There can be multiple possible dimensions for a garden with an area of 11 square feet depending on its shape. For example, the garden could be 1ft by 11ft, 2ft by 5.5ft, or even a square with each side measuring 3.32 ft.
Explanation:The area of a garden is calculated by multiplying its length by its width. As the area of the garden is given as 11 square feet, possible dimensions for the garden could be 1 foot by 11 feet, 2 feet by 5.5 feet, or any other combinations that, when multiplied, give the result as 11 square feet.
Another way to look at it is that if you imagine the garden as a perfect square shape, each side would be approximately 3.32 feet since 3.32 multiplied by 3.32 equals roughly 11. This is because the square root of 11 is about 3.32.
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A mountain climber climbed down a cliff 50 feet at a time . He did this 5 times in one day . What is the overall change in his elevation ?
Six less than the product of 9 and a number is equal to 4
Given the point and it''s image, determine the scale factor. A (3, 6) A'' (4.5, 9) G'' (3, 6) G (1.5, 3) B (2, 5) B'' (1, 2.5).
Final answer:
The scale factors for the points given are 1.5 for A to A', indicating an enlargement, and 0.5 for B to B', indicating a reduction. G to G' also indicates a reduction with a factor of 0.5.
Explanation:
To determine the scale factor given the point and its image, you can find the ratio between the coordinates of the image and the original coordinates. Let's analyze the pairs of points you've provided:
A (3, 6) and A' (4.5, 9)
G (1.5, 3) and G' (3, 6)
B (2, 5) and B' (1, 2.5)
We can find the scale factor by dividing the x-coordinates of the image by the original x-coordinate and doing the same for the y-coordinates. For point A:
Scale factor for x: 4.5 / 3 = 1.5
Scale factor for y: 9 / 6 = 1.5
For point G, we see that it's actually the reverse (original to image), but you can still calculate:
Scale factor for x: 3 / 1.5 = 2
Scale factor for y: 6 / 3 = 2
Lastly, for point B:
Scale factor for x: 1 / 2 = 0.5
Scale factor for y: 2.5 / 5 = 0.5
So, the scale factors for A to A' and for B to B' are 1.5 and 0.5, respectively, showing that A to A' is an enlargement while B to B' is a reduction. For G to G', the reverse is a reduction with a factor of 0.5.
Answer:
-7(k+9)=9(k-5)-14k
a number x plus 9 is 3036 write equation solve for x
which of the following inequality has solution set
Need help with this one!!!
25/5 as a mixed number
what is 63.75 minus 13.25 please really need help.
What is equivalent to 5.300
can a sequence be both arithmetic and geometric?
A sequence can be both arithmetic and geometric, and this is illustrated where terms follow both an arithmetic and geometric progression.
Yes, a sequence can be both arithmetic and geometric. An example of such a sequence is when the terms of the sequence follow both an arithmetic progression, where the difference between consecutive terms is constant, and a geometric progression, where each term after the first is found by multiplying the previous term by a fixed, non-zero number.
A car traveled 63 miles on 3 gallons of gas. What proportion can you set up to determine how many miles, m, the car can travel on 7 gallons of gas?
3.4 divided by 0.16728
x/21 = 3/63 solve the proportion
there are some numbers that can be made into only one array. Find all of these numbers up to 50.
Multiplication Property of Inequality -1/2x<-12 simplify it all the way through
The manager at Jessica's Furniture Store is trying to figure out how much to charge for a couch that just arrived. If the couch was bought at a wholesale price of $113.00 and Jessica's Furniture Store marks up all furniture by 45%, at what price should the manager sell the couch?
Answer: The manager sold the couch at $163.85.
Step-by-step explanation:
Since we have given that
Wholesale price of the couch = $113.00
If Jessica's Furniture Store marks up all furniture by 45%.
So, Increment in whole sale price is given by
[tex]\frac{45}{100}\times 113\\\\=\frac{5085}{100}\\\\=\$50.85[/tex]
So, the manager sold the couch at the price is given by
[tex]\$113.00+\$50.85\\\\=\$163.85[/tex]
Hence, the manager sold the couch at $163.85.
You have 10,600 to 10,425 find the percent decrease
Is the product of an irrational number with a rational number always an irrational number??
Write out the sample space for the given experiment. use the letter b to indicate boys and g for girls. a couple plans to have 33 children.
An example of one possible outcome in the sample space:
[tex]\[ \text{bgbbggbggbgbgbggbbgbgbgbbggbgbgb} \][/tex]
To create the sample space for the given experiment, where a couple plans to have 33 children, we'll represent the possible outcomes using the letters "b" for boys and "g" for girls. The sample space for having 33 children can be represented as a sequence of "b" and "g", where each letter represents the gender of a child. Since there are 33 children, the sample space will consist of all possible sequences of 33 "b"s and "g"s.[tex]\[ \text{bgbbggbggbgbgbggbbgbgbgbbggbgbgb} \][/tex]
Each letter in the sequence represents the gender of a child, with "b" indicating a boy and "g" indicating a girl. The sample space consists of all possible sequences of 33 "b"s and "g"s, representing all possible combinations of boys and girls the couple could have among their 33 children.What is the relationship between the 6s in 660, 472?
Answer:
1st 6 is 1/10 of 2nd 6 and 2nd 6 is 10 times the 2nd 6.
Step-by-step explanation:
We are asked to find the relationship between the 6s in 660,472.
Upon looking at our given number, we can see that 1st see is in 10 thousands place and 2nd 6 is in hundred thousands place.
Place value of 1st 6: 60,000
Place value of 2nd 6: 600,000
Let us compare our both numbers as:
We can see that 600,000 is 10 times greater than 60,000, therefore, 1st 6 is 1/10 of 2nd 6 and 2nd 6 is 10 times the 2nd 6.
What is the next number in the sequence: 4, 11, 25, 53...?
Answer:
109
Step-by-step explanation:
Given that there is a sequence of numbers as
4,11,25,53,...
We have to find the next number.
To find the next number, let us see the pattern from the given four numbers
We have
I number = 4
II number = 4+7
III number = II number + 2(7)
Iv number = III number +4(7)
So if we guess this pattern continues the next number namely v number would be
V number = IV number +8(7)
=53+56
109
i.e. I number is added by 7, II number by 2(7), III number by 2^2(7)
hence next number 2^3(7)
Answer is 109
The next number in the sequence is:
109Obtaining the sequenceAs can be seen, the first number is a selected number, which in this case is four, to which seven are added to obtain:
4 + 7 = 11Then double 7 is added to that number, that is 14, with which you get:
11 + 14 = 25The double of 14 is added to that number, which is 28, so the next number is: 25 + 28 = 53And to get the next number, double 28 must be added, which is 56, therefore:
53 + 56 = 109By this reason, the next number in the sequence is 109.
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Prime factorization practice all factors 1.- 25 2.- 49 3.- 7 4.- 13 5.- 24 6.- 48 7.- 168
calculate each of the following by using scientific notation and product rule. write the answer in scientific notation. 2.3 x 10^4 times 4.2 x 10^6
40.8 gallons of paint among 8 containers
divide the two
40.8 / 8 = 5.1 gallons per container
what is bigger 4/5 or 5/9
The time to fly between new york city and chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. what is the probability that a flight is less than 135 minutes
If g(x)=5x-3 and h(x) = x find (goh) (4)
In this composition, we first apply the function h, which is simply the identity function, to the input 4, resulting in 4. Then, we apply the function g to this result. As g(x) = 5x - 3, g(4) equals 17. Hence, (g◦h)(4) = 17.
To find (g◦h)(4), which represents the composition of functions g and h evaluated at x = 4, we first need to find h(4), then substitute the result into g(x).
Given h(x) = x, h(4) = 4.
Now, we substitute h(4) into g(x).
So, g(h(4)) becomes g(4).
Given g(x) = 5x - 3, substituting x = 4 into g(x), we get g(4) = 5(4) - 3 = 20 - 3 = 17.
Therefore, (g◦h)(4) = 17.
A factory produces 5−packs of pencils. To be within the weight specifications, a pack of 5 pencils should weigh between 60 grams and 95 grams. Each package has a mass of 15 grams. Enter a compound inequality to represent the mass of a single pencil in a pack. Can each pencil have a mass of 10.5 grams?
The compound inequality will be: [tex]9\leq x\leq 16[/tex], where [tex]x[/tex] is the mass of a single pencil and each pencil can have a mass of 10.5 grams.
Explanation
Suppose, the mass of a single pencil in the pack is [tex]x[/tex] gram.
So, the total mass of 5 pencils will be: [tex]5x[/tex] grams.
Each package has a mass of 15 grams. So, the total weight of the pack of 5 pencils [tex]=(5x+15)[/tex] grams.
To be within the weight specifications, a pack of 5 pencils should weigh between 60 grams and 95 grams. So, the compound inequality will be..........
[tex]60\leq 5x+15\leq 95\\ \\ 60-15\leq 5x+15-15\leq 95-15\\ \\ 45\leq 5x\leq 80\\ \\ \frac{45}{5}\leq \frac{5x}{5}\leq \frac{80}{5}\\ \\ 9\leq x\leq 16[/tex]
So, the compound inequality to represent the mass of a single pencil in a pack will be: [tex]9\leq x\leq 16[/tex], where [tex]x[/tex] is the mass of a single pencil.
Let f(x) = 2x - 7 and g(x) = -6x - 3. Find f(x) + g(x) and state its domain.
Answer:
[tex]\( f(x) + g(x) = -4x - 10 \).[/tex]
To find the domain of [tex]\( f(x) + g(x) \)[/tex], we need to consider the values of [tex]\( x \)[/tex] for which the function is defined. Since [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] are both linear functions, their domain is all real numbers.
So, the domain of [tex]\( f(x) + g(x) \)[/tex] is [tex]\( \mathbb{R} \)[/tex] , which means that [tex]\( x \)[/tex] can be any real number.
Explanation:
To find [tex]\( f(x) + g(x) \)[/tex] , we simply add the functions [tex]\( f(x) \) and \( g(x) \)[/tex] together:
[tex]\[ f(x) + g(x) = (2x - 7) + (-6x - 3) \][/tex]
Now, let's simplify:
[tex]\[ f(x) + g(x) = 2x - 7 - 6x - 3 \][/tex]
[tex]\[ f(x) + g(x) = (2x - 6x) + (-7 - 3) \][/tex]
[tex]\[ f(x) + g(x) = -4x - 10 \][/tex]