Answer:
6 bags for $25
Step-by-step explanation:
25/6 = 4.16666666667 = $4.17 per bag
35/8 = 4.375 = $4.37 per bag
The better deal for the bags of apples is at the market
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
To determine which is the better deal, we can compare the prices per bag of apples at the market and the orchard.
At the market:
Price of 6 bags of apples = $25
Price per bag of apples = $25 / 6 ≈ $4.17 (rounded to two decimal places)
At the orchard:
Price of 8 bags of apples = $35
Price per bag of apples = $35 / 8 ≈ $4.38 (rounded to two decimal places)
Comparing the two prices per bag of apples, we can see that the price per bag at the market is $4.17, while the price per bag at the orchard is $4.38.
Hence , the better deal is at the market where you can buy 6 bags of apples for $25, resulting in a lower price per bag compared to the orchard.
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ3
What is the additive inverse of 4 (- 4?
The additive inverse of 4 is -4. This means that when 4 is paired with -4, the two numbers cancel each other out and the result is 0.
The additive inverse of a number is the opposite of that number. For example, the additive inverse of 4 is -4. This means that when two numbers are added together and one of them is 4 and the other is -4, the result will be 0. This is because the two numbers cancel each other out. The same is true for any number and its additive inverse. For example, 8 and -8 added together will also result in 0. Additive inverses are an important part of algebra and can be used to solve equations. By understanding the concept of additive inverses, you can easily manipulate equations and solve for unknowns. This is due to the fact that when two numbers are added together and one of them is the additive inverse of the other, the result will always be 0.
Learn more about inverse here
https://brainly.com/question/13715269
#SPJ4
The positive number a is 2,001% of the sum of the positive numbers b and c, and b is 87% of c. What percent of b is a?
Therefore , the solution of the given problem of percentage comes out to be percentage of b is 4301%.
A percentage is what?In mathematics, a percentage is a number of ratio that is stated as a portion of 100. Also occasionally used are the abbreviations "pct.," "pct," with "pc." To denote it, though, the percent symbol "%" is frequently employed. The % amount has no dimensions. Because percentages contain a numerator of 100, they are effectively fractions. A number should be followed by the % sign (%) to show that it represents a percentage. For instance, someone would receive a 75% grade if you properly solved 75 out of 100 questions on a test. To determine percentages, divide the amount of money by the total, and then multiply the result by 100. The percentage is calculated by multiplying the ratio (value/total) by 100%.
Here,
a =2001/100 * (b+c)
and
b= 87/100*c
thus putting value of b in a
=>a = 2001/100*(87/100*c + c)
=> a= 2001/100 * 187/87 * b
=>a/b = 374187 / 8700 * 100 = 4301%
and
Now percentage of b is 4301%.
Therefore , the solution of the given problem of percentage comes out to be percentage of b is 4301%.
To know more about percentage visit:
https://brainly.com/question/28269290
#SPJ1
Where is midpoint theorem used?
The midpoint theorem is used in a variety of mathematical fields, but it is primarily used in geometry and algebra.
In geometry, the midpoint theorem is used to find the midpoint of a line segment, which is the point that is exactly halfway between the two endpoints of the segment. The theorem states that the coordinates of the midpoint of a line segment can be found by averaging the coordinates of the endpoints.
For example, if the endpoints of a line segment have coordinates (x1, y1) and (x2, y2), the coordinates of the midpoint would be ((x1 + x2)/2, (y1 + y2)/2).
In algebra, the midpoint theorem can be used to find the equation of a line when the coordinates of the endpoints of a line segment are known. The equation of a line can be represented in the form of y = mx + b, where m is the slope and b is the y-intercept.
The slope of the line can be found by taking the difference of the y-coordinates of the two endpoints divided by the difference of the x-coordinates of the two endpoints. The y-intercept of the line can be found by using the midpoint of the line segment and the slope of the line.
In Calculus, the midpoint theorem is used in optimization problems. Optimization problems are used to find the maximum or minimum value of a function.
The midpoint theorem is used to find the critical points of the function, which are the points where the function reaches its maximum or minimum value. The critical points are found by taking the derivative of the function and equating it to zero.
Learn more about midpoint theorem:
https://brainly.com/question/25686058
#SPJ4
Andrew is paid 4$ per hour for the first 30 hours he works each week. he makes 5$ per hour for each hour he works over 30 hours per week. in other words, total wages= fixed wages for 30 hours + additional wages at 5$ per hour.
Part A
Write a function that gives Andrews total wages when he works more than 30 hours. use the variables w for wages and h for hours.
Answer: For the first 30 hours, Andrew will earn 4 (30) = $120. For each additional hour beyond 30 that Andrew works, he will earn 5 (h - 30). Therefore, the function that gives Andrew's total wages when he works more than 30 hours is
Step-by-step explanation: For the first 30 hours, Andrew will earn 4(30) = $120. For each additional hour beyond 30 that Andrew works, he will earn 5(h - 30). Therefore, the function that gives Andrew's total wages when he works more than 30 hours is:
w = 120 + 5(h - 30).
So, if he works 35 hours, he will earn:
120 + 5(35 - 30) = 120 + 5(5) = 120 + 25 = $145.
If he works 42 hours, he will earn:
120 + 5(42 - 30) = 120 + 5(12) = 120 + 60 = $180.
I hope this helps!
Greg’s parents bought a $350.00 savings bond when he was born. When he turns 3030, the bond’s value will have increased 125%. How much will the savings bond be worth on Greg’s thirtieth birthday?
Using percentages we know that the savings bond will be worth $787.5 on Greg's 30th birthday.
What is the percentage?In mathematics, a quantity or ratio known as A% stands for a percentage of 100.
There are several different ways to depict a dimensionless connection between two numbers, including ratios, fractions, and decimals.
To represent percentages, the symbol "%" is typically written after the number.
So, we know that:
The bond is $350.
The return is 125% when Greg turns 30.
Then, the amount after she turns 30 will be as follows:
350/100 * 125
437.5
Bonds value: 437.5 + 350 = $787.5
Therefore, using percentages we know that the savings bond will be worth $787.5 on Greg's 30th birthday.
Know more about percentages here:
https://brainly.com/question/9553743
#SPJ1
What is the slope of y =- 5x 5?
The slope of the given equation [tex]y = -5x^5[/tex] is [tex]-25x^4[/tex].
To find the slope of the equation [tex]y = -5x^5[/tex], you need to take the derivative of the equation with respect to x. The slope of the equation represents the rate of change of y with respect to x, that is how y changes as x changes.
The derivative of [tex]y = -5x^5[/tex] can be calculated using the power rule, which states that if f(x) = [tex]x^n[/tex] then f'(x) = [tex]nx^{(n-1)}[/tex], the slope of the equation is [tex]-55x^4[/tex].
So, the slope of the equation [tex]y = -5x^5[/tex] is [tex]-25x^4[/tex].
Here, note that this equation represents a polynomial function of degree 5, which means that it is a function that has the highest power term of [tex]x^5[/tex]. Also, the slope of a polynomial function is always a polynomial function of one degree lower than the original function.
Read more about Slope:
brainly.com/question/28645794
#SPJ4
Please help!! Find f(-3) - 2
Hint: find f(-3) first and then subtract 2.
The solution for f(-3) - 2 in the function when the function f(x) = 4 − (x + 3)⁵ is 2
How to determine the solution for f(-3) - 2 in the function?From the question, we have the following equation that can be used in our computation:
f ( x ) = 4 − ( x + 3 )^5
To make the equation legible, we need to rewrite it
So, we have the following representation
f(x) = 4 − (x + 3)⁵
Also from the question, we have
f(-3) - 2
This means that the value of x is -3, and we calculate f(x) when x = -3
Substitute the known values in the above equation, so, we have the following representation
f(x) - 2 = 4 − (x + 3)⁵ - 2
So, we have the following equation
f(-3) - 2 = 4 − (-3 + 3)⁵ - 2
There are constants to add or subtract to both sides of the equation
However, there is no factor to multiply or divide from both sides of the equation
So, we have the following representation
f(-3) - 2 = 4 − (0)⁵ - 2
Solving further, we have
f(-3) - 2 = 4 - 2
Evaluate the difference
f(-3) - 2 = 2
Hence, the solution is 2
Read more about functions at
brainly.com/question/28277110
#SPJ1
Complete question
Given that f ( x ) = 4 − ( x + 3 )^5
Find f(-3) - 2
Hint: find f(-3) first and then subtract 2.
A cooking group made 240 oz of spaghetti sauce to sell at a county fair. The group can pour the sauce into small jars that hold 8 oz and large jars that hold 16 oz. The group leader made a sketch to show the line representing the different combinations of jar sizes the group can use. The x-axis represented the number of small jars and the y-axis represented the number of large jars. The group leader labeled only the intercepts.
The points that the cooking group leader did label are (0,15) and (30,0). Thus, the correct answer is C.
As your first step, find the function that best represents x and y:
x is the number of 8-ounce jars x.y is the number of 16-ounce jars.Hence, the function is:
8x + 16y = 240The group leader labeled (0,15) on the y-axis, which means that when the number of small jars is 0, the group can use 15 large jars. This means that 15 large jars can hold 240 oz of spaghetti sauce, which is true since:
8x + 16y = 240(15x0) + (16x15) = 2400 + 16 x 15 = 24015 x 15 = 240The group leader also labeled (30,0) on the x-axis, which means that when the number of large jars is 0, the group can use 30 small jars. This means that 30 small jars can hold 240 oz of spaghetti sauce, which is true since:
8x + 16y = 240(8x30) + (16x0) = 2408 x 30 + 0 = 2408 x 30 = 240The function that represents this line is 8x + 16y = 240, where x is the number of small jars and y is the number of large jars. The line passes through (0,15) and (30,0) as the two intercepts.
This question should be written as:
A cooking group made 240 oz of spaghetti sauce to sell at a county fair. The group can pour the sauce into small jars that hold 8 oz and large jars that hold 16 oz. The group leader made a sketch to show the line representing the different combinations of jar sizes the group can use. The x-axis represented the number of small jars and the y-axis represented the number of large jars. The group leader labeled only the intercepts. Which points did the group leader label?
A. (0,8) and (16,0) B. (0,30) and (15,0) C. (0,15) and (30,0) D. (0,16) and (8,0)The correct answer is C.
Learn more about x axis here: brainly.com/question/27946240
#SPJ4
Question
Which statement describes the relationships between x and y in these two equations?
y = 10x
y = x + 10
In y = 10x the value of y is twice the value of x, and in y = x + 10 the value of y is 10 more than the value of x.
What is an Equations?
Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
y = 10x, we can say that the algebraic equation represents "the value of y is twice the value of x.
Also, for the equation y = x + 10, we can say "the value of y is two more than the value of x.
Hence, In y = 10x the value of y is twice the value of x, and in y = x + 10 the value of y is 10 more than the value of x.
Learn more about equations, by the following link
brainly.com/question/2972832
#SPJ1
How many solutions does -3=2x²-8x+8 have
Answer:
no real solutions
Step-by-step explanation:
the easiest method would be to graph the equation and see how many intersection points with the x-axis there are; that represents the number of solutions
when we graph the equation we first want to add 3 to each side of the equation to get the following:
y = 2x²-8x+11
what we see is that the parabola does not intersect the x-axis at all; therefore, there are no 'real' roots or solutions
Answer:
Step-by-step explanation:
x =(4-√24)/4=1-1/2√ 6 = -0.225.
Is the triangle with sides 25 cm 5 cm and 24 cm a right triangle?
The triangle with sides 25cm, 5cm and 24cm is not a right triangle.
Now, According to the question:
Let us assume that :
ABC is a right triangle,
A = 25cm
B = 5 cm
C = 24 cm
We have to find if the given sides of a triangle form a right triangle.
By using Pythagoras theorem for a right triangle,
[tex]A^2 = B^2+C^2[/tex]
[tex](25)^2 = (5)^2 + (24)^2[/tex]
LHS:[tex](5)^2 + (24)^2[/tex]
= 25 + 576
= 601
RHS:[tex](25)^2[/tex]
= 625
LHS ≠ RHS
Since, the Pythagorean theorem does not apply, the given sides do not form a right triangle.
Therefore, the triangle with sides 25cm, 5cm and 24cm is not a right triangle.
Learn more about Right Triangle at:
https://brainly.com/question/29285631
#SPJ4
When is the boundary line of the graph of an inequality in two variables part of the solution?
The boundary line of the graph of an inequality in two variables is part of the solution when the line is a solid line
What is the meaning of inequality in math?A mathematical statement stating the relationship in terms of greater than, larger than or equal to, less than, or less than or equal to between two numbers or algebraic expressions is known as an inequality.
Inequality representation using a solid line and a dotted line
Inequality plots that use the < or > symbols features a dashed line and this shows the boundary lines are not a part of the solution.
An inequality marked with the symbol "or" such as greater than or equal to or less than or equal to is represented by a solid line boundary line and the region is included in the solution.
Learn more about inequality interpretation at:
https://brainly.com/question/29723628
#SPJ1
Shayna and Arjun each improved their yards by planting grass sod and geraniums. They bought
their supplies from the same store. Shayna spent $16 on 2 ft² of grass sod and 1 geraniurn, Arjun
spent $73 on 1 ft² of grass cod
WL
fta of grass sod and the
So on solving the provided question, we can say that by equation Shayna : [tex];5x + 10y = $175[/tex] and Brenda : [tex]9x + 4y = $147[/tex]; cost = [tex]$11/ft^2[/tex] of grass, $12/geranium
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
the equation, that will be formed are
Shayna : [tex];5x + 10y = $175[/tex]
Brenda : [tex]9x + 4y = $147[/tex]
[tex]5x + 10y = $175 \\ 5x = $175 - 10y\\(5x/5) = ($175/5) - (10y/5) = > x = $35 - 2y\\9x + 4y = $147 = > 9($35 - 2y) + 4y = $147\\ $315 - 18y + 4y = $147\\$315 - $147 = 18y - 4y \\ $168 = 14y = > y = $12\\ 5x + 10y = $175 = > 5x + 10($12) = $175 = > 5x + $120 = $175 \\5x = $175 - $120 = > 5x = $55 = > x = $11[/tex]
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
Earth approximately 33x 107 miles from the sun. Saturn is approximately 8.87 x 108 miles from the sun. About how much farther is S
from the sun than Earth is?-
OA 794x107 miles
OB 724x10 miles
0 43×10 miles
OD 4.3x10 miles
Reset
Next
What is the percent of increase from 5 to 7?
The percentage increse in value from 5 to 7 is 40 %
What is Percentage ?A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.
Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:
use the unitary approach.by adjusting the fraction's denominator to 100.It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary technique.
The initial value is 5
Final value = 7
Increse in value 7-5 = 2
Percentage increse is [tex]\frac{2}{5}* 100 = 40 \ \% \\[/tex]
The percentage increse in value from 5 to 7 is 40 %
To learn more about Percentage refer to :
https://brainly.com/question/29163532
#SPJ1
which pair of expressions are equivalent.
a) 3(x+ 2) and 3x + 2
b) 4d+ 2e and 8d +e
c) f+f+f+g and 3fg
d) b+b+ 3c and 2b +3c
Answer:
d) b+b+3c and 2b+3c
Step-by-step explanation:
b+b=2b
2b+3c=2b+3c
what does it mean to round to the nearest cent
Answer:
wrong - $32.547
right - $325.47
Step-by-step explanation:
Basically, if the number in the tens place (145) is 5 or higher the nearest would be the next ten or hundred up, if lower than 5 it goes back down.
Rounding cents is basically the same. as rounding Example:
$14.345
(This is not a vaild amount of money because once you reach a hundred cents you have another dollar. So you will move the decimal point over to the left.)
$143.45
More examples:
incorrect - $23.8678
correct - $2386.78
incorrect - $89.264
correct - $892.64
Rounding is something like rounding to the nearest ten or hundred here's an example:
14 to the nearest ten is 10
16 to the nearest ten is 20
284 to the nearest hundred is 300
104 to the nearest hundred is 100
(Hope this helps. Sorry if this confused you further)
The height of a kicked ball can be modeled by the quadratic function h = - 0 .01x^2 + 1.18x + 2. The horizontal distance traveled by the ball in feet is represented by x, and h is the height of the ball in feet. Approximately how far does the ball travel horizontally by the time it hits the ground?
The horizontal distance covered by the ball is 119.5 ft.
What is a quadratic equation?It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Given that the height of a kicked ball can be modeled by the quadratic function h = - 0 .01x² + 1.18x + 2. The horizontal distance traveled by the ball in feet is represented by x, and h is the height of the ball in feet.
The horizontal distance covered by the ball will be calculated as,
h = - 0 .01x² + 1.18x + 2
Equate h to zero and solve for the distance x,
- 0.01x² + 1.18x + 2 = 0
Use the quadratic formula,
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x = \dfrac{-1.18\om\sqrt{(1.18^2)-(4\times(-0.01)\times2}}{2\times-0.01}[/tex]
[tex]x=\dfrac{-1.18\pm\sqrt{1.4+0.08}}{-0.02}[/tex]
x = ( -1.18 - 1.21 ) / 0.02
x = 119.5 ft
The horizontal distance will be 119.5 ft.
To know more about quadratic equations follow
https://brainly.com/question/1214333
#SPJ1
at a football game, a vender sold a combined totalf of 248 sodas and hot dogs. the number of sodas sold was three times the number of hot dogs sold. find the number of sodas and hot dogs sold.
Answer:
Number of soda = 186
Number of hot dog= 62
Step-by-step explanation:
Let us take number of sodas as x and number of hot dogs as y
Then
x + y = 248 [Equation 1]
and
3y = x
Hence,
3y -x = 0 [Equation 2]
By adding [Equation 1 & 2]
(+x -x) 3y + y = 248 + 0
4y = 248
4 4
y = 62
Substitute y= 62 in [Equation 1] to get
x + y = 248
x + 62 = 248
x = 248 - 62
x = 186
Solve these simultaneous equations.
y=x
y=x²-6
Answer:
solutions for these simultaneous equations are x = 6 and y = x = 6, or x = 1 and y = x = 1
Step-by-step explanation:
To solve these simultaneous equations, we need to find the values of x and y that satisfy both equations.
Given:
y = x
y = x² - 6
We can substitute the first equation into the second:
x = x² - 6
we can subtract x from both sides to get:
0 = x² - 7x + 6
Then we can factor it:
(x-6)(x-1) = 0
Therefore x = 6 or x = 1
So the solutions for these simultaneous equations are x = 6 and y = x = 6, or x = 1 and y = x = 1
There are two solutions, (6,6) and (1,1)
The point of intersection of angle bisectors of a triangle is called .
A . circumcentre
B. incentre
C. orthocentre
D. centroid
The point of intersection of a triangle's angle bisectors is known as the incentre.
What exactly is an incentre?The incentre is the point where the triangle's three angle bisectors meet at a single point. For more understanding, draw a triangle. Name each angle with A, B, and C. Place P in the triangle's center. The point that connects A to P, B to P, and C to P is the angle bisector of a triangle. Point P is the intersection of all of the lines mentioned above. The explanation leads us to the conclusion that the incenter is the center of the triangle pointed out by P.Then, what is the explanation of the other options?The point of intersection where the three perpendicular bisectors meet or intersect is called the circumcenter.The point of intersection where the three triangle’s altitudes meet or intersect is called the orthocentre. The point of intersection where the triangle’s three median values meet or intersect is called the centroid. The letter G is usually used to denote the centroid.Learn more about incentre in triangle:
https://brainly.com/question/29756751
#SPJ4
The number of calls received by an office on Monday morning between 8:00 AM and 9:00 AM has a mean of 2. Calculate the probability of getting no more than 4 calls between eight and nine in the morning. Round your answer to four decimal places
The probability of getting no more than 4 calls between eight and nine in the morning is 0.9473
How to calculate the probability of getting no more than 4 calls?
This is a Poisson distribution problem with a mean of 2.
In a Poisson distribution, the probability that X successes is given by:
P(X = x) = [e^(-λ) × λˣ] / x!
where x is the number of successes
e = 2.71828 is the Euler number
λ is the mean
The number of calls received by an office on Monday morning between 8:00 AM and 9:00 AM has a mean of 2 i.e. λ = 2
P(X ≤ 4) = ([e⁻²× 2⁰]/0!) + ([e⁻²× 2¹]/1!) + ([e⁻²× 2²]/2!) + ([e⁻²× 2³]/3!) + ([e⁻²× 2⁴]/4!)
P(X ≤ 4) = 0.9473
Learn more about Probability distribution on:
brainly.com/question/29405205
#SPJ1
What is prime multiple of 10?
A multiple of 10 cannot be equals to a prime number. Multiple of 10 is always equals to a composite number.
As given in the question,
Multiple of a given number 10 are equals to :
10 , 20 , 30, 40, 50, ........, so on.
Prime number are those numbers which have only two factors one and the number itself.
Number 10 itself is not a prime number.
Factors of 10 are equals to :
1, 2, 5, 10
More than two factors.
All the Multiples of 10 cannot be a prime number as they have more than two factors.
Multiple of 10 represents the composite number.
Therefore, multiple of 10 cannot be equals to a prime number they are composite number.
Learn more about multiple here
brainly.com/question/24327297
#SPJ4
Jean Junction i elling jean at 15% off the regular price the regular price i $25 per pair what i the dicount amount
The discount amount is $3.75 ($25 x 15% = $3.75).
1.Calculate the discount: Regular price x discount percentage = discount amount
2. Plug in the values: $25 x 15% = $3.75
3.The discount amount is $3.75.
The discount amount can be calculated by taking the regular price and multiplying it by the discount percentage. For example, if the regular price is $25, and the discount percentage is 15%, the discount amount can be calculated by multiplying the regular price by the discount percentage ($25 x 15% = $3.75). Therefore, the discount amount is $3.75. This calculation can be used to calculate the discount amount for any given regular price and discount percentage.
Learn more about amount here
https://brainly.com/question/8082054
#SPJ4
What is the range of the given function?
((-2, 0), (-4, -3), (2, -9), (0, 5), (-5, 7))
A (x/x = -5, -4,-2,0,2)
B (uly = -9,-3,0,5, 7)
C lr=-9, -5,-4.-3,-2.0,2,5,7
D g1g=-9,-5,-4,-3,-2,0,2,5,7
Answer: B (-9, -3, 0, 5, 7)
Step-by-step explanation:
Victoria has tiles that measure 20 centimeters by 12 centimeters. If she wants to arrange them to form the smallest possible square, without cutting or overlapping any of the tiles, how many centimeters long will each side of the square be?
The dimensions of each side of the square will be 4 centimeters long.
To determine the smallest possible square that can be formed from the tiles without cutting or overlapping them, you will need to find the greatest common divisor (GCD) of the two dimensions of the tile (20 cm and 12 cm).
The GCD represents the largest size of a square that can be formed without cutting or overlapping the tiles.
The GCD of 20 and 12 can be found using the Euclidean algorithm:
Divide 20 by 12. The quotient is 1 and the remainder is 8.
Divide 12 by 8. The quotient is 1 and the remainder is 4.
Divide 8 by 4. The quotient is 2 and the remainder is 0.
Since 4 is the last non-zero remainder, it is the GCD of 20 and 12.
Thus, each side of the square will be 4cm long.
Learn more about the Greatest Common Factor here:
brainly.com/question/18905667
#SPJ1
Rick melted a cube and made a cone with it. The amount of melted liquid left after making the cone wa 49 cm
The volume of the cube before it was melted is greater than 49cm^3
The amount of melted liquid left after making the cone is 49 cm^3.
A cone is a three-dimensional shape that has a circular base and a single vertex or point. The amount of liquid remaining after making a cone can be calculated by comparing the volume of the cone to the volume of the cube.
The volume of a cone can be calculated using the formula:
V = (1/3) * pi * r^2 * h
Where V is the volume of the cone, pi is a mathematical constant (approximately 3.14), r is the radius of the circular base, and h is the height of the cone.
However, we don't have information about the radius or height of the cone, we only know the volume of melted liquid left after making the cone is 49 cm^3.
We can use this information to determine the volume of the cube before it was melted and compare it with the volume of the cone.
The volume of a cube can be calculated using the formula:
V = s^3
Where V is the volume of the cube, s is the length of one side of the cube.
Let's call Vc the volume of the cube before it was melted and Vcon the volume of the cone
Vc - Vcon = 49 cm^3
Therefore, the volume of the cube before it was melted is greater than 49cm^3
To learn more about the volume of cube and cone,
Visit; brainly.com/question/495173
#SPJ4
Anna and julia each take a bycicle trip. Anna ride 20 mile in 1 1/3 hour. Julia ride 246 mile in 16 hour. Which rider ha the lower unit rate? by how much?
Julia has lower rate than anna by 0.375 miles/ hour
A rate is a ratio that is used for comparing two different kinds of quantities which have different units. On the other hand, the unit rate illustrates how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. In fact, unit rate is said to be the amount of something in each unit or per unit. Let us understand this using some examples:
40 miles/2 hours = 20 miles/hour, Unit rate is 20 miles per hour
160 words/4 minutes = 40 words/minutes, Unit rate is 40 minute per minute
To compare the unit rate of the two riders, we need to determine the number of miles per hour for each of them.
For Anna, the unit rate is 20 miles / 1 1/3 hour = 15 miles/hour.
For Julia, the unit rate is 246 miles / 16 hours = 15.375 miles/hour.
So, Julia has a lower unit rate than Anna by 0.375 miles/hour.
To learn more about unit rate visit-
brainly.com/question/29781084
#SPJ4
When writing a piecewise function from a graph how do you determine the domain of each rule?
When writing a piecewise function from a graph, the domain of each rule is determined by the x-values of the graph.
A piecewise function is a function that is defined by different rules for different ranges of the input (x-values). Each rule corresponds to a different interval of the domain.
To determine the domain of each rule when writing a piecewise function from a graph, you can use the following steps:
Identify the intervals of the x-axis where the graph changes behavior.
Write the domain of the function for each interval.
Write the rule for each interval of the domain.
For example, if a graph has a behavior change at x = 1, x = 3, and x = 5, then the domain of the function can be written as:
f(x) = {
y1, x < 1
y2, 1 ≤ x < 3
y3, 3 ≤ x < 5
y4, x ≥ 5
}
The domain for each rule is the interval of x-values between the changes in behavior. In this example, the first rule applies to x values less than 1, the second rule applies to x values between 1 and 3, the third rule applies to x values between 3 and 5, and the fourth rule applies to x values greater than or equal to 5.
Here, note that when writing a piecewise function, it is important to make sure that there are no gaps or overlaps in the domain of the function and that the x-values where the graph changes behavior are included in the domain of at least one of the rules.
Read more about piecewise function:
brainly.com/question/18499561
#SPJ4
What is the additive inverse of 924?
The Additive Inverse of 924 is -924
⇒ The number that, when added to 924, will result in a sum of zero is the additive inverse of 924. The formula to solve the issue where x is the additive inverse of 924 is as follows:
924 + x = 0
⇒ When we solve the preceding equation for x, we obtain x = -924. As a result, the answer to the question "What is the additive inverse of 924?" is -924.
∴Therefore Additive Inverse of 924 = -924
Learn more about Additive Inverse:
https://brainly.com/question/1548537