Suppose the tangent line to the curve
y = f(x)
at the point
(1, 1)
has the equation
y = 7 − 6x.
If Newton's method is used to locate a solution of the equation
f(x) = 0
and the initial approximation is x1 = 1, find the second approximation x2.

33.7618% is the geometric mean annual increase for the period

Rate of Increase Over Time(GM)=[tex]\sqrt[n]{value end period / value start period }[/tex] -1

In 1985, there were 326,030 cell phone subscribers in the United States. By 2008, the number of cell phone subscribers increased to 262,359,000. we have to find  the geometric mean annual increase for the period

from 1885 to 2008 that is (2008- 1885=23 ) in 23 years the GM become

therefore n= 23

value of start period = 326030

value of end period = 262359000

rate of increase over time GM= [tex]\sqrt[23]{262359000/326030} -1[/tex]

                                                 = 1.337618 -1

                                                  =0.337618

rate of increase is 33.7618% per year

33.7618% is the geometric mean annual increase for the period

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Answer:

  31/45 lb

Step-by-step explanation:

You want to know the weight of a 5/9 lb bag after 2/15 lb of fruit are added to it.

Fractions can be added when they have a common denominator. Here, the denominator will need to have factors of 3² = 9 and 3·5 = 15. It can be ...

   3·3·9 = 45

Using this denominator, the fractions are ...

  bag weight = 5/9 lb = 25/45 lb

  fruit weight = 2/15 lb = 6/45 lb

The total weight of the fruit and the bag is ...

  total weight = 25/45 lb + 6/45 lb = 31/45 lb

With the fruit, the bag weighs 31/45 pounds.

Polygon A's area is 1/25 times of Polygon B's area.

In geometry, a polygon is a two-dimensional closed shape with straight sides that is flat or plane. It doesn't have any curved edges.

Now, as per the given question;

The formula of the scale factor is given as;

Area of Polygon B = (scale factor)²×(Area of Polygon A).

The scale factor is given as 5.

(Area of Polygon B)  = (5)²×(Area of Polygon A)

Further simplifying;

(Area of Polygon B) = (25)×(Area of Polygon A)

or,

Area of Polygon A = (1/25)×Area of Polygon B

Therefore, the area of polygon A is found to be 1/25 times times the area of the polygon B.

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Answer:

x=1

Step-by-step explanation:

Number of bags of sand needed to cover the area of circular pool is 51 bags.

A circle is a round-shaped figure that has no corners or edges.

Now it is given that,

Diameter of pool, D = 14 feet

So, Area of pool = π(D/2)²

⇒  Area of pool = π(14/2)²

⇒  Area of pool = π(7)²

⇒  Area of pool = 153.86 square feet

Now given Area of 1 bag = 3 square feet

So, number of bags required = Area of pool / Area of 1 bag

⇒ number of bags required = 153.86/ 3

⇒ number of bags required = 51.28

⇒ number of bags required ≈ 51

Thus, Number of bags of sand needed to cover the area of circular pool is 51 bags.

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Answer:

D. [tex]2^9[/tex]

Step-by-step explanation:

[tex]2^6*2^3 = 2^9[/tex]

We can just add the exponents together.

If it were continued another 120 minutes past this, it would be

[tex]2^9*2^3 = 2^1^2[/tex]

4-3i^2

Step-by-step explanation:

Answer:

3/30 for 66 lo siento I core help you

[tex]\frac{1}{2^{4} }[/tex]  is simple form of the equation.

What in mathematics is a linear equation?

Simply solve this equation = [tex](2^{4}) ^{-1}[/tex]

multiply the powers   = [tex]2^{-4}[/tex]

now right on simple form  = [tex]\frac{1}{2^{4} }[/tex]

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The interval where the function is negative is:

(-5 - √19 , -5 + √19)

That is the solution set of the inequality.

Here we have the following inequality:

x^2 + 10x + 5 < 0

So we want to find the values of x for which the quadratic function is negative.

To do so, we can solve:

x^2 + 10x + 5 = 0

The solutions are given by the quadratic formula:

x = (-10 ± √(10^2 - 4*6))/(2*1)

x = (-5 ± √19)

notice that the quadratic has positive leading coefficient, so it open upwards, then the function is below zero between the two roots, on the interval:

-5 - √19 < x < -5 + √19

Then the correct option is D.

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Sticker price refers to the published tuition and fees, whereas net price refers to the amount the student actually pays after financial help which is much lower than the sticker price.

The sticker price of a college education is the entire annual cost. This cost covers the whole cost of tuition every year, books, lodging, and board, as well as any other charges the campus may levy, such as a parking permit or library card fee.

In this report, there are two prices listed: a sticker price and a net price. The sticker price of a college education is the entire annual cost. Every year's full tuition, books, housing, and board are included in this amount.

Hence sticker price refers to the published tuition and fees

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Answer: 8 = g

Step-by-step explanation:

56 divided by 7 = g

8 = g

a) The minimum 75% of commuters in Boston has a commute time within 2 standard deviation of the mean.

b) The minimum 60.93% of commuters in Boston has a commute time within 1.6 standard deviation of the mean.

c) Commute times within 1.4 standard deviation are lie between 15.48 to 38.72.

Explanation:

Given that

To find

So, according to the question

We know that

                            = (1- [tex]\frac{1}{k^2}[/tex] )×100

a) What is the minimum percentage of commuters in Boston has a commute time within 2 standard deviation of the mean?

                            = (1- [tex]\frac{1}{2^2}[/tex] )×100

                            = (1- [tex]\frac{1}{4}[/tex] )×100

                            = ( [tex]\frac{4-1}{4}[/tex] )×100

                            =  [tex]\frac{3}{4}[/tex] ×100

                            = 3 × 25

                            = 75%

b) What minimum percentage of commuters in Boston has a commute time within 1.6 standard deviation of the mean?

                            = (1- [tex]\frac{1}{1.6^2}[/tex] )×100

                            = (1- [tex]\frac{1}{2.56}[/tex] )×100

                            = ( [tex]\frac{2.56-1}{2.56}[/tex] )×100

                            =  [tex]\frac{1.56}{2.56}[/tex] ×100

                            = 1.56 × 39.06

                           = 60.93%

c) What are the commute times within 1.4 standard deviation?

     commute times  = 27.1 ± (1.4×8.3)

                                 = 27.1 ± 11.62

      for + sign,

                                 = 27.1 + 11.62

                                 = 38.72

      for - sign,

                                 = 27.1 - 11.62

                                 = 15.48

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Based on the fact that Gina has $10.00 to spend, if she only buys oranges, the number of oranges she can buy is 29.41176 oranges.

The number of oranges that Gina can buy when she visits her local farm to buy apples and oranges for a fruit salad can be found as:

= Amount that Gina has to spend / Price of oranges

Solving for the total amount of oranges gives:

= 10 / $0.34

= 29.41176 oranges.

The full question is:

Gina visits her local farm stand to buy apples and oranges to make a fruit salad. She has​ $10.00 to spend. If she buys only oranges and oranges are $0.34 how much oranges can she buy

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It should be noted that Ruby will be able to reach the fish

It should be noted that sea level simply means the sea base level that is used for measuring the elevation and the depth on the Earth.

It should be noted that Ruby looks over the edge of her boat and sees fish 0.4 meter below the surface of the water and Ruby holds a 1-meter long net at 0.5 meter above sea level.

It should be noted that he will be able to each the fish. This will be illustrated as:

=1m - (0.4 + 0.5)

= 1 - 0.9

= 0.1m

Therefore, the long net is enough to reach the fish.

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Ruby looks over the edge of her boat and sees fish 0.4 meter below the surface of the water. If Ruby holds a 1-meter long net at 0.5 meter above sea level. Can she reach the fish?

Answer:

[tex]\frac{-10}{7}[/tex]

Step-by-step explanation:

Use the formula

m= [tex]\frac{y2-y1}{x2-x1}[/tex]

another way to say this is Δy divided by Δx

Δ means "change in"

m = slope

The y2 value is -7

The y1 value is 3

The x2 value is 5

The x1 value is -2

Plug those values in the formula

m = [tex]\frac{(-7)-3}{5-(-2)}[/tex]

Simplify

m = [tex]\frac{-10}{7}[/tex]

The slope is [tex]\frac{-10}{7}[/tex]

The distance covered by the falling freely body from rest will be 48 feet.

The study of motion without considering the mass and the cause of the motion.

When a body falls freely from rest, the distance it travels straight changes as the square of the time (air resistance excluded). If something is dropped 192 feet from the summit of a tower, it lands on the ground in 8 seconds.

We know that the acceleration is due to gravity (g = 32 ft/s²).

d ∝ t²

d/t² = constant

Then the distance covered by the falling freely body from rest will be given as,

d / 4² = 192 / 8²

d / 16 = 192 / 64

d = 16 x 192 / 64

d = 48 feet

The distance covered by the falling freely body from rest will be 48 feet.

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Given parabola [tex]y=-2(x+3)^{2} +8[/tex]  have vertex (-3,8)

axis of symmetry :x=-3

x intercepts (-1,0),(5,0)

y intercepts (0,-10)

Maximum value (-3,8)

Range is y[tex]\leq 8[/tex] or (-∞,8]

Parabola is increasing in (-∞,-3) and decreasing in (-3,∞)

How to identify parabola type from vertex form and its attributes?

The parabola equation y=ax²+bx+c

The parabola equation in its vertex form is

y = a(x - h)² + k, where

a  is same as the a coefficient in the standard form;

(h, k)  is coordinates of the vertex of parabola

h and k can be calculated as

h = - b/(2a)

k = c - b²/(4a)

If a is negative the parabola opens downward and if a is positive the the parabola opens upward

Axis of symmetry : x= h

For  a parabola y=ax²+bx+c if a<0  then the range is y [tex]\leq k[/tex] and if a>0 then range is y[tex]\geq k[/tex]

For Maximum and minimum value , if a<0 then vertex is the maximum value and if a>0 then vertex is the minimum value.

For given equation [tex]y=-2(x+3)^{2} +8[/tex]

As this equation is in vertex form

h=-3, a=-2, k=8

Therefore, vertex = (-3,8)

For x intercept put y=0

Then [tex]y=-2(x+3)^{2} +8\\y\\=-2x^{2} -12x-10\\y=0\\\\x=-1,-5\\put x=0 \\y= -10[/tex]x intercepts (-1,0),(5,0)

y intercepts (0,-10)

Axis of symmetry : x= -3

[tex]y=-2(x+3)^{2} +8\\y=-2x^{2} -12x-10[/tex]

As a is negative therefore range is y[tex]\leq 8[/tex] or (-∞,8]

As a is negative therefore vertex (-3,8) is the maximum value

f'(x)= -4x-12

f'(x)=0 gives x= -3

f'(x)>0 in (-∞,-3), parabola is increasing in (-∞,-3)

f'(x)<0 in (-3,∞), parabola is decreasing in (-3,∞)

Please find the graph attached.

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Answer:

me not soluesan match huiudresst

Answer: 24.33 units

Step-by-step explanation: If we appropriately measure the distance between the points we can depict a parallelogram with 2 sides measuring 6.083 units and 2 others measuring 4 units. We multiply 4 x 6.083 and get the area: 24.33 units

Answer: 24

Step-by-step explanation: As the formula to solve this equation is A= 1/2 | [(x1y2) - (x2y1)] + [(x2y3) - (x3y2)] + [(x3y4) - (x4y3)] + [(x4y1) - (x1y4)]

Which would be (with the numbers)

[(-3 x 4) - 1 x 4)] + [(1 x -2) - (0 x 4)] + [(10 x 2) - (-4 x -2)] + [(-4 x 4) - (-3 x -2)]

which lowers down too

(-12 - 4) + (-2 - 0) + (0 - -8) + (-16 - 6)

Then that gets us (absolute values) of

|-16| + |-2| + |8| + |-22|

using absolute values that gets us to

16 + 2 + 8 + 22

Which is equal to 48.

Don't forget to divide by 2 because we need half of it as it says in the beginning of the formula (A = 1/2)

So that gives us the answer of 24.

Hope this helped :)

Also, this could help by labeling each coordinate as a (X, Y) Number

[-3(x1) , 4(y1)}  (you could write the x and y part above it)

And then you go down the list and label each as either x1 , x2 , x3 , x4 (for the left side of comma) and then y1 , y2, y3 , y4 (for the right side of the comma)

Answer: -2, -6/11

Step-by-step explanation:

[tex]11x^2 +28x=-12\\\\11x^2 +28x+12=0\\\\(11x+6)(x+2)=0\\\\x=-2, -6/11[/tex]

The mass of the tow chain will be equal to 12.96 kg.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given that 6.0m of Grade 70 bow chain, which has a diameter of 3/8" and weighs 2.16 kg/m.

The mass of 1 m chain = 2.16 kg

Mass of 6-meter chain = 2.16 x 6

Mass of 6-meter chain = 12.96 kg

Therefore, the mass of the tow chain will be equal to 12.96 kg.

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The solution to the inequality is x ≤ 3

The compound inequality is given as:

5x ≤ -30 and 5x ≤ 15

Divide both sides of the individual inequality in the compound inequality by the coefficient of the variable x

So, we have

x ≤ -6 and x ≤ 3

One of the above inequalities can be true

x ≤ 3 is a proper set of x ≤ -6

So, the solution to the inequality is x ≤ 3

See attachment for the graph of the inequality

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Answer:

x<0; x>0

Step-by-step explanation:

Basically, anything but zero, depending on what a is.

Answer:

x = ± [tex]\sqrt{a}[/tex]

Step-by-step explanation:

x² = a ( take square root of both sides )

x = ± [tex]\sqrt{a}[/tex]

A--->A'=(-2,6)

B--->B'=(7,3)