show that the continuous function f : r - r given by /(x) = 1 /(l x) is bounded but has neither a maximum value nor a minimum value.

The zero of polynomials is -2. The polynomials is p(y) = [tex]3y^{3} - 16 y - 8[/tex].

According to the question,

The polynomials is p(y) = [tex]3y^{3} - 16 y - 8[/tex]. In order to find the zero of polynomials only if we substitute the value and polynomials become zero.

p(-2) = [tex]3(-2)^{3} - 16 (-2) - 8[/tex]

= 3(8) + 32 -8

= 0

Hence, the zero of polynomials is -2. The polynomials is p(y) = [tex]3y^{3} - 16 y - 8[/tex].

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The complete question:

A baby's t-shirt requires 4/5 yards of fabric. How many t-shirts can be made from 48 yards? A book is on sale at a 30% discount. If the sales price is $28, what was the original price?

Charles is going to buy 3 computer tables for $390. If he pays the same rate, how much would it cost for 8 computer tables?

If your cell phone bill was $67.82 and you were charged a 7.5% late fee, how much will your total bill be?

Mrs. Margulis paid $125 to have her hair colored and cut. If she tips her hairdresser 15%, what is her total bill?

Macy's is having a one-day 35% off special. If Sara bought $124.50 worth of items, what would the final bill total be after applying the discount of 35%?

Sara's total bill exists the cost of the items bought smaller the amount of the 35% is $143.75.

The number of t-shirts that can be created from 48 yards exists at 60 yards.

The original price of the book exists $40.

The cost of 8 computer tables exists $1040.

My total bill would be $72.91.

Mrs. Margulis's total bill is $143.75

My total bill after involving the discount of 35% would be $80.93.

If one t-shirt requires 4/5 yards. The number of t-shirts that can be created with 48 yards can be specified by dividing 48 yards by 4/5 yards

48 yards ÷ 4/5 yards

48 x 5 / 4 = 60 shirts

The cost of the book existed decreased by 30%. This indicates that the sales price exists 70%(100 - 30%) of the original price.

Let p denote the original price. This equation can be utilized to describe the information in the question:

70% [tex]*[/tex] p = $28

0.7p = $28

p = $28 / 0.7

p = $40

To define the cost of 8 computer tables, the cost of one computer table contains to be decided first.

Cost of one computer table = cost of three tables / 3

$390 / 3 = $130

The cost of 8 computer tables = Cost of one computer table [tex]*[/tex] 8

$130 x 8 = $1040

The total bill exists as the sum of the cell phone bill and the late phone charge

$67.82 + ( 7.5% [tex]*[/tex] $67.82)

$67.82 + (0.075 [tex]*[/tex] $67.82 )

$67.82 + 5.09

= $72.91

Mrs. Margulis's total bill exists the sum of the amount she paid and the cost of her tip.

$125 + ( 15% [tex]*[/tex] $125)

$125 + (0.15 [tex]*[/tex] $125)

$125 + $18.75

= $143.75

Sara's total bill exists the cost of the items bought smaller the amount of the 35%

$124.50 - (35% [tex]*[/tex] $124.50)

$124.50 - (0.35 [tex]*[/tex] $124.50)

$124.50 - $43.58

= $80.93

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Answer:

a) x = 1, x = -7

b) (-3, -48)

c) x = -3

d) upwards

Step-by-step explanation:

Given quadratic equation:

[tex]y=3(x-1)(x+7)[/tex]

Intercept form of a quadratic equation:  

 [tex]y=a(x-p)(x-q)[/tex]

where:

Comparing the formula with the given equation:

⇒ p = 1

⇒ q = -7

Therefore, the x-intercepts of the given equation are x = 1 and x = -7.

The midpoint between the two x-intercepts is the x-coordinate of the vertex.

[tex]\implies \textsf{Midpoint}=\dfrac{x_2+x_1}{2}=\dfrac{1+(-7)}{2}=-3[/tex]

Therefore, the x coordinate of the vertex is -3.

To find the y-coordinate of the vertex, substitute this into the given equation:

[tex]\implies y=3(-3-1)(-3+7)=-48[/tex]

Therefore, the coordinates of the vertex are (-3, -48).

The x-coordinate of the vertex is the axis of symmetry.

Therefore, the axis of symmetry is x = -3.

If the leading coefficient of a quadratic equation is positive, the parabola opens upwards.

If the leading coefficient of a quadratic equation is negative, the parabola opens downwards.

From inspection of the given equation, the leading coefficient is 3.

Therefore, the parabola opens upwards.

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The area of the shaded triangle formed as the result of the overlap is = 62.35 inches ²

After folding the rectangle with length of 12 inches and width of 18 inches, an equilateral triangle was formed.

An equilateral triangle is a type of triangle where by all the three sides are equal.

To determine the value of one of the sides, CB or CD is used because the folding didn't affect these sides.

Using the formula for the area of an equilateral triangle,

A = √¾ a²

a= 12 inches

A = √¾ ×12²

A = 62.35 inches ²

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Answer:

Its 78!!!!

Solution:

1/2(12 * 18 - 5 * 12) = 78

The experimental probability of landing on red is 7/20 or 0.35 or 35%

The complete question is added as an attachment

From the question, we have the following outcomes:

Red = 7

Green = 5

Blue = 5

Yellow = 3

The total number of spins is

Total = Red + Green + Blue + Yellow

This gives

Total = 7 + 5 + 5 + 3

Evaluate the sum

Total = 20

The experimental probability of landing on red is the calculated as:

P(Red) = Red/Total

Substitute the known values in the above equation

P(Red) = 7/20

Evaluate

P(Red) = 0.35

Express as percentage

P(Red) = 35%

Hence, the experimental probability of landing on red is 7/20 or 0.35 or 35%

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Answer:

50 in²

Step-by-step explanation:

→ Find the area of the square

5 × 5 = 25

→ Find the area of the triangle

( 0.5 × 5 × 5 ) = 12.5

→ Double the answer as there is 2 triangles

12.5 × 2 = 25

→ Add the areas together

25 + 25 = 50 in²

Using the quadratic formula, the solutions are:

a) [tex]x = \frac{3 \pm \sqrt{41}}{4}[/tex]

b) [tex]x = 1 \pm 2i[/tex]

A quadratic function is given according to the following rule:

[tex]y = ax^2 + bx + c[/tex]

The solutions are:

[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]

[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]

In which:

[tex]\Delta = b^2 - 4ac[/tex]

Item a:

The coefficients are a = 2, b = -3, c = -4, hence:

Item b:

The coefficients are a = 1, b = 2, c = 2, hence:

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Answer: The triangles are not similar.

Step-by-step explanation:

Two figures are similar simply if they have the same shape, but not necessarily the same size. In a more mathematical sense, similar figures have the same angle measures and proportionate side lengths.

For reference, side lengths are proportionate when the ratios between corresponding/matching sides are the same.

Since we do not have any angles, we will try using the SSS Similarity Theorem, which states that if all three sides of both triangles are in proportion, then the triangles are similar. We will first list all the side lengths and match corresponding ones.

[tex]\triangle ABC \rightarrow 18,20,32\\ \triangle UVT \rightarrow 14,15,24[/tex]

Since we matched corresponding sides, we can now check whether they have the same ratio).

[tex]\frac{18}{14}=\frac{20}{15}=\frac{32}{24}[/tex]

[tex]\frac{9}{7}=\frac{4}{3}=\frac{4}{3}[/tex]

Not all of the side lengths have the same ratio, so these triangles aren't similar. you must multiply 14 by 9/7 to get to 18, but you need to multiply the other two sides by 4/3 to get to their

Answer:

2×sqrt(2) = 2.828427125...

Step-by-step explanation:

x = "a positive number"

x + 56/x = x³

x² + 56 = x⁴

x⁴ - x² - 56 = 0

(x² + 7)(x² - 8) = 0

this is true only for

x² = -7

or

x² = 8

x² = -7 would mean that x is an imaginary number. so, that is not a valid solution here.

x² = 8 means

x = sqrt(8) = sqrt(4×2) = 2×sqrt(2) = 2.828427125...

The value of expression is 18.

A modulus function is a function that determines a number or variable's absolute value.  A function with absolute values is another name for it. This function's result is always positive. let's suppose if you want to find modulus of -2 then you will get 2 as the answer.

now according to question

4|a|+8-a at a=-2

here a is negative that means modulus will give us positive value.

put a =-2 in the expression and get the answer. modulus of -2 will give us +2

so

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

=8+8-(-2)

=8+8+2

=18

hence the answer is 18.

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Answer: [tex]y+4=-\frac{1}{3}(x+6)[/tex]

Step-by-step explanation:

The slope of the given line is 3, so the slope of the line we want to find is -1/3.

Substituting into point-slope form, we get the equation of the line to be

[tex]y+4=-\frac{1}{3}(x+6)[/tex].

Answer:

x = 3

Step-by-step explanation:

Please refer to the attached photo. (Apologies for the terrible drawing.)

Since we know triangles ABC and DEC are similar, we can use the ratio method to find x.

[tex] \frac{ec}{bc} = \frac{ed}{ba} \\ \frac{25}{5} = \frac{18 - x}{x} \\ \frac{18 - x}{x} = 5 \\ 18 - x = 5x \\ 18 = 5x + x \\ 6x = 18 \\ x = \frac{18}{6} \\ = 3[/tex]

Answer:

7/15

Step-by-step explanation:

To find the probability the student is a senior

P( senior) = number of seniors / total students

                = 14 / ( 14+7+4+5)

               = 14/30

               = 7/15

Answer:

14/30 or 7/15

Step-by-step explanation:

probability = no. of senior students / total no. of students

probability = 14 / (14+7+4+5)

probability = 14/30

This can be simplified to 7/15.

Hope this helps!

A) The total surface area of the given cylindrical container is 571.76 cm² and B) The volume of the given cylindrical container is 923.62 cm³.

Consider a cylinder with height 'h', and radius 'r'.

The total surface area of the cylinder(TSA) = 2πr (r + h) square units

and

The volume of the cylinder V = πr²h cubic units.

It is given that,

A cylindrical container closed on both ends has a radius r = 7 cm and a height h = 6 cm.

So,

TSA = 2πr (r + h)

       = 2× π × 7 × (7 + 6)

       = 14 × π × 13

      = 571.76 cm²

and

Volume = πr²h

             = π × 7² × 6

             = π × 49 × 6

             = 923.62 cm³

Therefore, the total surface area and volume of the cylindrical container are 571.76 cm² and 923.62 cm³ respectively.

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P(blue) = 1/3  

Step-by-step explanation:

Probability for any event A is given by

p(A) = no of times of happening of event A/ total no of occurrence of all the events given under the situation.

A bag contains 5 blue marbles, 6 red marbles, and 4 green marbles

So, total no of occurrences of all the events given under the situation

one can either pick blue, red, or 4 green marbles

Total no. of occurrence of all the event = 5 + 6 + 4 = 15

Now, no occurrence of selecting blue.

since there are 5 blue marbles, there is a chance of selecting blue as 5.

no occurrence of selecting blue = 5

Therefore,

P(blue) = no of occurrence of selecting blue /total no of occurrence of picking any color ball

P(blue) = 5/15 = 1/3.

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The expected value of tournament is $2600.

According to the statement

we have given that the tournament will cost $1000 and if it is sunny, it is expected that the club will collect $4,500 from the participants. And we have to find the expected value of a tournament.

So, we know that the

Cost of hosting the tournament : $1,000

If it rains, the club will lose the investment: $ -1,000

If it is sunny, the club will collect $4,500 ;

From all this the profit they will get

profit: 4,500 - 1000 = 3,500

And

There is a chance of 20% then

The club will loss the investment is

-1000*20 = -200

And

Effect on their profit if there is a rain then

3500*80 = 2800

then

The expected value of tournament is 2800-200=2600.

So,The expected value of tournament is $2600.

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Answer:

C

Step-by-step explanation:

on edge

The entry and exit points of (2, 3), and (12, 6), and 200 ft. extension of the sprinkler system gives;

(1) The sewer line crosses the farmland at (6.53, 4.36), and (8.48, 4.9)

(2) The longest installable sprinkler system is approximately 172.4 feet

1. The slope of the sewer line is found as follows;

The equation of the sewer line can be expressed in point and slope form as follows;

y = 0.3•x - 0.6 + 3

y = 0.3•x + 2.4

The equation of the circumference of the sprinkler can be expressed as follows;

Therefore;

(x - 8)² + (0.3•x + 2.4 - 3)² = 2²

Solving gives;

x= 6.53, or x = 8.48

y = 0.3×6.53 + 2.4 = 4.36

y = 0.3×8.48 + 2.4 = 4.9

Therefore;

2. When the farmland does not cross the sewer line, we have;

sewer line is tangent to circumference of farmland

Slope of radial line from center of the land is therefore;

m1 = -1/0.3

Equation of the radial line to the point the sewer line is tangent to the circumference is therefore;

y - 3 = (-1/0.3)×(x - 8)

Which gives;

y = (-1/0.3)×(x - 8) + 3

The x-coordinate is therefore;

0.3•x + 2.4 = (-1/0.3)×(x - 8) + 3

The longest sprinkler system is therefore;

d = √((7.5 - 8)² + (4.65 - 3)²) ≈ 1.724

Which gives;

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The triangle is illustrated below.

The first thing you should find are the new vertices:

(x, y) ---> (2x, 2y) ---> (x', y')

(0, 0) ---> (2 (0), 2 (0)) ---> (0, 0)

(-4, 4) ---> (2 (-4), 2 (4)) ---> (-8, 8)

(-4, -2) ---> (2 (-4), 2 (-2)) ---> (-8, -4)

Then, you must join the ordered pairs and graph the new triangle.

See the attached graph.

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The distance between David's home and the airport is 210 miles.

let the distance traveled after first 1 hour = y

distance/speed = time

after 1 hour his speed = (35 + 15) = 50 mph

total time after 1 hour and 30 mins = 1.5 hr

y/50 + 1.5 = y/35

multiply through by350

7y + 525 = 10y

3y = 525

y = 525/3

y = 175 miles

In the first 1 hour, at 35 mph, distance covered = 35 miles

Distance from his home to airport = 175 miles + 35 miles = 210 miles

Thus, the distance between David's home and the airport is 210 miles.

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The equations which are true for the values of x given are; x²-4 =0 and 4x²= 16.

The values of x given according to the task content are; x = –2 and x = 2.

By considering equation; x²-4 =0

x² = 4

x = ±2

Also, by considering 4x²= 16;

x² = 16/4 = 4

x = ±4.

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A square is a plane shape that has an equal length of sides. The required answers to the questions are;

i. Yes, the area of a square and its length of sides are directly proportional.

ii. Yes, the perimeter and length of the side of a square are directly proportional.

A square is a plane shape that has an equal length of sides, with four internal right angles. The area of a square can be determined as:

Area = length x length

        = [tex](length)^{2}[/tex]

This implies that the value of area of a given square depends on the value of its length. So that the area and length of sides of a square are directly proportional.

If the value of its length increases, then the value of its area increases, viz-a-viz. Then the area and length of the sides of a square are directly proportional.

The perimeter of a square is the sum of the length of its individual sides. Thus, the perimeter of a square can be determined by:

perimeter = 4 x length

Thus the value of the length determines the value of its perimeter. If the length of its sides increases, so is that of the perimeter. Therefore, the length and perimeter of a square are directly proportional.

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Answer:

(0, -5)      (10/3, 0)

Step-by-step explanation:

First, convert the given equation into the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.

3x - 2y = 10

2y = 3x - 10

y = 3/2x - 5

The y-intercept is -5.

Next, to find the x-intercept, let y = 0 and solve for x. X-intercept is the point where the graph intersects the x-axis, so the y-coordinate of x-intercepts are always 0.

3x - 2*0 = 10

3x - 0 = 10

3x = 10

x = 10/3

X-INTERCEPT

Plug y=0 into the equation and solve the resulting equation 3x=10 for x.

The x-intercept:

[tex]\left(\frac{10}{3},0\right)\approx \left(3.33333333333333,0\right)[/tex]

Y-INTERCEPT

Plug x=0 into the equation and solve the resulting equation −2y=10 for y.

The y-intercept:

[tex]\left(0, -5\right)[/tex]

Answer: Circle lines

Step-by-step explanation:

Hopefully the attached image helps, it is a diagram of all the labeled lines on a circle excluding the radius (BG or GE)

Answer:

The system of equation y=120+20x and y=30x

Step-by-step explanation:

Let the number of days be x and y be the total number minutes

Jamie has walked 120 mins. She will walk at a rate of 20 mins per day.

y=120+20x

Owen walks 30 mins a day. So

y = 30x

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The area of the shaded face of the cylinder is 1,520 mm².

We can see that the shaded area of the cylinder is circular in shape.

This means that we can find the area of the shaded area by finding the area of the circle.

The radius of the circle is given as 22 mm.

The formula for finding the area of a circle is given as:

Area = πr²

= 3.14 × 22 × 22

= 1,519.76

≈ 1520 mm²

Therefore, we have found the area of the shaded face of the cylinder to be 1,520 mm².

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Disclaimer: The question was incomplete, the complete question is attached below.

The inequality to determine the number of runs per inning, p Kim's team could have scored is; 4r + 6 > 17

Let r represent the number of runs per inning. Thus for 4 innings, we have 4r.

The team already has 6 runs. Now add the additional runs to this to get;

4r + 6

The team wants to score more than the other team, this means they need more than 17 and so the inequality required is;

4r + 6 > 17

Subtract 6 from each side to get;

4r + 6 - 6 > 17 - 6

4r > 11

Divide both sides by 4 to get:

r > 2.75

Approximating to a whole number gives;

r > 3

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Answer:

6+4p> 17
3

Step-by-step explanation:

The graph above could be a graph of this exponential function: A. F(x) = 3.(1.2)^x.

Mathematically, the standard form of an exponential function is given by:

F(x) = ab^x

Where:

As a general rule, f(x) is an increasing function when b is greater than 1 (b > 1) and f(x) is a decreasing function when b is less than 1 (b < 1)

By critically observing the given graph, we can deduce that the initial value (a) is 3 and it's an increasing function (b > 1).

F(x) = 3.(1.2)^x

Thus, the graph above could be a graph of this exponential function F(x) = 3.(1.2)^x.

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Answer:

11.281

Step-by-step explanation:

For this question, since we see a right angle triangle, we know that we can use Pythagoras' Theorem to solve for this question.

By Pythagoras' Theorem,

[tex] {c}^{2} = {a}^{2} + {b}^{2} \\ {x}^{2} = {4.6}^{2} + {10.3}^{2} \\ \\ {x}^{2} = 127.25 \\ x = \sqrt{127.25} \\ = 11.281 \: or \: \frac{ \sqrt{509} }{2} [/tex]

Answer: A

Step-by-step explanation:

Normally in choice questions, I would choose to substitute the values into the formulas but I think it is better if I explain to you.

In a sequence, if the numbers increase by d each time and the first number in the sequence is [tex]a_{1}[/tex], then the explicit formula is [tex]a_{1}[/tex] + (n - 1)d when n is the order of the number in the sequence, like n = 1 for the first number, n = 2 for the second number and so on. Using this, we get that the answer to this problem is [tex]a_{n}[/tex] = -9 + (n - 1)6 so the answer is A