HELP ME PLZ
Using V = lwh , find an expression in factored form for the volume of this prism. Explain the general steps you used to arrive at this answer.
Answers
First factor each of the expressions in the numerators and then multiply those in the numerators putting them over those in the denominator. It turns out those in the denominators (in this problem) cannot be factored. When you do this you are left with:
[tex]\frac{(x)(x-1)(2x-5)(6x)(4x+1)}{(4x+1)(x-1)} [/tex]
You can divide out (sometimes called cancelling out) those terms expressions that are in both the numerator and the denominator. That leaves you with:
[tex]\frac{(x)(2x-5)(6x)} {1}[/tex] which we can clean up by multiplying x and 6x in the numerator.
Thus, the volume of the prism is: [tex]6 x^{2} (2x-5)[/tex]
We do not multiply this out because it is now written as a product and thus factored (as you were asked).
The volume of the prism with the given dimensions is;
V = 12x³ - 30x²
We are given that the formula for the volume of a cube is;
V = Lwh
where;
L is length
w is width
h is height
We are given;
L = (24x² + 6x)/(x -1)
w = 2x - 5
h = (x² - x)/(4x + 1)
This means that;
V = [(24x² + 6x)/(x - 1)] × (2x - 5) × [(x² - x)/(4x + 1)]
Now, let us factorize the terms that can be factorized;
(24x² + 6x)/(x - 1) can be factorized into; [6x(4x + 1)/(x - 1)]
Similarly;[(x² - x)/(4x + 1)] can be factorized into [x(x - 1)/(4x - 1)]
Using the factorized terms to get the volume now;
V = [tex]\frac{6x(4x + 1)}{x -1} * (2x - 5) * \frac{x(x - 1)}{4x + 1}[/tex]
(x - 1) will cancel out and also 4x + 1 will cancel out to give;
V = 6x * x * (2x - 5)
V = 6x²(2x - 5)
V = 12x³ - 30x²
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Related Questions
PLEASE HELP!
The phone case you want to buy is marked down 30%, and you have a 25% off coupon. You pay $42.00. Can this equation be used to find the original price of the phone case? If so, what is the original price of the item? Explain. (5 points) 3/4(0.7c) = 42
Answers
Yes, the equation provided can be used to calculate the original price of the phone case. After solving the equation, we found out that the original price of the phone case was approximately $80.
Explanation:Yes, the equation you provided, 3/4(0.7c) = 42, can certainly be used to find the original price of the phone case (c). The equation is obtained by recognizing that you're receiving two discounts: a 30% or 0.3 discount off the original price (leaving 70% or 0.7 of the original price) and then a 25% or 0.25 discount (meaning you're paying 75% or 0.75 of the price after the first discount).
To find the original price, you want to solve this equation for 'c'. That would involve dividing both sides by 3/4(0.7) equaling to 0.525. So, it will look like: 42 ÷ 0.525 = c. Doing the calculation, c equals approximately $80.
Therefore, the original price of the phone case was $80.
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What is the slope of the line that passes through the points (2, 3) and (–2, 6)?
Answers
An Investor invested a total of $2,600 in two mutual funds. One fund earned 7% profit while the other earned 3% profit. If the investor’s total profit was $150, how much was invested in each mutual fund?
Answers
let x = amount invested at 3%
so, (2600 - x) is invested at 7%
.07 *(2600 - x) + .03 *(x) = 138
182 - .07x + .03x = 138
-.07x + .03x = 138 - 182
-.04x = -44
-.04x / -.04 = -44 / -.04
x = 1,100
so amount invested at 7% is (2600 - 1100) or 1500
consequently amount invested at 3% is 1100
$1,100 invested at 3%
$1,500 invested at 7%
The money invested in both of the funds are $800 and $1800 respectively.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100.
Suppose the money invested in one of the funds be x.
Then, in the other fund the investment is (2600 - x).
Now, the equation for the total profit from both investments can be obtained as,
7% × x + 3% × (2600 - x) = 150
⇒ 7/100 × x + 3/100 × (2600 - x) = 150
⇒ 4x/100 = 150 - 78
⇒ x = 1800
Thus, the investment in the other fund is 2600 - 800 = $800.
Hence, the investment for both the funds are $800 and $1800 respectively.
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Answer the manager one
Answers
(Please help HURRY!) (Don't delete this!) (I WILL GIVE BRAINY!)
1. ABC undergoes a dilation, with a scale factor of 8, to form A'B'C'.
Side A'B' is 8 times the length of side AB.
What is the area of A'B'C', compared to the area of ABC?
A. The area of A'B'C' is 1/8 of the area of ABC
B. The area of A'B'C' is 1/64 of the area of ABC
C. The area of A'B'C' is 8 times the area of ABC
D. The area of A'B'C' is 64 times the area of ABC
2. DEF undergoes a dilation, with a scale factor of 4, to form D'E'F'.
Side D'E' is 8 times the length of side DE.
What is the area of D'E'F', compared to the area of DEF?
A. The area of D'E'F' is 1/4 of the area of DEF
B. The area of D'E'F' is 1/16 of the area of DEF
C. The area of D'E'F' is 4 times the area of DEF
D. The area of D'E'F' is 16 times the area of DEF
3. ABC undergoes a dilation, with a scale factor of 3, to form A'B'C'.
Side A'B' is 3 times the length of side AB.
What is the area of A'B'C', compared to the area of ABC?
A. The area of A'B'C' is 1/3 of the area of ABC
B. The area of A'B'C' is 1/9 of the area of ABC
C. The area of A'B'C' is 3 times the area of ABC
D. The area of A'B'C' is 9 times the area of ABC
Answers
2. C
3. I think B
area of triangle is = 1/2 * base * altitude
1- each side is made 8 times
so the net change in area is 64 times
The area of A'B'C' is 64 times the area of ABC
2- each side is made 4 times
so the net change in area is 16 times
The area of D'E'F' is 16 times the area of DEF
3- each side is made 3 times
so the net change in area is 9 times
The area of A'B'C' is 9 times the area of ABC
Rewrite the following equation in slope-intercept form. 10x − 17y = -12 Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
y = (10/17) x + (12/17)
Explanation:
The slope-intercept form has the following formula:
y = mx + c
where:
m is the slope
c is the y-intercept
The given is:
10x - 17y = -12
To put this in slope-intercept form, we need to isolate the y as follows:
10x - 17y = -12
17y = 10x + 12
y = (10/17) x + (12/17)
where:
m is the slope = 10/17
c is the y-intercept = 12/17
Hope this helps :)
10x = -12
X = -12/10 = -6/5
X=0
-17y=-12
Y= 12/17
Use 3.14 for and round your final answer
Answers
4/3 x 3.14 x 8 ^{3}
4/3 x 3.14 x 512
4/3 x 1607.68
2143.57 (I also got 2144.66 if the first one doesn't work)
2 × 7/8 as a model how do I draw it as a model
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You can draw 8 tiles, and color in 7.
Draw that two times.
That’s one way, but that might not be the way you learned it.
Hope this helped anyways!
Describe the differences between vertical and adjacent angles
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and adjacent lines are 2 angles that have a common endpoint and common sides
There are 56 trees in an apple orchard. They are arranged in equal rows. There are 8 trees in each row. How many rows of apple trees are there? Which equation can be used to solve this problem?
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56 divided by 8 is 7
Hope this helped :)
Two points are located at (−9,−8) and (−6,−4) . Complete the equations below to show how you can use the Pythagorean theorem to find the distance between these two points.
Answers
The distance between two points in a coordinate plane can be found using the Pythagorean theorem. For the points (-9,-8) and (-6,-4), the distance is 5 units.
Explanation:The Pythagorean theorem can be used to find the distance between two points in a coordinate plane. To find the distance between the points (-9,-8) and (-6,-4), we can consider the horizontal and vertical differences as the legs of a right triangle. The horizontal difference is 3 and the vertical difference is 4.
Using the Pythagorean theorem, we have:
a^2 + b^2 = c^2
3^2 + 4^2 = c^2
9 + 16 = c^2
25 = c^2
c = sqrt(25) = 5
Therefore, the distance between the two points is 5 units.
what was sal finding when he plugged t=10 into the expression 5t+3?
a. The cost of 10 tickets
b. The cost of 53 tickets
c. The number of tickets that would cost 10 dollars
d. The number of tickets that would cost 53 dollars
Answers
Answer:
a. The cost of 10 tickets
Step-by-step explanation:
We don't know what the expression is supposed represent, but the answer choices suggest that ...
c = 5t +3
represents the cost of t tickets. Then, when t=10, c = 53 will represent the cost of 10 tickets.
what is the sum of the finite arithmetic series ? 7.6+6.3+5+3.7+2.4+1.1+(-0.2)+(-1.5)
Answers
Good luck :)
[tex]\text{Consider the sum of the finite arithmatic series}\\ \\ 7.6+6.3+5+3.7+2.4+1.1+(-0.2)+(-1.5)\\ \\ \text{We know that the sum of the finite arithmatic series }\\ \\ a_1,a_2, a_3, ..., a_n \text{ is given by the formula}\\ \\ S_n=\frac{n}{2}\left ( a_1+a_n \right )\\ \\ \text{here in the given series, we can see that }a_1=7.6, \ a_n=-1.5 \text{ and}\\ \text{the number of terms is, }n=8. \text{ so using above formula, we get}[/tex]
[tex]S_8=\frac{8}{2}\left ( 7.6+(-1.5) \right )\\ \\ =4\left ( 7.6-1.5 \right )\\ \\ =4\left ( 6.1 \right )\\ \\ =24.4[/tex]
Hence the sum of the finite Arithmetic series is: 24.4
What’s 5/9 rounded to the nearest half
Answers
Hope this helped☺☺
The round off to nearest half is 1/2.
What is Round off?Although the term "rounding" is a general one, we typically use the terms "round up" or "round down" to indicate whether the number has gone up or down after being rounded. The supplied number is said to be rounded up when the rounded number is increased, and it is said to be rounded down when the rounded number is dropped.
Given:
The fraction = 5/9.
Now, rounded to the nearest half is 1/2
we know 9 halved value is 4.5 which is much closer to 5.
So, we can write it as 5/10 = 1/2.
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Four friends share 3 apples equally. what fraction of an apple does each friend get
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This would be 1/4 * 3, or 3/4 of an apple.
The length of cherries vegetable garden is 6.56 meters. The width of the garden is 6.6 meters. What is the answer
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....................................................................
A small plastic storage container is in the shape of a cylinder. It has a diameter of 7.6 centimeters and a height of 3 centimeters. What is the volume of the storage cylinder
Answers
(3.14)(3.8)^2(3)
136.0248
The volume of the cylinder with given diameter and height is 136.02 cm³.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
Given that, the diameter of a cylinder =7.6 cm and the height of a cylinder = 3 cm.
Radius =7.6/2 =3.8 cm
We know that, the volume of a cylinder is πr²h
Now, volume = 3.14×3.8²×3
= 136.02 cm³
Therefore, the volume of the given cylinder is 136.02 cm³.
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Find the distance between (6,-3) & (-1, 7) on the CCS
Answers
Answer:
9 or (5,4)
Step-by-step explanation:
Just subtract it on each side :)
can someone help ?? please
Answers
What is the slope of the line passing through the point (-3,-1) and the origin?
Answers
Select the statement that best justifies the conclusion based on the given information. Conclusion: l1 and l 2 intersect only at point P. A line contains at least two points. Through any two different points, exactly one line exists. If two lines intersect, then their intersection is exactly one point. If two lines intersect, then exactly one plane contains both lines.
Answers
If two lines intersect, then their intersection is exactly one point
Explanation:
Let's take a look at the choices:
Choice A: A line contains at least two points.
The statement is true. However, it is not related to intersection between lines. Therefore, this choice is wrong
Choice B: Through any two different points, exactly one line exists
This postulate is true. However, it does not relate directly to the intersection between lines. Therefore, this choice is wrong
Choice C: If two lines intersect, then their intersection is exactly one point.
This statement is known as theorem 1-1. It describes the intersection between two lines.
Therefore, this statement is correct.
Choice D: If two lines intersect, then exactly one plane contains both lines.
The conclusion given is related to points created due to intersection between lines. This option is therefore excluded as it describes planes.
Hope this helps :)
Answer:
If two lines intersect, then their intersection is exactly one point.
Step-by-step explanation:
Audrey is buying a nee car for $32,998. She plans to make a down payment of $4,200. If she's to make a monthly payments of $525 for the next five years, what APT has she paid?
Answers
4,200+525(60)=
4,200+31,500=35,700
Which equation will help you solve this problem?
A band performed at halftime during the football game.
There were 64 band members marching in 8 equal rows.
How many band members were in each row?
Answers
So the answer is that 8 members was in each row.
Answer:
There are 8 band members in each row
Step-by-step explanation:
Given : A band performed at halftime during the football game.
There were 64 band members marching in 8 equal rows.
To Find : How many band members were in each row?
Solution :
Let there are x members in each row .
Since there are 8 rows
So, no. of members in 8 rows = 8x
We are also given that there are 64 band members .
⇒[tex]8x=64[/tex]
⇒[tex]x= \frac{64}{8}[/tex]
⇒[tex]x= 8[/tex]
Thus there are 8 band members in each row
Solve: 3(20 + 5y) = - 30.
y = -10
y = - 18
y = 2
y = -6
Answers
The answer to your question would be
Y= -18
This is because 3x20 is 60
so then it would be 60 + 3x5y= -30
it has to be a negative number because 60 is greater than -30
then you would add the absolute values which would be 60+30=90
And divide that by 5 which is 18, but then you have to add back on the negative sign.
Please help me with these!!!
Simplify these expressions:
a) 3 2/3x-4/5(x- 3 3/4)
b) 2 1/4x+(4 1/3x-7 4/5) divided by 2 3/5
c) 8x-1 1/7 (1 1/3x-12)
d) 11 4/7x+(5x- 2 2/5)
Answers
Answer:
A) 2 13/15 x + 3
B) 2 7/12 x - 7 4/5 over 2 3/5
C) 5 16/21 x - 18 6/7
D) 16 4/7 x - 2 2/5
Step-by-step explanation:
Evaluate.
4+(5-3)5+7
Answers
Hey there!
4 + (5 - 3) 5 + 7
= 4 + (2)(5 + 7)
= 4 + 2(5) + 7
= 4 + 10 + 7
= 14 + 7
= 21
Therefore, your answer is: 21
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
irrational number of 5
Answers
Hope this helped
~Melis
Which equals 2.2360679....
solve the compound inequality
Answers
You want x alone, so subtract 4 from each of the 3 parts.
[tex] -3 \le x + 4 \le 13 [/tex]
[tex] -3 - 4 \le x + 4 - 4 \le 13 - 4 [/tex]
[tex] -7 \le x \le 9 [/tex]
[tex] x \ge -7 [/tex] and [tex] x \le 9 [/tex]
Which expression is equivalent to 32?
Answers
Final answer:
The expression equivalent to 32 might refer to a mathematical manipulation or a unit conversion. In equations, 32 is what remains when you subtract 32 from one side of an equation like x + 32 = 64. Meanwhile, in conversions, multiplying the number of quarts by 32 gives you the equivalent volume in fluid ounces.
Explanation:
The expression is equivalent to 32 and could be interpreted in different contexts. Using mathematical manipulation, when you subtract 32 from both sides of an equation, the equality holds. For example, if you have an equation like x + 32 = 64, subtracting 32 from both sides gives us x = 64 - 32, which simplifies to x = 32. This demonstrates an application of the principle that you can add or subtract the same number from both sides of an equation without changing its solution.
In relation to conversion between different units of measurement, specifically volume, when you convert quarts to fluid ounces, the conversion factor is 32 because there are 32 fluid ounces in one quart. Consequently, to find how many fluid ounces are in a given number of quarts, you multiply the number of quarts by 32. For example, 4 quarts equal 4 × 32, which is 128 fluid ounces.
Furthermore, when dealing with electrical resistance, 'equivalent resistance' is another situation where the number 32 might be relevant. Depending on the context and the specific details of an electrical circuit, one of the listed equivalent resistances may be the correct answer to a problem involving calculating the total resistance.
solomon has read 1/3 of his book. He finishes the book by reading the same amount eat night for 5 nights what fraction of the book does he read each of the 5 nights?
Answers
Final answer:
Solomon has 2/3 of the book left to read. To finish it over 5 nights, he needs to read 2/15 of the book each night.
Explanation:
Solomon has read 1/3 of his book already. To finish the remaining 2/3 of the book in 5 nights, we need to calculate the fraction of the book he should read each night. Since he has to evenly distribute the remaining portion over 5 nights, we will divide 2/3 by 5.
Here's the calculation step-by-step:
First, represent the remaining part of the book as a fraction, which is 2/3.
To divide this fraction by 5, we multiply the denominator by 5. This gives us (2/3) × (1/5).
Multiplying these fractions, we get (2 × 1) / (3 × 5), which simplifies to 2/15.
Thus, Solomon reads 2/15 of the book each night for the next 5 nights.