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 nearest tenth as needed.)

Answer:

∴ x = 6.40 units (to 3sf)

Step-by-step explanation:

Following the Pythagoras' Theorem,

 x² = 4² + 5²

∴ x = 6.40 units (to 3sf)

Step-by-step explanation:

Using Triangle Intersection Theorem,

2(LM)=2+x

[tex]2(2x - 11) = 2 + x[/tex]

[tex]4x - 2 2 = 2 + x[/tex]

[tex]3x = 24[/tex]

[tex]x = 8[/tex]

Answer:

[tex] x =\dfrac{7+\sqrt{41}}{4},\dfrac{7-\sqrt{41}}{4} [/tex]

Step-by-step explanation:

The given equation is ,

[tex]\longrightarrow 7x = 2x^2+1[/tex]

We can rewrite it as ,

[tex]\longrightarrow 2x^2-7x + 1=0 [/tex]

On comparing with the standard form of quadratic equation [tex] ax^2+bx + c [/tex] , we have ;

On using the quadratic formula , we have;

[tex]\longrightarrow x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\\[/tex]

[tex]\longrightarrow x =\dfrac{-(-7)\pm\sqrt{(-7)^2-4(2)(1)}}{2(2)} \\[/tex]

[tex]\longrightarrow x =\dfrac{7\pm\sqrt{49-8}}{4}\\ [/tex]

[tex]\longrightarrow x =\dfrac{7\pm\sqrt{41}}{4}[/tex]

separate the solutions ,

[tex]\longrightarrow x =\dfrac{7+\sqrt{41}}{4},\dfrac{7-\sqrt{41}}{4} [/tex]

And we are done !

The required implicit differentiation is given as dy/dx = -4x/3.

Given that,
To determine the implicit differentiation of the given function 4 = 2x² + 3y.

The method of determining the derivative of an implicit function by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol

Here,
4 = 2x² + 3y
Differentiate with respect to x on both sides,
d4/dx = d[2x²]/dx + 3dy/dx
0 = 4x + 3dy/dx
dy/dx = -4x/3

Thus, the required implicit differentiation is given as dy/dx = -4x/3.

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The probability that the region will be hit by a hurricane in 3 consecutive years is; 0.000343

The binomial probability is defined as the probability of exactly x successes on n repeated trials, with p probability. The general formula for binomial probability distribution is;

P(X = x) = ⁿCₓ * pˣ * (1 - p)^(n - x)

where;

P(X = x) is binomial probability

x is number of times for a specific outcome within n trials

ⁿCₓ is number of combinations

p is probability of success on a single trial

n is number of trials

Now, we are given that the probability of success for a particular region in Mexico being hit by hurricane is 0.07. Thus;

P(three consecutive years hurricane) = 0.07 * 0.07 * 0.07 = 0.000343

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Answer:

  common denominator = 2·3·5

Step-by-step explanation:

You want the factorization of the common denominator of 2/3+7/10.

The denominators of the fractions in the given sum are 3 and 10. Their prime factors are ...

  3 = 3

  10 = 2·5

The common denominator factors will be the product of the unique factors in the above list:

  common denominator = 2·3·5

__

Additional comment

Using the common denominator, the sum is ...

  20/30 +21/30 = 41/30 = 1 11/30

An adjacency matrix is defined as the square matrix that is used to describe the finite graph

An adjacency matrix is defined as the square matrix that is used to describe the finite graph which is also an example of graph theory.

The adjacency matrix is made up of rows and columns which is used to represent a simple labelled graph. it is also called connection matrix.

The properties of an adjacency matrix include the following:

The adjacency matrix can be used to represent indirect or direct graph.

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An adjacency matrix is a square matrix used to describe the finite graph.

An adjacency matrix is a square matrix used to describe a finite graph, which is also a kind of graph theory.

The adjacency matrix, which consists of rows and columns, is used to depict a basic labeled graph. It is also known as a connection matrix. The adjacency matrix can represent either an indirect or direct graph.

An adjacency matrix has the following properties:

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By the use of the distributive property, we have the result obtained as 6xy - 6xz.

The term distributive property has to do with the process by which we can remove the brackets that may sometimes occur in a mathematical expression. It is the way by which we can be able to rewrite the mathematical expression without adding the brackets thereby making mathematical operations much easier.

We have the expression; 6x (y - z)

Multiplying through by 6x we have;

6xy - 6xz

Using the distributive property, we obtain; 6xy - 6xz

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Answer:

g = -5

z = -4

z = 2.1

t = -36

Step-by-step explanation:

-4 = g +1  Subtract 1 from both sides

-5 = g

z - 4 = -8  Add 4 to both sides

z = -4

10.5 = 5z  Divide both sides by 5

2.1 = z

-9 = t/4  Multiply both side sby 4

-36 = t

The EF is the diameter. Then the area of the circle is  113.04  square meters.

circle :

A circle is a circular shape without corners or line segments. In terms of geometry, it has the shape of a closed curve.

EF = diameter

EF = 12 meter

then, radius  = d/2 = 12/2 = 6 meter

Area of the circle is calculated  as:

area = πr²

area = 3.14 x 6 x 6

area = 113.04 square meter

The given que is incomplete . The correct question is given as :

The EF is the diameter. If EF measures 12 meters, the approximate area of circle B is square meters.

The EF is the diameter. Then the area of the circle is  113.04  square meters.

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Answer:

a = 48°

Step-by-step explanation:

Forming the equation,

→ 42° + a = 90°

Now the value of a will be,

→ 42° + a = 90°

→ a = 90° - 42°

→ [ a = 48° ]

Hence, the value of a is 48°.

⇒The quadratic equation has already been factorized in such a way that the factors are equal to 0 ∴ they won`t be an need to multiply out, since you would still have to come back to the factorizing part.

⇒Let us solve for x now.

[tex]\sqrt{x} +2 =0\\\sqrt{x} =-2\\No\\ solution[/tex]

⇒There is no way that a square root of a number can result in a negative number... that is why the answer was a no solution.

[tex]\sqrt{x} -2=0\\\sqrt{x} =2\\(\sqrt{x} )^{2} =(2)^{2} \\x=4[/tex]

⇒The solution to the quadratic equation is only and only 4.

Answer:

(32, 8)

Step-by-step explanation:

Substitute 4y for x in x + y = 40 and solve for y. Then find x.

[tex]4y + y = 40[/tex]

[tex]5y = 40[/tex]

[tex]y = 8[/tex]

[tex]x = 4(8) = 32[/tex]

The area between z = -1.71 and z = 0.08 is 0.4883, in median .

What is median ?

The value of the middle observation found after the data are arranged in ascending order is referred to as the median of the data. In many cases, it is challenging to take all of the facts into account when representing something, and in these cases, median is helpful. The median is one of the simple to compute statistical summary metrics. The median is also known as the place average since it uses the data that is in the centre of a sequence to determine its value.

=> P(-1.71 < Z < 0.08 ) = P(Z < 0.08 ) - P(Z < -1.71)

= 0.5319 - [1 - P(Z < 1.71)]

= 0.5319- [1 - 0.9564]

= 0.4883

Hence, the area between z = -1.71 and z = 0.08 is 0.4883.

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Over 48.6 hours are worked by 2.28 percent of faculty members each week.

Given that,

In a college, a full-time faculty member typically puts in 43 hours each week.

We have to find how many faculty members work more than 48.6 hours each week, assuming the standard deviation is 2.8 hours.

The Z-score determines the measure's standard deviations away from the mean. After calculating the Z-score, we look at the p-value associated with it in the z-score table. This p-value is the probability that the measure's value is smaller than X, or the percentile of X. By subtracting 1 from the p-value, one can determine the likelihood that the value of the measure is greater than X.

In a college, a full-time faculty member typically puts in 43 hours each week. 2.8 hour standard deviation.

This means μ=43 and σ=2.8

What proportion of academic staff employees put in more than 58.6 hours each week.

When X = 48.6, the proportion is calculated by deducting 1 from the p-value of Z.

So,

Z=X-μ/σ

Z=48.6-43/2.8

Z=5.6/2.8

Z=2

Z=2 has a p-value of 0.9772

1 - 0.9772 = 0.0228

0.0228*100% = 2.28%

Therefore, Over 48.6 hours are worked by 2.28 percent of faculty members each week.

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Answer:

Step-by-step explanation: formula is (y2 - y1) / (x2 - x1)

so in this case it is: (4-(-4) / (-8 - 2) -> 8/-10 -> -4/5(final solution)

The decimal equivalent of 13/10 is 1.3

Decimal:

Decimal is referred as the numbers, which consist of two parts namely, a whole number part and a fractional part separated by a decimal point. For example, 12.5 is a decimal number.

Give,

Here we have the fraction 13/10

And we need to find the decimal equivalent to the fraction.

In the given fraction, we have to use the long division method in order to get the decimal for,

The steps for the long division is as follows:

1) Set up the problem with long division bracket. Put dividend inside bracket and divisor on outside left.

2) 10 goes into 13 (1-times). Put a 1 in the next place of quotient and multiply 10 by 1 to get 10.

Subtract 10 from 13 to get remainder (13-10=3).

3) Now, bring down 0 from the dividend, to make 30. 10 goes into 30 (3-times). Put a 3 in the next place of quotient and multiply 10 by 3 to get 30.

Subtract 30 from 30 to get remainder (30-30=0).

Therefore, the decimal equivalent to 13/10 is 1.3

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Step-by-step explanation:

3x + 2y = -18

Set y = 0

3x + 2 × 0 = -18

3x + 0 = -18

3x = -18

x = -6

.: the x-intercept = -6

You can choose to put it in coordinate form (-6, 0).

[tex]Answer: \boxed {(-6,0)}[/tex]

Step-by-step explanation:

The x-intersection coordinate of the equation 3x+2y=-18 is (x,0)

Hence, y=0

3x+2(0)=-18

3x+0=-18

3x=-18

Divide both parts of the equation by 3:

x=-6

Thus, (-6,0)

The fraction that Martha has left to make matching throw pillows is 3 1/6 yards.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.

From the information given, Martha had 12 2/3 yards of drapery material. She used 3/4 of it to make the drapes for her family room.

Since 3/4 has been used, the fraction left will be gotten by subtracting the fraction that had already been used from the total fraction that she has. In this case, it should be noted that this will be illustrated as:

Total fraction that Martha has - The fraction that has been used

= 1 - 3/4

= 1/4

Therefore, the fraction will be the fraction that is left multiplied by the yards of drapery material that Martha had at the beginning. This will be:

= Fraction unused × Total yards of material

= 1/4 × 12 2/3

= 1/4 × 38/3

= 19/6

= 3 1/6

The fraction is 3 1/6 yards.

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Answer:

f(-7) = 18

f(-3) = 14

f(4) = 7

Step-by-step explanation:

f(-7)

l-7-8l + 3

l-15l + 3

15 + 3

18

F(-3)

l-3-8l + 3

l-11l + 3

11 + 3

14

F(4)

l4-8l + 3

l-4l + 3

4 + 3

7

From the given details of Manuel wooden crates , where x represents the number of crates and y represents the cost then equation represents the given situation is given by y = 10x + 5.

As given in the question,

Given details of Manuel wooden crates :

Number of crates  : 2       4       6         8

Cost in dollars       : 25     45      65      85

From the given table where x represents the number of crates and y represents the cost :

(x₁ , y₁) = ( 2, 25)

(x₂ , y₂) = ( 4, 45)

For the given situation equation is given by :

( y - y₁) / (x- x₁) = (y₂ - y₁) / (x₂ - x₁)

⇒( y - 25) / (x -2) = (45 -25)/ (4 -2)

⇒(y -25) / (x -2) = 10

⇒y - 25 = 10(x-2)

⇒ y = 10x +5

Therefore, from the given details of Manuel wooden crates , where x represents the number of crates and y represents the cost then equation represents the given situation is given by y = 10x + 5.

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Answer: (0,0),  (-5,0),  (2,0)

Step-by-step explanation:

c(t)=4t⁴+12t³-40t²

1) t=0

c(t)= 4(0⁴)+12(0³)-40(0²)

c(t)=4(0)+12(0)-40(0²)

c(t)=0+0+0

c(t)=0

Thus (0,0)

2) c(t)=0

4t⁴+12t³-40t²=0

Divide both parts of the equation by 4:

t⁴+3t³-10t²=0

t²(t²+3t-10)=0

t²=0

t=0

Thus (0,0)

t²+3t-10=0

t²+(5t-2t)-10=0

(t²+5t)-(2t+10)=0

t(t+5)-2(t+5)=0

(t+5)(t-2)=0

t+5=0

t=-5

Thus (-5,0)

t-2=0

t=2

Thus (2,0)

Step-by-step explanation:

the slope-intercept form is

y = ax + b

with "a" being the slope, and "b" being the y-intercept (the y- value when x = 0).

so, we have

y = x - 8

The solution of the equation 3x(x - 3) = 12 will be 4 and negative 1.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The equation is given below.

3x(x - 3) = 12

Simplify the equation, then we have

3x(x - 3) = 12

x(x - 3) = 4

x² - 3x - 4 = 0

Factorize the equation, then we have

x² - 3x - 4 = 0

x² - 4x + x - 4 = 0

x(x - 4) + 1(x - 4) = 0

(x - 4)(x + 1) = 0

x = 4, -1

The solution of the equation 3x(x - 3) = 12 will be 4 and negative 1.

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Answer: [tex]\frac{11}{5}[/tex]

Step-by-step explanation

(y2-y1)/(x2-x1)

which means (5-(-6))/-4-(-9)=[tex]\frac{11}{5}[/tex]

The first term [tex]a_{1}[/tex] = 2 and the sum of first 30 terms [tex]s_{30}[/tex] = 930

Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value.

Arithmetic sequence is gotten by adding a known term by a constant value.

if [tex]a_{33}[/tex] = 66 and d = 2 and [tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n -1)d and n = 33

Then

[tex]a_{33}[/tex] =  [tex]a_{1}[/tex] + 32d,

making  [tex]a_{1}[/tex] subject of the equation we have

[tex]a_{1}[/tex] =66 - 32 x 2

[tex]a_{1}[/tex] = 66 - 64

[tex]a_{1}[/tex] = 2

if n = 30,  [tex]a_{1}[/tex] =-2, d = 2

Then

[tex]a_{30}[/tex] = 2 + ( 30 - 1) x 2

[tex]a_{30}[/tex] = 2 + 29 x 2

[tex]a_{30}[/tex] = 60

if [tex]s_{n}[/tex] = n/2([tex]a_{1}[/tex] + [tex]a_{n}[/tex])

Then,

[tex]s_{30}[/tex] = n/2 ( [tex]a_{1}[/tex] + [tex]a_{30}[/tex]) where n = 30

[tex]s_{30}[/tex] = 30/2( 2 + 60)

[tex]s_{30}[/tex] = 930

In conclusion, the sum of he first 30 terms is 930 and the first term is 2

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Answer:

the interior angles of a triangle add to be 180 degrees.

the value of angle x = 36 degrees

the value of angle y = 84 degrees

The gradient of the function at the point (-1 -7) is 3a - 6.

What is the gradient of the function?

A function's gradient is also known as its slope, and the slope (of a tangent) at a given point on a function is known as its derivative.

We have,

g(x) = ax³ + 3x² + bx + c

Take the derivative of the function with respect to x, then substitute the x-coordinate of the point of interest in for the x values in the derivative to find the gradient.

to know the gradient of the function ax³ + 3x² + bx + c at the point (-1, -7) we would do the following:

Take the derivative with respect to x:

g'(x) = 3ax² + 6x + b

Substitute the x-coordinate (x = -1)in for x:

gradient = 3a(-1)² + 6(-1) + b = 3a - 6

So the gradient of the function at the point (-1 -7) is 3a - 6.

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