Answers
Note that:
• All numbers whose final digit is 0 or an even number are divisible by 2
,• All numbers whose final digit is 0 are divisible by 10
,• 498 is divisible by 2 but not divisible by 5 and 10
,• 151 is not divisible by any of 2, 5, or 10
,• 150 is divisible by al of 2, 5, and 10
The complete table is uploaded below
Related Questions
Question 1 (1 point)
What integer represents a rise in temperature of 19°?
O a -|-191
Ob
-19
Oc
19
Od
-|19|
Answers
The integer which represents the rise in temperature of 19° is -|19|
Positive, negative, and zero numbers all fall under the category of integers. The word "integer" is a Latin word that signifies "whole" or "intact." Therefore, fractions and decimals are not considered to be integers.
A number without a decimal or fractional element is known as an integer, which encompasses both positive and negative numbers, including zero. The following are some examples of integers: -5, 0, 1, 5, 8, 97, and 3,043. Z denotes a collection of integers,
hence the correct form is answered.
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two cards are drawn without replacement from a standard deck of 52 playing cards what is the probability of choosing a club and then without replacement a spade
Answers
occurringGiven a total of 52 playing cards, comprising of Club, Spade, Heart, and Spade.
[tex]\begin{gathered} n(\text{club) = 13} \\ n(\text{spade) =13} \\ n(\text{Heart) = 13} \\ n(Diamond)=\text{ 13} \\ \text{Total = 52} \end{gathered}[/tex]Probability of an event is given as
[tex]Pr=\frac{Number\text{ of }desirable\text{ outcome}}{Number\text{ of total outcome}}[/tex]Probability of choosing a club is evaluated as
[tex]\begin{gathered} Pr(\text{club) = }\frac{Number\text{ of club cards}}{Total\text{ number of playing cards}} \\ Pr(\text{club)}=\frac{13}{52}=\frac{1}{4} \\ \Rightarrow Pr(\text{club) = }\frac{1}{4} \end{gathered}[/tex]Probability of choosing a spade, without replacement
[tex]\begin{gathered} Pr(\text{spade without replacement})\text{ = }\frac{Number\text{ of spade cards}}{Total\text{ number of playing cards - 1}} \\ =\frac{13}{51} \\ \Rightarrow Pr(\text{spade without replacement})=\frac{13}{51} \end{gathered}[/tex]Thus, the probability of both events occuring (choosing a club, and then without replacement a spade) is given as
[tex]\begin{gathered} Pr(\text{club) }\times\text{ }Pr(\text{spade without replacement}) \\ =\frac{1}{4}\text{ }\times\text{ }\frac{13}{51} \\ =\frac{13}{204} \end{gathered}[/tex]Hence, the probability of choosing a club, and then without replacement a spade is
[tex]\frac{13}{204}[/tex]
Given AABC with vertices A(7, 7) B(-5, 3) and C(3,-5),
1) If BE is a median, then point E is located at what coordinate?
2) If AL is a median, at what coordinate would L be located?
3) If LP is a perpendicular bisector, what would be the slope of LP?
4) An altitude is always.
to the side of the triangle.
Answers
ABC's vertices are points A, B, and C. ABC's sides are made up of the AB, BC, and CA segments.
How to calculate vertices of ABC?Determine the length of the median across vertex A of triangle ABC, which has vertices A (7,3), B (5,3), and C.
Assume M(x,y) represents the ABC median from A to BC.
M will be the point at which BC splits in half.
x 1 =5, y1 =3
x 2 =3,y2 =−1
Using the midpoint formula, x=(x 1 + x 2)/2
∴x=(5+3)/2=8/2=4
Using the midpoint formula, y=(y 1 + y 2 )/2
∴y=(3+(−2))/2=2/2=1
Consequently, M's coordinates are (4,1).
The distance formula reads d(AM)=
By distance formula, d(AM)= √[(x2 - x1)² + (y2 -y1)²]
x1 = 7,y1 = -3
x2 = 4,y2 = 1
∴d(AM) = √[(4- 7)² + (1 - (-3)²]
∴d(AM) = √(-3)² + (4)² = √9 + 16
∴d(AM) = √25 = 5
As a result, the median AM is 5 units long.
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Select the correct difference.-325 - (-725)4 z4 25-10 25-45
Answers
Given:
-325 - (-725)
We know that negative negative equals positive
(- -) = +
Therefore, we have:
-325 - (-725)
= -325 - -725
= -325 + 725 = 400
ANSWER:
400
Factorise 49n^3 -- 25m^3
Answers
Factorization of 49n^3 -- 25m^3 is (5m + 7n) × (5m - 7n)
A difference of two perfect squares, A2 - B2 can be factored into (A+B×(A-B)
(A+B) • (A-B)
= A2 - AB + BA - B2
= A2 - AB + AB - B2
= A2 - B2
AB = BA is the commutative property of multiplication.
- AB + AB equals zero and is therefore eliminated from the expression.
⇒ 25 is the square of 5
⇒ 49 is the square of 7
⇒ m2 is the square of m1
⇒ n2 is the square of n1
Hence, The Factorization is (5m + 7n) × (5m - 7n)
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Kyle can wash the car in 30 minutes. Michael can wash the car in 40 minutes. Working together, can they wash the car in less than 16 minutes?
Answers
Step-by-step explanation:
Kyle can do in 1 minute 1/30 of the work.
Michael can do in 1 minute 1/40 of the work.
the whole work is 1.
how much can they do together in 16 minutes ?
16×1/30 + 16×1/40 = 8/15 + 2/5 = 8/15 + 3/3 × 2/5 =
= 8/15 + 6/15 = 14/15
which is less than 1 = 15/15.
so, as they cannot even do the whole work in 16 minutes, they cannot do it in less than 16 minutes either.
Logarithm 6) If log 5 = A and log 3 = B, find the following in terms of A and B:
Answers
Given the following parameters:
log 5 = A
log 3 = B
According to the law of product and quotient of logarithm as shown:
[tex]\begin{gathered} \log AB=\log A+\log B \\ \log (\frac{A}{B})=\log A-\log B \\ \log A^b=b\log A \end{gathered}[/tex]Applying the laws of logarithm in solving the given logarithm
[tex]\begin{gathered} a)\log 15 \\ =\log (5\times3) \\ =\log 5+\log 3 \\ =A+B \end{gathered}[/tex]For the expression log(25/3)
[tex]\begin{gathered} b)\log (\frac{25}{3}) \\ =\log (\frac{5^2}{3}) \\ =\log 5^2-\log 3 \\ =2\log 5-\log 3 \\ =2A-B \end{gathered}[/tex]For the expression log135
[tex]\begin{gathered} \log (135) \\ =\log (5\times27) \\ =\log (5^{}\times3^3) \\ =\log 5^{}+\log 3^3 \\ =\log 5+3\log 3 \\ =A+3B \end{gathered}[/tex]For the expression log₅27
[tex]\begin{gathered} \log _527 \\ =\frac{\log 27}{\log 5} \\ =\frac{\log 3^3}{\log 5} \\ =\frac{3\log 3}{\log 5} \\ =\frac{3B}{A} \end{gathered}[/tex]For the expression log₉625
[tex]\begin{gathered} \log _9625 \\ =\frac{\log 625}{\log 9} \\ =\frac{\log 5^4}{\log 3^2} \\ =\frac{4\log 5}{2\log 3} \\ =\frac{\cancel{4}^2A}{\cancel{2}B} \\ =\frac{2A}{B} \end{gathered}[/tex]For the value of 15, this can be expressed as shown. Since:
[tex]\begin{gathered} \log 5=A;10^A=5 \\ \log 3=B;10^B=3^{} \end{gathered}[/tex]Since 15 = 5 × 3, writing it in terms of A and B will be expressed as:
[tex]\begin{gathered} 15=5\times3 \\ 15=10^A\times10^B \\ 15=10^{A+B} \end{gathered}[/tex]The table below gives the dimensions of a statue and a scale drawing of the statue.Find the scale factor of the drawing to the real statue.Write your answer as a fraction in simplest form.Height (inches)Length (inches)Scale factor:Drawing8006Statue6448 I need help with this math problem.
Answers
Given:
Find-:
The scale factor
Explanation-:
The scale factor is:
[tex]S.F.=\frac{\text{ Status}}{\text{ Drawing}}[/tex][tex]S.F.=\frac{64}{8}\text{ or }\frac{48}{6}[/tex]So, the scale factor is:
[tex]\begin{gathered} S.F.=\frac{64}{8}\text{ or }\frac{48}{6} \\ \\ S.F.=8\text{ or }8 \\ \\ S.F.=8 \end{gathered}[/tex]The scale factor is 8.
calculate the average speed of a lion that runs 45 m in 5 seconds
Answers
Answer:
9 m /s
Step-by-step explanation:
To find the speed, take the distance and divide by the time
45 m/ 5 s
9 m /s
Answer:
[tex] \sf9ms ^{ - 1} [/tex]
Step-by-step explanation:
[tex] \sf \: Average \: speed = \frac{ Total \: distance }{Total \: Time}[/tex]
Let us find the average speed now.
[tex] \sf \: Average \: speed = \frac{ Total \: distance }{Total \: Time} \\ \sf \: Average \: speed = \frac{ 45m }{5s} \\ \sf \: Average \: speed = 9ms ^{ - 1} [/tex]
i inserted a picture of the question, i can give you the answer to the previous question if it helps. C(t) = -0.30(t-12)^2 + 40
Answers
Answer:
F(t) = -0.54(t - 12)² + 104
Explanation:
We know that C(t) = -0.30(t - 12)² + 40 and F(t) = 9/5C(t) + 32
Then, we can replace C(t) on the equation of F(t) to get
[tex]\begin{gathered} F(t)=\frac{9}{5}C(t)+32 \\ F(t)=\frac{9}{5}(-0.30(t-12)^2+40)+32 \\ F(t)=\frac{9}{5}(-0.30)(t-12)^2+\frac{9}{5}(40)+32 \\ F(t)=-0.54(t-12)^2+72+32 \\ F(t)=-0.54(t-12)^2+104 \end{gathered}[/tex]Therefore, the new function F(t) is
F(t) = -0.54(t - 12)² + 104
For the expression, which of the following is the coefficient of the term involving the variable x. x^3/2 + 4y + 5z²1. 3/22. 23. 34. 1/2
Answers
Given the expression:
[tex]\text{ }\frac{x^3}{2}+4y+5z^2[/tex]The term that involves the variable x is x^3/2.
Let's determine its coefficient:
[tex]\text{ }\frac{x^3}{2}\text{ = }\frac{1}{2}x^3[/tex]Therefore, the coefficient of the term that involves the variable x is 1/2.
Which of the following lines is not perpendicular to y = –1.5x + 11?A. y =2/3x + 5B. 3y = 2x – 9C. 2y = 3x + 10D. –2x + 3y = 7
Answers
B. 3y = 2x – 9
is not perpendicular to the given line.
Explanation:The slopes of perpendicular lines are negative reciprocals
Given the line
y = -1.5x + 11
The slope is -1.5 or -3/2
Any line perpendicular to the one above must have its slope as 2/3
A. The slope is 2/3 . CORRECT
B. The slope is 2/3. CORRECT
C. The slope is 3/2. WRONG
D. The slope is 2/3. CORRECT
Nate's age is six years more than twice Connor's age. If the sum of their ages is 24 find each age
Answers
Answer:
12
Step-by-step explanation:
nate's age=6
connor's age =6+6=12
Nate's age +connor's age =24
Nate's age=24÷3=8
connor's age=8+8=16
the sum of thier ages =24
can someone help and explain how to do this. Ive been stuck in this lesson for days. This is so confusing and hard.
Answers
when x = 0:
y = 0/2 = 0
when x = 2:
y = 2/2 = 1
when x = 4:
y = 4/2 = 2
when x = 6:
y = 6/2 = 3
Joe borrowed $9,000 from the bank at a rate of 7% simple interest pa year. How much interest did he pay in 5 years? In 5 years, Joe pays ? In Interest
Answers
Principal = 9000
Interest rate = 7% = 0.07
Time = 5 years
Simple interest formula:
A = P(1 + rt)
In this case:
A = 9000(1 + 0.07*5) = 9000(1 + 0.35) = 9000(1.35) = 12150
Interest = A - P = 12150 - 9000 = 3
There is a population of 205 tigers in a national park. They are being illegally poached at the rate of 7tigers per year.Assume the population is otherwise unchanging, write a linear model using "P" for population and "t" fortime.What does the t-intercept signify?NOTE: This answer will NOT be automatically graded and will appear as a 0 until the instructor hasgraded it.Question Help: Message instructorSubmit Question
Answers
Solution.
Initial population = 205
After 1 year, population = 205 - 7 = 198
After 2 years , population = 198 - 7 = 191
After 3 years , population = 191 - 7 = 184
We can generate a table of value for the changes
[tex]\begin{gathered} Slope\text{ of the line, m = }\frac{198-205}{1-0} \\ m=-\frac{7}{1} \\ m=-7 \end{gathered}[/tex]One point on the line = (0, 205)
[tex]\begin{gathered} The\text{ equation of the linear model can be gotten using the formula} \\ y-y_1=m(x-x_1) \\ y-205=-7(x-0) \\ y-205=-7x \\ y=-7x+205 \\ Replacing\text{ y with P and x with t} \\ The\text{ linear model is P = -7t + 205} \end{gathered}[/tex]The t-intercept signifies the time when the population of the tiger will be zero. That is the time when there will be no more tigers in the park
Answer:
Step-by-step explanation:
bbbbbbbbbbb
4.5x + 5 = (if x = 4)
Answers
Answer:
23
Step-by-step explanation:
George shot the basketball 20 times in his game on Saturday. Of those 20 shots, he made 15.
What percentage of the shots did George make?
Answers
George made 75 percent of the shots.
First, let us understand the percentage:
A percentage is a fraction of a whole expressed as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent.
To determine a percentage, we need to divide the portion of the whole by the whole itself and multiply by 100.
We are given the following:
George shot the basketball 20 times in his game on Saturday.
Of those 20 shots, he made 15.
We need to find the percentage of the shots George made.
The percentage of shots George made is given by:
Percentage = 15 / 20 * 100 = 15 * 5 = 75 %
So, 75 % of the shots did George make.
Thus, George made 75 percent of the shots.
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Find an equation of the line that satisfies the conditionPasses through (-1,-3) and (4,2)
Answers
The points given are:
(-1, -3) and (4, 2)
Coordinates are:
x₁ =-1 y₁=-3 x₂ = 4 y₂ = 2
First, let's find the slope(m) of the equation using the formula below:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]=\frac{2+3}{4+1}=\frac{5}{5}=1[/tex]Next, find the inetercept of the equation by substituting x =-1 y=-3 m = 1 into y=mx+ b
-3 = 1(-1) + b
-4 = -1 + b
Add 1 to bothside
-4+1 = b
-3 = b
b = -3
We can now form the equation of the line by simply substituting the value of m and b into y=mx+ b
y = x - 3
Therefore, the equation of the line that satisfies the condition is y = x - 3
GG is considering two websites for downloading music. The costs are detailed here.
Website 1: a yearly fee of $15 and $5 for each download
Website 2: $7 for each download
Select the equation for Website 1.
Responses
y=15x+5
y=5x+15
y=−7x
y=7x
Answers
The equation for Website 1 is y = 15 + 5x option (A) is correct if yearly fee of $15 and $5 for each download
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
GG is considering two websites for downloading music.
Website 1: a yearly fee of $15 and $5 for each download
Let x be the number of downloads
Equation for the website 1:
Total cost is y
y = 15 + 5x
Thus, the equation for Website 1 is y = 15 + 5x option (A) is correct if yearly fee of $15 and $5 for each download
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Radiation machines used to treat tumors produce an intensity of radiation that variesinversely as the square of the distance from the machine. At 3 meters, the radiationintensity is 62.5 milliroentgens per hour. What is the intensity at a distance of 2.6 meters?The intensity is(Round to the nearest tenth as needed.)
Answers
Answer: Intenisy = 83.2 milliroentgens per hour
Let the intensity from the radiation = I
Let the distance = d
The intensity is inversely proportional to the square of its distance
[tex]\begin{gathered} I\text{ }\propto\text{ }\frac{1}{d^2} \\ \text{Introducing a proportionality constant} \\ I\text{ = }\frac{k\text{ x 1}}{d^2} \\ I\text{ = }\frac{k}{d^2} \\ \text{When I = 62.5 , d = 3} \\ \text{From the above equation} \\ K=I\cdot d^2 \\ K\text{ = 62.5 }\cdot(3)^2 \\ K\text{ = 62.5 x 9} \\ K\text{ = 562.5 } \\ \text{ Find the intensity wen D = 2.6 meters} \\ I\text{ = }\frac{k}{d^2} \\ I\text{ = }\frac{562.5}{(2.6)^2} \\ I\text{ = }\frac{562.5}{6.76} \\ I\text{ = 83. 2 milliroentgens per our} \end{gathered}[/tex]Write the equation in standard form for the circle passing through (-7,7) centered at theorigin.
Answers
Step 1
State the equation of a circle
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where
h= -7
k= 7
Step 2
Find r
r is the distance between the origin and (-7,7)
Distance between 2 points is
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2^{}}[/tex][tex]\begin{gathered} \text{where} \\ x_2=0 \\ x_1=-7 \\ y_2=0 \\ y_1=7 \end{gathered}[/tex]Hence the distance is given as
[tex]\begin{gathered} d=\sqrt[]{(0-(-7))^2+(0-7)^2} \\ d\text{ =}\sqrt[]{49+49} \\ d=\sqrt[]{98} \\ d=7\sqrt[]{2} \end{gathered}[/tex]Hence r =7√2
Step 3
Write the equation in standard form after substitution.
[tex]\begin{gathered} (x-(-7))^2+(y-7)^2=(7\sqrt[]{2})^2 \\ (x+7)^2+(y-7)^2=(7\sqrt[]{2})^2 \end{gathered}[/tex]Please help quickly
Answers
The equation of the function in standard form is y = 3x -12.
How to write the equation of a function in a standard form when two points are given?
1. First find the slope using the slope formula, m = (y₂ - y₁) / (x₂ - x₁)
2. Find the y-intercept by substituting the slope and the coordinates of 1 point into the slope-intercept formula, y = mx + b.
3. Write the equation using the slope and y-intercept.
Here, we have
Points (2,-6) and (5, 3)
First we find the slope using the slope formula, m = (y₂ - y₁) / (x₂ - x₁), we get
m = (3 + 6) / (5 - 2)
m = 3
then, we find the y-intercept by substituting the slope and the coordinates of 1 point into the slope-intercept formula, y = mx + b.
we get,
-6 = 3*2 + b
-6 - 6 = b
b = 12
Now, we write the equation using the slope and y-intercept
we get,
y = mx + b
y = 3x - 12
Hence, the equation of the function in standard form is y = 3x -12.
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A file that is 273 megabytes is being downloaded. If the download is 15.6% complete, how many megabytes have been downloaded? round your answer to the nearest tenth.
Answers
1750 megabytes has been downloaded.
What do you mean by percentage?
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If you need to calculate the percentage of a number, divide the number by the whole number and multiply by 100. Percentages therefore mean 1 in 100. The word percent means around 100. Represented by the symbol '%'.Percentages have no dimension. Hence it is called a dimensionless number.
It is given that 273 megabytes has been downloaded and it is 15.6% of complete.
Let x be the complete storage
15.6% of x = (15.6/100) × x
(15.6/100) × x = 273
x = (273/15.6) × 100 = 2730/15.6 = 1750
Therefore, 1750 megabytes has been downloaded.
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Given (x – 7)2 = 36, select the values of x.
Answers
Answer:
x = 1 , x = 13
Step-by-step explanation:
(x - 7)² = 36 ( take square root of both sides )
x - 7 = ± [tex]\sqrt{36}[/tex] = ± 6 ( add 7 to both sides )
x = 7 ± 6
then
x = 7 - 6 = 1
x = 7 + 6 = 13
I NEED HELP WITH THIS
Answers
Answer:
see explanation
Step-by-step explanation:
given that W varies jointly with l and d² then the equation relating them is
W = kld² ← k is the constant of variation
(a)
to find k use the condition W = 6 when l = 6 and d = 3 , then
6 = k × 6 × 3² = 6k × 9 = 54k ( divide both sides by 54 )
[tex]\frac{6}{54}[/tex] = k , then
k = [tex]\frac{1}{9}[/tex]
W = [tex]\frac{1}{9}[/tex]ld² ← equation of variation
(b)
when W = 10 and d = 2 , then
10 = [tex]\frac{1}{9}[/tex] × l × 2² ( multiply both sides by 9 to clear the fraction )
90 = 4l ( divide both sides by 4 )
22.5 = l
(c)
when d = 6 and l = 1.4 , then
W = [tex]\frac{1}{9}[/tex] × 1.4 × 6² = [tex]\frac{1}{9}[/tex] × 1.4 × 36 = 1.4 × 4 = 5.6
Determine the range of the following graph:
Answers
Answer:
R: {y | -11 ≤ y < 11}
Step-by-step explanation:
Range is going to include the possible output values in regards to the Y-axis on the graph. As far as when to use equal to and not, the open circle means it does NOT include that number, since the circle is not colored in on that number, while the full circle DOES include that number, and that is when you would introduce the equal than.
Hope this helps.
Divide f(x) = x^3 - x^2 - 2x + 8 by (x-1) then find f(1)
Answers
Division of f(x) = x³ - x² - 2x + 8 by (x-1) will have a quotient of x² - 2 and a remainder of 6.
What is the remainder theoremThe remainder theorem states that if f(x) is divides by x - a, the remainder is f(a).
We shall divide the f(x) = x³ - x² - 2x + 8 by x - 1 as follows;
x³ divided by x equals x²
x - 1 multiplied by x² equals x³ - x²
subtract x³ - x² from x³ - x² - 2x + 8 will result to -2x + 8.
-2x² divided by x equals -2
x - 1 multiplied by -2 equals -2x + 2
subtract -2x + 2 from -2x + 8 will result to a remainder of 6, and a quotient of x² - 2.
f(1) = (1)³ - (1)² - 2(1) + 8
f(1) = 1 - 1 - 2 + 8
f(1) = 6
Therefore, f(1) is a remainder of as x - 1 divides f(x) = x³ - x² - 2x + 8 resulting to a quotient of x² - 2 and a remainder of 6
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(A) How many ways can a 2-person subcommittee be selected from a committee of 8 people?
Answers
To solve this problem, we have to use the combination formula
[tex]C^r_n=\frac{n!}{r!(n-r)!}[/tex]Where r represents the number of people for the subcommittee (2), and n represents the total committee (8). Replacing this information, we have
[tex]C^2_8=\frac{8!}{2!(8-2)!}=\frac{8!}{2!(6)!}[/tex]Remember that factorials are solved by multiplying the number in a reversal way, as follows
[tex]C^2_8=\frac{8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{(2\cdot1)(6\cdot5\cdot4\cdot3\cdot2\cdot1)}=\frac{40,320}{2(720)}=\frac{40,320}{1,440}=28[/tex]Therefore, there are 28 ways to form a 2-person subcommittee from a committee of 8.ow 3. Hto What is the surface area of this triangular prism? 15 in. 12 in. 7 21 in 18 in. A. 846 in. B. 909 in. C. 1,062 in. D. 1,224 in. 2
Answers
To obtain the surface area of a triangular prism, the formula to employ is:
[tex]\begin{gathered} A_{triangular\text{ prism}}=2A_B+(a+b+c)h \\ \text{where A}_B=\sqrt[]{s(s-a)(s-b)(s-c)} \\ \text{where s=}\frac{a+b+c}{2} \\ a,b\text{ and c are sides of the triangular prism and h is the height} \end{gathered}[/tex]From the image, a=18in, b=21in, c =15in and h=12in
We have to obtain the value of 's' first, from the equation:
[tex]\begin{gathered} s=\frac{a+b+c}{2} \\ s=\frac{18+21+15}{2} \\ s=\frac{54}{2} \\ s=27in \end{gathered}[/tex][tex]\begin{gathered} \text{Then, we obtain the value of A}_B \\ A_B=\sqrt[]{s(s-a)(s-b)(s-c)} \\ A_B=\sqrt[]{27(27-18)(27-21)(27-15)} \\ A_B=\sqrt[]{27(9)(6)(12)} \\ A_B=\sqrt[]{17496} \\ A_B=132.27in^2 \end{gathered}[/tex]The final step is to obtain the area of the triangular, having gotten the values needed to be inputted in the formula;
[tex]\begin{gathered} A_{triangular\text{ prism}}=2A_B+(a+b+c)h \\ A_{triangular\text{ prism}}=(2\times132.27)+(18+21+15)12 \\ A_{triangular\text{ prism}}=264.54+(54)12 \\ A_{triangular\text{ prism}}=264.54+648 \\ A_{triangular\text{ prism}}=912.54in^2 \end{gathered}[/tex]Hence, the surface area of the triangular prism is 912.54 square inches