size of circle B using the radii of the circles.

⇒ scale factor = 16 ÷ 4 = 4

Dilate circle A by a scale factor of 4.

Therefore, the only answer option that is correct is:

Dilate circle A by a scale factor of 4.

Perimeter is the sum of the length of the sides used to make the given figure. The perimeter of the regular octagon is 8√58 units.

Perimeter is the sum of the length of the sides used to make the given figure.

For a regular octagon, the length of each side of the octagon is the same. Therefore, the length of a single side of the octagon is,

Length of the side of the octagon = √[(-4-3)² + (0 + 3)²] = √58

Now, the perimeter of the octagon is 8 times of√58.

Perimeter = 8 ×√58 = 8√58

Hence, the perimeter of the regular octagon is 8√58 units.

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The guest they can invite so that the cost they pay will be the same at both wedding catering halls is 18.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The given equation is

900+50x=450+75x

To solve;

900 - 450 = -50x +75x

450 = 25x

x = 450 /25

x = 18

The guest they can invite so that the cost they pay will be the same at both wedding catering halls is 18.

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Answer:

30%

Step-by-step explanation:

The unemployment rate is 30%

Step-by-step explanation:

please mark me as brainlest

Answer:

8

Step-by-step explanation:

We need to sort your set into Least-to-Greatest order.

4, 5, 5, 6, 10, 11, 12, 13

That is your set in least to greatest order.

Which 2 numbers are in the middle?

They are 6 and 10.

Now, we find the mean of 6 and 10.

(6+10)/2 = 8

8 is your median

Answer:

2 and 1/4 cups

Step-by-step explanation:

4 cups-5 cups

5 cups-?

(5×5)÷4=6 cups and 1/4

6 and 1/4-4=2 cups and 1/4