The maximum area that the farmer can enclose for the rectangular garden is 488 sq ft and the dimensions of the rectangular garden are 24ft and 12 ft respectively.

It is given that a farmer decided to enclose a rectangular garden with one side using the barn of a tree and other 3 sides with 48 ft of fencing.

Let the length of the rectangle be y and the breadth of the rectangle be u.

So **perimeter **of the fencing needed = y + 2u (as one side is barn)

∴ y + 2u = 48

⇒ y = 48 - 2u (equation 1)

Area = yu (equation 2)

Putting the value of variable y from equation 1 in equation 2 we have,

Area = (48-2u)u

∴ Area = 48u - 2[tex]u^{2}[/tex]

⇒ Area = -2[tex]u^{2}[/tex] + 48u

⇒ Area = -2([tex]u^{2}[/tex] - 24u)

⇒ Area = -2([tex]u^{2}[/tex] - 24u + 144) + 288 (using completing the square method)

⇒ Area = -2[tex](u-12)^{2}[/tex] + 288

So the maximum area is 288 sq units as for any value of u the area value will decrease as seen from the above equation.

So if Area = 288

Then yu = 288

⇒ u = 288/y equation 3

Putting this value in **Perimeter** equation 1 we have,

y = 48 - 2u

⇒ y = 48 - 2 x [tex]\frac{288}{y}[/tex]

⇒ [tex]y^{2} = 48y - 576[/tex]

⇒ [tex]y^{2} - 48y + 576 = 0[/tex]

⇒ [tex](y-24)^{2}[/tex] = 0

Solving we get y = 24 ft

Hence the value of u is calculated as follows:

⇒ u = 288 / y

⇒ u = 288/ 24 = 12 ft

The maximum area that the farmer can enclose is 488 sq ft and the dimensions of the rectangle are 24ft and 12 ft respectively.

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an acorn is falling from 13 feet in the air if it descends 4.8 feet every second write and solve the equation to determine how long it will take for the acorn to be 1 foot above the ground

It will take 6 **seconds **for the acorn to be 1 **foot above **the **ground**.

A **linear equation **is an algebraic equation of the **form **y=mx + b, where m is the **slope** and b is the** y-intercept**, and only a **constant **and a first-order (linear) **component **are **included**. The variables in the preceding equation are y and x, and it is occasionally referred to as a "**linear equation **of **two **variables."

A typical form **linear equation **is, for **instance**, 2x+3y=5. When an equation is provided in this format, finding both intercepts is rather simple (x and y).

Given:

acorn is falling from 13 feet

Every seconds it descends = 4.8 feet

let us **assume **that the **equation** for the distance **between **the acorn from the **ground **is

x =13 - 4.8 y

where is y is **time** in **seconds **and x is the **distance**

if x = 1 foot

1 = 13 -4.8y

-12 = -4.8y

y = -12 / -4.8

y = 2.5 seconds

Hence, it will take 6 **seconds **for the acorn to be 1 **foot **above the **ground**.

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Please simplify these equations

**Answer: **

**a) 81**

**b) 16807**

**c) 1010000000**

**d) 390630**

**These are all correct. I checked.**

the brain volumes () of 50 brains vary from a low of to a high of . use the range rule of thumb to estimate the standard deviation s and compare the result to the exact standard deviation of , assuming the estimate is accurate if it is within 15

The estimated **standard deviation** from the range rule is 145.5 cm3.As it is 29.8 cm3 smaller than the exact standard deviation, we consider that the estimation is not accurate enough.

Generally, brain **volumes** which are smaller than 921.1 cm3 can be considered significantly low and bigger than 1417.5 cm3 can be considered significantly high. Hence, brain **volume** of 1457.5 cm3 is bigger than the expected maximum, so it can be considered significantly high.

The calculation goes like this,

According to the range rule, the standard deviation and range, or the distance between the maximum and smallest value, are roughly inversely proportional:

[tex]s=R/4[/tex]

If we have a sample of 50 brains **volumes**, and they range from 910 cm3 to 1492 cm3, we can estimate the **standard deviation** as:

[tex]s=max-min/4[/tex]

s=1492-910/4=582/4=145.5

The exact standard deviation is 175.3 cm3.The difference is 175.3-145.5=29.8 cm3, so the estimation is not accurate enough.

The range rule of thumb states that we should anticipate a maximum value that is approximately two **standard deviations** above the mean and a lowest value that is approximately two standard deviations below the mean. The expected ranges are as follows given our mean volume of 1169.3 cm3 and standard deviation of 124.1 cm3:

Min= M-2s=1169.3-2*124.1=921.1

Max=M+2s=1169.3+2*124.1=1417.5

The brain capacity of 1457.5 cm3 can be regarded as significantly high because it is higher than the predicted maximum.

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Please help!

Find the value of x and y

We can conclude that the value of **angle **y is 70° and x is 35°.

So, a measure of 'x':

We can see that ∠BAC = ∠DAE (Inversely opposite angles)

∠BAC = ∠DAE = 40°We can observe that △DAE is an isosceles triangle with ∠2x and ∠y beingLet 2x be y for instance:

y + y + 40 = 1802y = 180 - 402y = 140y = 140/2y = 70°Now, we know that y = 70 and similarly 2x = 70.

Now, solve for 'x' as follows:

2x = 70x = 70/2x = 35°Therefore, we can conclude that the value of **angle **y is 70° and x is 35°.

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Eight workers are hired to weed a field by

hand. Each is given a plot which is 9×7

meters in size. What is the total area of

the field?

**Step-by-step explanation:**

1.work out area of a single plot

[tex]area = 9 \times 7[/tex]

[tex]area = 63m ^{2} [/tex]

2.multiply the area by the amount of workers

[tex]total \: area = 63 \times 3[/tex]

[tex]total \: area \: = 189m ^{2} [/tex]

The total area of the field is 198 m squared

Jake has 30 fish in his aquarium. Emi has 1/3 the number of fish that Jake has and 1/2 the number of fish that Tobin has.

If the three students combined all their fish in the school's new aquarium, how many fish would there be?

Using** Linear equation**, The** total** number of** fishes i**n the aquarium is found to be **50**.

Linear equation is an equation containing** one unknown variable** with **power one** and** constants**.

The **standard form** of an linear equation in **one variable** x is :

ax + b = 0 , where a, b are **constants**

x= -b/ a is** solution **if this equation or we can solve this equation by adding or subtracting**, multiplying,** dividing** same number** to both sides.

Given that** number** of fishes jake has in the aquarium = 30

And that number of fishes Emi has is 1/3 the number of fish that jake has .

Therefore, **Number **of fishes that Emi has = 1/3 (30) = 10

Also given that Emi has 1/2 the number of fish that Tobin has .

Let Tobin has x fishes

⇒ 1/2(x) = Number of fishes Emi has

⇒ (1/2)x = 10, this is an** linear equation** in x

**Multiplying **both sides by 2, We get:

⇒ 2× (1/2)x = 2 ×10

⇒ x = 20

∴ Tobin has 20 fishes

If the three students combined all their fish in the school's aquarium,

the** Total number** of fishes = 30+20+10 =** 50**

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Can somebody trade lease help me I’m late on my work in school

The **slopes** for each couple of **points** are summarized below:

How to understand slopes in lines

Geometrically speaking, **slopes** in lines indicates the grade of **steepness** of the line itself. The **slope** of the **line** can be determine by knowning the coordinates of two distinct** points** set on **Cartesian plane** and using the **secant line formula**, whose definition is shown below:

m = Δy / Δx

Where:

m - SlopeΔx - Change in independent variable.Δy - Change in dependent variable.Now we proceed to answer on each case:

**Case 1**

m = [3 - (- 1)] / [3 - (- 3)]

m = 4 / 6

m = 2 / 3

**Case 2**

m = (- 2 - 1) / [2 - (- 2)]

m = - 3 / 4

**Case 3**

m = [2 - (- 4)] / [- 4 - (- 1)]

m = 6 / (- 3)

m = - 2

**Case 4**

m = Undefined, as Δx = 0.

**Case 5**

m = [3 - (- 1)] / (3 - 2)

m = 4

**Case 6**

m = 0, as Δy = 0

**Case 7**

m = (6 - 9) / (1 - 4)

m = - 3 / (- 3)

m = 1

**Case 8**

m = [- 5 - (- 1)] / [- 2 - (- 4)]

m = - 4 / 2

m = - 2

**Case 9**

m = (- 9 - 3) / (5 - 5)

m = - 12 / 0

m = Undefined

**Case 10**

m = (9 - 1) / (8 - 2)

m = 8 / 6

m = 4 / 3

**Case 11**

m = [- 6 - (- 8)] / (7 - 14)

m = 2 / (- 7)

m = - 2 / 7

**Case 12**

m = [- 3 - (- 3)] / (8 - 4)

m = 0 / 4

m = 0

**Case 13**

[8 - (- 4)] / (2 - x) = - 3

12 = - 3 · (2 - x)

12 = - 6 + 3 · x

18 = 3 · x

x = 6

**Case 14**

(4 - y) / (3 - 10) = - 2 / 7

(4 - y) / (- 7) = - 2 / 7

4 - y = - 2

y = 6

**Case 15**

(4 - 1) / (x - 7) = 3 / 4

3 / (x - 7) = 3 / 4

x - 7 = 4

x = 11

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Write an equation for a parabola that passes through the point (2,2) and has a vertex of (3,1)

The **equation **of the **parabola **will be;

y = (x - 3)² + 1

**What is mean by Parabola?**

A **parabola **is a set of points in the plane which are **equidistant **from the directrix and **focus**.

Given that;

The **vertex **of the parabola = (3 , 1)

A **parabola **passes through the **point **(2,2).

Now,

Since, The **equation **of **parabola **in vertex form is;

y = a (x - h)² + k

Where, (h , k) are vertex of the parabola.

So, The **equation **of **parabola **with **vertex **(3, 1) will be;

y = a (x - 3)² + 1

And, It passes through the point (2,2).

So we substitute the value of (2, 2) in place of (x, y) as;

2 = a (2 - 3)² + 1

2 = a + 1

a = 2 - 1

a = 1

Substitute the value of a in above equation, we get;

The **equation **of **parabola **as;

y = (x - 3)² + 1

Therefore, The **equation **of the **parabola **will be;

y = (x - 3)² + 1

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what is the answer to this? :(5x^4)^3

**Answer:**

it is 25 or 35

**Step-by-step explanation:**

Ms. Yoto is putting together bags of fruit that contain 1 pear for every 2 apples. How many apples are there in a bag if there is a total of nine pieces of fruit (using algebraic formulas).

The **number** of apples in the bag are 6

**What are algebraic equations?**

**Algebraic** **equation** are the **equation** containing coefficients and variable Which can be solved by various method like **substitution** and **elimination**.

We are given that, Ms. Yoto is putting together bags of fruit that contain 1 pear for every 2 apples.

Also the total number of fruits in the bag are 9

Now mr. Yoto is putting 3 fruit at a time and the bag contains total of 9 fruits that means 3 such sets were put

in each set there were 2 apples and 1 pear

Hence there were 6 apples and 3 pear

Hence the number of apples in the bag is 6

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Which answer is an equation in point-slope form for the given point and slope?

Point: (5, 9); Slope: 2

Responses

y−9=2(x−5)

y−5=2(x+9)

y−9=2(x+5)

y+9=2(x−5)

The **equation** which forms the correct **slope-point **form equation is

y - 9 = 2( x - 5). Thus, **option (1)** is the answer.

The point-slope form is a method that uses the** slope **of the line and a random **coordinate** on any point of the line to create an equation of that line.

The equation in the point-slope form is written in the format: [tex]y-y_{1}=m(x-x_{1})[/tex] , where **m** is the **slope** and [tex]x_{1}[/tex] and [tex]y_{1}[/tex]are the **coordinates** of the point on the line.

The given slope is 2, the x-coordinate is 5, and the y-coordinate is 9. There will be **no addition** symbol in the equation. There is only a subtraction of the coordinates in the equation form. Since options 2, 3, and 4 have addition signs, they do not show the correct equation.

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Mrs. Walter wanted to plant one daffodil for every 3 tulips in her garden. If she planted 20 daffodils, how many tulips did she plant?

**Answer:**

60 tulips

**Step-by-step explanation:**

1 daffodils : 3 tulips

Since she planted 20 daffodils

20 × 3 = 60 tulips

the perimeter of triangle abc is 90. if ab= 5x+1, bc= 2x+13 and ac = x+4 what type of triangle is abc

As all the **length **of each side of given triangle are **unequal **so the given triangle is **scalene **triangle

A triangle's perimeter is defined as the total length of its boundary.

The **perimeter **of a triangle is the **sum **of all three **sides**.

Here given that there is a triangle name ABC and the triangle ABC has the perimeter of 90.

∴ Sum of sides of triangle ABC will equal to the perimeter of triangle ABC

∴ **AB + BC + AC = 90**

As we have AB = 5x + 1, BC = 2x + 13, AC = x + 4

∴ 5x + 1 + 2x + 13 + x + 4 = 90

∴ 8x + 18 = 90

∴ 8x = 90 - 18

∴ 8x = 72

∴ x = 72/8

∴ x = 9.

So we get **AB **= 5x + 1 = 5(9) + 1 =45 + 1 = **46**.

**BC **= 2x + 13 = 2(9) + 13 = 18 + 13 = **31**.

**AC **= x + 4 = 9 + 4 = **13**.

As all the **length **of each side are **unequal **so the given triangle is **scalene **triangle as an **scalene triangle **is a triangle in which all three side **lengths **are **different **and all three **angle **measurements are **different**. However, the sum of all **interior **angles is always equal to **180 **degrees. Therefore, it **satisfies **the angle sum property of triangles.

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45 is divisible by which of the following numbers? (1 point) 1, 5, 8 1, 2, 3 1, 2, 5 1, 3, 5, 9

**Answer:**

1,3,9,5

**Step-by-step explanation:**

**Answer:**

9, 5, 1, 3

**Step-by-step explanation:**

i forgot my vocabulary

But i still know decent engrish

91.276-4.319

to the nearest whole number

**Answer:**

that's a good question

**Step-by-step explanation:**

I believe it is 87

Explanation: 91.276-4.319=86.957 then by rounding that number to the nearest whole is 87…

Explanation: 91.276-4.319=86.957 then by rounding that number to the nearest whole is 87…

Answer the two questions in the photo for easy points ( will mark brainliest if correct )

[10] D

A** counter-example** is an **example **that shows the **argument **can have true **premises **and a false **conclusion**.

Option D shows someone who is good at math, but isn't an engineer. This is a **counter-example**.

[11] B

Similar to the previous question, options A, B, and D are all dogs. However, option C is not a dog and also has four legs. Therefore, it is a **counter-example**.

GEOMETRY HELP ASAP

F (x,y) = (...,...)

1. y or -x

2. -x or y

The **function** which can be the **reflection** along y-axis will be F(-x, y).

A **function** may be defined as an expression in which for every input variable x there is only one output variable y. The input variable is known as **independent** variable and output variable is known as **dependent** variable. **Reflection** may be defined as the changes which occur on a graph for a given **curve**. If reflection of a point occurs along **x axis**, then there will be change in the y coordinate and if reflection along **y axis**, then there will be change in the x coordinate. We have a function F(x, y) and we need to find** reflection** along y axis so there will be change in the x coordinate, so new **function** will be F(-x, y).

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2/4 x 1/3 because i need help

**Answer:**

5/6

**Step-by-step explanation:**

Step 1: Find the GCD (greatest common denominator)

12

Step 2: multiply your factions to represent this

[tex]\frac{2x3}{4x3} = \frac{6}{12} \\[/tex] , [tex]\frac{1x4}{3x4} = \frac{4}{12}[/tex]

Step 3: add the numerators:

[tex]\frac{6}{12} + \frac{4}{12} = \frac{10}{12}[/tex]

Step 4: reduce your fraction

[tex]\frac{10}{12} = \frac{5}{6}[/tex]

Hope that helps

**Fraction multiplication**

**2/4 x 1/3**

*We*** reduce the fraction 2/4** *to its*** lowest expression by extracting and canceling 2.**

**1/2 x (1/3)**

**Multiply 1/2 by 1/3** *(to do this,* **multiply** the **numerator by the numerator** *and the* **denominator by the denominator).**

**1 x 1/2 x 3 =====> ***Multiply*

**1/6 ====>** Answer

the question is in the photo! :)

**Answer:**

2

**Step-by-step explanation:**

So to get the answer we need to figure out what x is

2×2=4

so x has to be 2

What is the average rate of change of the equation g(x)=−x2+2x−4 from x = 2 to x = 5

The average **rate of change** of the **equation** g(x) =−x²+2x−4 from x = 2 to x = 5 is -15 .

The **average of change** of the **function** f(x) from x=a to x=b is given by the formula

Average rate of change = (f(b)-f(a))/(b-a)

In the question ,

it is given that

the **function** is g(x) =−x²+2x−4

we need to find g(2) and g(5) .

g(2) = −(2)²+2(2)−4

= -4 + 4 -4

= -4

g(5) = −(5)²+2(5)−4

= -25 +10 -4

= -15 -4

= -19

So , Average rate of change = (g(5) - g(2))/(5-2)

Substituting the values , we get

**Average rate of change **= (-19 - (-4))/3

= (-19+4)/3

= -15/3

= -5

Therefore , the average **rate of change** of the **equation** g(x) =−x²+2x−4 from x = 2 to x = 5 is -15 .

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Which system of inequalities is graphed below?

System of **inequalities** are :

y> [tex]x^{2} -4[/tex] and y > [tex]x^{2} +3[/tex]

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In an isosceles triangle ABC, the measure of vertex angle C is 30° more than the measure of each base angle. Find the measure of each angle of the triangle

**Answer:**

30 + x + x + x = 180

so, 30 + 3x = 180

sub 30 on both sides

3x = 150

divide 3 on both sides

x = 50

Given the equation 6(8g + 2) + 45 = 153, write a scenario similar to Parts A and B that could be represented by the equation. Solve for g and explain what each number in the equation represents, including the solution.

The **value** for **g** is 2, meaning that each family bowled 2 games.

How to **solve linear equations**?

Given that the **largest power** of the **variable** (or pronumeral) in these equations is **1**, **linear equations **are also known as **first-degree equations**. A line on the quadratic system is represented by a linear equation. This equation's general form is axe + b = 0, where a, b, and x are all integers and x is the variable. The y-axis is parallel to this form of equation's single solution, which it symbolizes.

The **steps** that should be followed while **solving linear equations** are listed below:

1) We must first determine which variable we need to isolate.

2) Next, make a distinction between variables and constants.

3) Arrange the constants on the right and the variables on the left.

4) Using established axioms, we carry out algebraic operations to determine the variable's value.

Given, the **equation** is **6(8g + 2) + 45 = 153**

Following the steps in the available literature, we have the equation as:

6(8g + 2) + 45 = 153 ⇒ 48g + 12 + 45 = 153 ⇒ 48g = 153 - 45 - 12 = 96

⇒ g = 96/48 ⇒ g = 2

Thus, **g **as suggested will **determine** number of **times** each **family** **bowled**.

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Suppose James has a credit card with a balance of $4289. Each month, the credit card company charges 5% interest. James pays off all new purchases that he makes each month without paying off the old balance or its interest. He wants to know what the balance on his credit card will be one year from now. Is this situation an example of exponential growth or exponential decay?

The **balance **on his **credit card **will be the **amount **of $4076.56 one **year **from now.

Simple interest is defined as **interest **paid on the original **principal **and calculated with the following formula:

S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100

First, we must compute James' **monthly charges **on his **balance **of 4289.

Principal = 4289

Rate = 5%

Time = 1 month = 1/12 year

Simple interest = 4289×5×1/12×100 = 17.87

The **monthly charge **is 17.87,

So the yearly charge would be: 12 × 17.87 = $214.44

His credit card **balance **one **year **from now = Principal - Interest

⇒ 4289 - 214.44

⇒ 4076.56

In one year, his credit card **amount **will be 4076.56.

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what are the answer to these questions

( 1 ) The **y-intercept** for the **first **graph is 50. The **correct **option is B.

( 2 ) The **y-intercept** for the **second **graph is 12. The **correct **option is C.

( 3 ) The **y-intercept** for the third **graph **is 0. The **correct **option is C.

A **coordinate **plane is a 2D plane that is formed by the **intersection **of two **perpendicular **lines known as the x-axis and y-axis. A **coordinate** system in **geometry **is a method for determining the positions of the points by using one or more **numbers **or coordinates.

The** y-intercept** of the **first **graph:-

y = mx + c

m= ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( 350 - 50 ) / ( 4 ) = 75

y = mx + c

50 = 75 x 0 + c

c = 50

The** y-intercept** of the **second **graph:-

y = mx + c

m= ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( 30 - 12 ) / ( 4 ) = 4.5

y = mx + c

12 = 4.5 x 0 + c

c = 12

The** y-intercept **of the **third **graph:-

y = mx + c

m= ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( 6 - 3 ) / ( ( 8 - 4 ) = 3 / 4

y = mx + c

3 = ( 3 / 4) x 4 + c

c = 0

Therefore, the** y-intercept** of all the **graphs **is calculated above.

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select graph for solution of open sentence click until correct graph appears [×]=2

Given:

[tex]|x|=-2[/tex]Let's graph the the absolute value equation.

From the equation let's solve for x.

Since |x| = -2, there is no possible value of x that can satisfy this equation. This is because an absolute value can never be a negative number.

Therefore, we can say there is no solution.

This absolute value equation can not be graphed.

**ANSWER:**

**No solution**

auto pistons at wenming chung's plant in shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. from sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows:

The **value** of the **mean **is 155.96mm

**Calculation** of the mean is:

n=5

Mean= [tex]\frac{\sum fx}{n}[/tex]

Mean=[tex]\frac{156.9+153.2+153.6+157.5+158.6}{5}[/tex]

Mean=779.8/5

Mean=155.96mm

The question was incomplete, the complete question is given below:

Auto pistons at Wenming Chung's plant in shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. from sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows:

Day Mean X(mm) Range R (mm)

1 156.9 4.2

2 153.2 4.6

3 153.6 4.1

4 157.5 4.8

5 158.6 4.7

What is the value of mean in **mm**, (round your response to 2 decimal places)

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Mark has downloaded four times as many songs on his music player as Chloe. If Mark has 40 songs, how many songs does Chloe have?

**Answer:**

Chloe has 10 songs.

**Step-by-step explanation:**

40 ÷ 4 = 10

Select the equation of the line that goes through point (4,−2) and is parallel to the equation 2x+5y=15.

A. -2/5x + y= -18/5

B. -5/2x + y= -12

C. 2/5x + y= -2/5

D. 5/2x + y= 8

Answer: 2/5x + y = -2/5

Answer: C

Solution: 2x+5y=15; (4, -2); parallel

Parallel lines have the same slope.

Subtract 2x on both sides to get 5y on one side

5y=-2x+15

Now divide 5y into both sides to get y by itself

Now you got y=-2/5x+15

Solve for b by substituting -2 in for y and 4 in for x

-2=-2/5(4)+b

-2=-8/5+b

+8/5 +8/5

-2/5=b

So b=-2/5

y=-2/5x-2/5

Add 2/5x on both sides

2/5x+y=-2/5

Answer: C

Solution: 2x+5y=15; (4, -2); parallel

Parallel lines have the same slope.

Subtract 2x on both sides to get 5y on one side

5y=-2x+15

Now divide 5y into both sides to get y by itself

Now you got y=-2/5x+15

Solve for b by substituting -2 in for y and 4 in for x

-2=-2/5(4)+b

-2=-8/5+b

+8/5 +8/5

-2/5=b

So b=-2/5

y=-2/5x-2/5

Add 2/5x on both sides

2/5x+y=-2/5

If a car is traveling at 65 miles per hour, then

how far does it travel in 2 hours?

**Answer:**

130 miles

**Step-by-step explanation:**

65×2=130 So if I am driving at a rate of 65 mph then in one hour I drive 65 miles. Since it is in 2 hours I will have driven 130 miles.

**Answer:**

130 miles.

**Step-by-step explanation:**

so it said that the car is traveling 65 miles per hour and it wants to know how far it would go in 2 hours. so if 1 hour is 65 miles if we multiply it by two then we will get

65 miles = 1 hour

130 miles = 2 hours

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