A student claims that a linear-quadratic system of equations has three solutions. Explain the error the student made.

For this case we have that by definition, the equation of the line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It is the slope of the line

b: It is the cut-off point with the y axis

We have two points through which the line passes:

[tex](x_ {1}, y_ {1}) :( 8,5)\\(x_ {2}, y_ {2}): (- 6,5)[/tex]

We found the slope:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {5-5} {- 6-8} = \frac {0} {- 14} = 0[/tex]

The slope is zero.

Thus, the equation is of the form:

[tex]y = b[/tex]

We substitute one of the points and find b:

[tex](x, y) :( 8,5)\\5 = b\\b = 5[/tex]

Finally, the equation is:

[tex]y = 5[/tex]

Answer:

[tex]y = 5[/tex]

Answer:

y=5

Step-by-step explanation:

The chemist should use 86.13 liters of the 15% solution,

47.29 liters of the 35% solution,

94.58 liters of the 65% solution to obtain a mixture of 228 liters containing 25% acid, using 2 times as much of the 65% solution as the 35% solution.

To solve this problem, we need to find how many liters of each solution should be used to obtain a mixture of 228 liters containing 25% acid, using 2 times as much of the 65% solution as the 35% solution. Here's how we can approach the problem:

Let's assume that we need to use x liters of the 15% solution, y liters of the 35% solution, and z liters of the 65% solution.

From the problem statement, we know that:

x + y + z = 228 (since we need a total of 228 liters of the mixture)

z = 2y (since we need to use 2 times as much of the 65% solution as the 35% solution)

0.15x + 0.35y + 0.65z = 0.25(228) (since we need the final mixture to contain 25% acid)

We can use these equations to solve for x, y, and z. Here's how:

Substitute z = 2y into the first equation to get x + y + 2y = 228, which simplifies to x + 3y = 228.

Rearrange this equation to get x = 228 - 3y.

Substitute z = 2y into the second equation to get 0.15x + 0.35y + 0.65(2y) = 0.25(228), which simplifies to 0.15x + 1.15y = 74.4.

Substitute x = 228 - 3y into this equation to get 0.15(228 - 3y) + 1.15y = 74.4, which simplifies to 34.2 - 0.3y = 74.4 - 1.15y.

Rearrange this equation to get 0.85y = 40.2, which simplifies to y = 47.29.

Substitute y = 47.29 into z = 2y to get z = 94.58.

Substitute y = 47.29 and z = 94.58 into x + 3y = 228 to get x = 86.13.

Therefore, the chemist should use 86.13 liters of the 15% solution, 47.29 liters of the 35% solution, and 94.58 liters of the 65% solution to obtain a mixture of 228 liters containing 25% acid, using 2 times as much of the 65% solution as the 35% solution.

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It takes 3.2 pounds of steel to make one pot.

Step-by-step explanation:

Given,

It takes 800 pounds to manufacture 250 steel pots, therefore,

250 pots = 800 pounds

For calculating steel used for making one pot,

1 steel pot = [tex]\frac{800}{250}[/tex]

[tex]1\ steel\ pot=3.2\ pounds[/tex]

It takes 3.2 pounds of steel to make one pot.

Keywords: division, unit rate

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Answer:

cos60° = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Using the trigonometric identity

sin²x + cos²x = 1 ⇒ cos x = [tex]\sqrt{1-sin^2x}[/tex]

Given

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex], then

cos60° = [tex]\sqrt{1-(\frac{\sqrt{3} }{2})^2 }[/tex] = [tex]\sqrt{1-\frac{3}{4} }[/tex] = [tex]\sqrt{\frac{1}{4} }[/tex] = [tex]\frac{1}{2}[/tex]

Final answer:

The cosine of 60 degrees is 1/2.

Explanation:

To find cos 60 degrees, we can use the trigonometric identity: cos² 0 = 1 - sin² 0. Since sin 60 degrees = √3/2, we can substitute this value into the equation:

cos² 60 degrees = 1 - (√3/2)²

cos² 60 degrees = 1 - (3/4)

cos² 60 degrees = 1/4

cos 60 degrees = ±√(1/4)

cos 60 degrees = ±1/2

However, since 60 degrees is in the first quadrant, cos 60 degrees is positive:

cos 60 degrees = 1/2

Required polynomial of degree four having zeros as -2 , 4 , 4 , 8 is [tex]f(x)=x^{4}-14 x^{3}+48 x^{2}+32 x-256[/tex]

Need to determine a polynomial of degree 4 and the zeros are -2, 4 , 4 and 8

Let the required polynomial be represented by f(x)

The factor theorem describes the relationship between the root of a polynomial and a factor of the polynomial.

If the polynomial p(x) is divided by cx−d and the remainder, given by p(d/c), is equal to zero, then cx−d is a factor of p(x).

-2 is zero of a polynomial means when x = -2, f(-2) = 0, so from factor theorem we can say that  

=> x = -2 that is x + 2 = 0 is factor of polynomial f(x)

4 is zero of a polynomial means when x = 4, f(4) = 0 , so from factor theorem we can say that  

=> x = 4 that is x -4 = 0 is factor of polynomial f(x)

4 is zero of a polynomial means when x = 4, f(4) = 0 , so from factor theorem we can say that  

=> x = 4 that is x -4 = 0 is factor of polynomial f(x)

8 is zero of a polynomial means when x = 8, f(8) = 0 , so from factor theorem we can say that  

=> x = 8 that is x -8 = 0 is factor of polynomial f(x)

So now we have four factors of polynomial f(x) that are (x + 2), (x -4) , (x -4) and (x – 8)

And as given that degree of polynomial f(x) is 4  

Now f(x) is equal to product of factors

[tex]\begin{array}{l}{\Rightarrow f(x)=(x+2)(x-4)^{2}(x-8)} \\\\ {=>f(x)=(x+2)\left(x^{2}-8 x+16\right)(x-8)} \\\\ {=>f(x)=(x+2)\left(x^{3}-8 x^{2}+16 x-8 x^{2}+64 x-128\right)} \\\\ {=>f(x)=(x+2)\left(x^{3}-16 x^{2}+80 x-128\right)} \\\\ {=>f(x)=x\left(x^{3}-16 x^{2}+80 x-128\right)+2\left(x^{3}-16 x^{2}+80 x-128\right)} \\\\ {=>f(x)=x^{4}-16 x^{3}+80 x^{2}-128 x+2 x^{3}-32 x^{2}+160 x-256} \\\\ {=>f(x)=x^{4}-14 x^{3}+48 x^{2}+32 x-256}\end{array}[/tex]

Hence required polynomial of degree four having zeros as -2 , 4 , 4 , 8 is [tex]f(x)=x^{4}-14 x^{3}+48 x^{2}+32 x-256[/tex]

Answer:

j=-37

Step-by-step explanation:

step 1

Find the slope of the given line

we have

[tex]2x+3y=21[/tex]

Convert to slope intercept form

Isolate the variable y

subtract 2x both sides

[tex]3y=-2x+21[/tex]

divide by 3 both sides

[tex]y=-\frac{2}{3}x+7[/tex]

The slope is

[tex]m=-\frac{2}{3}[/tex]

step 2

we have the points

(2,-9) and (j,17)

Find the slope

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

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

substitute

[tex]m=\frac{17+9}{j-2}[/tex]

[tex]m=\frac{26}{j-2}[/tex]

Remember that

If two lines are parallel then their slope are equal

therefore

[tex]\frac{26}{j-2}=-\frac{2}{3}[/tex]

[tex]26(3)=-2(j-2)\\78=-2j+4\\2j=4-78\\2j=-74\\j=-37[/tex]

Answer:

k is -1

Step-by-step explanation:

-12(k+4) = 60

-12k-48=60

-12k=12

k=-1

Answer:

k= -9

Step-by-step explanation:

[tex] - 12(k + 4) = 60 \\ - 12k + - 48 = 60 \\ - 12k = 108 \\ k = - 9[/tex]

Answer:

6.83 miles

Step-by-step explanation:

The length of the third side is approximately: [tex]\[\boxed{2.256 \, \text{miles}}\][/tex]

To find the length of the third side of a triangular course with a given angle between two sides, we can use the Law of Cosines.

[tex]\[c^2 = a^2 + b^2 - 2ab \cos(\gamma)\][/tex]

We want to find the length of the third side c

First, we need to plug in the values into the Law of Cosines formula:

[tex]\[c^2 = (3.5)^2 + (2.5)^2 - 2 \cdot 3.5 \cdot 2.5 \cdot \cos(40^\circ)\][/tex]

Calculate each term:

[tex]\[(3.5)^2 = 12.25\][/tex]

[tex]\[(2.5)^2 = 6.25\][/tex]

[tex]\[2 \cdot 3.5 \cdot 2.5 = 17.5\][/tex]

Using a calculator, we find:

[tex]\[\cos(40^\circ) \approx 0.7660\][/tex]

Substitute all the values into the equation:

[tex]\[c^2 = 12.25 + 6.25 - 17.5 \cdot 0.7660\][/tex]

[tex]\[c^2 = 18.5 - 13.405\][/tex]

[tex]\[c^2 = 5.095\][/tex]

Finally, take the square root of both sides to find c

[tex]\[c = \sqrt{5.095} \approx 2.256\][/tex]

Therefore, the length of the third side is approximately:

[tex]\[\boxed{2.256 \, \text{miles}}\][/tex]

Number of adult tickets sold = 17

Number of student tickets sold =32

Number of senior citizen tickets sold = 51

Given that a certain school sells:

adult tickets = $ 8 ; student tickets = $ 5 and senior citizen tickets = $ 6

Let the number of adult tickets sold be "a"

Let the number of student tickets sold be "b"

Let the number of senior citizen tickets sold be "c"

For one game 100 tickets were sold for $ 600

Number of adult tickets sold + number of student tickets sold + number of senior citizen tickets sold = 100

a + b + c = 100 ------ eqn 1

Number of adult tickets sold  x price of one adult ticket +  number of student tickets sold x  price of one student tickets +  number of senior citizen tickets sold x price of one senior citizen tickets = 600

8a + 5b + 6c = 600  ----- eqn 2

There are 3 times as many adult tickets sold as senior citizen tickets

Hence we get,

3a = c  -------- eqn 3

Put eqn 3 in eqn 1 we get,

a + b + 3a = 100

4a + b = 100

b = 100 - 4a  ----- eqn 4

Substitute eqn 3 and eqn 4 in eqn 2, we get

8a + 5(100 - 4a) + 6(3a) = 600

8a + 500 - 20a + 18a = 600

6a = 600 - 500

a = 16.67 that is approximately 17

a = 17

Substitute a = 17 in eqn 3,

3(17) = c

c = 51

Substitute a = 17 in eqn 4,

b = 100 - 4(17) = 100 - 68 = 32

b = 32

Thus we get:

number of adult tickets sold = a = 17

number of student tickets sold = b = 32

number of senior citizen tickets sold = c = 51

The maximum profit is $854

Profit is the difference between the revenue and the cost price of an item. It is given by:

Profit = selling price - cost price

Since x represent the profit made by the company, is related to the selling price of each widget, x and it is given by the formula:

y = -3x² + 155x - 1148

At maximum profit, dy/dx = 0, hence:

dy/dx = -6x + 155

0 = -6x + 155

6x = 155

x = 25.83

The maximum profit is at gotten when the selling price of each widget is 25.83. Hence:

y = -3(25.83)² - 155(25.83) - 1148

y = $854

Therefore the maximum profit is $854

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To find equivalent fractions, multiply the numerator and denominator of a given fraction by the same number to achieve the desired denominator. For example, 3/4 becomes 9/12 and 1/2 becomes 3/6 when transformed to have denominators of 12 and 3 respectively.

To solve the question of completing each equation so that it shows equivalent fractions, we will use the concept of multiplying the numerator and denominator of a fraction by the same number to find an equivalent.

For the fraction 3/4, to find its equivalent with a denominator of 12, we would multiply both the numerator and denominator by 3, because 4 times 3 equals 12. Thus, we get the equivalent fraction: 3/4 = 9/12.

To find an equivalent fraction for 1/2 with a denominator of 3, we multiply both the numerator and denominator by 3/6 because 2 times 3 equals 6. The equivalent fraction is 1/2 = 3/6.

If we need an equivalent for 2/1 with a denominator of 4, we multiply both the numerator and denominator by 4 because the common denominator we are aiming for is 4. The equivalent fraction is then 2/1 = 8/4.

Note that we always ensure the multiplication factor makes the denominators equal, since that is the requirement for fractions to be equivalent.

The equivalent fractions are:

1. [tex]\( \frac{1}{4} = \frac{3}{12} \)[/tex]

2. [tex]\( \frac{4}{5} = \frac{8}{10} \)[/tex]

3. [tex]\( \frac{1}{6} = \frac{2}{12} \)[/tex]

To complete each equation and show equivalent fractions, we need to find the missing numerator or denominator that, when filled in, will make the fractions equivalent.

1. [tex]\( \frac{1}{4} = \frac{3}{12} \)[/tex]

  Explanation: To find an equivalent fraction for [tex]\( \frac{1}{4} \)[/tex] with a denominator of 12, we notice that we can get from 4 to 12 by multiplying 4 by 3 (4 * 3 = 12). So, to make the fractions equivalent, we also multiply the numerator by 3 (1 * 3 = 3). This gives us [tex]\( \frac{3}{12} \)[/tex], which is equivalent to [tex]\( \frac{1}{4} \)[/tex].

2. [tex]\( \frac{4}{5} = \frac{8}{10} \)[/tex]

  Explanation: To find an equivalent fraction for [tex]\( \frac{4}{5} \)[/tex] with a denominator of 10, we notice that we can get from 5 to 10 by multiplying 5 by 2 (5 * 2 = 10). So, to make the fractions equivalent, we also multiply the numerator by 2 (4 * 2 = 8). This gives us [tex]\( \frac{8}{10} \)[/tex], which is equivalent to [tex]\( \frac{4}{5} \)[/tex].

3. [tex]\( \frac{1}{6} = \frac{2}{12} \)[/tex]

  Explanation: To find an equivalent fraction for [tex]\( \frac{1}{6} \)[/tex], we want the denominator to be 12. To do this, we notice that we can get from 6 to 12 by multiplying 6 by 2 (6 * 2 = 12). So, to make the fractions equivalent, we also multiply the numerator by 2 (1 * 2 = 2). This gives us [tex]\( \frac{2}{12} \)[/tex], which is equivalent to [tex]\( \frac{1}{6} \)[/tex].

The complete question is given below:

Complete each equation below so that it shows equivalent fractions.

1/4 = __/12

4/5 = __/10

1/6 = __/__

Answer:

Approximately 7.9 feet.

Step-by-step explanation:

cos 10 = x / 8     where x is the required distance.

x = 8 cos 10

= 7.878 feet.

Answer:

Length = 25 inches and width = 15 inches.

Step-by-step explanation:

Let us assume that the length of the rectangle is L inches and the width of the rectangle is W inches.

Now, the area of the rectangle is A = LW = 375 sq. inches ........... (1)

Now, given that the length to width ratio of the rectangle is 5 : 3.

Let L = 5x and W = 3x, then from equation (1) we get,

(5x)(3x) = 375

⇒ 15x² = 375

⇒ x² = 25

⇒ x = 5 {Neglecting the negative root, as length can not be negative}

Now, Length = L = 5x = 25 inches and Width = W = 3x = 15 inches. (Answer)

594.15

Step-by-step explanation:

To find the sale price of the iPhone 11, we first calculate the amount of discount which comes to $104.85 and subtract this from the original price. The sale price of the iPhone 11 is therefore $594.15.

The question is about computing the sale price of an iPhone 11 which originally costs $699.00, given that a discount of 15 percent is provided. In mathematical terms, you would be required to find 15% of $699.00 and subtract that amount from the original price to get the sale price.

So, first, determine the amount of discount: 15 / 100 * $699.00 = $104.85. Next, subtract this discount from the original price: $699.00 - $104.85 = $594.15. So, the sale price of the iPhone 11 would be $594.15.

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Answer:

51/44 OR 1 7/44

Step-by-step explanation:

In adding fractions with unlike denominators, you have to find a common factor. In this case, I'll choose 44 because 11 times 4 is 44. So, whatever you do to the bottom must be done to the top as well. 11 times 4 is 44, so 10 times 4 is 40. The new fraction is 40/44. We'll do the same for the other fraction. 4 times 11 is 44, so 1 times 11 is 11. The new fraction is 11/44. Now we can add since we have common factors. 40/44 plus 11/44 is 51/44, which can be simplified to 1 7/44.

Answer:

Yes 1/3 is a rational number.

Explanation:

in mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Hence, 1/3 is a rational number.

Answer:

Yes, it is a rational number.

Step-by-step explanation:

A rational number is any number that can be expressed as a ratio of integers. Even a fraction in which both the numerators and denominators are both integers but the denominator can never ever be less than 0.

I hope this helped you!

Answer:

9.4(3.5 - 2.6x) = -0.4(5.5 + 4.85x)​

Step-by-step explanation:

x = 1.56

Sorry I didn't show my work, my computer won't let me upload pictures right now. I hope this helps!

Answer:

The probability that Aaron goes to the gym on exactly one of the two days is 0.74

Step-by-step explanation:

Let P(Aaron goes to the gym on exactly one of the two days) be the probability that Aaron goes to the gym on exactly one of the two days.

Then

P(Aaron goes to the gym on exactly one of the two days) =

P(Aaron goes to the gym on Saturday and doesn't go on Sunday) +

P(Aaron doesn't go to the gym on Saturday and goes on Sunday)

P(Aaron goes to the gym on Saturday and doesn't go on Sunday) =

P(the probability that Aaron goes to the gym on Saturday)×P(If Aaron goes to the gym on Saturday the probability that he does not go on Sunday)

=0.8×0.7=0.56

Thus, P(Aaron doesn't go to the gym on Saturday and goes on Sunday) = P(The probability that Aaron doesn't go to the gym on Saturday)×P(if Aaron does not go to the gym on Saturday the probability he goes on Sunday)

=0.2×0.9=0.18

Then

P(Aaron goes to the gym on exactly one of the two days) =0.56 + 0.18 =0.74

Answer:

0.74

Step-by-step explanation:

i just did it now on my maths-watch homework

Answer:

The answer is 300. Use an online calculator.

Step-by-step explanation:

Answer:300

Step-by-step explanation:

Write your equation down in long division format and the see how many times you can get 7 into 2,100 and then you put 300 at the top and that’s how you solve a perfect division equation.

Answer:

step by step explanation:64^3x=512^2x+12

64^3x-512^2x=12

2^18x-2^18x=12

0=12

There is no solution for x in the given quadratic equation.

The equation which is of 2nd degree is known as quadratic equation.

Example: ax^2 + bx + c = 0 (quadratic equation)

               Here a, b, c are known quantities and x is variable.

               Here a can't be 0.

The equation given in the question is:

  64^3x =512^2x+12

 (8^2)^3x = (8^3)^2x + 12

 (8)^6x = (8)^6x + 12

There is no value of x, which will satisfy the equation hence it has no solution.

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Answer:

[tex]\large\boxed{\dfrac{11}{14}}[/tex]

Step-by-step explanation:

[tex]\dfrac{\frac{11}{2}}{7}=\dfrac{11}{2}\div7=\dfrac{11}{2}\div\dfrac{7}{1}=\dfrac{11}{2}\cdot\dfrac{1}{7}=\dfrac{(11)(1)}{(2)(7)}=\dfrac{11}{14}[/tex]

Answer:

Step-by-step explanation:

[tex]\frac{\frac{11}{2}}{7} = \frac{11}{14}[/tex]

[tex]\frac{11}{14} = 0.7857142...[/tex]

I hope this helps!

the answer is 173 square units

Answer: 84 un squared

Step-by-step explanation:

area of parallelogram = bh

area = 14 x 6 = 84 un squared

RootIndex 12 StartRoot 8 EndRoot Superscript x

12th root of 8^x = (12th root of 8)^x

[tex]\sqrt[12]{8^{x}} = \left(\sqrt[12]{8}\right)^{x}[/tex]

=========================================

Explanation:

The general rule is

[tex]\sqrt[n]{x} = x^{1/n}[/tex]

so any nth root is the same as having a fractional exponent 1/n.

Using that rule we can say the cube root of 8 is equivalent to 8^(1/3)

[tex]\sqrt[3]{8} = 8^{1/3}[/tex]

-----

Raising this to the power of (1/4)x will have us multiply the exponents of 1/3 and (1/4)x like so

(1/3)*(1/4)x = (1/12)x

In other words,

[tex]\left(8^{1/3}\right)^{(1/4)x} = 8^{(1/3)*(1/4)x}[/tex]

[tex]\left(8^{1/3}\right)^{(1/4)x} = 8^{(1/12)x}[/tex]

-----

From here, we rewrite the fractional exponent 1/12 as a 12th root. which leads us to this

[tex]8^{(1/12)x} = \sqrt[12]{8^{x}} [/tex]

[tex]8^{(1/12)x} = \left(\sqrt[12]{8}\right)^{x} [/tex]

Answer:

C 8 x/3

Step-by-step explanation:

Answer:

12 magazines

Step-by-step explanation:

cost over magazines

12.00    =      36.00    

   4                   ?

12*3=36      whatever you do to the numerator you do it to the denominator  

4*3=12

12 magazines

and im correct so gmany you better not delete my answer

Answer:

12 magazines

Step-by-step explanation:

12 (1/4) = 3

36 (1/3) =  12

Answer:

2/5

Step-by-step explanation:

if one red ball was pulled that mean that now we have 2 red balls 2 green balls and 1 blue ball

and the sum of them is 5 and we have 2 . Soo it is 2/5

Answer:

150=6x

Step-by-step explanation:

Let x = height of the tree.

Set up the ratio %28Height%29%2F%28Shadow%29+=5%2F6=x%2F30

Since a%2Fb=c%2Fd means ad=bc,

5%2F6=x%2F30 means 5%2A30=6%2Ax

150=6x

Answer:

The answer is 25/31 because it equals 56

Final answer:

The smaller number is 25 and the larger number is 31, obtained by setting up an equation with x for the smaller number and x + 6 for the larger one, to represent the described relationship.

Explanation:

To solve the problem, let's denote the smaller number as x and the larger number as x + 6, because the problem states that the larger number is 6 more than the smaller number. The sum of the two numbers is given as 56, so we can set up the following equation:

x + (x + 6) = 56

This simplifies to:

2x + 6 = 56

Subtract 6 from both sides to get:

2x = 50

Now, divide both sides by 2 to find x:

x = 25

Since x is the smaller number, the larger number would be x + 6. Plugging in the value of x, we get:

Larger number = 25 + 6 = 31

Therefore, the smaller number is 25 and the larger number is 31.

To find the sum of 3.14 and 4.83, simply add the two numbers together: 3.14 + 4.83 equals 7.97.

The sum of 3.14 and 4.83 can be calculated by performing a simple addition of the two numbers:

3.14

+ 4.83

-------

 7.97

So, the sum of 3.14 and 4.83 is 7.97.

Answer:

False

True

Step-by-step explanation:

Initially, there were 50 bacteria. It is observed that the bacteria triple in population every 8 hours.

Therefore, the situation can be interpreted as  

[tex]f(x) = 50\times (3)^{\frac{x}{8} }[/tex] .......... (1)

where, f(x) represents the population of bacteria after x hours.

So, the model equation [tex]f(x) = 3 (50)^{\frac{x}{8}}[/tex] is false. (Answer)

Again, from the equation (1) we get, after 36 hours, the bacteria population will be given by [tex]f(36) = 50 \times (3)^{\frac{36}{8}} = 7014.8[/tex] ...... (2)

So, 7014.8 ≈ 7015 is the population of bacteria after 36 hours.  

Hence, this statement is true. (Answer)

Answer:

The original fraction was less than 1/2. Since the result was a mixed number, the original fraction must have contained less than 1 unit of 1/2.

Step-by-step explanation:

The fraction will be less than 1/2. An example will be 1/2 divided by 1/3. You'll need to do 1/2 x 3/1, which will result in 3/2, or 1 1/2.

The original fraction was greater than 1/2. Dividing by 1/2 is the same as doubling, so for the result to be a mixed number, the original fraction must have exceeded 1/2.

The original fraction was greater than 1/2. Since the result was a mixed number, the original fraction must have contained more than 1 unit of 1/2.

This is because when you divide a fraction by 1/2, you are essentially doubling that fraction. If the original fraction were less than or equal to 1/2, doubling it would still result in a fraction that is less than or equal to 1 (not a mixed number). Therefore, in order for the result to be a mixed number, the original fraction must have been more than 1/2. For example, if the original fraction was 3/4 (which is greater than 1/2), when divided by 1/2, the result would be 1 1/2, a mixed number.

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