The rate of change, y=−√x−4 +5 , is expressed as 1/5−2i/5 .The square root of a number is the number itself.
what is a square root ?A number can be obtained by multiplying the square root by itself. Square root is represented by the symbol sqrt, which stands for square root of, end square root. The reverse of squaring an integer is finding its square root. The result of multiplying a number by itself yields its square value, whereas the square root of a number can be found by looking for a number that, when squared, yields the original value. If 'a' is the square root of 'b,' then a a = b.
given
Use the average rate of change formula to substitute.
(√1)−(√−4) / (1)−(−4)
Condense the phrase.
1/5−2i/5
The rate of change, y=−√x−4 +5 , is expressed as 1/5−2i/5 .The square root of a number is the number itself.
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7x-2y=10 slope intercept form
Answer:
7/2
Step-by-step explanation:
7x – 2y = 10
using ( y = mx + b) as our guideline
where m is the slope
7x – 2y = 10
subtract 7x from both sides
7x – 7x – 2y = 10 – 7x
–2y = 10x – 7x
when arranged in slope form
–2y = –7x + 10
divide both sides by (–2) to get y
[tex] \frac{ \\ - 2y}{ - 2} = \frac{ - 7x}{ - 2} + \frac{10}{ - 2} [/tex]
[tex]y = \frac{ \\ 7y}{2} - 5[/tex]
[tex]the \: slope \: will \: be \: \frac{ \\ 7}{2} [/tex]
This is our answer.
i hope i
What is the rule for an acute triangle?
Answer:
it must be less than 90 degrees
A farmer sells 8. 5 kilograms of apples and pears at the farmer's market. 3/4 of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market? Express your answer in fraction and decimal form. Solve on paper. Then check your work on Zearn. The farmer sold kg or kg of pears
In fraction form, this is 6.375/8.5, or 3/4.In decimal form, this is 0.75.
What is fraction?Fraction is a mathematical expression which represents a part of a whole. It consists of a numerator and a denominator which are separated by a fraction bar. The numerator is the number of parts and the denominator is the total number of parts in the whole. Fractions can be used to represent parts of a whole number or parts of a physical object. Fractions can also be used to express ratios or rates.
To solve on paper, we can use the following equation:
Pears = 8.5 kg - (3/4 x 8.5 kg)
Pears = 8.5 kg - (6.375 kg)
Pears = 2.125 kg
Therefore, the farmer sold 2.125 kg of pears at the farmer's market in fraction form, and 0.75 in decimal form.
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Which explanation can be used to informally derive the formula for the volume of a cylinder? Responses A cylinder consists of 2 circles on the top and the bottom. Determine the circumference of each circle and add the circumferences together. To get the body of the cylinder, multiply it by the height of the cylinder. A cylinder consists of 2 circles on the top and the bottom. Determine the circumference of each circle and add the circumferences together. To get the body of the cylinder, multiply it by the height of the cylinder. A cylinder is similar to a triangular prism except it does not have edges. The volume of a cylinder can be found by using the volume of a triangular prism. However, instead of using the base length of the triangle, use the radius of the cylinder. A cylinder is similar to a triangular prism except it does not have edges. The volume of a cylinder can be found by using the volume of a triangular prism. However, instead of using the base length of the triangle, use the radius of the cylinder. A cylinder is approximately equivalent to 3.5 spheres of the same radius stacked on top of each other. The volume of a cylinder is the volume of a sphere times 3.5. A cylinder is approximately equivalent to 3.5 spheres of the same radius stacked on top of each other. The volume of a cylinder is the volume of a sphere times 3.5. A cylinder is like a stack of circles. The volume of a cylinder would be the area of the circle times the height of the cylinder. The height of the cylinder represents how many circles are in the stack. A cylinder is like a stack of circles. The volume of a cylinder would be the area of the circle times the height of the cylinder. The height of the cylinder represents how many circles are in the stack.
The explanation can be used to informally derive the formula for the volume of a cylinder, which is the correct answer would be option (D).
What is a cylinder?Usually, a cylinder was a three-dimensional solid, one of the most fundamental curvilinear geometric forms. It is a prism with a circle as its basis in elementary geometry. In some recent fields of geometry and topology, a cylinder can alternatively be defined as an infinite curved surface.
Given that, Which explanation can be used to informally derive the formula for the volume of a cylinder
We know that the volume of a cylinder = πr²h
So, consider option (D).
A cylinder is similar to a circular stack. The volume of the cylinder would be equal to the area of the circle multiplied by the cylinder's height. The height of the cylinder reflects the number of circles in the stack.
Therefore, we get the formula πr²h, where πr² represents the area of the circle and h the height of the circle.
Hence, With this reasoning, we may get the formula for cylinder volume informally.
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PLEASE HELP PICTURE ATTACHED
Given the diagram below, which statement is true?
A. /1 and /2 are vertical angles and supplementary.
B. /2 and /3 are complementary angles and congruent.
C. /1 and /3 are vertical angles and congruent.
D. /2 and /4 are supplementary angles and congruent.
Therefore , the solution of the given question of triangle comes out to be the only true option is A.
Triangle definitionAny three points in a plane can be connected to create triangles, which have three sides and three angles. They were one of the very first geometric shapes to be studied. They are particularly important because any polygon, whether it has four, five, six, or n sides, may be split into a triangle.
Here,
Because angles 1 and 2 are close to one another, they are neighboring angles.
A They share a side and are near to each other, making them neighboring angles.
B. The angles are complimentary (add to 90 degrees) False—Angle 2 has a 90 degree angle.
C. They are additional angles. (add to 180) They do not create a straight line, which is untrue.
D. Vertical angles describe them. (Contrary angles) False, they are not created through the intersection of lines.
Therefore , the solution of the given question of triangle comes out to be the only true option is A.
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Adrianne is reading a book. She reads 275 pages and has 155 pages to go. How many pages p is Adrianne’s book? Write and solve an equation to find the book’s length in pages
There will be a total of 430 pages in the book or the length of the book in pages = 430.
Adrianne reads 275 pages
She is left with 155 pages.
So, for converting the above in form of an equation,
Let us assume that the total pages in the book be x
Let us assume that the total number of pages she read = a
Assuming that the total remaining pages that she does not read = b
So, the total number of pages will be = total pages which she read + total remaining pages.
=> x = a+b
Now, solving the values given in the questions,
The value of a = 275 and the value of b = 155
So, the total number of pages in the book = 275+155 = 430
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Problem Solving Quick Check
A recipe for macaroni and cheese takes 3 tablespoons of milk and 2 tablespoons of butter Simon is going to make 5 batches of the macaroni and cheese for a family dinner how many cups of milk are
required? tpoint)
os
o
0.94 cups of milk is required for 5 batches of the macaroni and cheese.
Given that the recipe for macaroni and cheese takes:
3 tablespoons of milk
and 2 tablespoons of butter
To find: the number of cups of milk required
Let m be the number of cups of milk is required to make 5 batches of the macaroni and cheese.
a batch of the macaroni and cheese require 3 tablespoons of milk .
So by unitary method for 5 batches of the macaroni and cheese,
(5 × 3) = 15 tablespoons of milk is required.
We know that 1 US Cup = 16 US tablespoons
So by unitary method,
m = 15/16 cups of milk
m = 0.94 cups of milk
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y=-2x + 11 and y= 4x + 2
(Answer for 100 brainlist!!)
Just solve the x value for the frist equation and the y value for the secound equation
x=-1.5
y=8
the answer is in the picture below
The coordinates of 3 of the vertices of a parallelogram are (-3, 4), (-2, 1), and (2, 6). What is the equation for the
line containing the side opposite the side containing the first two vertices? (Remember, opposite sides of a
parallelogram are parallel.)
The equation for the side of the line that contains the first two vertices' opposite side is 3x+y=12
Given that,
Three of a parallelogram's vertices have the coordinates (-3, 4), (-2, 1), and (2, 6).
We have to find what is the equation for the side of the line that contains the first two vertices' opposite side.
We know that,
The equation of the line is
y=mx+b
Here, we find m and d
Take the points (-3,4) (-2,1)
m = y₂-y₁ / x₂-x₁
m = 1 - 4 / -2-(-3)
m = -3 / 1
m = -3
Now take point (2,6)
6 = -3(2) + b
6 = -6 + b
6 + 6 = b
12 = b
We get m =-3 and b=12
The equation will be y=-3x+12
3x+y=12
Therefore, the equation for the side of the line that contains the first two vertices' opposite side is 3x+y=12
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The length of a rectangle is 3cm longer than its width.
If the perimeter of the rectangle is 58 cm, find its length and width.
The length and width of the rectangle will be 16 centimeters and 13 centimeters, respectively.
What is the perimeter of the rectangle?Let W be the rectangle's width and L its length.
The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be
Perimeter of the rectangle = 2(L + W) units
The length of a rectangle is 3cm longer than its width. If the perimeter of the rectangle is 58 cm. Then the equations are given below.
L = 3 + W ...1
2(L + W) = 58
L + W = 29 ...2
From equations 1 and 2, then we have
3 + W + W = 29
2W = 26
W = 13 cm
Then the length of the rectangle will be given as,
L = 3 + 13
L = 16 cm
The length and width of the rectangle will be 16 centimeters and 13 centimeters, respectively.
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a farm house has 11 animals some are goats and some are ducks there are 34 legs all together how many ducks and goats
There are 11 animals on a farm, some of which are goats, while others are ducks. The total number of legs on the ducks and goats is 34.
Explain about the Expression?An expression, often known as an algebraic expression, is any mathematical statement that contains variables, numbers, and an arithmetic operation between them. For instance, the word m in the given equation is separated from the terms 4m and 5 by the arithmetic symbol +, as is the variable m in the expression 4m + 5.
In mathematics, an expression is referred to as an algebraic expression if it contains variables, constants, and algebraic operations (addition, subtraction, etc.). Expressions are made up of multiple terms.
Functions, variables, and numbers make up an expression (such as addition, subtraction, multiplication or division etc.) It is possible to contrast phrases and expressions.
There are 11 animals, and they have a combined total of 34 legs.
Set G and D to the number of goats and ducks, respectively.
Consequently, G = 11 - D when G + D = 11, and vice versa.
therefore 4G + 2D = 34
Using the value as a stand-in for G, we obtain 4(11 - D) + 2D = 34.
By expanding, we have 34 - 44 - 4 + 2D.
The answer is D = 5. Thus, G equals 6.
Proof (5 x 2) plus (6 x 4) equals 34.
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A retail store sold a case of candles for $17.85 that had been marked up 110%. What was the original price of the table
The original price of the case of candles before markup was $8.50.
Markup price is the price that comes after setting up additional layer of pricing on the original price of a good. In this case also markup price is there. To find the original price of the case of candles before markup, we can use the following formula:
Original price = Marked up price / (1 + markup percentage)
In this case, the original price would be:
$17.85 / (1 + 110%) = $17.85 / 2.10 = $8.50
So the original price of the case of candles before markup was $8.50.
Thus, Original price is $8.5
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Grace was born in 1995. How old will she be in 2027
Answer:
Grace will be 32 years old in 2027.
Answer: she will be 32 years old.
Step-by-step explanation:
Does 4 8 and 12 make a triangle?
No, 4, 8, and 12 are not valid side lengths for a triangle. So 4, 8 and 12 does not make a triangle.
In order for a shape to be a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the triangle inequality theorem.
If a triangle has sides of length 4, 8, and 12, then the triangle inequality theorem would be:
8 + 12 > 4 (true, as 8+12 =20)
12 + 4 > 8 (true, as 4+12=16)
4 + 8 > 12 (false, as 4+8 =12)
Since 4 + 8 = 12, and 12 is not greater than 4 or 8, a triangle cannot be formed with sides of length 4, 8, and 12.
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Is an isosceles triangle always 60 degrees?
No, an isosceles triangle is not always 60 degrees. The angles of an isosceles triangle must be equal, but the overall measure of the angles can be any value greater than 0 degrees.
A triangle having two equal sides and two equal angles is known as an isosceles triangle.. The equal sides create two equal angles that are opposite each other. The two equal angles are the only two angles that define an isosceles triangle. There is no specific measure for the angles of an isosceles triangle, so the angles do not necessarily have to be 60 degrees and The angles can be any value greater than 0 degrees. The two equal angles, however, must be equal in measure to make the triangle an isosceles triangle. Therefore, an isosceles triangle is not always 60 degrees.
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A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle.
A triangle ABC is shown. The base of the triangle extends into a straight line. The angle formed between this straight line and the edge of the triangle is marked as p. The angle adjacent to p is marked as o, and the other two angles inside the triangle are marked as m and n.
Step 1: m∠m + m∠n + m∠o = 180 degrees (sum of angles of a triangle)
Step 2: m∠p − m∠o = 90 degrees (alternate interior angles)
Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p
Step 4: So, m∠m + m∠n = m∠p
In which step did the student first make a mistake and how can it be corrected? (4 points)
a
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (corresponding angles)
b
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles)
c
Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles)
d
Step 2; it should be m∠o + m∠p = 180 degrees (supplementary angles)
Answer:
C. Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles)
Step-by-step explanation:
The student first made a mistake in step 2. In order to check if the sum of the measures of the two remote interior angles of a triangle is equal to the measure of the exterior angle, it is necessary to use the property of alternate exterior angles. Alternate exterior angles are angles that are on opposite sides of the transversal and between the same parallel lines, so they are congruent. The measure of alternate exterior angles is always equal to 180 degree. Therefore, the correct statement in step 2 is that m∠o + m∠p = 180 degrees (alternate exterior angles)
Hope this helps
Suppose a shoe factory produces both low-grade and high-grade shoes. The factory produces at least twice as many low-grade as high-grade shoes. The maximum possible production is 500 pairs of shoes. A dealer calls for delivery of at least 100 high-grade pairs of shoes per day. Suppose the operation makes a profit of Birr 2.00 per a pair of shoes on high-grade shoes and Birr 1.00 per pairs of shoes on low-grade shoes. How many pairs of shoes of each type should be produced for maximum profit? Hint: Let x denote the number of high-grade shoes. Let y denote the number of low-grade shoes.
but can you make it clear more please
The total number of pairs of shoes produced should be 500 (the maximum possible production). The profit per day should be maximized, so we need to solve the following system of equations:
2x + 1y ≥ 100 (the number of high-grade shoes should be at least 100)
x + y = 500 (the total number of pairs of shoes produced should be 500)
Solving for x and y, we get:
x = 400 (high-grade shoes)
y = 100 (low-grade shoes)
Therefore, the factory should produce 400 pairs of high-grade shoes and 100 pairs of low-grade shoes for maximum profit.
How to optimize a factory’s production process to maximize profit?To optimize a factory's production process to maximize profit, the factory should focus on increasing efficiency and reducing costs. This can be done by streamlining processes, automating tasks, and utilizing data-driven decision making. Additionally, the factory should focus on reducing waste, lowering overhead costs, and developing cost-saving strategies. Finally, the factory should focus on finding new markets and expanding its customer base to increase revenue.
How to calculate the break-even point for a factory?The break-even point for a factory is the point where total revenue equals total costs. This can be calculated by subtracting the total variable costs (costs that change with production, such as raw materials and labor) from the total fixed costs (costs that are not affected by production, such as rent, insurance, and equipment). The difference is the break-even point, which is the total revenue needed to cover all costs and generate a profit.
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How do you find area?
Answer:
You do length time width
can someone please help ( check link for question )
Hence, The equation of the line is y=5x/3-3
What is the slope-intercept form of a line?The slope-intercept form of a line is represented by y=mx+c where m=slope and c is the y-intercept of the line
Given here: The line 3x+5y=15 , Rearranging in the slope intercept form we get y=-3x/5+3 and thus slope of the line that is perpendicular to this line must be equal to 5/3 and it passes through (3,2) then we get the equation of the line as y=5x/3+c and putting (3,2) in the equation we get the value of c as c=-3
∴ The equation of the line is y=5x/3-3
Hence, The equation of the line is y=5x/3-3
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A rectangle has a perimeter of 16 centimeters. The lengths of the sides of the rectangle are between 1 centimeter and 7 centimeters. If x represents the length of a side of the rectangle, then the rectangle's area is represented by x(8-x) square centimeters. Suppose a square is constructed to have the same area as this rectangle. The length of a side of the square is represented by centimeters. What is the range of possible perimeters of the square? Round answers to the nearest hundredth of a centimeter.
The range of possible perimeters of the square=10.583
What is area of a rectangle?Area of a rectangle (A) is the product of its length (l) and width (w).
A= l. w
here, we have,
A rectangle has a perimeter of 16 centimeters.
The lengths of the sides of the rectangle are between 1 centimeter and 7 centimeters.
let, x represents the length of a side of the rectangle,
then the rectangle's area is represented by x(8-x) square centimeters.
i.e. area of square = 8x-x^2
the side = √x(8-x)
perimeter= 4×√x(8-x)
Hence, the range of possible perimeters of the square=10.583
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What is negation example?
Let's say we have an expression P^A then the negation of P^A will be not( P^A ). This is an example of negation.
As the name suggests negation means the negative of a term or expression and it comes under the branch of mathematical logical reasoning.
When not word is added in front of an expression it becomes the opposite , this is how we negate something. A statement is only admissible if it is always true or always false.
It is sometimes required in mathematics to find the inverse of a particular mathematical statement, this is when negation is used. Negation thus, refers to the process of determining the inverse of a given assertion.
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The number of left-handed people in the world is one-tenth the number of right-handed people. The percent of right-handed people is nine times the percent of left-handed people and ambidextrous people combined. What percent of people are ambidextrous
According to question we can say that 1% percent of people are ambidextrous.
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
Let 'x' represent the percentage of left-handed people.
Let y represent the percentage of right-handed people.
Let z represent the percentage of ambidextrous people.
x = y/100
100x = y
y/100 = 9( x/100 + z/100)
y = 9x + 9Z
10x = 9x + 9z
x = 9z
x+y+z = 100
11x + x/9 = 100
100x/9 = 100
x = 9
z = 1%
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if x is a binomial random variable with n=10 and p=0.8, the mean value of x is _____.
Answer:
8
Step-by-step explanation:
[tex]\bar{x}=np=10(0.8)=8[/tex]
Jason and Marie both travel 300 miles. Jason drove at an average speed of 10 miles per hour faster than Marie and made the trip in one hour less time. Find the average speeds of both cars.
Answer:
jason: 60mph
marie: 50mph
Step-by-step explanation:
let jason drive at x miles per hour
let marie drive at x-10 miles per hour
let jason drive for y hours
let marie drive for y+1 hours
distance = speed * time
for jason:
300 = x * y
for marie:
300 = (x-10) * (y+1) = x*y + x - 10y -10
300 = x*y
divide both sides by x to solve for y
300/x = y
plug this into the second equation
300 = (x-10) * (300/x+1) = 300 -3000/x +x -10
300 = 300 -3000/x +x -10
subtract 300 from both sides
0 = -3000/x + x - 10
multiply both sides by x to get rid of the denominator
0 = x^2 -10x -3000
factor
0 = x^2 - 60x +50x -3000
0 = x(x-60) + 50(x-60) = (x+50)(x-60)
x = 60 or -50
x cannot be negative so x = 60mph
marie = 60-10 = 50mph
Solve the following system of equations algebraically:
y = x² - 15x + 60
y=x-3
Since the square root of a negative number does not exist in the real numbers, there are no real solutions for x. Therefore, the system of equations has no solutions.
Define Algebric expression.An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.
What is variables and constants ?A constant has a fixed value and does not vary over time. For instance, the size of a shoe, a piece of clothing, or any other article of clothing will never alter. x+y = 8 is an algebraic equation, and 8 is a constant that cannot be altered. Variables are concepts that change or fluctuate throughout time.
To solve this system of equations algebraically, we can substitute y = x-3 into the first equation
y = x² - 15x + 60
x-3 = x² - 15x + 60
x² - 16x + 63 = 0
We know that this quadratic equation has no real solutions because its discriminant (b^2 - 4ac) is negative, so the system of equations has no real solutions.
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Q 9-1 Pythagorean Theorem and Trig
A girl is 20 ft. east of her school and her bike is 21 ft. south of the school. How far is she from her bike? Round to the nearest hundredth.
Answer: 29 ft
Step-by-step explanation:
Based on the description we are given. we know that we can form a right triangle, where 20 and 21 are the legs. The length from the girl to the bike would be the hypotenuse. To do this, we need to use the Pythagorean Theorem, which is [tex]a^2+b^2=c^2[/tex], where a and b are legs, and c is hypotenuse. We can go ahead and plug them in.
[tex]20^2+21^2=c^2[/tex] [exponent]
[tex]400+441=c^2[/tex] [add]
[tex]841=c^2[/tex] [square root both sides]
[tex]c=29[/tex]
Therefore, the distance from the girl to the bike is 29 ft.
At the movie theatre, child admission is $5.10 and adult admission is $8.90. On Sunday, 156 tickets were sold for a total sales of $1145.20. How many child tickets were sold that day?
let y = number of child tickets so the total 0f 34 child tickets is sold at that day.
Define substitution.To calculate an expression's value by substitution, integers are substituted for letters in the expression.
Define expression.Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
let x = number of adult tickets
let y = number of child tickets
x = 4y (four times as many adult tickets as child tickets
8.4x + 5.1y = 1315.8
but we can substitute 4y for x
8.4(4y) + 5.1y = 1315.8
33.6y + 5.1y = 1315.8
38.7y = 1315.8
y = 34 and x = 4Y
x = 136
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(PLS HELP, URGENT, IT'S DUE IN 12 MINUTES!!!!)
Kara can run 3 miles in 25.5 minutes. At this rate, how long would it take her to run 2 miles? Diana's answer: If I subtract 1 mile from 3 miles, I get 2 miles, so if I subtract 1 minute from 25.5 minutes, I get 24.5 minutes. Kara takes 24.5 minutes to run 2 miles. Is Diana's answer correct? Explain pls!
Answer:25.5 divided by 3= answer I think
Step-by-step explanation:
The table below shows the times taken for
a group of athletes to finish a 200 m race.
Work out the percentage of the athletes
who took more than 28 s to finish the race.
Time, t(s)
24
26
28
30
Frequency
3
6
9
7
Therefore , the solution of the given problem of percentage comes out to be athletes who took move 285 to finish the race is 64%.
Define percentage.A percentage is what is used to describe a fraction of a whole when it is stated as a number range between 0 and 100. 100% of something, 50% of something, and 0% of something are all equal. After dividing the portion of the whole by the entire, multiply the result by 100 to arrive at a percentage.
Here,
For the table to get the total frequency is:
=> 3+6+9+7
=>9+9+7
=>25
The frequency greater than 285 is
9+7 = 16
So,
the percentage of the athletes who took move 285 to finish the race is:
=> 16/25 * 100
=> 0.64 * 100
=> 64%
Therefore , the solution of the given problem of percentage comes out to be athletes who took move 285 to finish the race is 64%.
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Building blocks are in the shape of a cube. The dimensions of the building blocks are based on the length of the packaging box, which is defined as [tex]\frac{1}{12} x^{2}[/tex] centimeters, where x is the length of the packaging box. What is the volume of a building block in terms of x?
ily whoever answers right <3
The volume of the building block in terms of x is V = x⁶/1728
What is volume?Volume is the amount of space a substance occupies.
What is the volume of a building block in terms of x?Since building blocks are in the shape of a cube. The dimensions of the building blocks are based on the length of the packaging box, which is defined as x²/12 centimeters, where x is the length of the packaging box.
Since the building blocks are in the shape of a cube, its volume is the volume of a cube.
What is the volume of a cube?The volume of a cube is given by V = L³ where L = length of side of cube.
To find the volume of the building block, since the length of the building block is L = x²/12, then we find the volume of the building block by substituting L into V.
So, V = L³
V = (x²/12)³
= x⁶/12³
= x⁶/1728
So, the volume of the building block is V = x⁶/1728
Learn more about volume of cube here:
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