The kinetic energy K (in joules) of a falling apple is represented by K=v squared divided by 2 where v is the speed of the apple (in meters per second). How fast is the apple traveling when the kinetic energy is 32 joules?

Answer:

Step-by-step explanation: Add pic so ppl can help

To model the relationship between the number of months, t, since opening the bank account and the total amount of money, a, deposited into the account, we can use the equation a = 500 + 500t.

To model the relationship between the number of months, t, since opening the bank account and the total amount of money, a, deposited into the account, we need to find the pattern. According to the information given, Ms. Gibson made an initial deposit of $500 and then deposited the same amount each month. This means that the total amount of money, a, deposited after a certain number of months, t, can be represented by the equation:

a = 500 + 500t

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She can enjoy her original 3/4 brownie divided into six equal parts, each constituting 1/8 of the delectable treat.

Deb possesses 3/4 of a brownie and intends to partition it into smaller portions, each equivalent to 1/8 of a brownie, allowing her to savor it throughout the day.

To determine the number of 1/8 portions she'll obtain, we can perform a simple division.

By dividing 3/4 by 1/8, we essentially multiply the numerator of 3/4 by the reciprocal of 1/8, which is 8/1.

This multiplication yields (3 * 8) / (4 * 1) = 24/4.

Simplifying further, we find that Deb will have 6 portions of 1/8 of a brownie.

Consequently, she can enjoy her original 3/4 brownie divided into six equal parts, each constituting 1/8 of the delectable treat.

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Question

Deb has 3/4 of a brownie. She wants to divide it up into 1/8 of a brownie so she can have it throughout the day. How many 1/8s will she have's will she have?

The reasonable estimate is 10.

We can approximate 915.25 to 900.

We can approximate 88.22 to 90.

Then we divide them: [tex]\frac{915.25}{88.22}\approx\frac{900}{90}=10[/tex].

So the reasonable estimate is 10.

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100 is not a reasonable estimate for the operation 915.25 divided by 88.22, as the actual answer is approximately 10.37. While estimates don't provide exact numbers, the difference here is too great for 100 to be considered reasonable, depending on the level of accuracy needed.

In mathematics, estimation is commonly used when you do not need the exact answer, but rather a ballpark number close to the actual value. The student's question revolves around whether 100 is a reasonable estimate for the operation 915.25 divided by 88.22. We can check this by performing the actual division: 915.25 / 88.22 equals approximately 10.37. Although this is not exactly 100, it is within an order of magnitude which might make the estimate reasonable depending on the context. Therefore, as a quick estimate, 100 might not be suitable for high-precision contexts.

It's important to understand how estimates work. Their value is not in providing exact numbers, but in giving a quick understanding of a situation, especially when the exact numbers are complex or cumbersome. Here, however, the difference between the actual result (10.37) and the estimate (100) is quite significant, which suggests that 100 might not be a reasonable estimate in this case, depending on the level of accuracy needed.

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When a figure is reflected across a line the orientation of the figure or shape changes when it is a reflected across a line. Also, the x-coordinate and y-coordinate change places

A reflection is a mirror image of the shape.

In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space

Given,

A figure is reflected across a line

The orientation of the figure or shape changes when it is a reflected across a line

Also, the x-coordinate and y-coordinate change places

Hence, When a figure is reflected across a line the orientation of the figure or shape changes when it is a reflected across a line. Also, the x-coordinate and y-coordinate change places

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The orientation of a figure changes when it is reflected across a line while its shape and size stay consistent, creating a mirror image with symmetry relative to the line of reflection.

When a figure is reflected across a line, its orientation changes, whereas the shape and size of the figure remain the same. The Law of Reflection implies that each point of the figure maintains its distance from the line of reflection but on the opposite side, creating a 'mirror image' or symmetric counterpart. This mirror image aligns with the original figure if an imaginary line were drawn perpendicular to the mirror (line of reflection) at each point, these perpendiculars would be equal in length on both sides. This reflection transformation is an example of a linear transformation, preserving the straightness of lines and parallelism of parallel lines.

Answer:

[tex]35\ pieces[/tex]

Step-by-step explanation:

we know that

To find the number of pieces of rope 4/7 of a yard, divide the total length of the rope by 4/7

we have that

The total length of the rope is 20 yards

so

[tex]\frac{20}{(4/7)}=\frac{20*7}{4}=35\ pieces[/tex]

Answer:

28 is the answer

Step-by-step explanation:

General Idea:

When we are working with word problems, we need to follow the below steps:

Step 1: Assign variable for the unknown that we need to find.

Step 2: Write a meaningful mathematical equation using the sentence given

Step 3: Solve the equation by Performing reverse operation by Undoing whatever is done to the variable. Solving means find the value of the variable which will make the equation TRUE.

Applying the concept:

Step 1: Let x be the number of books that Brett can afford without spending more than his gift voucher amount.

Step 2: Writing mathematical equation based on the given sentence "Brett has a $30 online gift voucher. He plans to buy as many books as he can. The cost of each book is $4. There is also a single shipping charge of $2"

[tex] Online \; Gift \; Voucher=Number \; of \; books \; \times \; Cost\;per \; Book \; + \; Single \; shipping \; charge [/tex]

[tex] 30=4x+2 [/tex]

Step 3: Solving equation

[tex] 4x+2=30\\ Subtract \; 2 \; on \; both \; sides\\ \\ 4x+2-2=30-2\\ Combine \; like \; terms\\ \\ 4x=28\\ Divide \; 4 \; on \; both \; sides\\ \\ \frac{4x}{4}= \frac{28}{4} \\ Simplifying \; fraction \; on \; both \; sides\\ \\ x=7 [/tex]

Conclusion:

The number of books that Brett can afford without spending more than his gift voucher amount is 7 !!

27/40 miles long was the bus ride.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

The store is 7⁄8 of a mile away from your house.

Distance covered by Walking = 1/5

and, the rest is covered by Bus.

So, the distance covered by Bus

= 7/8- 1/5

= 35/ 40- 8/40

= 27/40

Hence, 27/40 miles covered by Bus.

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Answer:

Step-by-step explanation:

Here we have to use the rate of depreciation, the initial value and the total time to find the final value with this formula

[tex]A=A_{0}(1-r)^{t}[/tex]

Where [tex]A[/tex] is the final value, [tex]A_{0}[/tex] is the initial value, [tex]r[/tex] is the rate of depreciation and [tex]t[/tex] is the time.

Replacing all values, we have

[tex]A=20300(1-0.0875)^{12}[/tex]

[tex]A=6765.35[/tex]

Therefore, after 12 years the car will value $6,765.35.

After the simplification of the  given radial expression [tex]\sqrt{\frac{64}{16}(\frac{y^{10} }{y^{12} } )\frac{h^{5} }{h^{5} } }[/tex] we get [tex]\frac{2}{y}[/tex].

A radical expression is defined as any expression containing a radical ([tex]\sqrt{}[/tex]) symbol.

The term underneath the radical symbol is called the radicand.

To solve a radical expression, simply take the the square root of the radicand.

According to the given question, we have a radical expression

[tex]\sqrt{\frac{64y^{10}h^{5} }{16y^{12} h^{5} } }[/tex]

=[tex]\sqrt{\frac{64}{16}(\frac{y^{10} }{y^{12} } )\frac{h^{5} }{h^{5} } }[/tex]                           ([tex]\frac{x^{m} }{x^{n} } =x^{m-n}[/tex])

= [tex]\sqrt{4(\frac{1}{y^{2} })(1) }[/tex]

= [tex]\sqrt{\frac{4}{y^{2} } }[/tex]

= [tex]\frac{2}{y}[/tex]

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Answer: 1032

Step-by-step explanation: you welcome

1.8p = 5.04

p = 5.04/1.8

p = 2.8

 it cost $2.80 per pound

Estella buys 1.8 pounds of walnuts for a total of $5.04. She solves the equation 1.8p=5.04 to find the price p in dollars of one pound of walnuts. what does one pound of walnuts cost?

Solution: Let the cost of one pound of walnuts= $p

So, The cost of 1.8 pound of walnuts=$1.8p

Whereas, The cost of 1.8 pound of walnuts=$5.04

So, 1.8p=5.04

Now, To solve for p, Let us isolate p

To isolate p, Let us divide by 1.8 on both sides

[tex] \frac{1.8}{1.8} p=\frac{5.04}{1.8} [/tex]

On dividing 5.04 by 1.8, we get 2.8

[tex] \frac{1}{1} p=\frac{2.8}{1} [/tex]

So, p=2.8

Cost of one pound walnuts is $2.80

Answer : The surface area of the package is, [tex]185.9inch^3[/tex]

Step-by-step explanation :

The given package is in cuboid shape. Now we have to calculate the surface area of the package by using volume of cuboid.

Formula used for volume of cuboid is:

[tex]V=2(lb+bh+hl)[/tex]

where,

V = volume of package

l = length of package = [tex]2\frac{1}{3}inch=\frac{7}{3}inch[/tex]

b = width of package = [tex]8\frac{1}{2}inch=\frac{17}{2}inch[/tex]

h = height of package = [tex]6\frac{3}{4}inch=\frac{27}{4}inch[/tex]

Now put all the given values in the above formula, we get:

[tex]V=2\times [(\frac{7}{3}\times \frac{17}{2})+(\frac{17}{2}\times \frac{27}{4})+(\frac{27}{4}\times \frac{7}{3})][/tex]

[tex]V=2\times [\frac{119}{6}+\frac{459}{8}+\frac{63}{4}][/tex]

[tex]V=185.9inch^3[/tex]

Therefore, the surface area of the package is, [tex]185.9inch^3[/tex]

Answer:

Its K ≥ 12

Step-by-step explanation:

Hope this helps! Have a good day!:) and happy St. Patrick's day lol