Find the equation of the line through (0, 2, 1) that perpendicular to both u =(4, 3, -5) and the z-axis. 5. Find an equation of the plane through P(-2, 3, 5) and orthogonal to n=(-1, 2, 4). 6. Find an equation of the plane passing through the points (-1, 1, 1), (0, 0, 2), and (3, -1, -2).
Answers
5. The equation of the plane through P(-2, 3, 5) and orthogonal to n(-1, 2, 4) is:
-x + 2y + 4z - 28 = 0.
6. The equation of the plane passing through the points (-1, 1, 1), (0, 0, 2), and (3, -1, -2) is:
-x - y - 2z - 2 = 0.
What is equation of plane?A plane's equation is a linear expression made up of the constants a, b, c, and d as well as the variables x, y, and z. The direction numbers of a vector perpendicular to the plane are represented by the coefficients a, b, and c.
5. To find the equation of the plane through point P(-2, 3, 5) and orthogonal to vector n(-1, 2, 4), we can use the point-normal form of a plane equation.
The equation of a plane in point-normal form is given by:
n · (r - P) = 0
where n is the normal vector of the plane, r represents a point on the plane, and P is a known point on the plane.
Substituting the given values, we have:
(-1, 2, 4) · (r - (-2, 3, 5)) = 0
Simplifying, we get:
(-1)(x + 2) + 2(y - 3) + 4(z - 5) = 0
Expanding and rearranging terms, we have:
-x - 2 + 2y - 6 + 4z - 20 = 0
Simplifying further, we get:
-x + 2y + 4z - 28 = 0
Therefore, the equation of the plane through P(-2, 3, 5) and orthogonal to n(-1, 2, 4) is:
-x + 2y + 4z - 28 = 0.
6. To find the equation of the plane passing through the points (-1, 1, 1), (0, 0, 2), and (3, -1, -2), we can use the point-normal form of a plane equation.
First, we need to find two vectors lying in the plane. We can do this by taking the differences between the points:
v₁ = (0, 0, 2) - (-1, 1, 1) = (1, -1, 1)
v₂ = (3, -1, -2) - (-1, 1, 1) = (4, -2, -3)
Next, we find the normal vector to the plane by taking the cross product of v₁ and v₂:
n = v₁ x v₂
Calculating the cross product, we have:
n = (1, -1, 1) x (4, -2, -3) = (-1, -1, -2)
Now we have the normal vector n = (-1, -1, -2), and we can use the point-normal form to write the equation of the plane. Choosing one of the given points, let's use (-1, 1, 1):
(-1, -1, -2) · (r - (-1, 1, 1)) = 0
Expanding and simplifying, we get:
-(x + 1) - (y - 1) - 2(z - 1) = 0
Simplifying further:
-x - y - 2z - 1 + 1 - 2 = 0
-x - y - 2z - 2 = 0
Therefore, the equation of the plane passing through the points (-1, 1, 1), (0, 0, 2), and (3, -1, -2) is:
-x - y - 2z - 2 = 0.
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Related Questions
T/F regardless of whether a distribution of scores that is symmetrically shaped has one mode or two modes, the mean value tends to be similar to the median value.
Answers
True
In a symmetrically shaped distribution of scores, regardless of whether it has one mode or two modes, the mean value tends to be similar to the median value.
When a distribution is symmetric, it means that the data is evenly distributed around the central point, resulting in a bell-shaped curve. In such cases, the mean, median, and mode are typically close to each other.
The mean is the arithmetic average of all the scores in a distribution, while the median represents the middle value when the scores are arranged in ascending or descending order. In a symmetric distribution, the mean and median are located at the exact center of the distribution.
If the distribution has only one mode, it means that there is one prominent peak or high point in the data. In this case, the mean and median will coincide with the mode and will be similar.
If the distribution has two modes, it means that there are two prominent peaks in the data, but they are symmetrical around the center. Even though there are multiple modes, the mean and median will still be similar and tend to be located between the two modes.
In summary, in symmetrically shaped distributions, regardless of the presence of one or two modes, the mean and median values are expected to be close to each other.
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Determine whether there is a profit or loss: revenue, $10,777; fixed cost, $8,041; and variable costs, $1,545.
Answers
Since the revenue of $10,777 exceeds the total cost of $9,586, so there is a profit of $1,191
To determine if there is a profit or loss, we need to consider the revenue, fixed costs, and variable costs. Revenue is the total income generated from sales. Fixed costs are expenses that do not change with the level of production or sales, such as rent, salaries, and insurance. Variable costs, on the other hand, are expenses that vary with the level of production or sales, such as raw materials and commissions.
To determine if there is a profit or loss, we need to calculate the total cost and subtract it from the revenue.
Total cost = Fixed cost + Variable cost
Total cost = $8,041 + $1,545 = $9,586
Profit/Loss = Revenue - Total Cost
Profit/Loss = $10,777 - $9,586 = $1,191
Since the result is positive, there is a profit of $1,191.
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cuanto es 5^3 - 3 √(375 ÷ 3) + (7 + 2)^2 - 9^11 ÷ 9^9
Answers
Consecuencia de 5^3 - 3 √(375 ÷ 3) + (7 + 2)^2 - 9^11 ÷ 9^9 es 91.46.
Sobre el número exponencialPotencias es una operación matemática para la multiplicación repetida de un número tanto como el rango. El rango de un número es un número que se escribe más pequeño y se ubica ligeramente hacia arriba. Basado en la semántica de escribir letras se llama superíndice, por ejemplo: 2², 3², 4³ y otros. En inglés, el exponencial se llama "potencia" o "exponente".
5³=125
3√(375:3) =3√125=3√5³= 3.5^3/2
(7+2) ²=9²=81
9¹¹÷9^9=9²=81
5³ - 3 √(375 ÷ 3) + (7 + 2)² - 9¹¹ ÷ 9^9= 5³-3.5^3/2+81-81 =125-3√125=125-(3(11.18) = 125- 33.54=91.46
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Answer each part. If necessary, round your answers to the nearest hundredth.
(a) It takes 51 pounds of seed to completely plant a 9-acre field.
How many acres can be planted per pound of seed?
acres per pound
(b) Christine runs 4 miles in 22 minutes.
How many minutes does she take per mile?
minutes per mile
Answers
Answer:4
Step-by-step explanation:
Answer:a) Given :
51 pounds of seed can be planted in = 9 acre field.
Per pound of seed =
We can convert 9/51 in simplest fraction by dividing top and bottom by 3.
We get
Therefore, 3/17 of an acrs can be planted per pound of seed.
b) $10 amount = 16 pounds of sugar.
$1 amount = 16/10 = 1.6 pounds of sugar.
Therefore, 1.6 pounds of sugar she got per dollar.
Step-by-step explanation:
PLEASE HURRY!
Which values from the given replacement set make up the solution set of the inequality?
m+7<18 ; {8, 9, 10, 11}
Responses
A. {8, 9, 10}
B. {8, 9}
C. {9, 10, 11}
D. {10, 11}
Answers
The values from the given replacement set make up the solution set of the inequality is {8, 9, 10]
How to solve inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
Let's solve the inequality to find the replacement set that make up the solution set of the inequality as follows:
m + 7 < 18
subtract 7 from both sides of the inequality
m + 7 < 18
m + 7 - 7 < 18 - 7
m < 11
Therefore, the set of value of m is less that 11.
The solution sets are {8, 9, 10}
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Fill in the blank 1.05 assignment
Answers
Answer:
Hey there!
The answer is -12
They are using the foil method, First, Outer, Inner, Last.
Let me know if this helps :)
The missing term is -12 in the given equation. which is the correct answer would be option (A).
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers.
The two factors are given in the question.
⇒ (2x - 3)(7x + 4)
We have to determine the polynomial of the given factors
⇒ (2x - 3)(7x + 4)
⇒ 2x (7x + 4) - 3(7x + 4)
Apply the distributive property of multiplication,
⇒ 2x × 7x + 2x × 4 - 3 × 7x - 3 × 4
⇒ 14x² + 8x -21x - 12
Comparing to the given equation, then we find the missing term is -12.
Therefore, the correct answer would be an option (A).
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What is the measure of ∠1
A: 56°
B: 73°
C: 107°
ANSWER FAST HURRY! WILL MARK BRAINLEIST WORTH 100 POINTS
Answers
Answer: 73
Step-by-step explanation:
Angle B is 180-107=73
Angle 1 is equivalent to B and it is 73
Answer:
C. ∠1 = 73°
Step-by-step explanation:
Angles on a straight line add up to 180°
Therefore:
⇒ ∠1 + 107° = 180°
Subtract 107° from both sides:
⇒ ∠1 + 107° - 107° = 180° - 107°
⇒ ∠1 = 73°
Quadrilateral RSTU is reflected across the line x = 1. Determine the coordinates of R’, S’, T’, and U’.
Quadrilateral R S T U plotted in the first quadrant of a coordinate plane. The vertices are at R (5, 2), S (4, 4), T (5, 6), and U (6, 4).
R’: (
,
)
S’: (
,
)
T’: (
,
)
U’: (
,
)
Answers
If quadrilateral RSTU is reflected across the line x = 1, then the coordinates of R’, S’, T’, and U’ are (-3, 2), (-2, 4), (-3, 6) and (-4, 4) respectively.
To reflect a point across the line x = 1, we can use the formula (2a - x, y), where (a, b) is the original point and x = 1 is the line of reflection.
Using this formula, we can find the coordinates of the reflected points as follows:
The x-coordinate of the line of reflection is 1, so the new x-coordinate for each point will be 2(1) - x = 2 - x.
The y-coordinate for each point will remain the same.
Therefore, the reflected coordinates are:
R' = (2(1) - 5, 2) = (-3, 2)
S' = (2(1) - 4, 4) = (-2, 4)
T' = (2(1) - 5, 6) = (-3, 6)
U' = (2(1) - 6, 4) = (-4, 4)
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Enter the value of
a
,
b
, and
c
if
x
2
−
x
−
1
=
0
Answers
Answer:
\(a=1\\b=-1\\c=-1\)
Step-by-step explanation:
Standard form:
\(ax^2+bx+c=0\)
Identify the values in:
\(x^2-x-1=0\)
\(a=1\\b=-1\\c=-1\)
What is the inverse of this trigonometric function?
y = sinx
y = cosx
y = arcsinx
y = arccosx
Answers
Answer:
D
Step-by-step explanation:
edge
The inverse of this trigonometric function is y = arccosx. Then the correct answer is option D.
What is a trigonometric function?The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths.
The given graph is represented by the function y = cosx. The inverse function will be y = arccosx.
Hence, the correct answer is option D.
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y = f(x) = 2x
Find f(x) when x = 1.
Enter the correct answer.
000
I
DONE
Clear all
000
E?
Answers
Answer:
2
Step-by-step explanation:
f(x) = 2x
Let x =1
f(1) = 2*1
f(1) = 2
Answer:
f(1)=2
Step-by-step explanation:
We are given the equation:
f(x)=2x
We also know that x=1. Therefore, we can substitute 1 in for every x.
f(1)= 2(1)
Multiply 2 and 1
f(1)=2
f(x) when x=1 is 2.
hello can somebody help please
Answers
Answer:
C 170
Step-by-step explanation:
A great-uncle has decided to give you a gift of $1,000. Being a financially savvy uncle, before giving you the money, he offers you a choice of the following: You can take the $1,000 today. You can wait five years and be given $1,200 instead 1. How will you decide if the offer presented by your great uncle is to your advantage? 2. Research interest rates for a savings account, checking account, and money market account at different financial institutions. Note the compounding period for each. How much would $1,000 be worth in each account in five years? 3. What are some factors that cause the value of money today to be different from its value in the future?
Answers
1. To decide if the offer presented by your great uncle is to your advantage, you need to consider the time value of money. This means that money available today is worth more than the same amount of money available in the future, due to the potential for earning interest or returns on the money. In this case, you need to compare the value of $1,000 today with the value of $1,200 in five years. If you can earn a rate of return greater than 4% over the next five years, it would be better to take the $1,000 today and invest it to earn a higher return. However, if you cannot earn a return greater than 4%, it would be better to wait and take the $1,200 in five years.
2. Interest rates and compounding periods will vary depending on the financial institution and type of account. As an example, let's assume that you are considering a savings account, checking account, and money market account with the following interest rates and compounding periods:
Savings account: 2% interest rate compounded annuallyChecking account: 0.1% interest rate compounded monthlyMoney market account: 2.5% interest rate compounded quarterlyUsing a compound interest calculator, the future value of $1,000 in each account after five years would be:
Savings account: $1,104.08Checking account: $1,005.02Money market account: $1,130.473. The value of money today can be different from its value in the future due to inflation, changes in interest rates, economic growth, and changes in the supply and demand for goods and services. Inflation is one of the biggest factors that can affect the value of money over time. If the rate of inflation is high, the value of money will decrease over time, meaning that the same amount of money will buy fewer goods and services in the future. On the other hand, if the rate of inflation is low, the value of money will increase over time, meaning that the same amount of money will buy more goods and services in the future. Interest rates can also affect the value of money, as higher interest rates can make it more attractive to save money, while lower interest rates can make it more attractive to borrow money. Economic growth and changes in the supply and demand for goods and services can also affect the value of money, as these factors can affect the overall price level of goods and services in the economy.
Which point can be the initial value of an application?
(0,5)
(7,12)
(5,0)
(-12,7)
Answers
Answer:
C maybe lemme know is its correct:)
Step-by-step explanation:
-102 = -8(6 – 4x) – 5x
Answers
Answer:
x= -2
Step-by-step explanation:
Hope this helps.
Answer:
-102 = (-8×6 -8×-4x) -5x ( this is only for explanation write only this way as given below)
-102 = -48+32x -5x
-102 = -48+27x
-102+48= 27x
-54 = 27x
x = -54/27
x = -2 Ans
Hope you like it!
Determine the domain of the following graph:
Please help :(
Answers
Answer:
[-11,11]
Step-by-step explanation:
the domain is all the values of the graph from left to right so [-11,11]
The line of best fit through a set of data is
ˆy=18.586−1.799xy^=18.586-1.799x
According to this equation, what is the predicted value of the dependent variable when the independent variable has value 60?
ˆy=y^= Round to 1 decimal place.
Answers
The given equation represents the line of best fit for a set of data. To find the predicted value of the dependent variable (y) when the independent variable (x) is 60, we substitute the value of x into the equation and calculate the corresponding y-value.
The equation ˆy = 18.586 - 1.799x represents the line of best fit. To find the predicted value of y when x = 60, we substitute x = 60 into the equation:
ˆy = 18.586 - 1.799(60)
ˆy = 18.586 - 107.94
ˆy ≈ -89.35
Therefore, the predicted value of the dependent variable (y) when the independent variable (x) has a value of 60 is approximately -89.35.
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Consider the limit lim (x,y)→(0,0)
2x 2
+y
3x 2
+y 2
and consider the approaches along y=0 and x=0. Which of the following is a correct conclusion of the two-line test? A. The approach y=0 yields the limit 2
3
while the approach x=0 yields 0 . Therefore the limit does not exist. B. The approach y=0 yields the limit 2
3
while the approach x=0 yields 0
0
. Therefore we cannot conclude whether the limit exists yet. C. The approach y=0 yields the limit 0 while the approach x=0 yields the limit 0 . Therefore the limit exists. D. The approach y=0 yields the limit 0 while the approach x=0 yields the limit 0 . Therefore we cannot conclude whether the limit exists yet. E. The approach y=0 yields the limit 0 while the approach x=0 yields the limit 0 . Therefore the limit does not exist.
Answers
The correct conclusion from the two-line test is: D. The approach y=0 yields the limit 0 while the approach x=0 yields the limit 0. Therefore we cannot conclude whether the limit exists yet.
Since the limit along the line y=0 is 0 and the limit along the line x=0 is also 0, we cannot determine the overall limit at (0,0) based on these two approaches alone. Further analysis or approaches may be needed to determine the existence and value of the limit.
The reason we cannot determine the overall limit at (0,0) based on the two approaches along y=0 and x=0 is that the limit can depend on the path taken to approach (0,0), not just the approaches along the coordinate axes.
In this case, when approaching along y=0, the limit is found to be 0, indicating that the function tends to approach 0 as (x,y) approaches (0,0) with y=0. Similarly, when approaching along x=0, the limit is also found to be 0, indicating that the function tends to approach 0 as (x,y) approaches (0,0) with x=0.
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help please number 7!! it’s using the pythagorean theorem
Answers
What is 5 rounded to the nearest whole number, explain why
Answers
Answer:
The answer is 10
Step-by-step explanation:
It is
Bill deposited $4000 into an account with 5.7% interest, compounded annually. assuming that no withdrawals are made, how much will he have in the account after 4 years?
Answers
After 4 years, with an initial deposit of $4000 and an annual interest rate of 5.7% compounded annually, Bill will have approximately $4,797.36 in his account.
To calculate the future value of the account after 4 years, we can use the formula for compound interest:
A = P\((1 + r/n)^(nt)\)
Where:
A = the future value of the account
P = the principal amount (initial deposit)
r = the annual interest rate (expressed as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, Bill deposited $4000, the annual interest rate is 5.7% (or 0.057 as a decimal), and the interest is compounded annually (n = 1). Plugging these values into the formula, we have:
A = 4000\((1 + 0.057/1)^(1*4)\)
≈ 4000\((1.057)^4\)
≈ 4000(1.2420449)
≈ 4797.36
Therefore, after 4 years, Bill will have approximately $4,797.36 in his account. It's important to note that this calculation assumes no additional deposits or withdrawals were made during the 4-year period.
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A basketball player scored 14 times during one game. She scored a total of 18 points, two for each two-point shot and one for each free throw. How many two-points shots did she make? How many free throws?
Answers
Answer:
i. 4 two-point shots
ii. 10 free throws
Step-by-step explanation:
Number of times scored = 14
total points made = 18
let her two-point shot be represented by x, and her free throw by y.
So that;
x + y = 14 .......... 1
But, two points for each two-point shot and one point for each free throw;
2x + y = 18 ......... 2
Subtract equation 2 from 1
2x - x + y - y = 18 - 14
x = 4
substitute the value of x in equation 1
4 + y = 14
y = 14 - 4
y = 10
x= 4, y = 10
Thus, she made 4 two-point shots, and 10 free throws.
Answer:
4 two-pointers and 10 free throws
Step-by-step explanation:
18 - 14 = 4
4 two-pointers = 8
10 free throws = 10 points
If angle p measures 60 degrees, what is the measure of angle C?
A)120
B)60
C)180
D)30
Answers
DO NOT ANSWER IF YOU DO NOT KNOW, Will give brainliest, like, comment, and 5 points to answer
Each of these is a pair of equivalent ratios, for each pair explain why they are equivalent. 5:1 and 15:3
10.2 and 25.5
198:1,287 and 2:13
Answers
Step-by-step explanation:
5:1 and 15:3 is equivalent because 5 ⋅ 3 = 15, and 1 ⋅ 3 = 3.
10.2 ⋅ 2.5 = 2.5.5 (This wasn't put into a ratio form.)
198:1,287 and 2:13 are equivalent because 198/99 = 2, and 1,287/99 = 13.
Uh need help
The ratio of the sale price of a jacket to the original price is 3:4. The original price is $64. What is the sale price?
Answers
Answer:
$48
Step-by-step explanation:
price of jacket : original price
3 : 4
If 64 = 4, we can find out 1.
64 / 4 = 16
16 x 3 = 48
16 x 4 = 64
48 : 64
sale price = $48
Hope this helps!
- profparis
Answer:
$48
Step-by-step explanation:
the 4 part of the ratio refers to the original price of $64 , then
$64 ÷ 4 = $16 ← value of 1 part of the ratio , then
3 parts = 3 × $16 = $48 ← sale price
An appliance store reduced the price of a refrigerator by 20% and then raised the prices by 10% from the lower price. What was the original price of the refrigerator, if the price was $70.49 ?
Answers
Answer: $80
Step-by-step explanation:
Let the original price of the refrigerator be represented by y.
We are told that an appliance store reduced the price of a refrigerator by 20%. This will be:
= y - (20% of y)
= y - (20/100 × y)
= y - (0.2 × y)
= y - 0.2y
= 0.8y
We are then told that the store then raised the prices by 10% from the lower price. This will be:
= 0.8y + (10% of 0.8y)
= 0.8y + (0.1 × 0.8y)
= 0.8y + 0.08y
= 0.88y
Since we told that now the price was $70.49, this means that we have to find the value of y using the above expression. This will be:
0.88y = $70.49
y = $70.49/0.88
y = $80.10
y = $80 approximately
The original price of the refrigerator is $80.
Solve for x. round your answer to the nearest whole degree.
Answers
Answer:
64°
Step-by-step explanation:
sin(x) = 17/19
take inverse sine of 17/19: \(sin^{-1}(17/19)\) = 63.475°
they want to the nearest whole degree, so it would be ≈ 64°
in 201520152015 the populations of city x and city y were equal. from 201020102010 to 201520152015, the population of city x increased by 20\ , percent and the population of city y decreased by 10\, percent. if the population of city x was 120{,}000120,000120, comma, 000 in 201020102010, what was the population of city y in 201020102010?
Answers
Answer:
Step-by-step explanation:
Answer:
The exact Population of the city Y in 2010 was 160,000.
Step-by-step explanation:
Given that,
1. In the year 2015, the populations of City X and City Y were equal.
2. City X population is increased by 20% and City Y population is decreased by 10% from 2010 to 2015.
3. Also, the population of City X was 120,000 in 2010
With the given data, calculation goes like this,
The population of City X in 2010 is 120000
Population Increased by 20% till 2015,
= 120000×120/100
= 144000
As Population of city Xand Y are same,
Population of city Y in 2015 would be 144000.
Population of Y in 2010 was decreased by 10%,
= 144000×100/90
=160000
Therefore, the Population of city Y in 2010 was 160,000.
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A rectangular field is 62 meters long and 48 meters wide. Diane estimates the length of the field to be 60 meters and
the width to be 45 meters. What is the percent error of Diane's estimated area measurement? Round your answer to
the nearest whole percent.
PLEASEEEEE SOMONE ANSWER THIS LIKE NOW
Answers
The percent error of Diane's estimated area measurement is 9%.
To find the percent error, we first calculate the actual area of the rectangular field:
Actual area = length × width = 62 × 48 = 2,976 square metersNext, we calculate the estimated area based on Diane's measurements:
Estimated area = estimated length × estimated width = 60 × 45 = 2,700 square metersThe absolute error is the difference between the actual and estimated areas:
Absolute error = |Actual area - Estimated area| = |2,976 - 2,700| = 276 square metersThe percent error is the absolute error divided by the actual area, multiplied by 100%:
Percent error = (Absolute error / Actual area) × 100% = (276 / 2,976) × 100% = 0.092 × 100% = 9%
Therefore, the percent error of Diane's estimated area measurement is 9% to the nearest whole percent.
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Find the surface area of each prism
Answers
Answer:
3. SA = 876 \(in^{2}\)
4. SA = 161 \(ft^{2}\)
Step-by-step explanation:
Number 3.
To find the total Surface Area, we need to know all the side lengths which are used to multiply to find the Area of each side. Then add the areas of all the sides to get the total SA.
To find side lengths:
Assuming the back triangle (24, 10 in) is congruent to the front triangle (26in.): First, Knowing the Pythagorean triples or the Pythagorean theorem, we can conclude that the short bottom leg in the triangle on the right (6, 10, x in) is 8 in. Secondly, to find the leg of the triangle with a hypotenuse of 24 inches, we subtract: 26 - 8 = 18 in.
Now we know all the (needed) side lengths.
To find the Surface Area:
Total SA = (12 x 26) + (12 x 24) + (12 x 10) + 2 x ((6 x 18 x 0.5) + (6 x 8 x 0.5))
= 312 + 288 + 120 + 2 x (54 + 24) = 720 + (2 x 78)
= 876 \(in^{2}\)
Number 4.
Same Idea: To find the Total SA, we need to know all the side lengths which are used to multiply to find the Area of each side. Then add the areas of all the sides to get the total SA.
Assuming the back triangle (7ft) is congruent to the front triangle (5x5 ft), then in this case, we already know all the needed side lengths.
To find the Surface Area:
Total SA = 2 x (8 x 5) + 2 x (5 x 5 x 0.5) + (7 x 8)
= 80 + 25 + 56
= 161 \(ft^{2}\)