The volume of a rectangular prism is (x4 + 4x3 + 3x2 + 8x + 4), and the area of its base is (x3 + 3x2 + 8). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism?
Answers
[tex] \frac{x^{4}+4x^{3}+3x^{2}+8x+4}{x^{3}+3x^{2}+8}=x+1-\frac{4}{x^{3}+3x^{2}+8}[/tex]
The height of the prism is [tex]x+1-\frac{4}{x^{3}+3x^{2}+8}[/tex]
If the volume of a rectangular prism is the product of its base area and height, than the height of the prism is given by:
[tex]h = (x+1)-\dfrac{4}{(x^3+3x^2+8)}[/tex]
Given :
Volume of rectangular prism [tex]= x^4+4x^3+3x^2+8x+4[/tex]
Base Area of a rectangular prism = [tex]x^3+3x^2+8[/tex]
[tex]\rm Volume = Base \;Area\times Height[/tex] ---- (1)
Solution :
The volume of prism is the amount of space a prism occupies. It has two same faces and other faces that resemble a parallelogram.
Let the height of the prism be h.
Now, substitute the value of base area and volume of the rectangular prism in the given equation (1).
[tex](x^4+4x^3+3x^2+8x+4) = (x^3+3x^2+8)\times h[/tex]
[tex]\dfrac{x^4+4x^3+3x^2+8x+4}{x^3+3x^2+8}=h[/tex]
[tex]h = \dfrac{((x+1)(x^3+3x^2+8)-4)}{(x^3+3x^2+8)}[/tex]
[tex]h = (x+1)-\dfrac{4}{(x^3+3x^2+8)}[/tex]
If the volume of a rectangular prism is the product of its base area and height, than the height of the prism is given by:
[tex]h = (x+1)-\dfrac{4}{(x^3+3x^2+8)}[/tex]
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Related Questions
fill in the blank with a symbol that makes this statement true 5/12 and 1/3
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sos
thanks in advance
Answers
9/12 = 3/4 or 0.75
Hope this helps :)
a used car lot has all vehicles on sale at a 15% discount. Which expression can be used to find the sale price of a vehicle with an original price of p dollars?
Answers
Answer:
a
Step-by-step explanation:
m,n
The required expression for the sales price is 0.85p.
Given that,
A used car lot has all vehicles on sale at a 15% discount. Which expression can be used to find the sale price of a vehicle with an original price of p dollars is to be determined.
The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
What is the cost price?
Cost price is the price the buyer pays to the seller for an object or product.
Here,
The original sales price of the card is p dollars,
There is a 15% discount on the sale of cars,
15 % discount,
= p 15/100
= 0.15p
Now, price after discount,
= p - 0.15p
= 0.85p
Thus, the required expression for the sales price is 0.85p.
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Chris is twice as old as Don, and next year the sum of their ages will be four times as much as Don’s age last year. Find their present ages.
Answers
Answer:
Chris is 12 years old and Don is 6 years old.
Step-by-step explanation:
;)
The present age of Don is 6 years old and Chris age is 12 years.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let's denote Don's current age as x.
As Chris is twice as old as Don, Then, Chris's current age is 2x.
Next year, their ages will be x+1 and 2x+1 respectively.
The sum of their ages will be four times as much as Don’s age last year.
(x+1) + (2x + 1) = 4(x-1).
Expanding and solving for x:
3x + 2 = 4x - 4
x = 6
So, Don is 6 years old and Chris is 2×6 = 12 years old.
Hence, the present age of Don is 6 years old and Chris age is 12 years.
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Please help and explain
Answers
the measure of two supplementary angles have a ratio of 5:4. What is the measure of the larger angles?
Answers
Curtis build a dog house with base shaped like a cube and a roof shaped like a pyramid. The cube has an edge lenght of 3 1/2 feet. The height of the pyramid is 5 feet. Find the volume of the doghouse rounded to the nearest tenth.
Answers
V1 = L ^ 3
Where,
L: length of the sides of the cube.
Substituting we have:
V1 = (3 + 1/2) ^ 3
V1 = 42,875 feet ^ 3
The volume of the pyramid is:
V2 = ((Ab) * (h)) / (3)
Where,
Ab: base area
h: height
Substituting we have:
V2 = (((3 1/2) * (3 1/2)) * (5)) / (3)
V2 = 20.41666667 feet ^ 3
The volume of the house is the sum of both volumes:
V1 + V2 = 42,875 feet ^ 3 + 20.41666667 feet ^ 3
V1 + V2 = 63.29166667 feet ^ 3
Nearest tenth:
V1 + V2 = 63.3 feet ^ 3
Answer:
The volume of the doghouse rounded to the nearest tenth is:
V1 + V2 = 63.3 feet ^ 3
Can someone please help me answer theses questions
Thank u so much
Answers
x^2 +3xyz -4
It meets the definition of a polynomial because it is a sum of products or constants, and all variables have non-negative integer powers.
what does these equation equal to [x+x]+[x+x+x]=blank and [x+x+x]+[x+x+x]=
Answers
[x+x+x] + [x+x+x] = [3x] + [3x] = 6x
Hope this helps :)
Answer:
[x+x] + [x+x+x] = [2x] + [3x] = 5x
[x+x+x] + [x+x+x] = [3x] + [3x] = 6x
Hope this helps :)
Danessa needs to compare the area of one large circle with a diameter of 8 to the total area of 2 smaller circles with a diameter one-half that of the large circle. Which statements about the areas are true? Check all that apply.
1.The radius of the large circle is 4.
2.The radii of the small circles are each 2.
3.The radii of the small circles are each 4.
4.The area of one small circle will be one-half of the area of the large circle.
5.The total area of the two small circles will equal that of the large circle.
6.The total area of the two small circles will be one-half of the area of the large circle.
Answers
Answer:
The answer is: 1, 2, and 6
Step-by-step explanation:
Answer with Step-by-step explanation:
Diameter of larger circle=8
Diameter of smaller circles=4
We know that radius is half times the diamketer
and Area=πr² where r is the radius
Radius of larger circle=4
Radius of smaller circles=2
Area of larger circle=π×4²
=16π
Area of two smaller circles=2×π×2²
= 8π=one-half the area of larger circle
Area of one small circle=π×2²
=4π=one fourth the area of larger circle
Hence, the correct options are:
1.The radius of the large circle is 4.
2.The radii of the small circles are each 2.
6.The total area of the two small circles will be one-half of the area of the large circle.
The table shows summary statistics for the dollar amounts spent by customers at two store locations over a period of 2 weeks.
Location Mean amount spent ($) Range ($)
A 84 15
B 97 25
Which conclusion is true?
Answers
Answer:
A.
Step-by-step explanation:
How do you tell a triangle is not a right triangle
Answers
So a right triangle is classified as a right triangle because it has one right angle. You can tell if it's not a right triangle by the angle measurements. If all the angles are above or below 90 degrees, it's not a right triangle. If one of the angles is 90 degrees, it's classified as a right triangle.
Hope this helps!
Write an equation of the line that is perpendicular to y = −4x + 8 and passes through the point (5, 1)
Answers
To start, we have to identify the slope of the perpendicular line. Perpendicular lines have opposite reciprocal slopes. Therefore, the slope of our new line will be 1/4.
Now, just substitute in the given point with our new slope and we can solve for B.
y = (1/4)x + b
1 = (1/4)5 + b
1 = 5/4 + b
-1/4 = b
Now that we have the slope and the y-intercept, we can put together our equation.
It is: y = (1/4)x - 1/4
Good luck,
MrEQ
how do I do identify calculate the area and perimeter for quadrilaterals
Answers
To calculate the area and perimeter of a quadrilateral, you need to know the shape of the quadrilateral and the lengths of its sides. The area can be calculated using different formulas depending on the shape, such as trapezoid, rectangle, parallelogram, or square. The perimeter is calculated by adding the lengths of all the sides.
To calculate the area and perimeter of a quadrilateral, we need to know the shape of the quadrilateral and the lengths of its sides.
1. Area:
Trapezoid: The area of a trapezoid can be calculated using the formula A = (base1 + base2) × height / 2, where base1 and base2 are the lengths of the parallel sides, and height is the distance between the parallel sides.Rectangle: The area of a rectangle is calculated by multiplying its length by its width, so A = length × width.Parallelogram: The area of a parallelogram is calculated using the formula A = base × height, where base is the length of one side and height is the perpendicular distance between the base and the opposite side.Square: The area of a square is calculated by multiplying the length of any side by itself, so A = side × side.2. Perimeter:
Trapezoid: The perimeter of a trapezoid is calculated by adding the lengths of all its sides.Rectangle: The perimeter of a rectangle is calculated by adding the lengths of its four sides, so P = 2 × length + 2 × width.Parallelogram: The perimeter of a parallelogram is calculated by adding the lengths of its four sides.Square: The perimeter of a square is calculated by multiplying the length of one side by 4, so P = 4 × side.Which answer shows a correct order to solve this story problem? Victor bought 3 sandwiches for $3.25 each, 3 bags of chips for $1.10 each, and a bottle of water for $1.99. He left the waiter a $2.25 tip. How much did Victor spend?
A. Step 1: Add the price of a sandwich to the price of the bottle of water. Step 2: Multiply that total by 3. Step 3: Add the total price of 3 bags of chips to that total. Step 4: Add the tip to the final total for all the items.
B. Step 1: Calculate the total price of the 3 sandwiches. Step 2: Calculate the total price of the 3 bags of chips. Step 3: Add $1.99 to total cost for the sandwiches and chips. Step 4: Add the tip to the final total for all the items.
C. Step 1: Add the price of a sandwich and a bag of chips. Step 2: Add $1.99 to total for the sandwiches and chips. Step 3: Multiply that total by 3. Step 4: Add the tip to the final total for all the items.
Answers
i really need help with this question
Answers
.. f(x) = x²
so g(x) would be
.. g(x) = 3x²
Jeannie ate 1/4 of an apple.kelly ate 2/4 of the apple.how much did they eat together
Answers
Answer:
3/4
Step-by-step explanation:
Which figure can be formed from the net?
Answers
Hope this helps
~ Jordan ~
The value of the digit in the hundreds place in the number 653841 is 1/10 the value of the digit in the thousands place in which number?
A) 748917
B) 749817
C) 784917
D) 797481
Answers
The graph show is
A)fails the vertical line test at (2,3) and (2,-2)
B) fails the vertical line test at (2,3) and (-1,3)
C) passes the vertical line test
So the line is
A) a function
B) not a function
Answers
A)fails the vertical line test at (2,3) and (2,-2)
Second Answer:
B) not a function
=========================================
Further Explanation:
It is possible to pass a single vertical line through this red curve. So it is not a function because it fails the vertical line test. One specific line goes from (2,3) to (2,-2) but there are infinitely other lines to choose from. In order to pass the vertical line test, it must be impossible to pass a vertical line through more than one point on the curve. A function is where any given input leads to exactly one output. In the case of (2,3) and (2,-2), the input x = 2 leads to more than one output (y = 3 and y = -2) at the same time
A=LW;for L. Solve for the indicated variable. Include all work in the answer.
Answers
A divided by W= L divided by W (cancels out)
Answer: A/W = L
Hope this helps! Can I get brainliest? lol
Solving for L , we get A/W= L
What are linear equations ?
Equations of degree 1 are called Linear Equation
To solve the above equation for the variable L . We need to isolate the variable on one side of the equation with the other terms on the other side
Given liner equation :
A= LW
In order to get L , need to isolate L and need to divide whole equation by W
A/W = LW/W
A/W= L
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different varieties of field daisies have numbers of petals that follow a fibonacci sequence.Three varieties have 13,21, and 347 petals.
How many petals do the next two varieties of field daisy have?
a. 42, 55
b. 47,60
c. 42,50
d. 55,89
Answers
I added 13+21 to get 34. Then add 21+34 to get 55. Then add 34+55 to get 89.
Answer: D
55,89
I just did it and I got it right
Step-by-step explanation:
simplify the expression 3 b 7 3b 21
Answers
A hot water heater measures 20" in diameter. What is the area of a metal base for the water heater, assuming a 2 inch overhang around the base of the water heater? (Round to the nearest tenth.) square inches.
Answers
If you add the extra 2 inches in each side and give the base a diameter of 24. The area comes out to 452.39. The answer is 452.39.
Area of the metal base of the water heater is equals to 452.6 square inches.
What is area of a circle?
"Area of a circle is the region enclosed by the circle in two dimensional plane."
Formula used
Area of a circle = πr²
Value of π = 22 /7
According to the question,
Given diameter = 20 inches
2 inches extended around the base of the water heater
New diameter = 24 inches
Therefore, radius = 12inches
Substitute the value of radius and π in the formula we get ,
Area of the base of the water heater = ( 22/ 7) ×(12)²
= 452.57 square inches
= 452.6 square inches (nearest tenth)
Hence, area of the metal base of the water heater is equals to 452.6 square inches.
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help please 40 points per question
Answers
x(x) = x²
x(9) = 9x
-2(x) = -2x
-2(9) = -18
x² + 9x - 2x - 18
simplify by combining like terms
x² + 9x - 2x - 18
x² + 7x - 18
x² + 7x - 18 is your answer
hope this helps
Ms Hendricks is buying a rectangular piece of land that is 2/5 mile on one side and 5/6 mile on an adjacent side. What is the area of the piece of land. help me please I don't get this
Answers
To find the area of an object, we need to multiply the two sidelengths together.
2/5 × 5/6 = 10/30
Now, we simplify.
10/30 = 1/3
So, your answer is 1/3 miles squared.
Hope this helps!
Final answer:
To find the area of Ms. Hendricks' rectangular land, multiply the lengths of the sides (2/5 mile and 5/6 mile), resulting in an area of 1/3 square mile.
Explanation:
The area of a rectangular piece of land is calculated by multiplying the length by the width. For Ms. Hendricks' piece of land, which measures 2/5 mile on one side (length) and 5/6 mile on an adjacent side (width), you would calculate the area by multiplying these two dimensions together:
Convert the fractions to have a common denominator if needed.Multiply the numerators of the fractions to find the numerator of the area.Multiply the denominators of the fractions to find the denominator of the area.Simplify the fraction if possible to find the final area in square miles.So, the calculation for the area would be:
(2/5) mile * (5/6) mile = (2*5)/(5*6) square miles = 10/30 square miles = 1/3 square mile.
Therefore, the area is 1/3 square mile.
A line with a slope of 1/4 passes through the points (9, -8) and (5, d). what is the value for?
Answers
d + 8 = 1/4x - 9/4
- 8 - 8
------------------------------
d = 1/4x - 17
I just realized that this is not the answer you are looking for. It's an equation, not a value. Sorry about that.
d = -9
Explanation:
The slope of the line can be calculated using the following formula:
slope = [tex] \frac{y2-y1}{x2-x1} [/tex]
We are given:
slope = [tex] \frac{1}{4} [/tex]
point (9,-8) representing (x1,y1)
point (5,d) representing (x2,y2)
Substitute with the givens in the above equation and solve for d as follows:
slope = [tex] \frac{1}{4} [/tex]
[tex] \frac{1}{4} [/tex] = [tex] \frac{d-(-8)}{5-9} [/tex]
[tex] \frac{1}{4} [/tex] = [tex] \frac{d+8}{-4} [/tex]
4(d+8) = -4
d + 8 = -1
d = -1 - 8
d = -9
Hope this helps :)
if a=37 degrees and b=6, find a.
A. 3.4
B. 4.5
C. 6.1
D. 2.5
Answers
To find the value of 'a' when a = 37 degrees and b = 6, trigonometry principles are used to calculate 'a' as approximately 34.08 degrees.
Given: a = 37 degrees and b = 6. To find a.
Using trigonometry: We can use the trigonometric ratio tangent to find a. tan(a) = b/c, where c is the hypotenuse. So, tan(37) = 6/c. Therefore, c = 6/tan(37) = 8.37. Hence, a = tan-1(b/c) = tan-1(6/8.37) ≈ 34.08 degrees.
Answer: Therefore, a = 34.08 degrees.
Divide £24.50 in the ratio 3:4
Answers
Step 2: Divide the money to be shared by the answer (this gives you the value of 1 share)
Step 3: Multiply the value of 1 share by each bit of the ratio
the answer is the £24.50 in the ratio 3:4 is £10.50:£14.00.
Final answer:
24.50 divided in the ratio 3:4 gives £10.50 and £14.00.
Explanation:
To divide £24.50 in the ratio 3:4, you first need to add the parts of the ratio together, which gives you 3 + 4 = 7 parts in total.
Then, you should divide the total amount of money by the total number of parts to find the value of one part.
In this case, £24.50 ÷ 7 = £3.50 per part.
Since the ratio is 3:4, you multiply the value per part by the number of parts for each portion of the ratio.
For the first part of the ratio, you multiply £3.50 by 3, giving £10.50. For the second part, you multiply £3.50 by 4, giving £14.00.
Hence, £24.50 divided in the ratio 3:4 gives £10.50 and £14.00.
Caitlin says that AC is the longest segment of fencing