Based on the analysis, the only absolute value equation or inequality that has a solution set that is not the empty set is |2x - 1| - 7 < -6.
Option A is the correct answer.
We have,
To determine which absolute value equation or inequality has a non-empty solution set, we can analyze each option:
|2x - 1| - 7 < -6:
Subtracting 7 from both sides, we get |2x - 1| < 1.
The absolute value of any real number is always non-negative, so the left-hand side is non-negative.
Since the right-hand side is also non-negative, the absolute value inequality is always true.
Therefore, this inequality has a solution set that is not the empty set.
|4x + 5| - 4 = -5:
Adding 4 to both sides, we get |4x + 5| = -1.
The absolute value of any real number is always non-negative, so the left-hand side is non-negative.
However, the right-hand side is negative, which is not possible.
Therefore, this equation does not have a solution, and the solution set is the empty set.
3|x + 2| - 2 = -3:
Adding 2 to both sides, we get 3|x + 2| = -1.
The absolute value of any real number is always non-negative, so the left-hand side is non-negative.
However, the right-hand side is negative, which is not possible.
Therefore, this equation does not have a solution, and the solution set is the empty set.
2|x - 5| - 4 < -8:
Adding 4 to both sides, we get 2|x - 5| < -4.
The absolute value of any real number is always non-negative, so the left-hand side is non-negative.
However, the right-hand side is negative, which is not possible.
Therefore, this inequality does not have a solution, and the solution set is the empty set.
Thus,
Based on the analysis, the only absolute value equation or inequality that has a solution set that is not the empty set is |2x - 1| - 7 < -6.
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ABC is equal to DEF and AB is equal to EF what type of triangle is ABC
Based on the information provided, the triangle ABC is an Isosceles triangle.
Understanding Isosceles TriangleIf triangle ABC is equal to triangle DEF and AB is equal to EF, it means that the corresponding sides and angles of the two triangles are congruent.
Based on the information given, we can conclude that triangle ABC is an isosceles triangle. An isosceles triangle is a triangle that has two sides of equal length. In this case, sides AB and EF are equal in length, making triangle ABC isosceles.
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cos 2x= ___. Check all that apply.
A. sin² x - cos²x
B. 1-2 cos²x
C. 1-2 sin² x
D. 2 cos²x - 1
Answer:
C and D
Step-by-step explanation:
[tex]\cos(2x)\\=\cos(x+x)\\=\cos(x)\cos(x)-\sin(x)\sin(x)\\=\cos^2(x)-\sin^2(x)\\=\cos^2(x)-(1-\cos^2(x))\\=2\cos^2(x)-1 \,\,\,\,\,\,\,\,\,\,\leftarrow \text{Option D}\\=2(1-\sin^2(x))-1\\=2-2\sin^2(x)-1\\=1-2\sin^2(x)\,\,\,\,\,\,\,\,\,\,\,\leftarrow \text{Option C}[/tex]
12
Select the correct answer.
The scatter plot represents the purchase prices and selling prices of X-ray machines made by five different manufacturers. Which of the following
points show errors of prediction or residuals?
OA.
OB.
O C.
O D.
Points (14, 25) and (15, 25)
Points (15, 25) and (18, 26)
Points (14, 25) and (16, 25)
Points (12, 24) and (18, 26)
Estimated Selling Price (in $1,000)
26.5
26-
25.5
25
24.5
24
23.5
10
11
12 13 14 15 16 17 18 19 20
Purchase Price (in $1,000)
The points on the scatter plot show the different predictions. The straight line drawn is called the line of regression.
Errors in prediction for each point can be determined by drawing a vertical line from the point to the line of regression. As seen in the image, all of the prediction points are found on the line except for points (14,25) and (16,25). Therefore, these points contain errors in prediction.
The graph that represent this data using the points is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The x and y values
Where
x = stars
y = price
To determine the graph that represent the data, we enter the x and y values in a graphing tool to create the graph
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Basic geometric shapes unit test part 2
Explain why m angle 4 is equal to the sun of the measure of the two nonadjancent interior angels
Angle 4 is equal to the sum of the measures of the two nonadjacent interior angles because of the corresponding angles theorem for parallel lines and a transversal.
Angle 4 can be considered as the sum of two nonadjacent interior angles because of the properties of parallel lines and a transversal line. When a transversal line intersects two parallel lines, it creates several pairs of corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles.
In this case, we have two parallel lines and a transversal line that intersects them.
Angle 4 is formed by the intersection of the transversal line with one of the parallel lines.
The two nonadjacent interior angles that we are interested in can be identified as the adjacent angles on the other parallel line, corresponding to the same transversal line.
According to the corresponding angles theorem, when two parallel lines are cut by a transversal line, the corresponding angles formed are congruent.
Therefore, the two nonadjacent interior angles that correspond to angle 4 are congruent.
Since congruent angles have the same measure, we can conclude that the measure of angle 4 is equal to the sum of the measures of the two nonadjacent interior angles.
This property holds true for any pair of parallel lines intersected by a transversal line.
It is a fundamental concept in geometry that helps us understand the relationships between angles formed by parallel lines and transversals, and it is useful in solving various geometric problems and proofs.
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If elephant grass grows 2 3/5
inches a day, how many inches will it grow in 7 days?
Fill in the table for the relation y = x^2 + 2x + 11.
y-intercept:
x-intercept(s):
axis of symmetry:
vertex:
domain:
range:
The table is attached below.
The given equation is,
y = x² + 2x + 11
The given equation is a quadratic equation
Now to find X intercept put y = 0
⇒ x² + 2x + 11 = 0
Now the discriminant is,
⇒ 2² - 4x1x11 = -11 < 0
Hence there is no real solution,
Thus,
There is no x intercept.
To find Y axis is,
put x = 0
y = 11
Hence the y intercept is 11
Now plot the graph of the given equation to find the axis of symmetry.
Then we get line of symmetry is x = -1
Domain: real number
Range : [10 , ∞)
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Adriana Graphic Design receives $1,650 from a client billed in a previous month for services provided. Which of the following general journal entries will Adriana Graphic Design make to record this transaction? Question 6 options: Account Title Debit Credit Cash 1,650 Accounts Receivable 1,650 Account Title Debit Credit Cash 1,650 Unearned Revenue 1,650 Account Title Debit Credit Accounts Receivable 1,650 Unearned Revenue 1,650 Account Title Debit Credit Accounts Payable 1,650 Design Revenue 1,650
The general journal entries Adriana Graphic Design should record the transaction as; Cash 1,650 Accounts Receivable 1,650.
Why should it fall under account receivable?When Adriana Graphic Design receives $1,650 from a client billed in a previous month for services provided, the firm is collecting an amount that was previously recognized as an account receivable.
In scenario provided, the firm will decrease its Accounts Receivable a debit entry, because Accounts Receivable is an asset account and assets decrease on the credit side and increase its - Cash account a credit entry, because Cash is also an asset account and assets increase on the debit side.
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Find slope of (- 6,1)and(8,-7)
The slope of the line passing through the points (-6, 1) and (8, -7) is -4/7.
What is the slope of the given points?Slope is simply expressed as change in y over the change in x.
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given the data in the question;
Point A: ( -6,1 )
x₁ = -6
y₁ = 1
Point B: ( 8,-7 )
x₂ = 8
y₂ = -7
Now, plug the given x and y values into the slope formula above and simplify:
[tex]Slope\ m = \frac{y_2 - y_1}{x_2 - x_1} \\\\Slope\ m = \frac{-7 - 1}{8 - (-6)} \\\\Slope\ m = \frac{-7 - 1}{8 + 6} \\\\Slope\ m = \frac{-8}{14} \\\\Slope\ m = -\frac{4}{7}[/tex]
Therefore, the slope of the line is -4/7.
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How would you find the volume of the figure represented by the given net? (Note: The area of each circular base is the same.)
Multiply (200.96)(22). or Add 1,105.28 + 200.96 + 22.
Answer:
(a) Multiply (200.96)(22).
Step-by-step explanation:
You want the volume of the cylinder with base area 200.96 mm² and height 22 mm.
VolumeThe volume is found using the formula ...
V = Bh
where B is the base area, and h is the height.
For base area 200.96 mm² and height 22 mm, the volume is ...
V = (200.96)(22) mm³
You find the volume by multiplying 200.96 and 22.
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Juan has twice as many video games as sam together they have 72 video games How many video games does Juan have
Answer: 48
Step-by-step explanation:
This isn't college
J=2S
J+S=72
3S=72
S=24
24*2=48
Juan has 48
Find all factors of polynomial
2x^3+x^2-2x-1; x+1
Answer:
The polynomial 2x^3 + x^2 - 2x - 1 can be factored as (x + 1)(2x^2 - x - 1).
Step-by-step explanation:
To find the factors of the polynomial 2x^3 + x^2 - 2x - 1, we can use synthetic division or long division to divide the polynomial by the factor x + 1.
Using synthetic division:
-1 | 2 1 -2 -1
| -2 1 1
___________________
2 -1 -1 0
The result of the division is 2x^2 - x - 1.
So, the polynomial 2x^3 + x^2 - 2x - 1 can be factored as (x + 1)(2x^2 - x - 1).
Answer:
Step-by-step explanation:
Solution
verified
Verified by Toppr
given, 2x
3
+x
2
−2x−1
=x
2
(2x+1)−1(2x+1)
=(x
2
−1)(2x+1)
=(x+1)(x−1)(2x+1)
complete the missing portions of the table. round to the nearest hundredth if necessary
The time period with the given principal, rate of interest and amount is 10 years.
Given that,
Principal = $1000, time period = 1 year and rate of interest =$40.
We know that, Simple interest = (Principal×Rate×Time)/100
48 = (1000×r×1)/100
4800=1000r
r=4800/1000
r=4.8%
Principal=$200, time period= 3 years and amount = $248
Simple interest = 248-200
= $48
48=(200×r×3)/100
4800=600r
r=4800/600
r=8%
Principal=$5000, rate of interest=2% and amount=$6000
Simple interest =6000-5000=$1000
Here, 1000=(5000×2×t)/100
1000=(100t)
t=10 years
Therefore, the time period with the given principal, rate of interest and amount is 10 years.
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Which of the following is the fourth vertex needed to create a rectangle with vertices located at (−4, −25), (−4, −12), and (−7, −12)?
(−12, 7)
(−7, −25)
(−7, 12)
(−25, 7)
Answer:
The fourth vertex needed to create the rectangle is (-7,-25).
Step-by-step explanation:
As per the property of a rectangle, the lengths of the opposite sides of a rectangle are the same.
Let,
point A=(-4,-25)
point B=(-4,-12)
point C=(-7,-12)
Thus, point D or the fourth vertex is (-7,-25).
Refer to the image for a better understanding.
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(-8x+10)-(3x to the power of 2 -x+6)
Simplification of the expression gives:
-3x² - 7x + 16
How to simplify algebraic expressions?Simplification is a way of determining an answer for a complex calculation that may involve numbers on division, multiplication, square roots, cube roots, plus and minus, etc.
We have the expression:
(-8x+10) - (3x²-x+6)
We can simplify as follow:
(-8x+10) - (3x²-x+6) = -8x+10 -3x²+x+6 (remove parenthesis)
= -3x² - 8x + x + 10 + 6 (collect like terms)
= -3x² - 7x + 16 (add/subtract like terms)
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Find m/JKL in OE.
A. 53°
B. 37°
C. 106°
D. 43°
L
E
74°
K
Answer:
A
Step-by-step explanation:
the inscribed angle JKL is half the measure of its intercepted arc
the sum of the arcs in a circle in a circle = 360°
since LK is a diameter the arc KL is equal to the measure of its central angle , that is
arc LK = 180° , then
LJ + JK + KL = 360°
LJ + 74° + 180° = 360°
LJ + 254° = 360° ( subtract 254° from both sides )
LJ = 106°
Then
∠ JKL = [tex]\frac{1}{2}[/tex] × 106° = 53°
|0.2x +0.6| <0.15
Answer quick
Answer(s):
Inequality Form:
-3.75 < x < -2.25
Interval Notation:
x ∈ ( -3.75, -2.25)
Step-by-step explanation:
Equation: |0.2x +0.6| <0.15
{0.2x + 0.6 > -0.15
{0.2x + 0.6 < 0.15
{(0.2x + 0.6) + (-0.6) > -0.15 + (-0.6)
{(0.2x + 0.6) + (-0.6) < 0.15 + (-0.6)
{0.2x + 0.6 - 0.6 > -0.15 - 0.6
{0.2x + 0.6 - 0.6 < 0.15 - 0.6
{0.2x > - 0.75
{0.2x < -0.45
{0.2x / 0.2 > - 0.75/0.2
{0.2x / 0.2 < - 0.45/0.2
{x > - 0.75/0.2
{x < - 0.45/0.2
{x > -3.75
{x < -2.25
-3.75 < x < -2.25
Answer: x ∈ ( -3.75, -2.25)
Hope this helps!
Daniel went to a petrol store and bought 15 litres of petrol for £24
Did he go to store X or store Y?
How much would 20 litres of petrol cost at the same station?
He went to station Y, and the cost for 20 liters is 32 pounds.
Did he go to store X or store Y?Here we know taht Daniel went to a petrol store, and bought 15 L of petrol for 24 pounds.
So we need to use the graphs of the linear relations to see which store he went to.
We can see that in store X, for 15L the cost is 28 pounds, and for store Y the cost is 24 pounds.
So the correct option is Y.
Now, for 20 litres in that station, (using the same graph) we can see that the cost will be C= 32 pounds.
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WILL MARK BRAINLIEST!!
In a baseball game, a batter standing at home plate sees the second baseman standing on the baseline between 1st and 2nd base as shown in the figure.
If θ=14∘, how far is the second baseman from second base?
Round to the nearest hundredth.
The distance to second base is approximately _________ feet.
The distance to second base is approximately 127.28 feet. Round to the nearest hundredth
How to determine the distance to second baseSince the angle is 45 degrees, the other side of the right triangle are equal, hence we have two sides of 90 ft to be used to find the hypotenuse
Using Pythagoras theorem given by the the formula
hypotenuse² = opposite² + adjacent²
plugging the values as in the problem
let x be the required distance
x² = 90² + 90²
x² = 16200
x = √16200
x = 90√2
x = 127.28 ft (to the nearest hundredth)
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PLEASE HELP!!!!!!
The box plot displays the number of flowers planted in a town last summer.
10
Flowers Planted In Town
13 14 15 16 17 18 19 20 21 22 23 24
Number of Flowers
Which of the following is the best measure of center for the data shown, and what is that value?
O The mean is the best measure of center and equals 12.
O The mean is the best measure of center and equals 10.
The median is the best measure of center and equals 12.
30 31
The median is the best measure of center and equals 10.
The best measure of center for the data shown is the median, and its value is 17.
The median is the best measure of center for the given data set. To find the median, we arrange the numbers in ascending order:
10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24
Since the data set has an odd number of values, the median is the middle value, which in this case is 17.
Therefore, the best measure of center for the data shown is the median, and its value is 17.
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answer the question on ixl I got
The first three pairs are of vertically opposite angles.
Given figure,
Vertical angles are the angles that are opposite to each other.
Hence the pairs of vertical angles will be opposite to each other as well as will be equal to each other.
So,
Vertical opposite angles are :
Option A
Option B
Option C
Thus 3 pairs will be considered for vertical angles .
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In the equation (x-3)²+(y-2)2=16, the radius of the circle is...
16
3
32
4
Step-by-step explanation:
This is of the form
(x-h)^2 + ( y-k)^2 = r^2 so r^2 = 16 means r = 4 units
A publishing company conducted a survey asking readers whether they use e readers. Of the 3000 readers surveyed, 1954 said they read books on e reader. The approximate sample proportion is? Which means that? %of the readers surveyed don’t use e readers
Approximately 34.87% of the readers surveyed don't use e-readers.
To find the approximate sample proportion of readers who use e-readers, we divide the number of readers who said they read books on e-readers (1954) by the total number of readers surveyed (3000):
Approximate sample proportion = Number of readers who use e-readers / Total number of readers surveyed
Approximate sample proportion = 1954 / 3000 ≈ 0.6513
To express this as a percentage, we multiply the sample proportion by 100:
Approximate sample proportion as a percentage = 0.6513 × 100
= 65.13%
Therefore, the approximate sample proportion of readers who use e-readers is approximately 65.13%.
This means that approximately 65.13% of the readers surveyed use e-readers.
To determine the percentage of readers who don't use e-readers, we subtract the sample proportion from 100%:
Percentage of readers who don't use e-readers = 100% - 65.13%
= 34.87%
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Convert the rectangular coordinates (5, 5√3) to polar coordinates, (r,θ), where r is positive and θ is expressed in radians and in the interval [0,2π)
*please answer in an ordered pair*
The polar coordinates (r, θ) for the given rectangular coordinates are
(10, π/3)
How to convert the coordinatesTo convert rectangular coordinates (5, 5√3) to polar coordinates (r, θ), we can use the following formulas:
r = √(x² + y²)
θ = arc tan (y/x)
Given the rectangular coordinates (5, 5√3), we have:
x = 5
y = 5√3
let's calculate the values
r = √(5² + (5√3)²
= √(25 + 75)
= √100
= 10
θ = arctan(5√3/5)
= arctan (√3)
= π/3 (since θ is in the interval [0,2π))
Therefore, the polar coordinates (r, θ) for the given rectangular coordinates are (10, π/3).
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Find m/DBC in OB.
A. 56°
B. 34°
C. 68°
D.
112°
A
B
D
68°
C
The measure of central angle DBC is 68 degree.
Hence, option C is correct.
In the given figure,
Measure of intercepted arc = 68 degree,
We have to find the measure of central angle DBC
We know that,
When two circle radii intersect in the center of a circle, they produce a vertex. These circle arms may begin at two distinct positions along the arc of such a circle. The two radii cross to produce a central angle, which serves to divide a circle into separate sectors.
A central angle is generated in the center of a circle when two radii within the circle overlap. As previously stated, a central angle in geometry is one whose vertex forms at the canter of the circle and whose arms cross the circle at two separate positions.
By connecting these two locations, an arc on the circle is formed. As a result, a central angle is the angle formed by an arc in the center of a circle.
Thus by property of central angles,
central angle = measure of intercepted arc
Hence,
⇒ m ∠DBC = 68 degree.
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Drag the tiles to the correct boxes to complete the pairs.
Add each pair of monomials and match it to the correct sum.
-15u³ +5u³
10u³+(-5u³)
-10³
-5u³
5²³
3
15u³
10u³+5u³ 5u³+ (-10u³)
100
The correct matches are:
-10u³ ⇒ -15u³ + 5u³
5u³ ⇒ 10u³ + (-5u³)
15u³ ⇒ 10u³ + 5u³
-5u³ ⇒ 5u³ + (-10u³)
For the expressions:
Expression 1:
-15u³ + 5u³
To add these expression taking u³,
⇒ (-15 + 5)u³
⇒ -10u³
Expression 2:
⇒ 10u³ + (-5u³)
To add these expression taking u³
⇒ (10 - 5)u³
⇒ 5u³
Expression 3:
⇒ 10u³ + 5u³
To add these expression taking u³
⇒ 15u³
Expression 4:
⇒ 5u³ + (-10u³)
To add these expression taking u³
⇒ (5 - 10)u³
⇒ -5u³
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The complete question is attached below:
-3 1/4 divided by 2 1/3
Answer:
Hi
Please mark brainliest ❣️
Step-by-step explanation:
-3 1/4 ÷ 2 1/3
Change to improper fraction
-13/4 ÷ 7/3
-13/4 × 3/7
-39/28 or -1 11/28
Ricardo invests $1500 into an account that earns interest compounded quarterly. After 10 years, he has $2721.03. What was' his annual interest rate?
Ricardo's annual interest rate is equal to 6%.
How to determine Ricardo's annual interest rate?In Mathematics and Financial accounting, compound interest can be calculated by using the following mathematical equation (formula):
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where:
A represents the future value.n represents the number of times compounded.P represents the principal.r represents the interest rate.t represents the time measured in years.By substituting the given parameters into the formula for compound interest, we have the following;
[tex]2721.03 = 1500(1 + \frac{r}{4})^{4 \times 10}\\\\1.81402=(1 + \frac{r}{4})^{40}[/tex]
By taking 40th root of both sides of the equation, we have:
1.01500002226 = 1 + r/4
r/4 = 1.01500002226 - 1
r = 0.01500002226 × 4
Interest rate, r = 0.06 × 100
Interest rate, r = 6%.
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Oliver spends $200 to produce some pineapples. He is able to sell each one for $6. If p represents the number of pineapples he must sell to make a profit, write an inequality and solve for p. Do not round your answer.
The inequality to solve for p is 6p > 600 and the solution is p > 100
How to write an inequality and solve for pFrom the question, we have the following parameters that can be used in our computation:
Selling price = $6 per apple
So, we have
Total = 6p
Also, we have
Spendings = $600
To make profit, we have
6p > 600
Divide by 6
p > 100
Hence, the inequality to solve for p is 6p > 600 and the solution is p > 100
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Which is the
4
graph of f(x) = 4[*?
-3-2--1₁-
-2-
2 3 4 5 6
4
1
1-2--11-
-2
2 3
56
4
2-11.
-2-
23
56
Option 2 is the correct graph for the function f(x) = [tex]4[(1/2)^{x}][/tex] .
Given ,
f(x) = [tex]4[(1/2)^{x}][/tex]
Mathematically the graph will of exponential in nature.
So,
Let us assume few values to understand the nature of graph.
Firstly,
Let x= 1
f(x) = [tex]4[(1/2)^{1}][/tex]
f(x) = 2
Let x = 2
f(x) = [tex]4[(1/2)^{2}][/tex]
f(x) = 1
Let x = 3
f(x) = [tex]4[(1/2)^{3}][/tex]
f(x) = 0.5
Thus from these values of f(x) corresponding to the values of x second graph will be correct .
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What is the surface area of the triangular prism 4 ft 5 ft 2 ft 3 ft
The surface area of the triangular prism is 137ft².
What is the surface area of the triangular prism?To get the surface area of a triangular prism, we will calculate the area of each face and then sum them up.
Base area = (4 ft * 5 ft) / 2
Base area = 20ft/2
Base area = 10 ft²
Since triangular prism has two triangular bases, the total area of the triangular bases is:
= 2 * Base area
= 2 * 10 ft²
= 20 ft².
Perimeter of the triangular base:
= 4 ft + 5 ft + 4 ft
= 13 ft
Face area = Perimeter * Height
Face area = 13 ft * 3 ft
Face area = 39 ft²
The total area of the rectangular faces is:
= 3 * Face area
= 3 * 39 ft²
= 117 ft².
The Surface area of the triangular prism will be:
= Total area of triangular bases + Total area of rectangular faces
= 20 ft² + 117 ft²
= 137 ft².
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