The length of a rectangle is five times its width. If the perimeter is at most 96 centimeters, what is the greatest possible value for the width?


Question 4 options:



2w + 2 • (5w) ≤ 96




2w + 2 • (5w) ≥ 96




2w + 2 • (5w) < 96




2w + 2 • (5w) > 96

Farmer Ed has 3,000 meters of fencing and wants to enclose a rectangular plot that borders on a river.The largest area that can be enclosed is 750,000 square meters.

To get the largest area that can be enclosed, we have to find the dimensions of the rectangular plot. Let's assume that the width of the rectangle is x meters.The length of the rectangle can be found by subtracting the width from the total length of fencing available:L = 3000 - x. The area of the rectangle can be found by multiplying the length and width:Area = L × W = (3000 - x) × x = 3000x - x²To find the maximum value of the area, we can differentiate the area equation with respect to x and set it equal to zero.

Then we can solve for x: dA/dx = 3000 - 2x = 0x = 1500. This means that the width of the rectangle is 1500 meters and the length is 3000 - 1500 = 1500 meters.The area of the rectangle is therefore: Area = L × W = (3000 - 1500) × 1500 = 750,000 square meters. So the largest area that can be enclosed is 750,000 square meters.

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You were on the right track, I totally understand why you'd get stuck where you are currently in the process. To start with, you technically found the wrong ratio between the two triangles. Your ratio is just 2x, while it should be 2x/5.

To start, let's find the ratio between triangle FEG and ABC by dividing angle F by and A:

\(R=\frac{2x}{5}\)

Now, multiply angle B by this ratio:

\((x+4)(\frac{2x}{5} )=\frac{2x^2}{5}+\frac{8x}{5}=\frac{2x^2+8x}{5}\)

We can now set this expression equal to angle E, as we have multiplied by the common ratio:

\(\frac{2x^2+8x}{5} =18\)

This looks rather daunting, but let's keep calm... you can do this!!

Start by subtracting 18 from both sides:

\(\frac{2x^2+8x}{5}-18=0\)

Now, let's get the whole expression under the denominator 5:

\(\frac{2x^2+8x-90}{5}=0\)

Notice that the denominator can now be removed:

\(2x^2+8x-90=0\)

Now, factor the equation (you could also use the quadratic eq if you want)

\(2(x-5)(x+9)=0\)

Notice that we have two potential values for x (5 and -9).

Think about this logically... If we use -9 and plug it in for x, we will end up with values of -5 degrees for an angle, which is impossible! Therefore 5 is the only valid answer!

I encourage you to also approach the problem from a different angle and use the common factor (5/2x) and multiply it by 18 :)

Answer:4

Step-by-step explanation:

Answer:

Step-by-step explanation:

You have to first, expand the brackets which gives you,
8x+8=8x-8+2x

Then you collect the like terms,
8x-8=10x-8

You have to try get x on one side, therefore you minus 8x.
-8=2x-8

You then add 8 from both sides,
0=2x

Lastly, you divide both sides by 2,
0.5 or 1/2=x

And that is your answer,
Hoped this helps,
Have a good day,
Cya :)

its a and c maybe. cuz im smart

Answer:

47

Step-by-step explanation:

Sub in 5 for y:

7+5(3+5)

7+5(8)

7+40

47

Answer:

96

Step-by-step explanation:

3 + 5 = 8

7 + 5 = 12

So, 12(8) is the same as 12 x 8.

12 x 8 = 96

The numbers x for which ||v + w|| = 2 are 16 and -167.

When v = 6i - 4j and w = xi + 6j, the numbers x for which ||v + w|| = 2 are given by the expression "||v + w||² = 4".

Explanation: It is known that ||u||² = u·u for any vector u. Thus,||v + w||² = (v + w)·(v + w) = v·v + 2v·w + w·w

Substituting the given values of v and w, we have

||v + w||² = (6i - 4j)·(6i - 4j) + 2(6i - 4j)·(xi + 6j) + (xi + 6j)·(xi + 6j)= 36i·i - 48i·j - 48j·i + 16j·j + 12xi·i + 72xi·j + 72j·i + 36j·j + x²i·i + 12xi·j + 36j·j= (36 + x²)i·i + (144 + 12x)j·i + (72 + 72x)i·j + (52)j·j

The above equation needs to be solved in order to get the values of x such that

||v + w|| = 2:||v + w||² = 4 ⇔ (36 + x²) + (144 + 12x) + 2(72 + 72x) + 52 = 4 ⇔ x² + 86x - 2672 = 0

The solutions for the above quadratic equation are x = 16 and x = -167.

Therefore, the numbers x for which ||v + w|| = 2 are 16 and -167.

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Answer:

Move on or try to find the answer using a different method or source.

Step-by-step explanation:

The single most reasonable next option for making progress towards the homework solution is to repeat the question soundlessly to yourself.

When faced with a challenging problem, repeating the question soundlessly to oneself is a technique known as "active rest" or "incubation." It allows the brain to continue processing the information subconsciously while temporarily shifting the focus away from the problem. This mental break can help reduce frustration and cognitive fatigue, which often occurs when tackling difficult tasks for an extended period.

Taking a quick nap or working late into the night without rest are not recommended options. Napping might be helpful in some situations, but if the schedule allows, a short mental break is more effective than a nap. Working late into the night without rest can lead to exhaustion, hindering clear thinking and problem-solving abilities.

Focusing harder on the problem may not be productive as it could lead to mental burnout. A brief break and returning with a fresh perspective can often lead to better problem-solving outcomes.

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------------The given question is incomplete, the complete question is:

"You are sitting down to do your homework. You work along, successfully solving the problems. But you then come across a problem that is more difficult. After spending fifteen minutes working on it, you begin to find yourself growing frustrated. What is the single most reasonable next option for you to take in order for you to make progress towards the solution?

Options:

- If your schedule allows for it, lie down for a few minutes and take a quick nap.

- Keep focusing on the problem harder and harder—you will eventually figure it out if you keep your attention on it

- Keep working late into the night—feeling exhausted, but NOT letting yourself sleep, will help you envision the solution.

- Repeat the question soundlessly to yourself."---------------

Answer:

1.  180°   ∑triangle angles=180°

2. 2x

3. 52°

Answer:

yes it is enough

Step-by-step explanation:

the tip costs $7 so in total the price comes to $77 which is less than the $80 he has

Answer:

8q+32r

Step-by-step explanation:

The expression  aₙ > 0 and lim n → [∞] aₙ + 1 is true.

The term expression in math is defined as a sentence with a minimum of two numbers or variables and at least one math operation.

Here we have given that if an > 0 and lim n→[infinity] an + 1 an < 1, then lim n→[infinity] an = 0.

And we need to check whether the given statement is true or not.

While we looking into the given question, we have identified the following expression,

=> lim n → [∞] aₙ + 1

Here we have also know that the value of aₙ > 0.

When we equate the given expression with zero, we have get the following expression,

=> lim n → [∞] aₙ + 1 = 0

=>  lim n → [∞] aₙ = -1

Here we have given the condition that,  aₙ >0, so

=> lim n → [∞] aₙ = 0

Therefore, the expression is zero.

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5, 10, 15, 20, 25, and 30 will be the multiples of 5 as  any integer that can be written as the product of 5 and a natural number is a multiple of 5.

Integers can be zero, a weighted combination, or a bad integer signified by a minus sign. An additive double of a complex value that it relates to is a negative number. Another group of arithmetic is usually denoted in mathematical notation by a bold Z and perhaps a bold "mathbb Z." An integer is a positive, bad, or zero number that is not a fraction (pronounced IN-tuh-jer). Integer examples were -5, 1, 5, 8, 97, and 3,043. Non-integer examples include the numerals 1.43, 1 3/4, 3.14, and more. A gathering of integer and their ecliptic is known as an integer set. Probabilities and decimals are not included in the set of integers.

given

5, 10, 15, 20, 25, and 30 will be the multiples of 5.

Because of this, we may say that any integer that can be written as the product of 5 and a natural number is a multiple of 5.

Examples include 140, 145, and 180, all of which may be obtained by multiplying 5 by a natural number, making them all multiples of 5.

5, 10, 15, 20, 25, and 30 will be the multiples of 5 as  any integer that can be written as the product of 5 and a natural number is a multiple of 5.

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Answer:

90°

Step-by-step explanation:

Ok, I get it now.

Draw two perpendicular lines. Starting at any of the right angles, name them 1, 3, 2, 4 going around in order.

Now you have vertical angles 1 and 2, vertical angles 3 and 4, and angle 3 is adjacent to angles 1 and 2. this is exactly what the description states.

Since angles 3 and 4 are right angles, then all angles are right angles.

m<1 = m<2 = m<3 = m<4 = 90

m<4 + m<1 - m<2 = 90 + 90 - 90 = 90

Answer: 90°

Answer : The incorrect step is, (A) step 1: -10 + 6x > 8

Step-by-step explanation :

The given expression is:

\(-4(\frac{5}{2}+\frac{3}{2}x)>8\)

Now solving this expression step by step.

First -4 distributed over parentheses.

\((-4\times \frac{5}{2})+(-4\times \frac{3}{2}x)>8\)

Now solving bracket term, we get:

\(-10-6x>8\)

Now taking like terms together, we get:

\(-6x>8+10\)

\(-6x>18\)

\(-x>3\)

Now multiplying this expression by (-1), we get:

\(x>-3\)

Thus, the incorrect step is, (A) step 1: -10 + 6x > 8

Answer:

A. Step 1: -10 + 6x > 8

Step-by-step explanation:

The correct way:

Step 1: Multiply both sides by \(-1\) (reverse the inequality)

\(\left(-4\left(\frac{5}{2}+\frac{3}{2}x\right)\right)\left(-1\right)<8\left(-1\right)\)

Step 2: Simplify

\(4\left(\frac{5}{2}+\frac{3}{2}x\right)<-8\)

Step 3: Divide both sides by 4

\(\frac{4\left(\frac{5}{2}+\frac{3}{2}x\right)}{4}<\frac{-8}{4}\)

Step 4: Simplify

\(\frac{5}{2}+\frac{3}{2}x<-2\)

Step 5: Subtract \(\frac{5}{2}\) from both sides

\(\frac{5}{2}+\frac{3}{2}x-\frac{5}{2}<-2-\frac{5}{2}\)

Step 6: Simplify

\(\frac{3}{2}x<-\frac{9}{2}\)

Step 7: Multiply both sides by 2

\(2\cdot \frac{3}{2}x<2\left(-\frac{9}{2}\right)\)

Step 8: Simplify

\(3x<-9\)

Step 9: Divide both sides by 3

\(\frac{3x}{3}<\frac{-9}{3}\)

Step 10: Simplify

\(x<-3\)

Answer:

4

Step-by-step explanation:

D (-1, -3) and F( 2, 3)

G (-4, -4)

Which point on the y-axis lies on the line that passes through point G and is parallel to line DF?

If the line is parallel to DF then they have the same slope.

slope of line DF is m= difference in y/ difference in x = (-3-3)/( -1-2) = -6/-3 = 2

so slope of line that passes trough G and is ║ with DF is also m= 2

From point G (-4, -4) we go with a slope of 2 until we get to the y-axis

So we go up 2 and 1 left, 2up and 1 left, ... until we get to the point (0, 4), because the slope = rise/run = rise 2/run 1

Answer:

n=-2

Step-by-step explanation:

As the sample size grows, the distribution of the sampled means becomes normally distributed option (C) is correct.

With simple random sampling, each component of the population has an equal chance of being selected for the sample.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

Suppose a simple random sample of size n is obtained from a population whose distribution is skewed right.

As we know, the distribution of sample means will be normally distributed even if the individual samples do not, according to the Central Limit Theorem, if the mean values for increasing sample sizes are determined.

Thus, as the sample size grows, the distribution of the sampled means becomes normally distributed.

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Pythagoras was an ancient Greek mathematician who founded the Pythagorean school of thought. The Pythagorean theorem is a fundamental concept in mathematics that is attributed to Pythagoras and his followers.

It states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. While this theorem is considered a cornerstone of mathematics today, it is important to understand that Pythagoras did not have access to the advanced mathematical tools and methods that we have today.

He had to rely on geometric constructions and reasoning to prove his theorem. Furthermore, Pythagoras believed that all numbers could be expressed as ratios of whole numbers, which is not always true in reality. Despite these limitations, the Pythagorean theorem has stood the test of time and continues to be a crucial tool in mathematics and other fields.

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Answer: Adult tickets were sold = 325

Step-by-step explanation:

Let, A = Number of adult tickets sold

S = Number of student tickets sold

Total number of tickets=599

Therefore:

                           A + S = 599

If, there were 51 fewer student tickets sold them adult tickets.

Since,

                            S=A-51

So, substitute A-51 for the value of the first equation.    

                            A+S=599    

                        A+(A-51)=599

Expanding to get:

                            2A-51=599

Solve to get:

                          2A=599+512

                          A=650A

                          A=325

So, A=325 adult tickets were sold.

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Answer:

A.)

 1.) b = h(2)

 2.) p = b - 3

B.) 10

C.) 5

Step-by-step explanation:

A.)

 1.) The birch tree is twice the size of the orange tree so, birch = orange * 2

 2.)  The peach tree is 3m shorter than the birch so, peach = birch - 3meters

B.) b = 5(2)

C.) 8 = 4(2)

     p = 8 - 3

Answer:

x ≈ 31.9

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos15° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{x}{33}\) ( multiply both sides by 33 )

33 × cos15° = x , then

x ≈ 31.9 ( to the nearest tenth )

The change in Emile's height is \(0 \frac{9}{10} \) cm in mixed number and 0.9 cm in simplified form.

Firstly finding the fractional form of old and new height.

Old height = \(3 \frac{7}{10} \)

Old height = ((3×10)+7/10

Old height = 37/10 cm

New height = \(4 \frac{3}{5} \)

New height = ((4×5)+3)/5

New height = 23/5

New height = 23/5 cm

Change in Emile's height = 23/5 - 37/10

Change in height = (23×2)-37/10

Change in height = 46 - 37/10

Change = 9/10

Representing the height in mixed number, \(0 \frac{9}{10} \) and simplified form as 0.9 cm.

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During these two years, Emile's height increased by 0.9 cm or 9/10 cm.

We will calculate the change in Emile's height using Subtraction. The formula that we will use is:

Change in height = Eighth-grade height - Seventh-grade height

Firstly, we will convert the height to a fraction.

Seventh-grade height = ((10×3)+7)/10

Seventh-grade height = 37/10 cm

Now,

Eighth-grade height = ((5×4)+3)/5

Eighth-grade height = 23/5 cm

Now, find the change in height by substituting the values in the formula.

Change in height = Eighth-grade height - seventh-grade height

                             =   23/5 - 37/10

Change in height = 23×2 - 37/10

Change = 46 - 37/10

Change = 0.9 cm

Therefore, the increase in height during these two years is 0.9 cm or 9/10 cm.

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Answer:

72

Step-by-step explanation:

First, we should probably break this shape down into 2 easier to work with shapes. The dimensions of these will be 4*9 and 6*6. I get 6 because when you break 4*9 off, you're also taking 4 off from the 10, giving you 6. Now just multiply and then add the area of both shapes. 4*9=36, and 6*6=36. 36+36=72, so that's your answer.

Hope this helps!

The subway car passes through 48 stations in 2hours

It is given that a subway car passes 4 stations every 10 mins.

Subway car is being referred to the metro system of New York city

It is known to us that an hour has 60 mins

We are given that subway car passes 4 stations every 10 mins

Therefore number of stations passed by subway car in 1 hour

= 60/10 x 4 = 24 stations

We are required to find the number of stations crossed by subway car in 2 hours

Therefore, number of stations crossed by subway car in 2 hours= 24 x 2

= 48  stations

Therefore, the subway car passes 48 stations in 2 hours

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Answer:

yah yeet yeet yah

Step-by-step explanation:

bring the fractions to a common denominator

The statement "new int[3]{1, 2, 3};" allocates an array of three initialized integers on the heap. This statement is True.

In C++, the "new" keyword is used to dynamically allocate memory on the heap. The statement "new int[3]{1, 2, 3};" allocates an array of three integers and initializes them with the values 1, 2, and 3.
The "new int[3]" part of the statement allocates memory for three integers on the heap. The square brackets [3] indicate that an array of size 3 should be allocated. The "int" specifies the type of the elements in the array.
The "{1, 2, 3}" part of the statement initializes the elements of the array with the specified values. In this case, the array elements are initialized to 1, 2, and 3 respectively.
By using the "new" keyword with the initialization values enclosed in curly braces, the array is allocated on the heap and the elements are initialized at the same time.L
Therefore, the statement "new int[3]{1, 2, 3};" does indeed allocate an array of three initialized integers on the heap, making the statement True.

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The length of the rectangle is 16 units long and the breadth is 14 units long. For a rectangle of length L and breadth b, the area is A = L×b

Let's take the breadth of the rectangle as x and the length x+2.

∴ we have,

L = x + 2

b = x

The area of this rectangle is

A = (x + 2)×x = x² + 2×x

As this area is equal to 168 square units.

Then,

168 = x² + 2×x

We can rewrite this below as

X² + 2×x - 168 = 0

This is a quadratic equation, and the solutions are given by Bhaskara's equation, such that for an equation of the form:

a×x² + b×x + c = 0

The solutions are given by

X= -b±√b²-4×a×c÷ 2+a

In our case, the solutions are

X= -2±√2²-4×1×(-168)÷2

= -2+26÷2

Then the two solutions are

x = (2 - 26)÷2 = -12

x = (2 + 26)÷2 = 14

we can conclude that

x = 14

Then the breadth of the rectangle is 14 units long, and the length is 14 + 2 = 16 units long.

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