If the graph shows a constant function, the value of f(x) will always be the same no matter which value does x take. It means: to graph the transformation of this function do an horizontal translation right 3 units (which would show the same graph, basically) and then do a vertical translation up 2 units
Solve the right triangle. Write your answers in simplified, rationalized form. DO NOT ROUND!
base = FG = root 30
perpendicular HG = x
angle = 45 degrees,
we know that
[tex]\text{tan}\theta=\frac{perpendicualr}{base}[/tex][tex]\tan 45=\frac{HG}{\sqrt[]{3}}[/tex][tex]\begin{gathered} 1=\frac{HG}{\sqrt[]{3}} \\ HG=\sqrt[]{3} \end{gathered}[/tex]so, the value of HG = root 3
I need help with my statistics homework " -compute the range ,sample variance,and sample standard deviation cost."
We need to find the range, sample variance, and sample standard deviation cost.
The range is already given: $247. It can be found by subtracting the least from the greatest value:
[tex]466-219=247[/tex]Now, in order to find the sample variance and the sample standard deviation, we first need to find the mean of the sample:
[tex]\text{ mean }=\text{ }\frac{415+466+400+219}{4}=\frac{1500}{4}=375[/tex]Now, we can find the sample variance s² using the formula:
[tex]s²=\frac{\sum_{i\mathop{=}1}^n(x_i-\text{ mean})²}{n-1}[/tex]where n is the number of values (n = 4) and the xi are the values of the sample.
We obtain:
[tex]\begin{gathered} s²=\frac{(415-375)²+(466-375)²+(400-375)²+(219-375)²}{4-1} \\ \\ s²=\frac{40²+91²+25²+(-156)²}{3} \\ \\ s²=\frac{1600+8281+625+24336}{3} \\ \\ s²=\frac{34842}{3} \\ \\ s²=11614 \end{gathered}[/tex]Now, the sample standard deviation s is the square root of the sample variance:
[tex]\begin{gathered} s=\sqrt{11614} \\ \\ s\cong107.8 \\ \\ s\cong108 \end{gathered}[/tex]Therefore, rounding to the nearest whole numbers, the answers are:
Answer
range: $247
s² = 11614 dollars²
s ≅ $108
what is the constant of proportionality in this proportional relationship? x 2 2-1/2 3 3-1/2 y 5/2 25/8 15/4 35/8. answer choices 4/5, 5/4, 4, 5
a proportional relationship has the following form:
yyy=
Space shuttle astronauts each consume an average of 3000 calories per day. One meal normally consists of a main dish, a vegetable dish, and two different desserts. The astronauts can choose from 11 main dishes, 7 vegetable dishes, and 12 desserts. How many different meals are possible?
Okay, here we have this:
Considering the provided information, we are going to calculate how many different meals are possible, so we obtain the following:
There are 11 ways to choose a main dish, 7 ways to choose a vegetable, 12 ways to choose the first dessert, and 11 ways to choose the second dessert. Then:
We multiply to find the possible number of combinations:
[tex]\begin{gathered} 11\cdot7\cdot12\cdot11 \\ =10164 \end{gathered}[/tex]Finally we obtain that there are 10164 different meals possible.
I think of a number.
I add 5 to it and then double the result.
I then subtract 10 from this answer.
I then subtract the original number I thought of.
Using algebra and a pronumeral to represent the number I think of, explain
why I get back to the number I started with.
Answer: [2(x + 5)] - 10 - x = 2x+10-10-x = 2x-x = x
Step-by-step explanation:
I think of a number, represented by the variable/pronumeral x.
I add 5 to it: x + 5
then double the result: 2(x + 5)
I then subtract 10 from this answer: [2(x + 5)] - 10
I then subtract the original number I thought of: [2(x + 5)] - 10 - x
Simplifying the expression will explain why you get the original number.
[2(x + 5)] - 10 - x = 2x+10-10-x = 2x-x = x.
Which operation results in a binomial?+(3y6 + 4)(9y12 - 12y6 + 16)ResetNextntum. All rights reserved.
Answer:
Explanations:
According to the question, we need to determine which of the signs will fit in that will make the expression a binomial.
In simple terms, a binomial is a two-term algebraic expression that contains variable, coefficient, exponents, and constant.
We need to determine the required sign by using the trial and error method.
Using the positive sign (+) first, we will have:
[tex]\begin{gathered} =\mleft(3y^6+4\mright)+(9y^{12}-12y^6+16) \\ =3y^6+4+9y^{12}-12y^6+16 \\ =3y^6-12y^6+4+9y^{12}+16 \\ =-9y^6+9y^{12}+20 \end{gathered}[/tex]Using the product sign, this will be expressed as:
[tex]\begin{gathered} (3y^6+4)\cdot(9y^{12}-12y^6+16) \\ (3y^6+4)\cdot\lbrack(3y^6)^2-(3y^6)(4)^{}+4^2)\rbrack \end{gathered}[/tex]According to the sum of two cubes;
[tex]a^3+b^3=\mleft(a+b\mright)•(a^2-ab+b^2)[/tex]Comparing this with the expression above, we will see that a = 3y^6 and
b = 4. This means that the resulting expression above can be written as a sum of two cubes to have;
[tex]\begin{gathered} (3y^6+4)\cdot\lbrack(3y^6)^2-(3y^6)(4)^{}+4^2)\rbrack^{} \\ =(3y^6)^3-4(3y^6)^2+4(3y^6)^2+16(3y^6)+4(3y^6)^2-16(3y^6)+4^3 \\ \end{gathered}[/tex]Collect the like terms:
[tex]undefined[/tex]Zaria is making pipe cleaner flowers for
her friends. She has 215 pipe cleaners.
How many flowers can she make with 3
pipe cleaners in each?
[?] flowers and pipe cleaners leftover
I
Answer
Enter
We can get the answer by dividing 215 by 3
What is dividing?
One of the four fundamental arithmetic operations, or ways to combine numbers to create new ones, is division. The other operations are multiplication, addition, and subtraction. The process of counting the instances in which one integer is included into the others is the most fundamental definition of the division of two natural numbers. This amount need not be an integer. For instance, if twenty apples are divided equally among four people, everyone will get five of them.
We can get the answer by dividing 215 by 3
215/3 = 71.67
Hence, 71 flowers are made
To know more about dividing, click on the link
https://brainly.com/question/1622425
#SPJ9
The following probability table shows probabilities concerning Favorite Subject and Gender. What is the probability of selecting an individual who is a female or prefers science?
Gender Favorite Subject Total
Math English Science
Male 0.200 0.050 0.175 0.425
Female 0.100 0.325 0.150 0.575
Total 0.300 0.375 0.325 1.000
Answer: 2
Step-by-step explanation: 0.300 0.375 0.325 1.000 = 2
Given the zeros of the following polynomial 2 +2i, 3, - 4 select the corresponding factors AND the polynomia O (x + 2i) (2 - 2i) (2 - 3)(x+4) o f(c) = 24 - 23 822 - 42 - 48 0 (2 – 2i) (x + 2i) (2+3)(– 4) 24 – 13 + 82 40 - 48 0 (0 - 2) (+2)(x - 3)(x +4) 24 - 23 - 822 + 4x + 48 1 3 N
a)
d)
1) Since the zeros of that polynomial were given, then we can write it into the factored form. Note that there are 4 zeros, so we can write:
[tex]\begin{gathered} (x-x_1)(x-x_2)(x-x_3)(x-x_4)=0 \\ (x-(-2i))(x-2i)(x-3)(x-(-4))=0 \\ (x+2i))(x-2i)(x-3)(x+4))=0 \end{gathered}[/tex]2) To find out the corresponding polynomial then we can expand it by rewriting "i" as -1
[tex]\begin{gathered} (x+2i))(x-2i)(x-3)(x+4) \\ (x+2i)(x-2i)=x^2+4 \\ (x-3)(x+4)=x^2+4x-3x-12 \\ (x^2+4)(x^2+x-12) \\ x^4+x^3-8x^2+4x-48 \end{gathered}[/tex]3) Hence, the answers are
a)
d)
[tex]x^4+x^3-8x^2+4x-48[/tex]Evaluate the expression whenb= 48 c= 7simplify as much as possible
Given:-
[tex]\frac{b}{3}+2c^2[/tex]To find the simplified value when b=48 and c=7.
So now we simplify the solution by substituting the values of b and c in the given equation and get the required solution.
So now we simplify. so we get,
[tex]\frac{b}{3}+2c^2=\frac{48}{3}+2\times7\times7=16+98=114[/tex]So the simplified solution is 114.
At a point on the ground 35 ft from base of a tree, the distance to the top of the tree is 1 ft more than 3 times the height of the tree. Find the height of the tree. The height of the tree is ___. (ft^3, ft^2, or ft)(Simply your answer. Round to the nearest foot as needed)
At a point on the ground 35 ft from the base of a tree, the distance to the top of the tree is 1 ft more than 3 times the height of the tree. Find the height of the tree
see the attached figure to better understand the problem
Applying the Pythagorean Theorem
(3h+1)^2=h^2+35^2
9h^2+6h+1=h^2+1,225
solve for h
9h^2-h^2+6h+1-1,225=0
8h^2+6h-1,224=0
Solve the quadratic equation
Using a graphing tool
the solution is
h=12 ftMultiply -5 1/2 × 7 5/6 =
You have to multiply:
[tex]-5\frac{1}{2}\cdot7\frac{5}{6}[/tex]First write the compound fractions as impropper fractions.
To do so, divide the whole number by one to express it as a fraction and add both fractions:
[tex]\begin{gathered} 5\frac{1}{2}=\frac{5}{1}+\frac{1}{2}\to\text{ common denominator 2} \\ \\ \frac{5\cdot2}{1\cdot2}+\frac{1}{2}=\frac{10}{2}+\frac{1}{2}=\frac{11}{2} \end{gathered}[/tex][tex]\begin{gathered} 7\frac{5}{6}=\frac{7}{1}+\frac{5}{6}\to\text{ common denominator 6} \\ \frac{7\cdot6}{1\cdot6}+\frac{5}{6}=\frac{42}{6}+\frac{5}{6}=\frac{47}{6} \end{gathered}[/tex]Rewrite the multiplication using the corresponding impropper fractions:
[tex]-\frac{11}{2}\cdot\frac{47}{6}[/tex]And solve the multiplication, numerator * numerator and denominator*denominator:
[tex]-\frac{11}{2}\cdot\frac{47}{6}=-(\frac{11\cdot47}{2\cdot6})=-\frac{517}{12}[/tex]While munching on some skittles, Bobby the Vampire lost a tooth that just so happened to be one of his fangs. He measured it to be 27 centimeters long. How long was his tooth in inches?
Answer: 10.6299
Step-by-step explanation:
There are 0.3937 inches in a cm., So, the length of the tooth in inches is [tex]27(0.3937)=10.6299 \text{ in }[/tex]
A country's population in 1994 was 182 million.In 2002 it was 186 million. Estimatethe population in 2004 using the exponentialgrowth formula. Round your answer to thenearest million.
we have the exponential formula
[tex]P=Ae^{(kt)}[/tex]so
we have
A=182 million ------> initial value (value of P when the value of t=0)
The year 1994 is when the value ot t=0
so
year 2002 -----> t=2002-1994=8 years
For t=8 years, P=186 million
substitute the value of A in the formula
[tex]P=182e^{(kt)}[/tex]Now
substitute the values of t=8 years, P=186 million
[tex]\begin{gathered} 186=182e^{(8k)} \\ e^{(8k)}=\frac{186}{182} \\ \text{apply ln both sides} \\ 8k=\ln (\frac{186}{182}) \\ k=0.0027 \end{gathered}[/tex]the formula is equal to
[tex]P=182e^{(0.0027t)}[/tex]Estimate the population in 2004
t=2004-1994=10 years
substitute the value of t in the formula
[tex]\begin{gathered} P=182e^{(0.0027\cdot10)} \\ P=187 \end{gathered}[/tex]therefore
the answer is 187 millionKatie opened a savings account and deposited 1,000.00 as principal the account earns 4% interest compounded quarterly what is the balance after 6 years
P = $1000
r = 4% = 4/100 = 0.04
t = 6 years
Therefore,
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=1000(1+\frac{0.04}{4})^{4\times6} \\ A=1000\times1.26973464853 \\ A=1269.73464853 \\ A=\text{ \$1269.73} \end{gathered}[/tex](2i) - (11+2i) complex numbers
The scale factor on a floor plan is 1 in8 ft. What is the actual distance represented by a 2.5 inches on the floor plan
Given:
Scale factor = 1 inch 8ft
Floor Plan measurement = 2.5 inches
Solution
We should re-write the scale factor in units of inches only.
Recall that:
[tex]1\text{ f}eet\text{ = 12 inches}[/tex]Then, the scale-factor in inch:
[tex]\begin{gathered} \text{Scale factor = 1 + 8 }\times\text{ 12} \\ =\text{ 1 + 96 } \\ =\text{ 97 inches} \end{gathered}[/tex]We can then find the actual distance by multiplying the represented distance (2.5 inches) by the scale factor.
So, we have:
[tex]\begin{gathered} \text{Actual distance = Represented distance }\times\text{ scale factor} \\ =2.5\text{ }\times\text{ 97} \\ =\text{ }242.5\text{ inches} \end{gathered}[/tex]Answer: Actual distance = 242.5 inches
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) And determine the quadrants of A+B and A-B.
Given that:
[tex]\cos A=\frac{5}{13}[/tex]Where:
[tex]0And:[tex]\cos B=\frac{3}{5}[/tex]Where:
[tex]0You need to remember that, by definition:[tex]\theta=\cos ^{-1}(\frac{adjacent}{hypotenuse})[/tex]Therefore, applying this formula, you can find the measure of angles A and B:
[tex]A=\cos ^{-1}(\frac{5}{13})\approx67.38\text{\degree}[/tex][tex]B=\cos ^{-1}(\frac{3}{5})\approx53.13\text{\degree}[/tex](a) By definition:
[tex]\sin \mleft(A+B\mright)=sinAcosB+cosAsinB[/tex]Knowing that:
[tex]\sin \theta=\frac{opposite}{hypotenuse}[/tex]You can substitute the known values into the equation in order to find the opposite side for angle A:
[tex]\begin{gathered} \sin (67.38\text{\degree)}=\frac{opposite}{13} \\ \\ 13\cdot\sin (67.38\text{\degree)}=opposite \\ \\ opposite\approx12 \end{gathered}[/tex]Now you know that:
[tex]\sin A=\frac{12}{13}[/tex]Using the same reasoning for angle B, you get:
[tex]\begin{gathered} \sin (53.13\text{\degree)}=\frac{opposite}{5} \\ \\ 5\cdot\sin (53.13\text{\degree)}=opposite \\ \\ opposite\approx4 \end{gathered}[/tex]Now you know that:
[tex]\sin B=\frac{4}{5}[/tex]Substitute values into the Trigonometric Identity:
[tex]\begin{gathered} \sin (A+B)=sinAcosB+cosAsinB \\ \\ \sin (A+B)=(\frac{12}{13})(\frac{3}{5})+(\frac{5}{13})(\frac{4}{5}) \end{gathered}[/tex]Simplifying, you get:
[tex]\begin{gathered} \sin (A+B)=\frac{36}{65}+\frac{20}{65} \\ \\ \sin (A+B)=\frac{36+20}{65} \end{gathered}[/tex][tex]\sin (A+B)=\frac{56}{65}[/tex](b) By definition:
[tex]\sin \mleft(A-B\mright)=sinAcosB-cosAsinB[/tex]Knowing all the values, you get:
[tex]\begin{gathered} \sin (A-B)=(\frac{12}{13})(\frac{3}{5})-(\frac{5}{13})(\frac{4}{5}) \\ \\ \sin (A-B)=\frac{36-20}{65} \\ \\ \sin (A-B)=\frac{16}{65} \end{gathered}[/tex](c) By definition:
[tex]\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\cdot\tan B}[/tex]By definition:
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex]Therefore, in this case:
- For angle A:
[tex]\tan A=\frac{12}{5}[/tex]- And for angle B:
[tex]\tan B=\frac{4}{3}[/tex]Therefore, you can substitute values into the formula and simplify:
[tex]\tan (A+B)=\frac{\frac{12}{5}+\frac{4}{3}}{1-(\frac{12}{5}\cdot\frac{4}{3})}[/tex][tex]\tan (A+B)=\frac{\frac{56}{15}}{1-\frac{48}{15}}[/tex][tex]\tan (A+B)=\frac{\frac{56}{15}}{-\frac{11}{5}}[/tex][tex]\tan (A+B)=-\frac{56}{33}[/tex](d) By definition:
[tex]\tan (A-B)=\frac{\tan A-\tan B}{1+\tan A\cdot\tan B}[/tex]Knowing all the values, you can substitute and simplify:
[tex]\tan (A-B)=\frac{\frac{12}{5}-\frac{4}{3}}{1+(\frac{12}{5}\cdot\frac{4}{3})}[/tex][tex]\tan (A-B)=\frac{\frac{16}{15}}{\frac{21}{5}}[/tex][tex]\tan (A-B)=\frac{16}{63}[/tex](e) Knowing that:
[tex]\sin (A+B)=\frac{56}{65}[/tex][tex]\tan (A+B)=-\frac{56}{33}[/tex]Remember the Quadrants:
By definition, in Quadrant II the Sine is positive and the Tangent is negative.
Since in this case, you found that the Sine is positive and the Tangent negative, you can determine that this angle is in the Quadrant II:
[tex]A+B[/tex]Rami practices his saxophone for 5/6 hour on 4 days each week.
How many hours does Rami practice his saxophone each week?
[] 2/[] Hr
Answer:
you take 5/6 and multiply it by 4/1.
which gives you 20/6
then reduce it by dividing the top number by the bottom number
which gives you 3 with a remainder of 2
you then place the remainder over the
This tells you he practicedfor 3 2/6
Step-by-step explanation:
Why is it incorrect to write {∅} to denote a set with no elements?
Answer:
It's incorrect because {∅} is saying that the set contains empty sets, which is not the same as saying the set is empty (which can be denoted by { } or ∅
Step-by-step explanation: It's all in the answer.
What is the value of f(3) on the following graph?
Answer
f(3) = -2
Explanation
We are asked to find the value of f(3) from the graph.
This means we are looking for the value of f(x) or y on the graph, at a point where x = 3.
From the graph, we can see that at the point where x = 3, y = -2
Hence, f(3) = -2
Hope this Helps!!!
what is the final cost of the purchase at discount heaven?
First, let's sum the single costs of each item.
[tex]32+32+20=84[/tex]Because they are buying 1 jacket, 2 pairs of jeans, and 1 vest. So, the subtotal of these items is $84. (At Discount Heaven)
Then, we apply a 7% sales tax.
[tex]84+0.07\cdot84=84+5.88=89.88[/tex]As you can observe, the sales tax is $5.88 for all the items purchased, and the total cost they have to pay is $89.88.
Use a calculator to find the values of X. Round sides to the nearest 10th and angles to the nearest whole number. Use sin or COS as appropriate.
Given the information about the triangle, we can use the cosine function on angle x to get the following:
[tex]\begin{gathered} \cos x=\frac{\text{adjacent side}}{hypotenuse}=\frac{7}{16} \\ \Rightarrow\cos x=\frac{7}{16} \end{gathered}[/tex]solving for x, we get:
[tex]\begin{gathered} \cos x=\frac{7}{16} \\ \Rightarrow x=\cos ^{-1}(\frac{7}{16})=64.1 \\ x=61.1\degree \end{gathered}[/tex]therefore, the value of x is 61.1
help meeeeeeeeeeeeeeeee
For the given function f(x) = x³ +x +1,g(x) =-x, composition of the given function is given by ( fog)(x) = -x³ -x +1 , ( g of)(x) = -(x³ +x +1).
As given in the question,
Given function :
f(x) = x³ +x +1
g(x) =-x
Composition of the given function is equal to :
(fog)(x) = f(g(x))
= f(-x)
= (-x)³ +(-x) +1
= -x³ -x +1
(g of)(x) = g(f(x))
=g(x³ +x+1)
= -(x³ +x+1)
Therefore, for the given function f(x) = x³ +x +1,g(x) =-x, composition of the given function is given by ( fog)(x) = -x³ -x +1 , ( g of)(x) = -(x³ +x +1).
Learn more about function here
brainly.com/question/12431044
#SPJ1
Camera has Alyssa price of $768.95 before tax the sales tax rate is 8.25% final total find the total cost of the camera with sales tax included round your answer to the nearest cent as necessary
We know that the listed price of the camera is $768.95 and the tax rate is 8.25%.
To find the total cost we must use the next formula
[tex]\text{Total cost }=\text{listed price before tax+(listed price before tax }\cdot\text{rate tax)}[/tex]Now, we must replace the values in the formula using that 8.25% = 0.0825
[tex]\text{Total cost}=768.95+(768.95\cdot0.0825)[/tex]Simplifying,
[tex]\text{Total cost}=832.39[/tex]ANSWER:
$O32
I need help on 3 it says find the value of x round each answer to the nearest tenth
In problem 3, we have a right triangle with:
• cathetus ,a = 7,,
,• cathetus ,b = x,,
,• and hypotenuse ,h = 9,.
Pigatoras Theorem states that:
[tex]h^2=a^2+b^2.[/tex]Where a and b are cathetus and h the hypotenuse.
Replacing the data of the problem in the equation above, we have:
[tex]9^2=7^2+x^2.[/tex]Solving for x the last equation, we get:
[tex]\begin{gathered} 81=49+x^2, \\ x^2=81-49, \\ x^2=32, \\ x=\sqrt[]{32}\cong5.7. \end{gathered}[/tex]Answer
The value of x to the nearest tenth is 5.7.
riangle QRS has vertices Q(8, −4), R(−1, 2), and S(3, 7). What are the coordinates of vertex Q after the triangle is reflected across the y-axiriangle QRS has vertices Q(8, −4), R(−1, 2), and S(3, 7). What are the coordinates of vertex Q after the triangle is reflected across the y-axi
17. A moving company charges a flat rate of $85 plus and additional $0.17 per mile driven. How far must the company drive to earn at least $100? Round to thenearest mile.x2 84x2 78x2 80x2 88
ANSWER
88
EXPLANATION
Let x be the miles driven and y be the earnings of the company when they drive for x miles.
If the company charges $0.17 per mile driven plus a flat rate of $85, then the total cost for moving x miles away is,
[tex]y=85+0.17x[/tex]Now, we have to find for how many miles, x, the company must drive to earn $100 or more,
[tex]85+0.17x\ge100[/tex]Subtract 85 from both sides,
[tex]\begin{gathered} 85-85+0.17x\geq100-85 \\ \\ 0.17x\ge15 \end{gathered}[/tex]And divide both sides by 0.17,
[tex]\begin{gathered} \frac{0.17x}{0.17}\ge\frac{15}{0.17} \\ \\ x\ge88.24 \end{gathered}[/tex]Hence, the company must drive for at least 88 miles to earn at least $100, rounded to the nearest mile.
Determine if the ordered pair provided is a solution to the linear system:3x+7y=1 and 2x+4y=0; (2,3) The system has no solution as the lines are parallel. The ordered pair (2, 3) is not a solution to the system. Yes, (2, 3) is a solution to the system. The system has no solution as the lines are perpendicular.
Answer:
The correct answer is:
The ordered pair (2, 3) is not a solution to the system.
Explanation:
The system given is:
[tex]\begin{cases}3x+7y={1} \\ 2x+4y={0}\end{cases}[/tex]If (2, 3) is a solution of the system, then replacing x = 2 and y = 3 on both equations should give a correct result and the same on both equatiions.
In the first equation;
[tex]\begin{gathered} 3\cdot2+7\cdot3=1 \\ 6+21=1 \\ 27=1 \end{gathered}[/tex]We can see that this result is not true, as 27 is not equal to 1.
In the second equation:
[tex]\begin{gathered} 2\cdot2+4\cdot3=0 \\ 4+12=0 \\ 16=0 \end{gathered}[/tex]Once again, a false result.
To see in the system has equations, let's solve for x in the second equation:
[tex]\begin{gathered} 2x+4y=0 \\ 2x=-4y \\ x=-2y \end{gathered}[/tex]Now, we can use substitution in the first equation:
[tex]3(-2y)+7y=1[/tex]And solve for y:
[tex]\begin{gathered} -6y+7y=1 \\ y=1 \end{gathered}[/tex]Now, we can find the value of x:
[tex]x=-2\cdot1=-2[/tex]The solution to the system is (-2, 1)
Thus, the correct option is "The ordered pair (2, 3) is not a solution to the system"
AMNP ~ AQRP N x + 8 28 M 24 P 3x - 9 R Create a proportion and find the length of side PR*
Using thales theorem:
[tex]\begin{gathered} \frac{24}{28}=\frac{x+8}{3x-9} \\ 24(3x-9)=28(x+8) \\ 72x-216=28x+224 \\ 44x=440 \\ x=\frac{440}{44} \\ x=10 \\ PR=3(10)-9=21 \end{gathered}[/tex]