Nancy wove a pot holder with a area of 80 square inches. The lengths and widths of the sides are whole numbers. Which dimensions make the most sense for a potholder? Explain

Answers

Answer 1

The pairs of numbers that multiply up to 80 are (1, 80), (2, 40), (4, 20), (5,16), and (8,10).
Since pot holders are normally close to squares, 8 by 10 makes the most sense

Answer 2

Final answer:

The dimensions of 8 inches by 10 inches make the most sense for a pot holder with an area of 80 square inches, as they are practical in size. This is similar to the concept of a square whose area scales by the square of the side length when dimensions are increased by a scale factor.

Explanation:

The student asked which dimensions make the most sense for a potholder with an area of 80 square inches where the lengths and widths are whole numbers. It's crucial to consider practical sizes that would be convenient for handling hot items without being too large or too small.

Common dimensions for a pot holder could be 8 inches by 10 inches since 8 x 10 equals 80 square inches, and these measurements are suitable for a pot holder. These measurements make sense as they provide enough space to protect hands from heat but are not excessively large, making them impractical. They are comparable to the measurements of a placemat, which is typically used in dining settings and is also manageable in size.

Comparing this to the information about squares and areas, if Marta has a square with side length 4 inches, its area would be 16 square inches. A similar square with side lengths that are twice as long (8 inches) would have an area of 64 square inches because the area is proportional to the square of the side length. Consequently, the area of the larger square is four times that of the smaller square (since 2 squared is 4).

This example of scaling dimensions and areas can assist in understanding how dimensions that are whole numbers relate to the area and the practical use of an object. The mentioned scale factor is integral in determining how the area increases with increased side lengths.

Related Questions

A video rental store charges $4 per day to rent a movie and $3 per day to rent a video game. During one summer, Tony paid a total of $140 to rent movies and video games from this store. If he rented twice as many video games as movies, how much did he spend on movie rentals during the summer?

Answers

Let's use the variables m and v for this:
4m + 3v = 140
v = 2m
Insert this variable:
4m + 3(2m) = 140
4m + 6m = 140
10m = 140
m = 14
One movie costs 4 dollars:
14*4 = 56
He spent $56 on movies

Suppose there is exactly one index k such that a[k] = x. what is the expected number of indices into a that we must pick before we find x and random-search terminates?

Answers

Suppose there is only one index k such that a [k] = x. What is the expected index number of indexes that must be selected before x and random search?

Evaluate the polynomial when x=4 y=-4
x^2-3y^2+2xy

Answers

[tex]x^2-3y^2+2xy\\\\for\ x=4\ and\ y=-4\\\\substitute\ the\ values\ of\ x\ and\ y:\\\\4^2-3\cdot(-4)^2+2\cdot4\cdot(-4)=16-3\cdpt16-32=16-48-32=-64[/tex]

An experienced roofer can work twice as fast as her helper. working together, they can shingle a new section of roof in 4 hours. how long would it take the experienced roofer, working alone, to complete the same job?

Answers

Final answer:

The problem solves for the time it would take the roofer to work alone, by first determining the shared work rate. The helper works at rate x and the roofer at rate 2x (twice as fast). They complete 1 roof in 4 hours working together, thus their combined rate is 1/12 roof per hour. So, the roofer’s individual rate is 1/6 roof per hour, meaning she can finish the job alone in 6 hours.

Explanation:

To solve this problem, we'll use the equation for work which is work = rate x time. Let's say the helper's rate of work as 1x and the roofer's rate as 2x, because the roofer can work twice as fast as the helper.

Bearing in mind that the total time it takes both of them to shingle the roof is 4 hours, according to the problem, we can represent this relationship as this equation: (2x + x) * 4 = 1 roof. This simplifies to 12x = 1, meaning the rate at which they work together is x = 1/12 roof per hour.

Thus, the roofer’s individual rate of work is 2x = 2/12 roof per hour = 1/6 roof per hour. Therefore, to calculate how much time it would take for the roofer to do the job alone, we simply divide the total task (1 roof) by the roofer’s rate of work, 1/(1/6) = 6 hours.

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Final answer:

By setting up and solving an algebraic equation based on the given conditions in the problem, we find that it would take the experienced roofer alone 3 hours to complete the same job.

Explanation:

The problem is related to work rate and could be solved using algebra. Let's denote by X the time (in hours) it takes for the helper to complete the job alone. Considering that an experienced roofer can work twice as fast as her helper, the roofer could complete the same job alone in X/2 hours. From the problem, we know that when working together, they can complete the job in 4 hours. This means that the amount of work they do together in one hour (1/4) is equal to the sum of the amounts of work done by each in one hour (1/X + 2/X). By solving this equation, we get X = 6. So, it would take the helper 6 hours to complete the job, which means it would take the experienced roofer half of this time, which is 3 hours.

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PLEASE HELP ME OUT ASAP!! I would really appreciate your help!

Answers

The first thing you need to do is get a graph for the corn. This one is not very good, but it will get you an answer. While the potatoes graph is going from 50000 to 40000 (slowly), the corn graph is going up like a rocket trajectory. So eventually, the Baker family will produce more corn than potatoes. That's D.

Answer D.

Problems with AB and C
A
The problem with A is that they won't always produce more potatoes than corn. That will happen only in the beginning.

B
Clearly B is wrong. The amount of corn in the beginning was 25000 pound. In the meantime potatoes were produced at a yearly rate of nearly 50000 pounds of potatoes.

C is wrong because of what A says.

A school table has 8 sides of equal lengths. if one side is 4 feet, what is the perimeter of the table?

Answers

Since the table has 8 sides that all have the same length then multiply 4 by 8 so the answer is 32

One side = 4 feet

4 x 8= 32

Eight sides = 32 feet

factor :
x^4 (x+4) + 9 (x+4)

Answers

[tex]x^4(x+4)+9(x+4)=(x+4)(x^4+9)[/tex]

A line segment with endpoints (-4,5) and (-2,2) is reflected about the y-axis. Write the coordinates of the endpoints after the segment has been reflected.

Answers

When reflection goes about y-axis, the x coordinate changes into its opposite.
(-4,5)---->(4,5)
(-2,2)----->(2,2)

A rain gutter is to be constructed of aluminum sheets 12 inches wide. After marking off a length of 4 inches from each edge, this length is bent up at an angle θ. The area A of the opening may be expressed as the function: A(θ) = 16 sin θ ⋅ (cos θ + 1). If θ = 45°, what is the area of the opening?

A. 4.8 in2
B. 20.8 in2
C. 19.3 in2
D. 9.0 in2

Answers

Answer is A. 4.8 in 2

Answer:

19.3

Step-by-step explanation:

took the test

Morgan uses 1/4 of her supply of raisins to make trail mix and 3/8 of her supply of raisins to make cookies. If Morgan uses 5 pounds of raisins, how many pounds of raisins are in her supply?

Answers

There are 8 pounds of raisins in Morgan's supply.

Let us say there are 'a' pounds of raisins in her supply.

What is a fraction?

Fraction is a manner to represent part of a whole.

Raisins used to make trail mix = 1/4 of a = 1/4 a

Raisins used to make cookies = 3/8 of a = 3/8 a

It is given that:

Morgan uses 5 pounds of raisins,

[tex]\frac{1}{4} a+\frac{3}{8} a=5[/tex]

[tex]\frac{5}{8} a = 5\\\\a=8[/tex]

Therefore, there are 8 pounds of raisins in Morgan's supply.

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Morgan's total supply of raisins is 8 pounds.

Let's denote the total supply of raisins by R. According to the problem, Morgan uses 1/4 of her supply to make trail mix and 3/8 of her supply to make cookies. Together, this amounts to a total of five pounds of raisins used.

We set up the equation to represent the total amount of raisins used:

1/4 R + 3/8 R = 5

We need to find a common denominator to combine the fractions. Here, the common denominator is 8:

(2/8) R + (3/8) R = 5

Combining the fractions gives:

(5/8) R = 5

To isolate R, we multiply both sides of the equation by the reciprocal of 5/8, which is 8/5:

R = 5 * 8/5

When we simplify, we get:

R = 8

So, Morgan's total supply of raisins is 8 pounds.

the ratio of keiths age to Jared's ages 3 to 5 if Keith is 24 years old how old is Jared please show how many you got this answer I will mark brainiest

Answers

Comment
You need to set up a direct proportion. You have to relate Keith and Jared's ages to the ratio you were given.

Givens
Keith is 24
Keith / Jared = 3/5
J = Jared

Solution
3/5 = 24 / J Cross multiply
3*J = 5 * 24 Combine factors on the right.
3J = 120 Divide by 3
J = 120 / 3
J = 40

Conclusion
Jared is 40 years old.

Which expression is equivalent to

Answers

The equivalent expression is [tex]log(\frac{1}{2} ) -log_{12}8+log_{12}w[/tex]

Logarithms and indices

To get the equivalent expressions for the given logarithmic function, we will use the following laws of logarithm:

Laws of logarithm[tex]logab=loga+logb\\ log(\frac{a}{b} )=loga -logb[/tex]

Given the logarithmic function:

[tex]log_{12}(\frac{1/2}{8w}) [/tex]

This can be further expressed as:

[tex]log_{12}(\frac{1/2}{8w} )[/tex][tex]log_{12}(\frac{1/2}{8w} )=log\frac{1}{2}-log8w [/tex]

Using the product law of logarithm

[tex]log_{12}(\frac{1/2}{8w}) =log(\frac{1}{2} ) -log_{12}8+log_{12}w[/tex]

Hence the equivalent expression is [tex]log(\frac{1}{2} ) -log_{12}8+log_{12}w[/tex]

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stumpy the skeleton goes for a bike ride every night in the cemetery. He rides 1/2 way around the cemetery and stops. Stumpy then bikes 3/4 of the way around before stopping again. he finishes his ride by biking another 3/8. how far around the cemetery does stumpy bike?

Answers

He bikes 13/8 of the cemetery

[tex]12 \times 778 [/tex]

Answers

Hope it helped you.
~~~~~~~~~~~~~~~~~~

778*12

Answer is=9336

-Charlie

Final answer:

To multiply 12 by 778, one needs to perform the standard multiplication process. Multiplying each digit of 12 by 778 individually and then adding the results provides the final answer, which is 9336.

Explanation:

The student's question involves performing a multiplication operation, specifically 12 multiplied by 778. To solve this without a calculator, one can use a standard multiplication technique as follows:

Write down the two numbers, with 778 above 12.

First, multiply 2 (the rightmost digit of the lower number) by 778 to get 1556.

Next, multiply 1 (the leftmost digit of the lower number) by 778 and remember to add a zero at the end (because it represents the tens place), which gives us 7780.

Add the two results, 1556 and 7780, to get the final answer, which is 9336.

The result of 12 times 778 is 9336.

Hey can you please help me posted picture of question

Answers

The correct answer is the option D.

The explanation is shown below:

1. As you can see in the figure attached, the blue parabola has the function f(x)=x^2. This is the patern function. By definition, this is the most basic function of the quadratics functions.

2. The red parabola is shifted 2 units to the -y axis and is wider than the first one, by multiplying the variable x. Therefore. As you can see, the correct function that represents this parabola is the function of the option D
3. If you want to verify it, you can give values to x and plot each point on a graph.

If you observe the two graphs you can note that:

a) F(x) is wider than G(x)
This can be obtained by multiplying the function by a value with magnitude less than 1.

b) F(x) is shifted down
This can be obtained by subtracting a number from the function value.

From the given option, only option D satisfies these conditions.

So, the correct answer is option D

use matrix method to solve x+4y=8 2x+y=9

Answers

In first equation, x has coefficient 1 and y has coefficient 4 and is equal to 8
In first equation, x has coefficient 2 and y has coefficient 1 and is equal to 9

So augmented matrix would looks like this:
[tex]\left[\begin{array}{cc|c}1&4&8\\2&1&9\end{array}\right][/tex]

Your goal is to transform matrix to look like this:
[tex] \left[\begin{array}{cc|c}1&0&x_{\text{answer}}\\0&1&y_{\text{answer}}\end{array}\right][/tex]

Steps to reach there:

Subtract first row from second row two times:
[tex]\left[\begin{array}{cc|c}1&4&8\\0&-7&-7\end{array}\right][/tex]

Multiple second row by -1/7:
[tex]\left[\begin{array}{cc|c}1&4&8\\0&1&1\end{array}\right][/tex]

Now subtract second row from first row 4 times:

[tex]\boxed{\left[\begin{array}{cc|c}1&0&4\\0&1&1\end{array}\right]}[/tex]

Which translate to
[tex]x+0y = 4\\\ \\0x+y=1[/tex]

So then x = 4 and y = 1.

Hope this helps.

which has more people a car that is 3/4 full or a car that is 1/4 full

Answers

A car that is 3/4 full because 3 outta the 4 seats are taken while 1/4 is only 1 outta the 4 seats are taken up. Hope it helps :).

A car of people 3/4 full would be more than a car of people 1/4 full because 3/4 is more than 1/4.

A camera manufacturer spends $2,100 each day for overhead expenses plus $9 per camera for labor and materials. The cameras sell for $14 each. a. How many cameras must the company sell in one day to equal its daily costs? b. If the manufacturer can increase production by 50 cameras per day, what would their daily profit be?

Answers

A. The profit for each camera itself is $5 a camera. So, to make $2,100 dollars they would have to sell 420 cameras (2,100 / 5 = 420).

B. If they sold an extra 50 cameras a day, since they make $5 a camera, that would give them an extra profit of $250 a day.

A. The company must sell 420 cameras, to make it equal to daily costs.
B. For making 50 more cameras each day, they'd make $250 dollars more per 50 cameras.

A. To find this, you can simply multiply 420 by $14. This will give you how much they make from selling that many cameras ($5,880). Next you need to multiply 420 by 9 (labor an material cost per camera), then add $2,100 (expenses). This will give you the same cost ($5,880), thus making them equal, and proving 420 is the answer.

B. To find this, you do the same steps as above, by replacing 420 with 470, (470*$14 = $6,580) and (470*9 + $2,100 = $6,330). Then you subtract $6,330 from $6,580. Thus getting $250.

I hope this helps!

Set A is the set of all positive multiples of 2 that are less than or equal to 20. Set B is the set of all positive multiples of 4 that are less than or equal to 20. How many elements are positive multiples of 4 that are less than or equal to 20, but are not positive multiples of 2?

Answers

A = {2, 4, 6, 8, 10, 12, 14, 16, 18}
B = {4, 8, 12, 16}

All elements of set B are also elements of set A.

Answer: None.
All multiples of 4 are automatically multiples of 2.

Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale.

Answers

sqrt(7^2 + (23/2)^2) = 13.5 (1 d.p.)

A house was valued at 398,000.over several the house increased by 0.08

Answers

Here's the equation to find the current price:
398000 + 0.08(398000)
We can make it simpler:
1.08(389000)
The current price is $420120

£600 is put in a bank. after a year the money has increased by 8% how much is now in the bank

Answers

increased = 8% x £600 = 0.08 x 600 = £48

Money in the bank now = £600 + £48 = £648

Answer: £648

The value of (a-1)+a^2-b^2/1-ab+2(a-b)/2b when a=2 and b=-1 is ?

Answers

The value of (a-1)+a^2-b^2/1-ab+2(a-b)/2b when a=2 and b=-1 will be evaluated as follows:
substituting the values in the expression we obtain:
(2-1)+2^2-(-1)^2/1-(2*(-1))+2(2-(-1))/(2(-1))
simplifying the above we get:
1+4-1/1-(-2)+2(2+1)/(-2)
=1+4-1+2(3)/(-2)
=1+4-1-3
=5-4
=1

Answer: 1

Final answer:

The value of the expression (a-1) + a^2 - b^2 / (1-ab) + 2(a - b) / (2b) when a=2 and b=-1 is -5/3.

Explanation:

To calculate the given expression when a=2 and b=-1, we first plug these values into the expression, which is (a - 1) + a^2 - b^2 / (1 - ab) + 2(a - b) / (2b). After substitution, it simplifies as follows:

The term (a - 1) becomes (2 - 1), which equals 1.

The term a^2 - b^2 becomes 2^2 - (-1)^2, which simplifies to 4 - 1 = 3.

The denominator 1-ab becomes 1 - (2)(-1), which equals 1 + 2 = 3.

The term 2(a - b) becomes 2(2 - (-1)), which is 2(3) = 6.

The denominator 2b becomes 2(-1), which is -2.

Now, the full expression simplifies to (1 + 3) / 3 + 6 / -2. Simplifying further, we get 4 / 3 + (-3), which equals to 4/3 - 3/1. After finding a common denominator, the expression simplifies to (4 - 9) / 3, which is -5/3.

Therefore, the value of the expression when a=2 and b=-1 is -5/3.

What number is 8.0007 • 10 ^6 in scientific notation?

Answers

8,000,700

Take the decimal and move it six spaces to the right.

[tex]8.0007*(10*10*10*10*10*10)=8000700[/tex]

Answer is 8000700

Hope it helped you.

-Charlie

what is the gcf of 12 78 and 90

Answers

The greatest common factor of 12, 78, and 90 is 6.

Factors are the numbers, that when multiplied with another number, equal the product.

Factors of 12: 1, 2, 3, 4, 6, and 12.
Factors of 78: 1, 2, 3, 6, 13, 26, 39, and 78.
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 20, 45, and 90.

The Greatest Common Factor is the highest factor shared among the products. Thus proving 6 is the GCF.

I hope this helps!

Part I: Angle Sum Relationships
Arrange the three congruent triangles so that angles 1 and 3 are adjacent to one another, and angle 2 is adjacent to angles 1 and 3.

B. What do you notice about the three angles?

C. What do they appear to form?

D. What can you conclude about the sum of the angles in a triangle?

Answers

The three angles are adjacent to each other.
They appear to form a straight line.
It means that the sum of the three angles of a triangle is appears to be 180 degrees.

Answer with explanation:

→→The three Angles form a Linear pair.That is

⇒∠1+∠2+∠3=180°

→→When these three congruent triangles are joined they form a Trapezoid.

→→Sum of angles in a trangle is given by Angle sum property Axiom of triangle which states that sum of the angles in a triangle is 180°.

Find the lowest common multiple of 28 and 210

Answers

Answer:

420

Step-by-step explanation:

210 = 14×15

28 = 14×2

The LCM wil be the product of unique factors;

... LCM = 14×15×2 = 420

The acronym CPCTC stands for “corresponding parts of congruent __________ are congruent.”

Answers

The Blank is: Triangles

Cpctc is Corresponding parts of congruent triangles are congruent.

It is used at the end of your proof to show two sides and two angles are congruent.

Hope this helps!

Answer: Triangles

Step-by-step explanation:

The CPCTC property of congruent triangles says that is two triangles are congruent then their corresponding angles and sides are congruent.

The acronym CPCTC basically stands for Corresponding Parts of Congruent Triangles are congruent.

It generally used two show any two corresponding segments or angles of two congruent triangles congruent.

Will give branliest!
Please help me!

The students in Mr. McIntyre’s class and the students in Mrs. Ramos’s class were asked how many pets they each have. The dot plots below show the results. Which compares the means of the data in the dot plots?

The mean for Mr. McIntyre’s class is about 2 more than the mean for Mrs. Ramos’s class.

The mean for Mrs. Ramos’s class is about 2 more than the mean for Mr. McIntyre’s class.

The mean for Mr. McIntyre’s class is about 1 more than the mean for Mrs. Ramos’s class.

The mean for Mrs. Ramos’s class is about 1 more than the mean for Mr. McIntyre’s class.

*The first picture is Mr. McIntyre’s Class
*The second picture is Mrs. Ramos’s Class

Answers

The mean can be calculated by adding all of the values and dividing that sum by the number of values you added. To take advantage of the way data is being collected, I am grouping the addends as, for example, 5(1), instead of writing out 1 + 1 + 1 + 1 + 1.

Mr. McIntyre's class mean is:
[tex]\frac{5(0)+5(1)+4(2)+ 1(3)}{5 + 5+4+1} = \frac{5+8+ 3}{15}= \frac{16}{15}= approx. 1.07[/tex]

Mrs. Ramos' class mean is:
[tex] \frac{1(0)+2(1)+2(2)+4(3)+3(4)+3(5)}{1+2+2+4+3+3} = \frac{2+4+12+12+15}{15}= \frac{45}{15}=3[/tex]

Based on these findings, we can conclude that the mean for Mrs. Ramos' class is about 2 more than the mean for Mr. McIntyre's class.

Answer:

If you are lazy like me the answer is B

Step-by-step explanation:

ur welcome :D

Hey can you please help me posted picture of question

Answers

This will be a Experimental probability as you are performing a small observation and selecting the favorable outcomes based on your observation.

Probability based on experiments or observation made in given scenario is known as experimental probability.

So, the answer is option A

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