A hat store sells 900 hats in its first year. If the number of hats it sells in the next year is 50% higher, how many hats will it sell in its second year?

Answer:

The fraction taken from 17 is [tex]$ \frac{16}{3}$[/tex].

Step-by-step explanation:

Let the fraction that is taken from 17 be 'a'.

Writing the given statement mathematically, we would have:

[tex]$ 17 - a = \frac{17}{3} +  6$[/tex]

⇒ 51 - 3x = 17 + 18

⇒ 51 - 3x = 35

⇒ 3x = 16

⇒ x = [tex]$ \frac{16}{3} $[/tex] is the answer.

Answer:

-17

Step-by-step explanation:

28 - 45 = -17$ in her account

The integer will represent the amount of money in Alaina’s account is -17 dollars.

Given that, Alaina has $28 in her account. She wants to purchase a pair of shoes that costs $45.

To subtract two integers, rewrite the subtraction expression as the first number plus the opposite of the second number.

Now, 28-45=-17

Therefore, the integer will represent the amount of money in Alaina’s account is -17 dollars.

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Answer:

6.5 yards total

Step-by-step explanation:

1.

Find the least common multiple (LCM) for the denominators. Because you have to make the denominators the same before you add the fractions, find a common multiple that they share. Then choose the lowest one. In this case the LCM is 6

2. Multiply the numerator and denominator to get like denominators. You'll need to multiply the entire fraction to make the denominator become the least common multiple. In this case multiply 2/3 by 2 = 4/6

3. Add the two fractions and the whole numbers

In this case: 2+ 3 =5

4/6 + 5/6 = 9/6

4. Now you have

5 + 9/6

5. Simplify 9/6 to 1 3/6 = 1 1/2

6. Add 5 + 1 1/2 = 6 1/2

Kristin has approximately 4 yards of plaid ribbon and 3 yards of polka-dot ribbon after rounding fractions to the nearest whole number, which totals to about 7 yards of ribbon in all. This estimation method is reasonable for handling fractions.

We are asked to estimate the total amount of ribbon Kristin has by adding together 3 2/3 yards of plaid ribbon and 2 5/6 yards of polka-dot ribbon. To estimate, we round each fraction to the nearest whole number. The 2/3 in 3 2/3 rounds up to 1, making it approximately 4 yards. The 5/6 in 2 5/6 rounds up to 1, making it approximately 3 yards. Adding these estimates together gives us 4 yards of plaid ribbon plus 3 yards of polka-dot ribbon, which equals to about 7 yards of ribbon in total.

Our estimate is reasonable because we rounded each fraction up to the nearest whole number, making for easy addition. It's also a common method to simplify calculations and get a sense for the magnitude of the sum. Since our original fractions were more than 1/2 (3/2 is 1 1/2, and 5/6 is nearly 1), rounding up provides a reasonable overestimate likely very close to the actual sum.

See explanation

Step-by-step explanation:

Given that Crystal sold b balloons, Aliya sold 2 more balloons than Crystal and Shamika sold twice as many balloons as Crystal then forming the expressions;

If Crystal sold b number of balloons then;

a) Number of balloons Aliya sold is 2 more than Crystal's .This means Aliya sold two more balloons added to what Crystal sold.mathematically, it will be = 2+b

b) Number of balloons Shamika sold is twice Crystal's.This means Shamika sold double the number of balloons Crystal sold.If Crystal sold b balloons, twice this number is =2b

c)Total number of balloons sold will be presented by the expression;

=b+2+b+2b=4b+2

The expression for total cost will be;

$2*(4b+2) =$900----------------------expression

d) solving the expression for total cost as

   2(4b+2)=900

    8b+4=900

     8b=900-4

     8b=896 -------divide both sides by 8 to get b

    b=896/8 =112 balloons  ----------value of variable b

e)

Crystal sold  b  balloons = 112 balloons

Shamika sold, 2b, =2*112 = 224 balloons

Aliya sold , 2+b balloons = 2+112 =114 balloons

f)By solving the expression for total cost , you obtain the value of variable b which represents the number of balloons sold by Crystal. Using the value of b, you can calculate the number of balloons for Shamika and Aliya using their expressions which represent number of balloons they sold.

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Answer:

Step-by-step explanation:

To find the composition of two functions F(G(x)), substitute the value of G(x) into F(x). The result for F(G(x)) in this case is -10x + 38.

This question pertains to the mathematical concept of functions. Specifically, you are being asked to find the composition of two functions, F(x) and G(x).

To find F(G(x)), you substitute the value of G(x) into the function F(x). Recall that G(x) = -2x + 9. So, you need to replace 'x' in F(x) = 5x -7 by the value of G(x). Thus, F(G(x)) = 5(-2x+9) - 7 = -10x + 45 - 7 = -10x + 38.

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Answer: 2.5 would be the answer

Answer:

Step-by-step explanation:

Here two equation of straight lines are given.

Two equations can intersect each other at a point.

The given equations are,

Equating both 1 and 2 we get,

[tex]10 - 5x = 3x + 2\\8x = 8\\x = 1[/tex]

Hence, from 1 we get, [tex]y = 3+2 = 5[/tex]

Answer:

1

Step-by-step explanation:

Correct question:  2x2 - 5x - 3 / 4x2 + 12x + 5 divided by 3x2 - 11x + 6 / 6x2 + 11x - 10.

As given: [tex]\frac{(2x^{2}-5x-3) }{(4x^{2}+12x+5 )} \div \frac{(3x^{2} -11x+6)}{(6x^{2}+11x-10) }[/tex]

Solving it by using quadratic equation.

= [tex]\frac{(2x^{2}-6x+1x-3) }{(4x^{2}+10x+2x+5) } \div \frac{(3x^{2}-9x-2x+6 }{(6x^{2}+15x-4x-10) }[/tex]

= [tex]\frac{(2x+1) (x-3)}{(2x+1) (2x+5)} \div \frac{(3x-2) (x-3)}{(2x+5) (3x-2)}[/tex]

To divide fraction take the reciprocal of divisor and multiply the dividend.

= [tex]\frac{(2x+1) (x-3)}{(2x+1) (2x+5)} \times \frac{(2x+5) (3x-2)}{(3x-2) (x-3)}[/tex]

We solve it to get 1 as it cancel fraction on both side.

Answer is 1.

Answer:

First part: C

Second part: 1

Step-by-step explanation:

                               Question # 1 Solution

Answer:

32≤x≤48 is the best estimate for the amount of money, x, that Erika has to pay to get to her destination. Hence, option D is correct.

Step-by-step Explanation:

Information Fetching and Solution Steps

As Erika estimates that she is 200 to 300 miles away from her destination, and car travels 25 miles per gallon of gas. So,

        i.e 200/25 = 8 gallons.

        As cost of each gallon being $4.00.

        So, 8 × 4 = 32$ is the amount she needed to make 200 miles.

        i.e 300/25 = 12 gallons.

        As cost of each gallon being $4.00.

        So, 12 × 4 = 48$ is the amount she needed to make 300 miles.

From the above calculation, we observe that 32$ and 48$ is the best estimate between 200 miles and 300 miles.

Therefore, 32≤x≤48 is the best estimate for the amount of money, x, that Erika has to pay to get to her destination. Hence, option D is correct.

                                   Question # 2 Solution

Answer:

Consultant B offers the cheapest price for a five hour session.

Hence, B. Consultant B is the correct option.

Step-by-step Explanation:

Analyzing the offer price of Consultant A, B and C for a Five hour session:

So, for five hour session, Consultant A is offering the price:

$160 + $75 + $75 + $75 + $75 = $460

So, for five hour session, Consultant B is offering the price:

$90 + $90 + $90 + $90 + $90 = 450 US$

So, for five hour session, Consultant C is offering the price:

$140 + $80 + $80 + $80 + $80 = $460

Comparing the price offers of Consultant A, B and C

So, by comparing the price offers of Consultant A, B and C, we determine that:

So, from this comparison, we conclude that Consultant B offers the cheapest price for a five hour session.

Hence, B. Consultant B is the correct option.

                             Question # 3 Solution

Answer:

They spent 4 nights at the hotel. Hence, option B is correct.

Step-by-step Explanation:

To determine:

how many nights did they stay at the hotel?

Information Fetching and Solution Steps

As the total amount they spent = $1,200

As $75 is the service charges as Jessica and Ashely purchased full room service for every night.

Per night charges = hotel chargers + service charges

Per night charges = $225 + $75 ⇒ $300

So, total nights will be calculated as:

Total nights = total amount they spent ÷ Per night charges

Total nights = $1,200 ÷ $300 ⇒ 4 nights

Therefore, they spent 4 nights at the hotel. Hence, option B is correct.

                                 Question # 4 Solution

Answer:

Hence, |h − 57.5| ≤ 7.5 is the absolute values which best represents this restriction, where ( h ) represents height. Hence, option A is correct.

Information Fetching and Solution Steps

Let us take the equation of following absolute value:

|h − 57.5| ≤ 7.5

We know h − 57.5 ≤ and h − 57.5 ≥ −50

h − 57.5 ≤ 7.5         (Condition 1)

h − 57.5 + 57.5 ≤ 7.5 + 57.5      (Add 57.5 to both sides)

h ≤ 65

h − 57.5 ≥ −7.5         (Condition 2)

h − 57.5 + 57.5 ≥ −7.5 + 57.5     (Add 57.5 to both sides)

h ≥ 50

So, h ≤ 65 and h ≥ 50

Solution Graph is also attached as shown in attached figure a.

Hence, |h − 57.5| ≤ 7.5 is the absolute values which best represents this restriction, where ( h ) represents height. Hence, option A is correct.

Using same methodology we observe that all other options B, C, and D brings wrong values which is as follows:

Hence, from all discussion, we conclude that |h − 57.5| ≤ 7.5 is the absolute values which best represents this restriction, where ( h ) represents height, as it brings h ≤ 65 and h ≥ 50. Hence, option A is correct.

Keywords: inequality, graph solution, absolute value

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Answer:

16

Step-by-step explanation:

4*(1/2)^2-3*(-5)

4*1/4+15

1+15=16

Answer:

Step-by-step explanation:

[tex]\text{Put the values of }\ x=\dfrac{1}{2}\ \text{and}\ y=-5\ \text{to the expression}\ 4x^2-3y:\\\\4\left(\dfrac{1}{2}\right)^2-3(-5)\qquad\text{use PEMDAS}\\\\=4\left(\dfrac{1}{2}\right)\left(\dfrac{1}{2}\right)+(-3)(-5)\\\\=4\!\!\!\!\diagup\left(\dfrac{1}{4\!\!\!\!\diagup}\right)+15\\\\=1+15\\\\=16[/tex]

Answer:

um whats the question

Step-by-step explanation:

Answer:

The second one

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

A function is where one x value only matches up to one y value.

Answer:

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

Step-by-step explanation:

The complete question is

The given line passes through the points (−4, −3) and (4, 1).

What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (−4, 3)?

step 1

Find the slope of the given line

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

(−4, −3) and (4, 1)

substitute the values

[tex]m=\frac{1+3}{4+4}[/tex]

[tex]m=\frac{4}{8}[/tex]

[tex]m=\frac{1}{2}[/tex]

step 2

Find the slope of the perpendicular line to the given line

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

so

[tex]m_1*m_2=-1[/tex]

we have

[tex]m_1=\frac{1}{2}[/tex] ---> slope of the given line

so

[tex]m_2=-2[/tex] ---> slope of the perpendicular line to the given line

step 2

Find the equation in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=-2[/tex]

[tex]point\ (-4,3)[/tex]

substitute

[tex]y-3=-2(x+4)[/tex] ----> equation in point slope form

Answer:

A

Step-by-step explanation:

did the edge quiz

Answer:

The graph in the attached figure

see the explanation

Step-by-step explanation:

we have

[tex]y=\sqrt{-x-3}[/tex]

we know that

The radicand must be greater than or equal to zero

so

[tex](-x-3)\geq 0[/tex]

solve for x

Adds 3 both sides

[tex]-x\geq 0+3[/tex]

[tex]-x\geq 3[/tex]

Multiply by -1 both sides

Remember that, when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol

[tex]x\leq -3[/tex]

so

The domain of the function is the interval (-∞,-3]

For x=-3 ---> the value of y=0

The range is the interval {0,∞)

therefore

The graph in the attached figure

Answer:

your answer is option A

Answer:

A is the correct answer... ten hundreths thousandths

βrainliest pleaseeeeeeeeeeeee

Answer:

6,561

Step-by-step explanation:

3x3=9

9x9=81

81x81=6,561

Final answer:

Georgia received 3 dimes on Tuesday, 9 on Wednesday, and 81 on Thursday, following a trend of tripling the amount each day. Continuing this pattern, she would receive 243 dimes on Friday.

Explanation:

The question involves identifying and extending a mathematical pattern. Here, we notice that the number of dimes Georgia receives each day is being multiplied by 3 to get the number of dimes for the next day. On Tuesday she received 3 dimes, on Wednesday this was multiplied by 3 to get 9 dimes, and on Thursday it was multiplied again by 3 to get 81 dimes. So, to find out how many dimes Georgia received on Friday, we simply continue this pattern and multiply Thursday's amount by 3.

3 dimes (Tuesday) * 3 = 9 dimes (Wednesday

9 dimes (Wednesday) * 3 = 81 dimes (Thursday)

81 dimes (Thursday) * 3 = 243 dimes (Friday)

Therefore, if this trend continued, Georgia would have received 243 dimes on Friday.

Answer:

Two quarters (50 cents)

Two dimes (20 cents)

Four pennies (4 cents)

Step-by-step explanation:

Guess and check.  

Rachel has two quarters (50 cents), two dimes (20 cents) and four pennies (4 cents) that amounts to 74 cents.

Money is any item or medium of exchange that is accepted by people for the payment of goods and services, as well as the repayment of loans.

A current medium of exchange in the form of coins and banknotes.

Given that, Rachel has 8 coins.

The amount of her coins is 74 cents.

Let us split 74 cents into 8 coins as follows

Two quarters (50 cents)

Two dimes (20 cents)

Four pennies (4 cents)

Therefore, Rachel has two quarters (50 cents), two dimes (20 cents) and four pennies (4 cents).

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Answer:

C. Select a number from {1, 2, 3, 4, 5, 6} and a vowel.

Step-by-step explanation:

Let's start this with a simple example: how many messages are possible using one number from {7, 9} and one letter from {a, b}. It will be 4 as 7a, 7b, 9a and  9b. This result can also come by multiplying the number of digits used and number of alphabets used - here number of digits are 2 (they are 7 and 9) and number of alphabets used are 2 (they are 'a' and 'b'). So 2 × 2 = 4.

[NOTE : In this question 7a and a7 are same]

Maximum number of options consists of vowels as letters so we will first find the number of digits needed if vowels are used as letters.

The number of vowels are 5 (they are 'a', 'e', 'i', 'o', 'u').

The number of possible precodes needed = 30

Let the number of digits needed be 'n'.

Then n × 5 = 30

∴ n = 6

Therefore the number of digits needed is 6 which is there in option C. The digits are {1, 2, 3, 4, 5, 6}

Therefore option C is the answer.

Answer:

See image

Step-by-step explanation:

Plato

Answer:

279J is the total amount of gravitational potential  energy gained by the box.

Step-by-step explanation:

Note: As you missed to add the diagram. So, I found and have attached the diagram as shown in figure a which is attached below, based on which I am answering your question. Hopefully, it would help understand the concept.

The energy stored in an object near the surface of the Earth due of its state in a gravitational field is termed as Gravitational potential energy.

The formula to get gravitational potential energy: [tex]Ep_}=mgh[/tex]

Here,

m = mass of the object normally measured in kg

g =  gravitational acceleration having constant value as 9.8 m/s²

h = height in m

As from the diagram a, we observe that object carries 155-newton force and at point B, the height is 1.80 m, as shown in figure a.

So,

      F = 155 N

      h = 1.80 m

From F = mg, we can get the mass of  object

       F = mg        ∵ g =  gravitational acceleration

      m = F/g

      m = 155/9.8 ⇒ m = 15.81

The gravitational potential energy is measured in joule which is abbreviated as 'J'.

The formula to get gravitational potential energy:

[tex]Ep_}=mgh[/tex]

[tex]Ep_}=(15.81)(9.8)(1.80)[/tex]

[tex]Ep_}=278.88J[/tex]  ≈ [tex]279J[/tex]

Therefore, 279J is the total amount of gravitational potential  energy gained by the box.

Keywords: potential energy, force

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∛128

Divide 128 by 2 to get 64

Now you have: ∛(64 *2)

Rewrite 64 as 4³

Now you have:

∛(4³ *2)

Pull Terms out of the radical to get the final answer:

4∛2

Answer:

Step-by-step explanation:

Solution: [tex]\frac{12}{13}[/tex]. The cosine of an acute angle of a right triangle is the adjacent side divided by the hypotenuse.

Answer:

[tex]2,400\pi[/tex] cubic units

Step-by-step explanation:

Given the cylinder has a base radius of 10 units.

And slant length of 26 units.

The formula for volume of an oblique cylinder is [tex]\pi r^2h[/tex]

Where [tex]r[/tex] is the radius and [tex]h[/tex] is the height of cylinder.

We will now find height of cylinder using following equation.

[tex](slant\ length)^2=(radius)^2+(height)^2[/tex]

[tex]26^2=10^2+(height)^2\\\\676=100+(height)^2\\\\676-100=(height)^2\\\\576=(height)^2\\\\\sqrt{576}=\sqrt{(height)^2}\\ \\24=height[/tex]

Now, the volume of cylinder would be

[tex]=\pi r^2h\\=\pi(10)^2\times24\\=\pi 100\times24\\=2400\pi[/tex]cubic units

The volume of the cylinder is 2,400pi cubic units

The formula for calculating the volume of a cylinder is expressed as:

V = πr²h

where:

r is the radius = 10units

h is the height

Since the cylinder is oblique, hence:

h² = 26² - 10²

h² = 676 - 100

h² = 576

h = 24 units

V = 22/7(10)² * 24

V = 2400 pi cubic units

Hence the volume of the cylinder is 2,400pi cubic units

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Answer:22/18 or 1 4/15

First, you have to find out how many pieces were eaten in all. This could be done with addition. 1/5+1/3= (3/15+5/15)= 8/15

Lastly, you have to find out how much they ate from 15 pieces. This could be done with subtraction. Since 15 is a whole number, the fraction for it would be 15/1. 15/1-8/15=(30/15-8/15)=22/18 or 1 4/15

Answer:

10 rectangles can fit in the square that has one side 10 cm long.

Step-by-step explanation:

Given:

Rectangle 5 cm multiply 2 cm .

Square that has one side 10cm long.

Now, to find the number of rectangle that can fits in the square.

So, for getting the number of rectangle we need to get the area first:

Area of rectangle as given 5 cm multiply 2 cm :

[tex]5\ cm\times 2\ cm=10\ cm^2[/tex]

Then the area of square as given side is 10 cm:

Area of square = (side)²

[tex]Area\ of\ square=10^2[/tex]

[tex]Area\ of\ square=100\ cm^2[/tex]

Now, for getting the number of rectangle we divide the area of square by area of rectangle:

Number of rectangle = Area of square ÷ Area of rectangle

[tex]Number\ of\ rectangle=100\ cm^2\div 10\ cm^2[/tex]

[tex]Number\ of\ rectangle=10.[/tex]

Therefore, 10 rectangles can fit in the square that has one side 10 cm long.

Answer:

The number of hot dogs sold was 35 and the number of sodas sold  was 52

Step-by-step explanation:

Let

x ----> the number of hot dogs sold

y ----> the number of sodas sold

we know that

[tex]x+y=87[/tex]

[tex]x=87-y[/tex] ----> equation A

[tex]1.50x+0.50y=78.50[/tex] ----> equation B

Solve the system by substitution

substitute equation A in equation B

[tex]1.50(87-y)+0.50y=78.50[/tex]

solve for y

[tex]130.50-1.50y+0.50y=78.50[/tex]

[tex]1.50y-0.50y=130.50-78.50[/tex]

[tex]y=52\ sodas[/tex]

Find the value of x

[tex]x=87-52=35\ hot dogs[/tex]

therefore

The number of hot dogs sold  was 35 and the number of sodas sold  was 52

Answer:

3: 6,9,12,15,18,21 and 24.

7: 14,21,28,35,42,49 and 56.

5: 10,15,20,25,30,35 and 40.

9: 18,27,36,45,54,63 and 72

4: 8,12,16,20,24,28 and 32.

Step-by-step explanation:

Given are the number at the beginning of each strings.

We need to write multiples of number on first light of string on rest of lights on the string.

3: [tex]3\times 1= 3 (given)[/tex]

[tex]3\times 2= 6\\3\times 3= 9\\3\times 4= 12\\3\times 5= 15\\3\times 6= 18\\3\times 7= 21\\3\times 8= 24[/tex]

7: [tex]7\times 1= 7 (given)[/tex]

[tex]7\times 2= 14\\7\times 3= 21\\7\times 4= 28\\7\times 5= 35\\7\times 6= 42\\7\times 7= 49\\7\times 8= 56[/tex]

5: [tex]5\times 1= 5 (given)[/tex]

[tex]5\times 2= 10\\5\times 3= 15\\5\times 4= 20\\5\times 5= 25\\5\times 6= 30\\5\times 7= 35\\5\times 8= 40[/tex]

9: [tex]9\times 1= 9 (given)[/tex]

[tex]9\times 2= 18\\9\times 3= 27\\9\times 4= 36\\9\times 5= 45\\9\times 6= 54\\9\times 7= 63\\9\times 8= 72[/tex]

4: [tex]4\times 1= 4 (given)[/tex]

[tex]4\times 2= 8\\4\times 3= 12\\4\times 4= 16\\4\times 5= 20\\4\times 6= 24\\4\times 7= 28\\4\times 8= 32[/tex]

Answer: It is the same distance from zero as the number she tells you.

Step-by-step explanation:

For this exercise it is important to remember the definition of opposite numbers.

Opposite numbers are defined as those numbers that are in opposite positions on a number line, but their distance from zero is the same. Then, one of them is positive and the other one is negative.

The sum of opposite numbers is zero.

For example, the following numbers are opposite:

 [tex]8[/tex] and [tex]-8[/tex]

 [tex]31[/tex] and [tex]-31[/tex]

 [tex]105[/tex] and [tex]-105[/tex]

Therefore, if Shanika says the opposite of a rational number, you can conclude that the number she is thinking is the same distance from zero as the number she tells you.

It is the same distance from zero as the number she tells you.

Step-by-step explanation:

The exponential expression 3^1/2 can be converted to radical form as √3. This is because the fractional exponent 1/2 equates to a square root and the base of the expression, 3, becomes the number under the square root symbol.

The expression 3^1/2 can be expressed in radical form by understanding that the exponent 1/2 represents a square root, which means the value inside the square root is being multiplied by itself to get the original number. Therefore, we rewrite this exponential term in radical form by placing the base, which is 3, under a square-root symbol, so 3^1/2 can be expressed as √3 in radical form. This is because the root, which corresponds to the denominator of the fractional exponent, is 2 (hence square root), and the radicand, which corresponds to the numerator of the fractional exponent, is 3.

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To convert the expression 3^1/2 to radical form, we need to find the square root of 3, which is represented as √3 or 3^(1/2).

Exponential expressions involve a base raised to an exponent. They are written in the form a^n, where "a" is the base and "n" is the exponent. These expressions represent repeated multiplication, where the base is multiplied by itself "n" times. Exponential functions play a crucial role in various mathematical and scientific contexts.

To convert the expression 3^1/2 to radical form, we need to find the square root of 3.

The square root of a number is a value that, when multiplied by itself, gives the original number.

In this case, the square root of 3 is represented as √3 or 3^(1/2).

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Answer:

16 cm

Step-by-step explanation:

Let the width be x

The length will be 3 x since the length is three times the width

Perimeter=2(l+w) where l is length and w is width

By substituting 128 cm for perimeter, x for w and 3 x for l then

128=2(3x+x)

128=8x

[tex]x=\frac {128}{8}=16[/tex]

Therefore, the width is 16 cm, the width is 16*3=48 cm

The correct answer is:

The greatest possible width for the rectangle, with length three times, is 16 cm, ensuring the perimeter doesn't exceed 128 cm.

Let's denote:

- Width of the rectangle as [tex]\( w \)[/tex] cm

- Length of the rectangle as [tex]\( 3w \)[/tex] cm (since it is three times the width)

The perimeter of a rectangle is given by:

[tex]\[ \text{Perimeter} = 2 \times (\text{Length} + \text{Width}) \][/tex]

Given the perimeter is at most 128 cm, we can write:

[tex]\[ 2 \times (3w + w) \leq 128 \][/tex]

Now, let's solve for [tex]\( w \)[/tex]:

[tex]\[ 2 \times (3w + w) \leq 128 \]\[ 2 \times 4w \leq 128 \]\[ 8w \leq 128 \]\[ w \leq \frac{128}{8} \]\[ w \leq 16 \][/tex]

So, the width of the rectangle must be less than or equal to 16 cm. Therefore, the greatest possible value for the width is 16 cm.