Answer:
£ 6904.13
Step-by-step explanation:
the final value is given by
[tex]8500 (0.90)[/tex] at the final of the first year
then you need to add (0.95) twice (one from second and one from third year)
Notice if the depreciation is 5% the final value is 0.95 of the initial value at the beginning of the year
finally:
[tex]8500 (0.90) (0.95)^2 = 6904.13[/tex] (rounded to nearest cent!)
Gerard wrote down the sum of squares of two (23?)2 + (1?2)² = 7133029 numbers, as shown. Unfortunately some of the digits cannot be seen because they are covered in ink. What is the last digit of the first number? (A) 3 (B) 4 (C) 5 (D) 6 (E) 7
Answer:
We know that (23x)² + (1y)² = 7133029. From the right hand side of the equation, we can see that the last digit of 7133029 is 9. Using this information, we can deduce that the last digit of (23x)² must be 9, because (1y)² can only end in 1, 4, 5, 6 or 9.
Now we know that the last digit of (23x)² is 9 and the last digit of 23x is 3. Therefore the last digit of x is 3.
So, the last digit of the first number is 3. And the answer is (A) 3
A group of 500 middle school students were randomly selected and asked about their preferred television genre. A circle graph was created from the data collected.
a circle graph titled preferred television genre, with five sections labeled drama 14 percent, sports 22 percent, documentaries, reality 20 percent, and sci-fi 20 percent
How many middle school students prefer the Documentaries television genre?
24
76
120
86.4
80 middle school students prefer the documentaries television genre.
None of the given options match exactly, but the closest one is 76.
What is circle graph?A circle graph, also known as a pie chart, is a type of chart that displays data as a circular diagram, divided into slices to represent proportions of a whole. Each slice of the circle represents a percentage of the total data being represented, and the entire circle represents 100% of the data.
According to question:Based on the circle graph, the percentage of students who prefer documentaries is 16% (as the percentage for documentaries is missing from the given options, we need to calculate it).
To find out the actual number of students who prefer documentaries, we need to multiply this percentage by the total number of students in the sample:
16% of 500 = (16/100) x 500 = 80
Therefore, 80 middle school students prefer the documentaries television genre.
None of the given options match exactly, but the closest one is 76.
Circle graphs are commonly used to show proportions or percentages of different categories within a dataset. They are useful for displaying data in a way that is easy to understand, and they are often used in business and finance, as well as in education and research.
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Using a minimum of three points, create two linear functions. Prove the line created works exclusively with the three points by justifying how the x-value and y-value fit into the equation for the line.
As we have proved that the line created works exclusively with the three points by justifying how the x-value and y-value fit into the equation for the line.
Let's start by defining what a linear function is. A linear function is an equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope represents the rate of change of the line, and the y-intercept represents the value of y when x is equal to zero. To create a linear function, we need two points on the line.
Now, let's create another linear function using points B and C:
slope (m) = (y₂ - y₁) / (x₂ - x₁) = (6 - 4) / (5 - 3) = 1
y-intercept (b) = y - mx = 4 - 1 * 3 = 1
Therefore, the linear function that passes through points B and C is also y = x + 1. We can check if point A lies on this line by substituting its x and y values into the equation:
2 = 1 + 1
This is true, so point A lies on the line created by points B and C. Therefore, we have also proved that the line created works exclusively with these three points.
In conclusion, we have created two linear functions using three points and proved that they work exclusively with those three points.
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Describe the possible echelon forms of the following matrix. A is a 2x2 matrix with linearly dependent columns Select all that apply (Note that leading entries marked with an X may have any nonzero value and starred entries (*) may have any value including zero)
a. 0 0
0 0
b. 0 x
0 0
c. x *
0 0
d. x *
0 x
The possible echelon forms of the given matrix are:
A matrix is in echelon form when it has leading nonzero entries in each row, with each row starting further to the right than the row above it. In the given matrix, the first row does not have any nonzero entries, so it does not meet this criterion. The second row does have a nonzero entry (x) so it can meet the criterion, provided that it is the leading entry.
This is the case for b. 0 x
0 0, c. x *
0 0, and d. x *
0 x.
The other criterion for echelon form is that all starred entries (*) may have any value including zero. This criterion is met in all three cases.
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Determine the number of 15 boxes in kilograms
Answer:
Step-by-step explanation:
150
Can you help me with this question please.
Answer:
[tex]x = 4\sqrt{3}[/tex]
Step-by-step explanation:
The triangle is right-angled
In a right-angled triangle, the following equality holds
[tex]\tan x = \dfrac{\text{Side Opposite x}}{\text{Side adjacent to x}}\\\\\tan 30 = \dfrac{4}{x}\\\\[/tex]
[tex]\tan 30 = \dfrac{1}{\sqrt{3}}\\\\\dfrac{1}{\sqrt{3}} = \dfrac{4}{x}\\\\[/tex]
Cross multiply:
[tex]1 \times x = 4 \times \sqrt{3}\\\\x = 4\sqrt{3}[/tex]
identify the symbols used for each of the following: (a) sample standard deviation; (b) population standard deviation; (c) sample variance; (d) population variance. if sample data consist of weights measured in grams, what units are used for these statistics and parameters?
(a) Symbol used for sample standard deviation is “s” or “σˆ” (s-hat). The unit for the sample standard deviation is grams, as it is calculated from a sample.
(b) Symbol used for population standard deviation is “σ” (sigma).The unit for the population standard deviation is also grams, as it is calculated for the entire population.
The population standard deviation is a parameter, which is a fixed value calculated from every individual in the population.
A sample standard deviation is a statistic. This means that it is calculated from only some of the individuals in a population. Since the sample standard deviation depends upon the sample, it has greater variability.
(c) Symbol used for sample variance is “s²” or “σ²ˆ” (sigma-hat squared). The unit for the sample variance is grams², as it is calculated from a sample.
(d) Symbol used for population variance is “σ²” (sigma squared). The unit for the population variance is also grams², as it is calculated for the entire population.
Population variance refers to the value of variance that is calculated from population data, and sample variance is the variance calculated from sample data.
Due to this value of denominator in the formula for variance in case of sample data is ‘n-1’, and it is ‘n’ for population data. As a result both variance and standard deviation derived from sample data are more than those found out from population data.
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on her way to visit her parents, jennifer drives 265 miles in 5 hours what is her average rate of speed in miles per hour?
Answer:
53 miles per hour
Step-by-step explanation:
To calculate Jennifer's average rate of speed in miles per hour, we can use the formula:
average speed = total distance / total time
In this case, Jennifer drove a total distance of 265 miles and it took her a total time of 5 hours, so:
average speed = 265 miles / 5 hours
Simplifying the expression, we get:
average speed = 53 miles per hour
Therefore, Jennifer's average rate of speed in miles per hour is 53 miles per hour.
Answer: 53 miles per hour
Step-by-step explanation:
To find Jennifer's average rate of speed in miles per hour, we divide the distance she traveled by the time it took her:
Average speed = distance ÷ time
Average speed = 265 miles ÷ 5 hours
Average speed = 53 miles per hour
Therefore, Jennifer's average rate of speed was 53 miles per hour.
Determine whether each of the following conditional statements is true or false. (a) If 10<7,10<7, then 3=43=4. (c) If 10<7,10<7, then 3+5=83+5=8. (b) If 7<10,7<10, then 3=43=4. (d) I…Determine whether each of the following conditional statements is true or false.(a) If 10<7,10<7, then 3=43=4.(c) If 10<7,10<7, then 3+5=83+5=8.(b) If 7<10,7<10, then 3=43=4.(d) If 7<10,7<10, then 3+5=83+5=8.
The given conditional statements are false, true, false, True.
They are determined by following:
(a) False - The statement "If 10<7,10<7, then 3=43=4" is false, since 10 is not less than 7.
(b) True - The statement "If 7<10,7<10, then 3=43=4" is true, since 7 is less than 10.
(c) False - The statement "If 10<7,10<7, then 3+5=83+5=8" is false, since 10 is not less than 7.
(d) True - The statement "If 7<10,7<10, then 3+5=83+5=8" is true, since 7 is less than 10.
Conditional statements are used in mathematics and logic to express relationships between events and conditions. These statements consist of an "if-then" structure, where the "if" clause is the antecedent or condition, and the "then" clause is the consequent or outcome.
The truth value of the conditional statement depends on whether the condition is true or false. If the condition is true, then the outcome is also true, and the statement is considered true.
If the condition is false, then the outcome may be true or false, and the statement is considered false. Conditional statements are widely used in mathematical proofs, programming, and reasoning to establish logical connections between different events and conditions.
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I need help somebody please
Answer: 54 square in
Step-by-step explanation:
I don't know if this is the same person but I answered this same question just now please check my profile or comment if you want the explanation
The ordering and transportation cost €C for components used in manufacturing process is approximated by the function below, where C is measured in thousands of dollars and is the order size in hundreds_ C(x) = s(x x+3 (a) Verify that C(3) C(6) _ c(3) (b) According to Rolle's Theorem, the rate of change of the cost must be for some order size in the interval (3 answer to the nearest whole number:) components Find that order size (Round vour Need Help? Ialkto Tutor
The value of x in the interval (3 < x < 6) for which the rate of change of the cost is zero.
(a) To verify that C(3) < C(6), we have to find the values of C(3) and C(6).The given function is C(x) = s(x x+3)The order size is measured in hundreds. So, when x = 3, the order size is 300 and when x = 6, the order size is 600.Therefore, C(3) = s(3 x 3+3) = s(18) and C(6) = s(6 x 6+3) = s(39)Now, as s(x) > 0, we can see that C(6) > C(3). Hence, C(3) < C(6).(b) According to Rolle's Theorem, the rate of change of the cost must be 0 for some order size in the interval (3 < x < 6).We know that the function is continuous and differentiable in the interval (3 < x < 6). Now, the rate of change of the cost is given by the derivative of the function C(x) with respect to x.C(x) = s(x x+3)C'(x) = s[1 + (x + 3) . 1] = s(1 + x + 3) = s(x + 4)As per Rolle's Theorem, there must exist a value of x in the interval (3 < x < 6) such that C'(x) = 0.So, s(x + 4) = 0x + 4 = 0x = -4Thus, the order size is -4 x 100 = -400. However, this is an absurd answer as the order size cannot be negative. Therefore, there is no value of x in the interval (3 < x < 6) for which the rate of change of the cost is zero.
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42 Développer chaque produit, puis réduire les expres-
sions obtenues.
A= 5x-3(x+12)
C = 2x² + x(4x - 5)
B=3x-6+7(2x+4)
D=4x²-x+x(5x-9)
a college student takes the same number of credits each semester. before beginning college, the student had some credits earned while in high school. after 2 semesters, the student had 45 credits, and after 5 semesters, the student had 90 credits. if c(t) is the number of credits after t semesters, write the equation that correctly represents this situation.
The equation that correctly represents this situation is c(t) = 45 + 45(t-2). This equation states that the total number of credits the student will have after t semesters is equal to 45 (the number of credits they had before beginning college) plus 45 times the number of semesters after two (t-2).
To explain this equation in more detail, we need to break it down. First, the student had some credits earned while in high school, so the equation starts off with c(t) = 45, which is the number of credits the student had before beginning college.
Next, 45(t-2) represents the number of credits earned in the additional semesters since college began. The t-2 part of the equation means that the total number of credits earned in the additional semesters starts at zero for t = 2. Then, for each additional semester, 45 credits are added. So, for example, when t = 5, 45 credits are added to the initial 45 credits the student had before beginning college, resulting in 90 credits.Therefore, the equation c(t) = 45 + 45(t-2) correctly represents this situation.
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60 mi / 1 hr = ? mi / 5 hr
Answer: 300 minuets
Step-by-step explanation:
Answer:
350
Step-by-step explanation:
60 miles is 1 hr. all it is, is a ratio. multiply 60 by 5 to get your answer; 350
the weights of bunches of bananas in the grocery store are normally distributed with a mean weight of 3.54 pounds and a standard deviation of 0.64 pounds. a random sample of four bunches is taken and the mean weight is recorded. which of the following is the mean of the sampling distribution for the mean of all possible samples of size four? a.0.89 b.1.27 c.3.54 d.5.53
The mean of the sampling distribution will be 3.54. Thus, the correct option is C.
The population means is equal to the mean of the sampling distribution for all feasible samples of size 4. In this instance, 3.54 pounds is shown as the population means.
This suggests that the mean weight of the population of banana bunches will be 3.54 pounds if we pick several random samples of size four, compute the mean weight for each sample, and then average those sample means.
The Central Limit Theorem, which asserts that the sampling distribution of the sample means approaches a normal distribution centered on the population mean as the sample size grows, is a fundamental idea in statistics.
Thus, the correct option is C.
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13
Select the correct answer.
Solve the following equation for x.-
x²-36=0
Ο Α.
OB.
OC.
O D.
X = 1; x = -36
x= -1; x = 36
x = -6; x = 6
x=-18; x = 18
Answer:
C.
Step-by-step explanation:
x² - 36 = 0
x = 6
6² = 6 x 6 = 36
So..
36 - 36 = 0
As there are so many equations in mathematics, it is a very broad subject. These are a few illustrations of typical mathematical equations: [tex]x = -6; x = 6[/tex]. Thus, option C is correct.
What is the equation used in maths?To solve the equation [tex]x² - 36 = 0[/tex] , we can use the difference of squares formula:
A, B, and C are constants in the quadratic equation: ax2 + bx + c = 0. A quadratic function, often known as a function with the form f(x) = ax2 + bx + c, can be solved using this equation to get its roots.
[tex]a² - b² = (a + b)(a - b)[/tex]
In this case, a² = x² and b² = 36, so we can write:
[tex]x² - 36 = (x + 6)(x - 6)[/tex]
Setting this expression equal to 0 and solving for x, we get:
[tex](x + 6)(x - 6) = 0[/tex]
[tex]x + 6 = 0 or x - 6 = 0[/tex]
[tex]x = -6 or x = 6[/tex]
Therefore, the solutions to the equation [tex]x² - 36 = 0[/tex] are [tex]x = -6[/tex] and [tex]x = 6.[/tex]
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I select two cards from a deck of 52 cards and observe the color of each (26 cards in the deck are red and 26 are black). Which of the following is the most appropriate sample space S for the possible outcomes? a. S-(red,red), (red,black), (black,red), (black,black) b. S - fred,black) c. S-(0, 1, 2) d. none of the above
The option a. S-(red,red), (red,black), (black,red), (black,black) is the most appropriate sample space S for the possible outcomes of selecting two cards from a deck of 52 cards
The most appropriate sample space S for the possible outcomes of selecting two cards from a deck of 52 cards and observing the color of each (26 cards in the deck are red and 26 are black) is given by option a. S-(red,red), (red,black), (black,red), (black,black).
Sample space S in probability theory denotes the set of all possible outcomes of an experiment.
In other words, the sample space S represents all possible outcomes of an experiment under consideration. For instance, in the current scenario,
These four possible outcomes are independent and equally likely events, and the sample space S for the possible outcomes is given by option a. S-(red,red), (red,black), (black,red), (black,black).
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Solve for x. using the tangent lines.
50 deg
X
x =[?]^
This equation shows that the value of x is equal to the y-value divided by the tangent of 50°.
What is tangent?Tangent is a line or plane that touches a curve or surface at a single point. It is a measure of the steepness of a curve or surface at a particular point. It is equal to the ratio of the change in the y-coordinate to the change in the x-coordinate of a point on the curve. Tangent is used in many areas of mathematics and physics, including calculus, geometry, and mechanics. It is also used to describe the rate of change in a function, as well as to define the angle between two intersecting lines.
The tangent line equation for a line with a slope of 50 degrees is y = tan(50°)x.
To solve for x, you must rearrange the equation to isolate x on one side of the equation.
To do this, divide both sides of the equation by tan(50°), giving the equation x = y/tan(50°). This equation shows that the value of x is equal to the y-value divided by the tangent of 50°.
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Edith's van can safely carry a maximum land of 920 kilograms.
She wants to use her van to carry
30 sacks of potatoes, each of mass 25 kilograms to the nearest kilogram
and
20 sacks of carots, each of mass 7. 5 kilograms to 1 decimal place
Can she definitely use her van safety in one journey?
You must show your working
(4 marks)
Yes, she can definitely use her van safety in one journey. The total weight is the weight of potatoes plus the weight of carots.
Given,
Number of sacks of potatoes = 30
Mass of each potato = 25
Total weight of Potatoes = 30 * 25
= 750
Number of sacks of carrots = 20
Mass of each Carot = 7.5
Total weight of Carrot = 20 * 7.5
= 150
(The total weight is the weight of potatoes plus the weight of carrots.)
So, total weight = 750 + 150
= 900
The maximum land which Edith can carry safely in the van is 920 kilograms.
∵ 900 < 920
∴ She can use her van safely.
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How many sides has a polygon if the sum of its
interior angles is 1440⁰
Answer:
10 sides
Step-by-step explanation:
We can use the formula for the sum of the interior angles of a polygon to solve this problem. The formula for the sum of the interior angles of a polygon with n sides, where S is the sum of the interior angles, and n is the number of sides of the polygon is:
S = (n - 2) x 180 degrees
If the sum of the interior angles is 1440 degrees, we can set this equal to the formula and solve for n:
1440 = (n - 2) x 180
Dividing both sides by 180, we get:
8 = n - 2
Adding 2 to both sides, we get:
n = 10
Therefore, a polygon with a sum of interior angles of 1440 degrees has 10 sides.
Select the correct answer.Adam constructed quadrilateral PQRS inscribed in circle O. How can he prove PQRS is a square?A.He needs to show only that the diagonals are perpendicular.B.He needs to show only that the diagonals are perpendicular and congruent.C.He needs to show only that the diagonals are perpendicular and bisect each other.D.He needs to show that the diagonals are perpendicular, congruent, and bisect each other.
Adam needs to show that the diagonals are perpendicular, congruent, and bisect each other.Therefore Option D is correct.
To prove that PQRS is a square, Adam needs to show that all four sides are congruent and that all four angles are right angles.
One way to do this is by showing that the diagonals of PQRS are perpendicular, congruent, and bisect each other.
If the diagonals are perpendicular, then opposite angles are congruent and the quadrilateral is a kite.
If the diagonals bisect each other, then opposite sides are congruent and the kite is a rhombus.
If the diagonals are also congruent, then all sides are congruent and the rhombus is a square.
Therefore, He needs to show that the diagonals of PQRS are perpendicular, congruent, and bisect each other to prove that PQRS is a square.
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Please help me as I’m struggling
Therefore , the solution of the given problem of pie chart comes out to be number of adults who selected math (15) outnumbered the number of minors. (10).
Explain pie charts.
A pie chart, also referred to as a circle diagram, is a graphical representation of each of the values of a particular variable or a method to condense a collection of nominal data. (e.g. percentage distribution). A circle with many parts makes up this kind of chart. Each segment represents a particular group.
Here,
for a two-way table: Party A, Party B, and Party C
Men make up 12 8 % of the population while women make up 16 %.
Total 28 15 19
32 ladies make up the group, to start with.
b) 16 female voters plan to support Party A.
Math, English, and science are studied by adults aged 15 to twenty-one and by children aged ten to ten.
Total 25 24 31
15 people selected math.
b) Reeshma is mistaken. The number of adults who selected math (15) outnumbered the number of minors. (10).
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find the number of outcomes in the complement of the given event. out of 344 high school students in their senior year, 175 are left-handed.
There are 169 outcomes in the complement of the given event.
To find the number of outcomes in the complement of the given event, which is that out of 344 high school students in their senior year, 175 are left-handed, you need to follow a few steps. So, let's get started. To find the number of outcomes in the complement of the given event, you will first find the total number of students that are right-handed, which can be found by subtracting the number of left-handed students from the total number of students:344 - 175 = 169Therefore, there are 169 right-handed students.
Next, to find the number of outcomes in the complement of the given event, you will need to subtract the number of outcomes in the given event from the total number of possible outcomes. Since the number of possible outcomes is equal to the total number of students, the number of outcomes in the complement of the given event can be found by subtracting the number of left-handed students from the total number of students:344 - 175 = 169 Therefore, there are 169 outcomes in the complement of the given event.
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what is the probability of choosing a red card or a king from a deck of 52 cards? for this event, choosing a red card or choosing a king, where choosing a red card and choosing a king may occur jointly, which rule applies?
The rule that applies here is the addition rule of probability, which states that the probability of the union of two events A and B is the sum of their individual probabilities minus the probability of their intersection
How do we calculate the probability?The probability of choosing a red card or a king from a deck of 52 cards is 8/52 or 2/13. To calculate this, we first need to determine the number of cards that are either red or a king. There are 26 red cards in a deck of 52 cards, so the probability of choosing a red card is 26/52 or 1/2. There are four kings in a deck of 52 cards, so the probability of choosing a king is 4/52 or 1/13.
However, we need to be careful to avoid counting the red kings (two of which exist in a deck of 52 cards) twice. To account for this, we subtract the probability of choosing a red king from the sum of the probabilities of choosing a red card and a king. The probability of choosing a red king is 2/52 or 1/26, so the probability of choosing a red card or a king is:
P(red card or king) = P(red card) + P(king) - P(red king)
P(red card or king) = 26/52 + 4/52 - 2/52
P(red card or king) = 28/52
P(red card or king) = 2/13
The rule that applies here is the addition rule of probability, which states that the probability of the union of two events A and B is the sum of their individual probabilities minus the probability of their intersection (i.e., the probability that they occur jointly).
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For what values of the variables must ABCD be a parallelogram?
The for the values of the variables x = 7 and y = 10, the given must be a parallelogram.
What is parallelogram?A quadrilateral having two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Also, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.
A parallelepiped is a three-dimensional shape with parallelogram-shaped faces. The base and height of the parallelogram determine its area.
For the given quadrilateral to be parallelogram the opposite sides need to be parallel and equal.
For the given quadrilateral we have:
2y - 16 = y - 6
2y - y = -6 + 16
y = 10
Also,
2x + 2 = y + 6
Substitute the value of y = 10:
2x + 2 = 10 + 6
2x = 16- 2
2x = 14
x = 7
Hence, the for the values of the variables x = 7 and y = 10, the given must be a parallelogram.
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What is the Smallest Positive Integer with at least 8 odd Factors and at least 16 even Factors?
Answer:
Step-by-step explanation:
120
The perimeter of a square is 16 cm find length , diagonal and area
Answer:
Step-by-step explanation:
we have perimeter 16
for perimeter 4+4+4+4 we add together it's 16
for area we have 4 times 16
Which operation is used to convert 245 liters to milliliters?
O Multiply by 1,000
O Multiply by 10,000
O Divide by 1,000
O Divide by 10,000
what is (2x+45)° x° = what?
Answer:
x = 45.
Step-by-step explanation:
Given a straight line with the equation.
First collect like terms:
2x + x = 180 - 45
Then calculate:
3x = 135
Finally after dividing both sides by 3:
x = 45
Can someone please help me on this i’ve been doing this for an hour
Step-by-step explanation:volume = 0.5 * b * h * length , where b is the length of the base of the triangle, h is the height of the triangle, and length is prism length
