A farmer with 350 meters of fencing wants to enclose a rectangular plot that borders on a river. If the farmer does not fence the side along the river, what is the largest area that can be enclosed? What are the dimensions of the enclosed area?
The width, labeled x in the figure, is ?
(Type an integer or decimal rounded to the nearest tenth as needed.)
The length, labeled 350-2 x in the figure, is?
(Type an integer or decimal rounded to the nearest tenth as needed.)
The largest area that can be enclosed is ?
(Type an integer or decimal rounded to the n
meters.
square meters.
cubic meters.

He should increase each dimension by 8 feet.

What is the area of a rectangle?

The area of the rectangle is the region enclosed by the perimeter of the rectangle and is equal to the product of length and width.

i.e. Area (A) = length(l) * width (w)

Given, a deck measurement is 12 feet by 10 feet

i.e. length (l) = 12 feet

width(w) = 10 feet

Area of deck (A) = 12*10 = 120 square feet

Let 'x' be the increased dimensions then,

new length = (12 + x) feet

new width = (10+x) feet

And, area of new dimensions = 3*120 = 360 square feet

So,  [tex](12 + x)*(10+x) = 360[/tex]

or, [tex]120+12x + 10x + x^{2} =360[/tex]

or, [tex]x^{2}+ 22x+120-360=0[/tex]

or, [tex]x^{2}+ 22x-240=0[/tex]

or, [tex]x^{2}+30x-8x-240=0[/tex]

or, [tex]x(x+30)-8(x+30)=0[/tex]

or, [tex](x+30)(x-8)=0[/tex]

Either, [tex](x+30)=0[/tex]            or, [tex](x-8)=0[/tex]

             [tex]x=-30[/tex]                        [tex]x=8[/tex] (Valid)

Hence, the increased dimension is 8 feet.

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The values of x are 1, 2, ±√-3.

Step-by-step explanation:

x⁵ + 5x³ + 5x - 2 = 0

x⁵ + 5x³ + 5x = 2

x ( x⁴ + 5x² + 5 ) = 2

x(x² + 1 )(x²+5 ) = 2

x = 2

(x² + 1 ) = 2

x² = 1

x = ± 1

(x²+5 ) =2

x² = -3

x = ±√-3

Hence, the values of x are 1, 2, ±√-3.

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Answer:

x = 0.35438 (5 d.p.)

Step-by-step explanation:

Given equation:

[tex]x^5+5x^3+5x-2=0[/tex]

Solve using the Newton-Rhapson method.

[tex]\boxed{\begin{minipage}{8 cm}\underline{The Newton-Rhapson iteration for solving f$(x) = 0$}\\\\$x_{n+1}=x_n-\dfrac{\text{f}\left(x_n\right)}{\text{f}\:'\left(x_n\right)}$\\\end{minipage}}[/tex]

If f(x) = 0 then:

[tex]\text{f}(x)=x^5+5x^3+5x-2[/tex]

Differentiate f(x) to find f'(x):

[tex]\implies \text{f}\:'(x)=5x^4+15x^2+5[/tex]

This means the iteration formula is:

[tex]x_{n+1}=x_n-\dfrac{{x_n}^5+5{x_n}^3+5{x_n}-2}{5{x_n}^4+15{x_n}^2+5}[/tex]

Let x₀ = 0.

Substitute this into the formula to find x₁:

[tex]\begin{aligned}\implies x_1&=0-\dfrac{(0)^5+5(0)^3+5(0)-2}{5(0)^4+15(0)^2+5}\\&=0-\dfrac{-2}{5}\\&=0.4\end{aligned}[/tex]

Substitute x₁ into the iteration formula to find x₂:

[tex]\begin{aligned}\implies x_2&=0.4-\dfrac{(0.4)^5+5(0.4)^3+5(0.4)-2}{5(0.4)^4+15(0.4)^2+5}\\&=0.4-\dfrac{0.33024}{7.528}\\&=0.3561317747\end{aligned}[/tex]

Repeat until the solution is found:

[tex]\implies x_3=0.354380602[/tex]

[tex]\implies x_4=0.3543780551[/tex]

[tex]\implies x_5=0.3543780551[/tex]

Therefore, the solution to the given equation is x = 0.35438 (5 d.p.).

The values of x that makes the inequality true are within the range x < -6

An inequality is a mathematical statement that shows that two quantities are unequal.

In such an expression the quantity at the left is either equal to and greater than, greater than, less than and equal to or greater than.

[tex]\frac{x + 6}{6 - x}[/tex]  < 0

By cross multiplying,

x + 6 < 0

x < -6

In conclusion, the values of x for which the inequality is true is x < -6

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Answer: C

Step-by-step explanation: for any of my edgen. people.

The sides of ∠1 are FG and FE, the vertex of ∠HFG is F and the names of ∠EFH are ∠F and ∠2

The figure represents the given parameter

From the question, we have

Angle = ∠1

The sides of ∠1 are the sides that extend from the vertex of angle 1

These sides are FG and FE

From the question, we have

Angle = ∠HFG

In the above representation, the angle can be expressed as

Angle = ∠F

This represents the vertex

So, the vertex is F

From the question, we have

Angle = ∠EFH

In the above representation, the angle can be expressed as

Angle = ∠F

Also, we have

Angle = ∠2

So, the names are ∠F and ∠2

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Answer:

38°

128°

Step-by-step explanation:

Complementary angles have measures that add to 90°.

Supplementary angles have measures that add to 180°.

comp: 90 - 52 = 38

sup: 180 - 52 = 128

Debemos tomar la integral definida de la diferencia entre las dos funciones en el intervalo dado.

Supongamos que queremos encontrar el area entre dos funciones f(x) y g(x) en un intervalo (a, b).

Vamos a suponer que f(x) > g(x) en todo el intervalo (a, b), entonces el area entre la funcion f(x) y g(x) en ese intervalo se calcula como:

[tex]\int\limits^b_a {(f(x) - g(x))} \, dx[/tex]

Si por ejemplo tuvieramos que para un valor c en el intervalo (a, b) se da que:

f(x) > g(x) en (a, c)

g(x) > f(x) en (c, b)

Entonces la integral sería:

[tex]\int\limits^c_a {(f(x) - g(x))} \, dx + \int\limits^b_c {(g(x) - f(x))} \, dx[/tex]

Y similarmente si debemos separar el intervalo mas segmentos.

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Answer:

x = 4 and y = 3

Step-by-step explanation:

You are looking for the value of x and y when: 2x - 3y = -1 and y = x - 1

Because you are given y in terms of x (the second equation given), substitute that into the first equation for y:

2x - 3y = -1 when y = x - 1

2x - 3(x - 1) = -1

expand left side:

2x - 3x + 3 = -1

combine x terms on left side:

-x + 3 = -1

subtract 3 from both sides:

-x + 3 - 3 = -1  - 3

-x = -4

divide both sides by -1:

-x/-1 = -4/-1

x = 4

now use x = 4 in one of the original equations to solve for y. For simplicity sake, we will use the second equation but the answer can also be found by substituting x = 4 into the first equation.

y = x - 1 when x = 4

y = 4 - 1

y = 3

Answer:

x = 4; y = 3

Step-by-step explanation:

2x - 3y = -1

y = x - 1

Copy the first equation.

Subtract x from both sides of the second equation and multiply both sides by 3. Write it below the first equation. Then add the equations eliminating y. Solve for x.

     2x - 3y = -1

+   -3x + 3y = -3

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

      -x        = -4

x = 4

Now substitute 4 for x in the second original equation and solve for y.

y = x - 1

y = 4 - 1

y = 3

Answer: x = 4; y = 3

Step-by-step explanation:

1. First things first, the binomial tells us the zeroes.

[tex] - (x - 2) {}^{2} = 0[/tex]

[tex](x - 2) {}^{2} = 0[/tex]

[tex]x - 2 = 0[/tex]

[tex]x = 2[/tex]

This root has a multiplicity of 2, so this root will "bounces off the x axis"

[tex](x + 4) = 0[/tex]

[tex]x = - 4[/tex]

Our x intercepts are

2 and -4

This root has a multiplicty of 1, so it will cross thorough the x axis.

Our leading degree is odd and we have a negative leading coefficient so

as x approaches ♾️, f(x) approaches negative ♾️

and as x approaches negative ♾️, f(x) approaches ♾️.

Our y intercept can be found by letting x=0,

so

[tex] - (0 - 2) {}^{2} (0 + 4) = - ( - 2) {}^{2} (0 + 4) = - (4)(4) = - 16[/tex]

So our y intercept is -16.

For Rational Functions, if the numerator and denominator share the same factor they are considered a removable discontinuity or hole.

Set it equal to 0.

[tex]x + 5 = 0[/tex]

[tex]x = - 5[/tex]

So we have a hole at x=-5.

Next, simplify the fraction.

[tex] \frac{x - 4}{x - 6} [/tex]

Now, plug in -5

[tex] \frac{ - 5 - 4}{ - 5 - 6} = \frac{ - 9}{ - 11} = \frac{9}{11} [/tex]

So we have a hole at (-5,9/11).

To find y intercept, let x=0,

[tex] \frac{0 - 4}{0 - 6} = \frac{2}{3} [/tex]

To find Vertical Asymptote, set denominator equal to 0

[tex]x - 6 = 0[/tex]

[tex]x = 6[/tex]

Draw a vertical dotted line at x=6

To find HA, this is the only case since the numerator and denominator has the same degree.

So using the leading coefficients, divide the numerator leading coefficient/ denominator leading coefficient.

The leading coefficient for both is 1 so

[tex]ha = \frac{1}{1} [/tex]

So our HA is y=1.

Draw a horizon tal dotted line at y=1

We have no slope asymptote.

The graph is above.

Part 3:

(3x-1)(2x+1)>0

[tex]3x - 1 = 0[/tex]

[tex]3x = 1[/tex]

[tex]x = \frac{1}{3} [/tex]

[tex]2x + 1 = 0[/tex]

[tex]2x = - 1[/tex]

[tex]x = - \frac{1}{2} [/tex]

We have three possible regions, when x is positive

Pick a random number less than -1/2 and plug it in the inequality to see if it true.

Let use -1

[tex](3( - 1) - 1)(2( - 1) + 1) = ( - 4)( - 1) = 4[/tex]

Since 4>0, Whenever x is less than -1/2, the function is positive (greater than zero)

Let's try the next region.

Let use 0

[tex](3(0) - 1)(2(0) + 1) = ( - 1)(1) = - 1[/tex]

So this solution won't work

Let try the next region, let use 1.

[tex](3(1) - 1)(2(1) + 1) = (2)(3) = 6[/tex]

Since 6>0, Whenever x is greater than 1/3, the function is positive(greater than zero).

Our answer is

(-oo,-1/2) U (1/3,oo).

Part 4:

We know x cannot be -2 because

[tex]x + 2 = 0[/tex]

[tex]x = - 2[/tex]

So -2 can not be in our answer.

[tex] \frac{x - 1}{x + 2} \leqslant 2[/tex]

[tex]x - 1 \leqslant 2(x + 2)[/tex]

[tex]x - 1 \leqslant 2x + 4[/tex]

[tex] - 5 \leqslant x[/tex]

So

[tex]x \geqslant - 5[/tex]

However x can not be -2. so we say

[-5,-2) U (-2,oo)

Answer:

[tex]-\frac{3}{\sqrt{7} } .[/tex]

Step-by-step explanation:

1) tanΘ=sinΘ/cosΘ;

[tex]2) \ cos \theta=^+_-\sqrt{1-sin^2 \theta}; \ = > \ cos \theta=^+_-\frac{\sqrt{7}}{4};[/tex]

3) if according to the initial condition Θ is in II-quadrant, then the cosΘ<0!

[tex]cos \theta=-\frac{\sqrt{7}}{4} ;[/tex]

4) finally,

[tex]tan \theta=\frac{sin \theta}{cos \theta}=-\frac{3}{\sqrt{7}}.[/tex]

The image distance is 33.3 cm and the magnification is 0.333  .

In the question ,

it is given that

since the lens is diverging

the focal length (f) = -50 cm

the distance between flower and diverging lens  (u) = -100

the formula to find the image distance is given by the equation

1/f = 1/v - 1/u

Substituting the values of f and u in the equation ,

we get

-(1/50) = 1/v - (-1/100)

1/v = -1/50 - 1/100

1/v = -3/100

v = -(100/3)

v = -33.33

formula for magnification = -(v/u)

= -(-33.33/100)

= 0.33

Therefore , The image distance is 33.3 cm and the magnification is 0.333  .

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The roots of the radical expression is given as 8, not defined, 10

What is radical expression?

a radical expression is defined as any expression containing a radical (√) symbol. Many people mistakenly call this a 'square root' symbol, and many times it is used to determine the square root of a number.

Given,

1. √64

we know 8 multiplied by 8 gives 64

√64 =8

2. ⁴√ -1

not defined

3. ³√1000

We know 10 multiplied by 10 =100

and 100 multiplied by 10 =1000

root of ³√1000 = 10

The radical form or number is

1. (⁴√ 1)⁷=1

2. ³ √-64=8i

3. (2⁹)¹/³=8

4. (11²)¹/² =11

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Answer:

[tex](3,0)[/tex]

Step-by-step explanation:

The ordered pair that satisfies both inequalities will lie in the region that is shaded by both inequalities.

The product of 110 × 298 by rounding each factor to the nearest hundred is 30,000.

When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done. The crucial figures are preserved when numbers are rounded off. Example: When rounded to the next hundredths place, 2.786 may be converted to 2.79. If 2.786 is rounded to the nearest tenths place, 2.8 is the result.

Given,

110 × 298

Rounding to the nearest hundred:

100 × 300

30,000

The product of 110 × 298 by rounding each factor to the nearest hundred is 30,000.

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The inequality that describes the relationship between the maximum amount Herman wants to spend and the total golf costs for the season is 450 + 18x ≤ 1000.

Herman can play for a maximum of 30 rounds, which will cost $990 in total.

Herman decides to take up golf. His golf club membership will cost $450 for the season, and he will be charged $18 for each round of golf that he plays. Herman has decided not to spend more than $1000 on golf for the season.

Let the number of rounds of golf Herman plays be represented by the variable "x". We can write the inequality as given below.

450 + 18x ≤ 1000

We can further simplify and solve this inequality.

18x ≤ 1000 - 450

18x ≤ 550

x ≤ 30.56

Hence, the maximum number of rounds of golf is 30. The total cost is calculated below.

C = $450 + $18*30

C = $450 + $540

C = $990

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Answer:

[tex]g(x)=|-x+1|-2[/tex]

Step-by-step explanation:

When reflecting over the [tex]y[/tex] axis, [tex]f(x) \to f(-x)[/tex].

[tex]f(x)=|x+1|-2 \implies g(x)=|-x+1|-2[/tex]

The equation would be g(x) = |-x+1| -2 reflecting the function over the y-axis.

Reflection across the y-axis is defined as reflecting a point across they = x,  the x-coordinate, and y-coordinate places, the line y = -x is the coordinates (-x, y).

So reflected across the y-axis: f(x) → f(-x),

⇒ (x,y) → (-x , y)

The function is given in the question

f(x) = |x+1| -2

We know that the reflected across the y-axis: f(x) → f(-x),

⇒ (x,y) → (-x , y)

g(x) = f(-x)

g(x) = |-x+1| -2

Thus, the equation would be g(x) = |-x+1| -2 reflect the function over the y-axis.

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Answer:

3.75%

Step-by-step explanation:

800+3.75%=830

The required equation of the line is 22x - 18.

A linear equation is defined as an equation in which the highest power of the variable is always one.

We take the two points (2, 26) and (5, 92) in the given table.

Let the required equation of the line is

⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

x₁ = 2, y₁ = 26

x₂ = 5, y₂ = 92

Substitute values in the equation, we get

y - 26 = (92-26/5-2)(x - 2)

y - 26 = 66/3(x - 2)

y = 22(x - 2) + 26

y = 22x - 44 + 26

y = 22x - 18

Therefore, the required equation of the line is 22x - 18.

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Answer:

inequality form: -4≤x<5

The matching angles are equivalent when the lines are parallel.

Here,

1. angles 6 and 7 are vertical angles.

2. angles 1 and 8 are alternate exterior angles.

3. angles 4 and 5 are alternate interior angles.

4. angles 2 and 6 are corresponding angles.

5. angles 6 and 8 are complimentary angles.

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Answer: B

Step-by-step explanation:

B

Answer:

n= 9,10,11,12,13

Step-by-step explanation:

Change the denominator to 16 so it can be common with n

1/2

1x8/2x8

8/16

3/4

3x4/4x4

14/16

Now we look at the numerators and see the new ones are 8 and 14 so all the numbers in between 8 and 14 are 9,10,11, 12, and 13

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The possible values of n are 9, 10, and 11.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

1/2 < n/16 < 3/4

Now,

Take 1/2 < n/16

1/2 < n/16

16/2 < n

8 < n ____(1)

Take n/16 < 3/4

n/16 < 3/4

n < 3/4 x 16

n < 12 ______(2)

From (1) and (2) we get,

8 < n < 12

This means,

The possible values of n are 9, 10, and 11.

Thus,

n values are 9, 10, and 11.

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Answer:

Step-by-step explanation:

x=-11we know thatPoints A,B,C,and D are collinear and positioned in that ordersoAD=AB+BC+CD -----> by addition segment postulatewe haveAB=2x+30AD=x=32substitute the given values and solve for xx+32 = (2x+43)Group terms that contain the same variable2x-x=32-43x=-11

1. The entire expression, 4x² + x + 3, is a sum with: 3 terms.

2. The coefficients of the expression are: 4 and 1.

The coefficient in a polynomial expression is described as the number that is multiplied by a variable.

For example, the term 5x has a variable of x that is multiplied by 5. Therefore, the coefficient of the term is 5.

Given the expression, 4x² + x + 3 that contains three terms, namely, 4x², x, and 3 .

Therefore, we can state that:

1. The entire expression is a sum that has 3 terms.

2. The coefficient of 4x² is 4. The coefficient of x is 1.

Therefore, we can state that, the coefficients are: 4 and 1.

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The range for this situation is {125, 150, ... 250}.

The range of a function includes all the possible output (y) values when the x value is substituted with a number.

The daily cost of hiring a lawn service = y

The number of hours mowing = x hours

Fixed cost per day = $100

Variable cost per hour = $25

Maximum hours of work per day = 6 hours

Minimum hour of work per day = 1 hour

y = 100 + 25x

y = 100 + 25(6)

y = 250

y = $250

For 5 hours, y = $225 (100 + 25(5)

For 4 hours, y = $200 (100 + 25(4)

For 3 hours, y = $175 (100 + 25(3)

For 2 hours, y = $150 (100 + 25(2)

For 1 hour, y = $125 (100 + 25(1)

Thus, the daily cost of hiring a lawn service ranges from  {125, 150, ... 250}.

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Answer:

Each movie costs $3.75 while each video game costs $5.50.

Step-by-step explanation:

Let the cost of each movie and the cost of each video game be $x and $y respectively.

6x + 5y = 50 ------ equation (1)

2x + 3y = 24 ------ equation (2)

Subtract 3 times of equation (2) from equation (1):

(6x + 5y) - 3(2x + 3y) = 50 - 3(24)

    6x + 5y -  6x - 9y = 50 - 72

                           -4y = -22

                            4y = 22

                           ∴ y = 5.5

Substitute y = 5.5 into equation (2):

2x + 3(5.5) = 24

            2x = 7.5

           ∴ x = 3.75

In a case whereby Henry incorrectly said the rate 1/4 hour/ 1/12 acre can be written as the unit rate 1/48 hour per acre the correct unit rate is 3hours per acre, he made the mistake by multiplying directly.

Rate  can be described as thequantity, or degree of something measured per unit of something else, the concept that will be used is the concept of rate.

The given rate will be   1/4 hour per 1/12 acre

but the per that was added implies division,

Then te rate will now be  1/4 hour ÷ 1/12 acre , then we can express as product as :1/4 hour * 12 /1 acre

Then we can simplify as : 3hours per acre

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This statement is false about metric system.

What is metric system?

matric systemare a group of two or more Lewis structure that represents a single polyatomic species.

Resonance is the ability of system to moves it's pi electron to the system .

Resonance structure are more significant beacuse they provide a much more realistic views of the shape of a molecule.

Each individua matric system is average into a resonance which is both true shape of the molecule .

Thus this statement is false about memetrictric system.

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