Final answer:
The surface area of the rectangular prism is represented as [tex]2x^2 + 16x[/tex] square units, and the volume as [tex]2x^3 + 6x^2[/tex]cubic units, based on the dimension formulas where the side lengths of the base are x and x+3, and the height is 2x.
Explanation:
The question involves finding the surface area and volume of a rectangular prism with dimensions based on the variable x. Given, the side lengths of the base are x and x+3, and the height is 2x.
Surface Area Calculation
The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l is length, w is width, and h is height. Substituting the given values, we get:
Top and Bottom Surface Area: 2(x)(x+3)
Front and Back Surface Area: 2(2x)(x+3)
Left and Right Surface Area: 2(x)(2x)
Adding these together yields the total surface area as [tex]2x^2 + 10x + 6x[/tex], which simplifies to [tex]2x^2 + 16x[/tex].
Volume Calculation
The volume of a rectangular prism is found using the formula V = lwh. For this prism, it translates to V = x(x+3)(2x), which simplifies to [tex]2x^3 + 6x^2.[/tex]
In conclusion, the surface area of the prism can be represented as [tex]2x^2 + 16x[/tex] square units, and the volume as [tex]2x^3 + 6x^2[/tex] cubic units.
Consider the following pair of equations: −x − y = −5 y = x + 1 If the two equations are graphed, at what point do the lines representing the two equations intersect? (−2, 3) (3, −2) (2, 3) (3, 2)
David and Amanda are trying to figure out how long they can live off their $12,350 savings if they spend $240 each month. They have each created an equation.
David's Equation Amanda's Equation
y = 12,350 - (240x) y = 12,350 + (240x)
Which person has the correct equation to model this linear relationship? (4 points)
a) Amanda's equation is correct, because their spending will be multiplied by the number of months and then added to their savings.
b) Amanda's equation is incorrect, because their spending will increase the amount of their savings.
c) David's equation is correct, because their spending will be multiplied by the number of months and then subtracted from their savings.
d) David's equation is incorrect, because their spending should be a fixed amount and should not be multiplied.
a right prism with a base perimeter of 9 units a height of 5 units and a total base of 16 square units has a surface area of how many square units?
A pyramid and prism have the same base area and height. The prism's base area is 8 square units and its height is 16 units. What is the volume of the pyramid? The volume of the pyramid is __________ cubic units. Enter the number that correctly fills in the blank in the previous sentence.
The volume of the pyramid with a base area of 8 square units and a height of 16 units is 42.67 cubic units.
The volume of a pyramid is calculated as one-third of the base area times the height. The base area of the given pyramid is 8 square units and the height is 16 units. Using the formula for volume V = rac{1}{3}Ah, where A is the base area and h is the height, the volume of the pyramid can be found as follows:
V = rac{1}{3} imes 8 imes 16
V = rac{1}{3} imes 128
V = 42.67 cubic units (rounded to two decimal places).
Therefore, the volume of the pyramid is 42.67 cubic units.
Bernard counted 8 posts along the side of the road. If the posts were 20meters apart how far is the first post from the last
What are the factors for 31
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Which expression represents the value, in dollars, of a certain number of dimes, d, and nickels, n? 0.10d + 0.05n 0.05d + 0.10n 0.15d + n 0.15dn
Answer:
0.10d+0.05n
Step-by-step explanation:
If the divisor is 40 what is the least three digit dividend that would give a reminder four
Tony is making small bags of bird sees from a larger bag that weighs 11.16 pounds. If he puts the same amount of seed in each of 6 bags, how much will each bag weigh?
99PTS (08.06)The data set shows the number of cars parked in the restaurant parking lot during the lunch hour each day for two weeks: 8 7 14 10 13 27 11 10 14 7 12 9 14 9 Which of the following statements is true based on the data set?
The area of a rectangle rug is (3x + 9) square units.Factor (3x + 39) to find possible dimension of the rug.?
Would be the (3x+39) factored out
3(x+13)
The possible dimension of the rug will be 3 and (x + 3).
What is expansion?
Expanded form is the term used in mathematics to refer to the process of expanding a number to convey the value of every digit and place value.
In mathematics, every real-world issue may be transformed into an equation, sometimes in the form of a factor, which must then be expanded to get a solution.
If you solve a factor by opening the bracket then you will go to get on some expanded term called expansion.
Area of rectangle = length × width
Given,
Area of rectangle rug = (3x + 9)
So,
length × width = (3x + 9)
length × width = 3(x + 3)
So out of 3 and (x + 3), one would be the length and one would be the width.
For more information about the expansion
brainly.com/question/14447197
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Ralph sold brownies for $0.27 a piece in order to earn money to buy baseball cards. If the cards cost $0.54 per pack, and if Ralph had no money left over after buying them, what is the least number of brownies he must have sold?
The diagonal of a square unit is x units. What is the Area of the square in terms of x
The area of a square with a diagonal x is (1/2)x² unit²
SquareA square is a quadrilateral (has four sides and four angles) in which opposite sides are equal and parallel. All the sides of a square have the same length and each angle measure 90 degrees.
let l represent the length of the side of the square and x be the length of the diagonal. Using Pythagoras theorem:
l² + l² = x²x² = 2l²l = x√(1/2)Area of square = l * l = x√(1/2) * x√(1/2) = x² * 1/2 = (1/2)x² unit²
The area of a square with a diagonal x is (1/2)x² unit²
Find out more on square at: https://brainly.com/question/8429946
The sum of 2/9 and 2 5/9 in simplest form is
Answer:
2 7/9
Step-by-step explanation:
Simplify open parentheses x to the 5 eighths power close parentheses to the 2 thirds power.
Answer:
[tex]x^{\frac{5}{12}}[/tex]
Step-by-step explanation:
[tex](x^{\frac{5}{8}})^{\frac{2}{3}}[/tex]
To simplify it we multiply the exponents inside with exponent outside
[tex](a^m)^n = a^{mn}[/tex]
[tex]\frac{5}{8} *\frac{2}{3}[/tex]
Cancel out 8 and 2
[tex]\frac{5}{4} *\frac{1}{3}[/tex]
[tex]\frac{5}{12}[/tex]
tex](x^{\frac{5}{8}})^{\frac{2}{3}}=\frac{5}{12}[/tex]
What is the equation of the line passing through the points (2, –1) and (5, –10) in slope-intercept form?
5 divided 1 squared plus 1
Answer: 6
Step-by-step explanation: Use a calculated bro
An empty rectangular tank, 40 cm long and 25 cm wide, contains 2 metal cubes of edge 10 cm. the tank is being filled with water flowing from a tap at a rate of 10 liters per minute. If it takes 3 minutes to fill up the tank, find the height of the tank.
The height of the tank is 0.5 cm.
Explanation:To find the height of the tank, we can use the formula:
Volume of water = base area × height
The base area of the tank can be found by multiplying the length and width: 40 cm × 25 cm = 1000 cm².
The volume of water flowing from the tap is given as 10 liters per minute, which is equivalent to 10000 cm³ per minute or 166.667 cm³ per second. Since it takes 3 minutes to fill up the tank, the total volume of water will be 3 minutes × 166.667 cm³ per second = 500 cm³.
Now, we can plug these values into the formula to find the height:
500 cm³ = 1000 cm² × height
Dividing both sides by 1000 cm² gives:
height = 0.5 cm
Therefore, the height of the tank is 0.5 cm.
A six-sided number cube labeled 1 through 6 is rolled 600 times. An odd number is rolled 272 times. Compare the experimental probability of rolling an odd number with the relative frequency of rolling an odd number and select one of the statements below that best describes the situation.
Answer:
Experimental probability and relative frequency are the same
Step-by-step explanation:
HELPPP PLEASEEEEEE!?!?!
a straight line is 180 degrees so we can find C by subtracting 140 from 180
180-140 = 40 degrees
all 3 inside angles need to equal 180 so now we have
180 = 40 + (2x) + (x+2)
180 = 40 +3x +2
180=42+3x
138=3x
x= 138/3 = 46
check : 2x= 2*46 = 92
x+2 = 46+2 = 48
92 +48 +40 = 180
so x = 46 degrees
so angle B = 2x46 = 92 degrees
DOES ANYONE KNOW THE ANSWER???
x varies directly as y, and x = 153 when y = 9. Find x when y = 13.
153/9 = x/13
153 x 13 = 1989
1989/9=221
x = 221
write an integer for the situation below : 13 feet below the sea level
Which class has 32% girls?
To find 19+(11+37) Lennie added 19 and 11. Then he added 37 to the sun.what property did he use
PLEASE HELP!
The graph below shows the height an elevator travels, y, in x seconds:
A graph is shown with x axis title as Time in seconds. The title on the y-axis is Height of Elevator Above Ground in feet. The values on the x-axis are from 0 to 5 in increments of 1 for each grid line. The values on the y-axis are from 0 to 125 in increments of 25 for each grid line. A line is shown connecting points on ordered pair 1, 25 and 2, 50 and 3, 75 and 4, 100. The title of the graph is Rate of Ascent.
What is the rate of change for the relationship represented in the graph?
50
25
fraction 1 over 25
fraction 1 over 50
The graph is not given , but with the help of information provided by you in the question:
X : 0 1 2 3 4 5 →→ Time in Seconds
Y : 0 25 50 75 100 125 →→Height of Elevator Above Ground in feet
Rate of change can be found by using two point slope form of line.
The slope of line joining two points [tex](x_{1},y_{1}) and (x_{2},y_{2})[/tex] is given by = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Taking two points (1,25) and (2,50) and finding the slope of line, that is Rate of change:
Rate of change = [tex]\frac{50-25}{2-1}=25[/tex]
Option (B) 25 is correct answer.
Which unit rate is the lowest price per ounce? Choice A: 25 ounces of potato chips for $3.49 Choice B: 40 ounces of potato chips for $4.79 Choice A Choice B The unit rates are equal. The unit rates cannot be determine
Answer:
B is the lowest price per ounce
Step-by-step explanation:
choice A is 14 cents per ounce, and choice B is 12 cents per ounce.
Which of the following coordinates of point C would make triangle ABC similar to triangle LMP ? Look at pic attached :) thank you .
What's equivalent to 3(8+7) 24+7 24+21 Please help