1. If f(x) and g(x) are inverse functions, then f(g(x)) = g(f(x)) = x. Finding the composite of the two functions will tell you if they are inverses.
2. To find the inverse of a function, swap x and y, then solve for y.
... x = 3y
... x/3 = y . . . . . matches f(x) = x/3
3. A function will pass the vertical line test. If its inverse is also a function, that, too, will pass the vertical line test. Since the inverse of a function is that function reflected across y=x, any inverse function that passes the vertical line test corresponds to an original function that passes the horizontal line test. (A vertical line reflected across y=x is a horizontal line.)
4. See 2.
... x = 3(y -2)³
... (x/3) = (y -2)³ . . . . divide by 3
... ∛(x/3) = y -2 . . . . .take the cube root
... 2+∛(x/3) = y . . . . .add 2
... f(x) = 2+∛(x/3) . . . . is the inverse
5. See 2.
... x = 2y -3
... x+3 = 2y . . . . . add 3
... (x+3)/2 = y . . . .divide by 2
... f(x) = (x+3)/2 . . . . is the inverse
A composite function is the combination of multiple functions.
The correct answers are:
Find the composite of the functions. The inverse of f(x) = 3x is [tex]f'(x) = \frac x3[/tex].All answers are trueThe inverse of [tex]f(x) = 3(x - 2)^3[/tex] is: [tex]f^{-1}(x) =2 + \sqrt[3]{\frac x3}[/tex]The inverse of [tex]f(x) =2x - 3[/tex] is [tex]f^{-1}(x) = \frac{x + 3}{2}[/tex]1. Test for inverse function
To test if two functions are inverse of one another, we simply find their composites.
Assume the functions are g(x) and h(x).
We simply test for [tex]g(h^{-1}(x))[/tex] and [tex]h(g^{-1}(x))[/tex]
If they are equal, then both functions are inverse functions
2. Inverse of f(x) = 3x
Rewrite as:
[tex]y = 3x[/tex]
Swap y and x
[tex]x = 3y[/tex]
Make y the subject
[tex]y = \frac x3[/tex]
Hence, the inverse function is: [tex]f'(x) = \frac x3[/tex]
3. True statements
A function has unique ordered pairs; so, it will pass the vertical line test.
Because it has unique ordered pairs, the inverse function will pass the vertical line tests, and the horizontal line tests.
Hence;
(b) All answers are correct
4. Inverse of [tex]f(x) = 3(x - 2)^3[/tex]
Rewrite as:
[tex]y = 3(x - 2)^3[/tex]
Swap x and y
[tex]x = 3(y - 2)^3[/tex]
Solve for y: Divide both sides by 3
[tex](y -2)^3 = \frac x3[/tex]
Take cube roots of both sides
[tex]y -2 = \sqrt[3]{\frac x3}[/tex]
Add 2 to both sides
[tex]y =2 + \sqrt[3]{\frac x3}[/tex]
Hence, the inverse function is: [tex]f^{-1}(x) =2 + \sqrt[3]{\frac x3}[/tex]
5. The inverse of [tex]f(x) =2x - 3[/tex]
Rewrite as:
[tex]y =2x - 3[/tex]
Swap x and y
[tex]x =2y - 3[/tex]
Solve for y: Add 3 to both sides
[tex]2y = x + 3[/tex]
Divide both sides by 2
[tex]y = \frac{x + 3}{2}[/tex]
Hence, the inverse function is: [tex]f^{-1}(x) = \frac{x + 3}{2}[/tex]
Read more about inverse functions at:
https://brainly.com/question/10300045
I want to know the value
Answer:
x = 2/5
Step-by-step explanation:
[tex]x^3=\dfrac{0.008}{0.125}=\dfrac{8}{125}=\dfrac{2^3}{5^3}\\\\x=\sqrt[3]{\dfrac{2^3}{5^3}}=\dfrac{\sqrt[3]{2^3}}{\sqrt[3]{5^3}}=\dfrac{2}{5}[/tex]
The value of x is 2/5.
Answer:
x = 2/5
Step-by-step explanation:
x^3 = .008/.125
Take the cubed root on each side
x^3 ^ (1/3) = (.008/.125) ^ 1/3
Using ( a/b) ^c = a^c / b^c and a^b^c = a^ (b*c)
x^(3 *(1/3)) = (.008) ^ 1/3 / (.125) ^ 1/3
x = (.008) ^ 1/3 / (.125) ^ 1/3
x = .2/.5
x = 2/5
A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror. The pipe is located 7 inches from the vertex of the mirror. Write an equation of the parabola that models the cross section of the mirror. Assume that the parabola opens upward.
A y=1/28x^2
B y=1/42x^2
C y=1/35x^2
D y=1/49x^2
Answer:
[tex]y= \frac{1}{28} x^2[/tex]
Step-by-step explanation:
A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror.
The pipe is located 7 inches from the vertex of the mirror.
The parabola is open upwards . the vertex of the parabola is (0,0)
and pipe is located 7 inches from the vertex (0,0)
7 inches is the focus of the mirror
The distance between the vertex and the focus = 7
Since parabola is upwards and vertex is (0,0) we use formula
[tex]4py = x^2[/tex]
Where p is the distance between the vertex and focus
p = 7 we know
[tex]4*7*y = x^2[/tex]
[tex]28y = x^2[/tex]
Now isolate y by dividing 28 on both sides
[tex]y= \frac{1}{28} x^2[/tex]
Simplify the polynomial by combining like terms.
xy−3x^3y−4xy^2+3x^2+7x^3y
Answer:
it should be 4x^3 y-4xy^2+xy+3x^2
Step-by-step explanation:
A ____________ has no dimension and is represented by a small dot.
Answer:
Point
Step-by-step explanation:
If you are referring to geometry
-7=7d-8 solve for the variable d
-7 = 7d - 8
Add 8 to both sides.
1 = 7d
Divide both sides by 7.
d = 1/7A tortoise is walking in the desert. It walks for 7.5 meters at a speed of 3 meters per minute. For how many minutes does it walk?
Answer:
2.5 min
Step-by-step explanation:
The tortoise takes 1 min/3 m.
7.5 × 1/3 = 2.5 min
A group of hikers buys 8 bags of mixed nuts. Each bag contains 3 1/2 cups of nixed nuts. The mixed nuts are shared evenly among 12 hikers. How many cups of mixed nuts will each hiker receive?
Answer:
Each hiker gets [tex]\frac{7}{3}[/tex] cups of mixed nuts.
Step-by-step explanation:
First, we need to find the total amount of cups by multiplying the number of bags with the amount of cups in each bag:
8 * 3.5 = 28
Now, we divide this by 12 to find the amount of cups per hiker:
28 ÷ 12 = [tex]\frac{7}{3}[/tex] or 2.3333
So each hiker gets [tex]\frac{7}{3}[/tex] cups of mixed nuts.
Find the rational roots of x^4 + 3x^3 + 3x^2 - 3x - 4 = 0
0, 1
1, 2
1, -1
-1, 2
Answer:
C. 1,-1
Step-by-step explanation:
The sum of the coefficient is 0 so x=1 is a root and (x-1) as a factor
so x^4+3x^3+3x^2-3X-4=(x-1)(x^3+4x^2+7x+4)
and the root of that is x=-1 and the factor is (x+1)
SO the answer is: x=1 and x=-1
Answer: -1, 1
Step-by-step explanation:
To solve the polynomial equation x^4 + 3x^3 + 3x^2 - 3x - 4 = 0, do a quick test of polynomials using 1 and -1 in place of x.
This gives the sum of coefficients as zero
Testing with 1: 1 + 3 + 3 - 3 - 4 = 0
Testing with -1: 1 + (-3) + 3 - (-3) - 4
= 1 - 3 + 3 + 3 - 4 = 0
This gives that both (x + 1) and (x - 1) are roots.
(x + 1)(x - 1) = x² - 1 {difference of two squares}
Dividing the polynomial x^4 + 3x^3 + 3x^2 - 3x - 4 by (x² - 1) results in x² - 3x + 4 as quotient. Factorizing this result would give complex roots.
Therefore, x² - 1 = 0
x² = 1
Taking square of both sides of the equation gives
x = ± 1
1 and -1 are the rational roots to the polynomial.
Which point on the graph is a direct variation equation in which k=12.4
(4,49.6)
(49.6,4)
(4,3.1)
3.1,4)
Answer:
The correct answer would be A) (4, 49.6)
Step-by-step explanation:
In order to find the equation, we first have to start with the base form of direct variation.
y = kx
Now we input the k value.
y = 12.4x
Now that we have this, we can try the ordered pairs and look for which satisfies the equation.
y = 12.4x
49.4 = 12.4(4)
49.4 = 49.4
Since this is the true statement, this is the ordered pair that works.
Answer:
(4,49.6)
Step-by-step explanation:
Choose the expression that mathematically represents the difference between ‘3 times a number’ and the quantity ‘5 times another number less 7’
a. 3x − (7 − 5x)
b. 3x − (5y − 7)
c. 3x − (5x − 7)
d. 3x − (7 − 5y)
Answer:
b. 3x - (5y -7)
Step-by-step explanation:
Let x represent "a number". Let y represent "another number."
The "3 times a number" is represented by 3x.
And "5 times another number less 7" is represented by 5y -7.
The difference between these quantities is the second subtracted from the first:
... 3x - (5y -7) . . . . matches selection b.
−5y=−5 THANKS
7x+6y=7
Is (5,1) a solution of the system?
Answer:
{x = 1/7 ,y = 1
Step-by-step explanation:
Solve the following system:
{-5 y = -5 | (equation 1)
{7 x + 6 y = 7 | (equation 2)
Swap equation 1 with equation 2:
{7 x + 6 y = 7 | (equation 1)
{0 x - 5 y = -5 | (equation 2)
Divide equation 2 by -5:
{7 x + 6 y = 7 | (equation 1)
{0 x+y = 1 | (equation 2)
Subtract 6 × (equation 2) from equation 1:
{7 x+0 y = 1 | (equation 1)
{0 x+y = 1 | (equation 2)
Divide equation 1 by 7:
{x+0 y = 1/7 | (equation 1)
{0 x+y = 1 | (equation 2)
Collect results: Answer: {x = 1/7 ,y = 1
Answer:
No
Step-by-step explanation:
The next test will be a hundred points total, but only forty questions will be asked. Some questions are worth two points each and the rest are four points each. How many of each questions is there?
Answer:
10 questions that are 4-point30 questions that are 2-pointStep-by-step explanation:
Numerical reasoning
If all questions were 2-point, the total score would be 80. It is 20 more than that. Each 4-point question that replaces a 2-point question will add 2 points to the score, so there must be 20/2 = 10 of them.
There are 10 4-point questions and 30 2-point questions.
_____
With an equation
Let x represent the number of 4-point questions. Then 40-x is the number of 2-point questions. The total number of points is ...
... 2(40-x) +4x = 100
... 2x +80 = 100 . . . . simplify
... 2x = 20 . . . . . . . . .subtract 80
... x = 10 . . . . . . . . . . divide by 2.
There are 10 4-point questions and 40-10=30 2-point questions.
Jason jumps from a plane at an altitude of 1000 m. His parachute opens after 10 seconds. The graph shows the relationship between the distance traveled and time. How far does he fall in 1 minute and 20 seconds? Continuous graph with the y axis labeled Distance (m) and the x axis labeled Time, min. The function consists of 3 lines, the first is almost vertical with a positive slope connecting the points 0,0, to approximately 1 of 6, 250. From that point the second line connects to the first and passes through the points 1,500, 2,800 and 2 1 over 3, 1000. From that point the function is horizontal.
600 m
Step-by-step explanation:The slope between 1 minute and 2 minutes is ...
... (800 -500)/(2 -1) = 300 . . . . . . m/min
Thus in 20 seconds, 1/3 minute, Jason will fall ...
... (1/3 min)·(300 m/min) = 100 m
This distance is in addition to the 500 m he has already fallen in the first minute.
In 1 min 20 sec, Jason falls 500 m + 100 m = 600 m.
_____
Comment on the graph
We don't expect Jason's rate of fall to change dramatically at the 2-minute mark. We suspect the last point should be (2 2/3, 1000).
What is the value of x?
Enter your answer in the box.
Since QC and BR are parallel, triangles CDQ and BDR are similar.
This means that corresponding sides are in proportion, so we have
[tex] BD \div QD = RD \div CD [/tex]
Substituting numbers, we have
[tex] 26+39 \div 39 = 18+x \div x \iff \dfrac{65}{39} = \dfrac{18+x}{x} [/tex]
Multiply both sides by [tex] 39x [/tex]
[tex] 65x = 39(18+x) [/tex]
Expand right hand side:
[tex] 65x = 702 + 39x [/tex]
Subtract 39x from both sides:
[tex] 26x = 702 [/tex]
Divide both sides by 26
[tex] x = \dfrac{702}{26} = 27 [/tex]
Just took the test and got the the correct answer *\(♡°▽°♡)/*
Look at the image down below!!
Krys bought x boxes of pastries to bring to a party. Each box contains 12 pastries. She decides to keep two boxes for herself. She brings 60 pastries to the party. Which equation can be used to find the number of boxes, x, Krys bought? a. 2x − 12 = 60 b. 12x − 2 = 60 c. 12x − 24 = 60 d. 24 − 12x = 60
Answer:
c. 12x − 24 = 60
Step-by-step explanation:
x is the number of boxes Krys bought.
12x is the number of pastries in those boxes. 2·12 = 24 is the number of pastries in the boxes Krys kept for herself. Then the number of pastries Krys brought to the party is ....
... 12x -24
We are told that number is 60, so we can use this equation to find x:
... 12x -24 = 60
Answer:
Option C : 12x − 24 =60
Step-by-step explanation:
Given :
Krys bought x boxes of pastries to bring to a party.
Each box contains 12 pastries.
She decides to keep two boxes for herself.
She brings 60 pastries to the party.
To Find : Equation can be used to find the number of boxes, x, Krys bought.
Solution :
Krys bought x boxes of pastries .
Each box contains 12 pastries.
So, total pastries she bought = 12 x
She decides to keep two boxes for herself.
Since 1 box contain 12 pastries .
Thus two box contains pastries = 12*2 =24 pastries
Now total pastries she bought is 12 x . Out of which she decides to keep 24 pastries . after keeping 24 pastries from 12 x pastries she bought 60 pastries to the party i.e.
⇒ 12 x - 24 = 60
Thus,Equation can be used to find the number of boxes, x, Krys bought:
12 x - 24 = 60
Hence Option C is correct .
A scientist is studying bacteria and records the number of bacteria over time. The scientists determines that the function N(t)=300(1.30) models the number of bacteria, N after t hours.
Which statement correctly interprets this model.
A. The number of bacteria is originally 300 and increases by 30%
B. The number of bacteria is originally 300 and decreases by 30 every hour
C. The number of bacteria is originally 30 and increases by 300 every hour
D. The number of bacteria is originally 30 and decreases by 300% every hour
Answer:
(A) The number of bacteria is originally 300 and increases by 30% every hour
Step-by-step explanation:
I am assuming the function should actually read:
[tex]N(t)=300\cdot 1.30^t[/tex]
(i.e., there should be a "t" in the exponent. if this is not the case please disregard my answer).
According to the above exponential function, the initial amount 300 grows as (1+0.3)*300=300+0.3*300. In other words it increases by 30% every hour (t).
Your answer choice (A) is likely a candidate, except I am missing "every hour" at the end (again, am assuming this was omitted by mistake)
Final answer:
The function N(t)=300(1.30)^t represents the bacterial growth model where the initial amount of bacteria is 300 and increases by 30% every hour.
Explanation:
Looking at the function N(t)=300(1.30)^t, this model describes the number of bacteria, N, after t hours. The base number, 300, indicates the initial quantity of bacteria, while the term (1.30)^t suggests that the population changes by a factor of 1.30 each hour, reflecting a 30% increase in the number of bacteria each hour. Therefore, the correct statement that interprets this model is:
A. The number of bacteria is originally 300 and increases by 30% each hour.
A triangle has vertices located at the coordinates (17,-3), (-7,11) and (17,11). What is the area of the triangle?
A. 40 sq units
B. 70 sq units
C. 96 sq units
D. 144 sq units
E. 168 sq units
E. 168 sq units
Step-by-step explanation:The legs of this right triangle have length 24 and 14, so the area is ...
... A = (1/2)bh = (1/2)(24)(14) = 168 . . . . sq units
The science club sold 24 t-shirts last week and 18 T-shirts this week. What is the percentage of decrease in the number of T-shirts sold?
a) 33%
b) 25%
c) 50%
d) 75%
Answer:
D) 75%
Step-by-step explanation:
75% of 24 = 0.75 x 24 = 18
help me plz i will apreciate
What is 9.36•10~4 in standard form
The number 9.36×10-4 in standard form is 0.000936. You convert from scientific notation to standard form by moving the decimal point to the left by the number equivalent to the exponent when the exponent is negative.
Explanation:
When asked what is 9.36×10-4 in standard form, we are being asked to convert a number from scientific notation to its regular number format. Scientific notation is a method of writing numbers that are too big or too small to be conveniently written in decimal form. To convert this to standard form, we move the decimal point to the left if the exponent is negative (or to the right if the exponent is positive) as many times as the value of the exponent.
In this case, we have a negative exponent (-4), so we move the decimal four places to the left:
9.36 -> 0.936 -> 0.0936 -> 0.00936 -> 0.000936
Therefore, 9.36×10-4 in standard form is 0.000936.
Write the equation for the parabola that has x− intercepts (−2−√2 ,0) and (−2+√2 ,0) and passes through the point(−1,1).
Answer:
f(x)= -x²-4x-2
Step-by-step explanation (this way is not the shortest one):
1. for intercept (-2-√2;0): a(-2-√2)²+b(-2-√2)+c=0
for intercept (-2+√2;0): a(-2+√2)²+b(-2+√2)+c=0
for the point (-1;1): a(-1)²+b(-1)+c=1
2. using the three record written above, it is possible to make up the system of equations and calculate 'a', 'b' and 'c':
[tex]\left \{ \begin{array}{ccc}a-b+c=1\\a(-2- \sqrt2)^2+b(-2- \sqrt2)+c=0\\a(-2+ \sqrt2)^2+b(-2+ \sqrt2)+c=0\end{array}[/tex]
[tex]\left \{ \begin{array}{ccc}a=-1\\b=-4 \\c=-2\end{array}[/tex]
3. the required equation is: -x²-4x-2
- 1 (multiplicity 3), 3 (multiplicity 4)
Answer:
-1,81
Step-by-step explanation:
Multiplicity of a number can be written as power
for example
-1(multiplicity 3) can be written as
[tex]-1^{3}[/tex]= -1
similiarly 3(multiplicity 4) can be written as
[tex]3^{4}[/tex]=81
The eleventh-degree polynomial (x + 3)4(x – 2)7 has the same zeroes as did the quadratic, but in this case, the x = –3 solution has multiplicity 4 because the factor (x + 3) occurs four times (that is, the factor is raised to the fourth power) and the x = 2 solution has multiplicity 7 because the factor (x – 2) occurs ... Can you do the rest on your own?
What would be the answer please help
PLZ HELP ASAP WILL MARK BRAINIEST
QUESTION 39
|-4| is a solution of x ≤ 4
True
False
QUESTION 43
The point (5, -1) is a solution of the equation: y = 2x − 11
True
False
Answer:
Question 39: False
Question 43: True
Step-by-step explanation:
Question 39
|-4| is a solution of x ≤ 4
|-4| ⇒ This mean the absolute value of 4. The sign s are neglected.
So, |-4| is not a solution of x ≤ 4.
Question 43
The point (5, -1) is a solution of the equation: y = 2x − 11.
To prove this we are to substitute the point (5, -1) in the equation y = 2x − 11.
y = -1 and x = 5
y = 2x − 11 ⇒ -1 = 2(5) -11
-1 = 10 - 11
-1 = -1
76.8% of what number is 32.64
Answer:
42.5
Step-by-step explanation:
76.8% × ? = 32.64
? =
32.64 ÷ 76.8% =
32.64 ÷ (76.8 ÷ 100) =
(100 × 32.64) ÷ 76.8 =
3,264 ÷ 76.8 =
42.5
To solve for the number that 76.8% of it equals 32.64, you can write an equation and solve for x: 0.768 * x = 32.64. Dividing both sides by 0.768 gives x = 42.5.
Explanation:The question asks about a percentage of a number, which is a math concept. If 76.8% of a number equals 32.64, you can use basic algebra to find that number. Let's call it 'x'. You can write it as an equation: 0.768 * x = 32.64. Solving for x, divide both sides of the equation by 0.768.
x = 32.64 /0.768
When you perform this calculation, you'll find that x is approximately 42.5. So, 76.8% of 42.5 is approximately 32.64.
Learn more about Percentage Calculation here:https://brainly.com/question/32197511
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Why is partitioning a directed line segment into a ratio of 1:3 not the same as finding 1/3 the length of the directed line segment?
The ratio given is part to whole, but fractions compare part to part.
The ratio given is part to part. The total number of parts in the whole is 3 – 1 = 2.
The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4.
The ratio given is part to whole, but the associated fraction is 1/3.
Answer:
The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4.
Step-by-step explanation:
I like to call the numbers in the ratio 1 : 3 "ratio units".
That is, the short length is 1 ratio unit long, and the longer length is 3 ratio units long. The total (whole) length is 1+3 = 4 ratio units long. Then the short length (1 ratio unit) is 1/4 of the whole length (4 ratio units).
_____
Coment on the answer wording
I think you need to be careful with terminology. The word "part" has a different meaning in the first answer sentence "... part to part" than it does in the second answer sentence "... parts in the whole ...".
In the first sentence, it refers to "a piece of the line, no matter its length." In the second sentence, it refers to "that length of the line represented by 1 in the ratio."
Using the Law of Detachment, find the conclusion for the following: If two triangles are similar, then their corresponding angles are congruent.
Triangle ABC and Triangle XYZ are similar.
Question 8 options:
AB≅XY
ABC≅XYZ
The statements are not valid.
Answer:
∠ABC ≅ ∠XYZ
Step-by-step explanation:
Given: ΔABC is similar to ΔXYZ.
If two triangles are similar, then
1. the corresponding angles are congruent
2. the corresponding sides are proportional
From the options given,
AB ≅ XY is not applicable for similar triangles. Hence the option is wrong.
∠ABC ≅ ∠XYZ since ΔABC ≅ ΔXYZ
Hence the answer is ∠ABC ≅ ∠XYZ
The sum of two numbers is 66 and the difference is 8 . What are the numbers?
Answer:
X = 37
Y = 29
Step-by-step explanation:
X + Y = 66
X - Y = 8
------
Solve second equation for X
X = Y + 8
Substitute for X in first equation
Y + 8 + Y = 66
2 * Y = 58
Y = 29
___
X - 29 = 8
X = 37
X = 37
Y = 29
Good Luck,
- I.A. -
Answer:
x = 37 and y = 29
Step-by-step explanation:
x + y = 66
x - y = 8
solve second equation for x
x = y + 8
substitute for x in first equation
y+8 +y = 66
2y = 58
y = 29
x - 29 = 8
x = 37
x = 37 and y = 29
Frog A eats 8 flies in 4 minutes, while Frog B eats 14 flies in 7 minutes. Which frog eats more flies per minute?
Neither one
Step-by-step explanation:Frog A's "unit rate" is ...
... (8 flies)/(4 minutes) = 2 flies/minute
Frog B's "unit rate" is ...
... (14 flies)/(7 minutes) = 2 flies/minute
Both rates are the same. Each frog eats 2 flies per minute.
Answer:
i dont like frogs
Step-by-step explanation:
The lengths of the sides of a triangle are 15 cm, 20 cm, 30 cm. What are the lengths of the sides of a similar triangle that has a perimeter of 26 cm ?
Answer:
6 cm,12 cm,8 cm
Step-by-step explanation:
add the perimeter of the first triangle to get 65
then divide 65 by 26 to get 2.5
then divide all the side lengths by 2.5
15/2.5=6
20/2.5=8
30/2.5=12
The lengths of the sides of a similar triangle that has a perimeter of 26 cm are 6 cm, 8 cm, and 12 cm and this can be determined by using the given data.
Given :
The lengths of the sides of a triangle are 15 cm, 20 cm, 30 cm.
The following steps can be used in order to determine the lengths of the sides of a similar triangle that has a perimeter of 26 cm:
Step 1 - The formula of the perimeter of the triangle is given below:
[tex]\rm P = a + b + c[/tex]
where a, b, and c are the length of the sides of the triangle.
Step 2 - Now, determine the perimeter of the triangle whose sides are 15 cm, 20 cm, 30 cm.
P' = 15 + 20 + 30
P' = 65 cm
Step 3 - Now, divide both the perimeters of the triangles, that is:
[tex]=\dfrac{65}{26}[/tex]
= 2.5
Step 4 - So, the side length of the sides of a similar triangle is given below:
[tex]\rm \dfrac{15}{2.5} = 6\;cm[/tex]
[tex]\rm \dfrac{20}{2.5}=8 \;cm[/tex]
[tex]\rm \dfrac{30}{2.5}=12\;cm[/tex]
For more information, refer to the link given below:
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