Let f(x) = 5x²-2 and let g(x) = 3x + 1. Find (f + g)(2).
(f+g)(2)= (Simplify your answer.)
Answers
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:(f+g)(x) = 5x² + 3x - 1 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: f(x) = 5 {x}^{2} - 2[/tex]
and
[tex]\qquad \tt \rightarrow \: g(x) = 3x + 1[/tex]
We need to find : (f + g) (x) = ?
[tex]\qquad \tt \rightarrow \: (f + g)(x) = f(x) + g(x)[/tex]
[tex]\qquad \tt \rightarrow \: (f + g)(x) = 5 {x}^{2} - 2 + 3x + 1[/tex]
[tex]\qquad \tt \rightarrow \: (f + g)(x) = 5 {x}^{2} + 3x - 1[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Related Questions
Find an equation for the graph sketched below.
Answers
The equation for the graph sketched below is given as y = -3(3)^x
Exponential equationThe standard form of an exponential equation is given as y = ab^x
Using the coordinate points on the graph (-1, 1) and (0, -3)
The equivalent equations are;
1 = ab^-1
-3 = ab^0
From equation2;
a= -3
Substitute into equation 1;
1 = ab^-1
1 = 3b^-1
1 =3/b
b =3
Determine the equation
y = ab^x
y = -3(3)^x
This gives the required exponential equation
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Please help me I was sick today and missed out on class and I don’t understand this question
Answers
i.
it is an corresponding angles
ii.
the realtion we have is that the angles are equal
iii.
4+10x=11x-1
or 4+1=11x-10x
5=x
iv
4+10x=4+10×5
=54
11x-1=11×5-1=54
Answer:
A)Corresponding angles (When two lines are crossed by another line (which is called the Transversal), the angles in matching corners are called corresponding angles
B)They are congruent to each other
C) 4+10x=11x-1
4=x-1
5=x
( we put them equal to each other because they are the same)
D)4+10(5)=
4+50=54
D)11(5)-1=
55-1=54
x = -CD/CD2-40 DC8x2 + 8x = -2Write the quadratic equation in standard form:( a )x2 + ( b )x+ C) = 0Identify the values of a, b, and c.b =Substitute these values into the quadratic formula and simplify:2( )a =C=
Answers
So the initial equation is:
[tex]8x^2+8x=-2[/tex]To writte the equation in the standard form we have to make it equal to 0, so we can add 2 in bout sides of the equation:
[tex]\begin{gathered} 8x^2+8x+2=-2+2 \\ 8x^2+8x+2=0 \end{gathered}[/tex]now, (a) is the number thas goes with the x^2, (b) is the number that goes with the x and (c) is the number that is alon, so:
[tex]\begin{gathered} a=8 \\ b=8 \\ c=2 \end{gathered}[/tex]Now we can substitute this numbers in the quadratic equation:
[tex]\begin{gathered} \frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \frac{-8\pm\sqrt[]{8^2-4(8)(2)}}{2(8)} \end{gathered}[/tex]and finally we can simplify the equation:
[tex]\begin{gathered} \frac{-8\pm\sqrt[]{64-64}}{16} \\ \frac{-8}{16}=\frac{-4}{8}=\frac{-2}{4}=-\frac{1}{2} \end{gathered}[/tex]Jerry made 8,700 mL of tomato soup. He packed 1.6 L of the soup for his kids' lunches. He then froze half of the remaining soup.How many milliliters of soup did Jerry freeze? Jerry froze ______mL of soup
Answers
7100 mL
Explanationto solve this we need to do a subtraction, note the unit must be the same, so
Step 1
convert 1.6 Liters into mL
to do this we need to use the equivalence:
[tex]\begin{gathered} 1000\text{ mL= 1 L} \\ so \\ \frac{1000\text{ mL}}{1\text{ L}} \end{gathered}[/tex]so,
a) convert 1.6 Liters into mm
[tex]\begin{gathered} 1.6\text{ L*\lparen}\frac{1000\text{ mL}}{1\text{ L}}\text{\rparen=1600 mL} \\ 1600\text{ mL} \end{gathered}[/tex]Step 2
b)now, we can do the subtraction:
so
soup she froze = total soup made - soup she packed
so, replace
[tex]\begin{gathered} frozen\text{ soup=8700 mL -1600 mL} \\ frozen\text{ soup=7100 mL} \end{gathered}[/tex]therefore, the answer is
7100 mL
I hope this helps you
Select all the equations that represent lines perpendicular to Y= 3x+4.A. Y= -1/3xB. 6x-2y=4C. 3y= -x+7D. X+3y=4E. y=3x-10
Answers
if two lines are perpendicular it is true that:
[tex]m1\cdot m2=-1[/tex]For the line:
[tex]\begin{gathered} y=3x+4 \\ m1=3 \end{gathered}[/tex]Let's check every line:
[tex]\begin{gathered} y=-\frac{1}{3}x \\ m2=-\frac{1}{3} \\ m1\cdot m2 \\ 3\cdot-\frac{1}{3}=-1=-1 \end{gathered}[/tex]So, A is a correct choice
[tex]\begin{gathered} 6x-2y=4 \\ y=3x-2 \\ m2=3 \\ m1\cdot m2 \\ 3\cdot3=9\ne-1 \end{gathered}[/tex]B is not a correct choice
[tex]\begin{gathered} 3y=-x+7 \\ y=-\frac{1}{3}x+\frac{7}{3} \\ m2=-\frac{1}{3} \\ m1\cdot m2 \\ 3\cdot-\frac{1}{3}=-1=-1 \end{gathered}[/tex]C is a correct choice
[tex]\begin{gathered} x+3y=4 \\ y=-\frac{1}{3}x+\frac{4}{3} \\ m2=-\frac{1}{3} \\ m1\cdot m2 \\ 3\cdot-\frac{1}{3}=-1=-1 \end{gathered}[/tex]D is a correct choice
[tex]\begin{gathered} y=3x-10 \\ m2=3 \\ m1\cdot m2 \\ 3\cdot3=9\ne-1 \end{gathered}[/tex]E is not a correct choice
2. Let f(x) = 5x² - 2x - 7.
(a) find f(0)
(b) find f(-3)
(c) find x if f(x) = 0
Answers
(B) Same calcul with -3 f(-3) = 25
(C) delta = b^2 - 4ac
= -2^2 - 4*5*(-7)
= 4 + 140
= 144 so delta>0 2 solutions
X1 = -10/10 = -1
X2 = 14/10 = 7/5
Answer:
A) f(0) = -7
B) f(-3) = 44
C) x = -1, (7/5)
Step-by-step explanation:
2. Let f(x) = 5x² - 2x - 7.
(a) find f(0)
f(x) = 5x² - 2x - 7
f(0) = 5(0)² - 2(0) - 7
f(0) = -7
(b) find f(-3)
f(x) = 5x² - 2x - 7
f(-3) = 5(-3)² - 2(-3) - 7
f(-3) = 5(9) - 2(-3) - 7
f(-3) = 45 + 6 - 7
f(-3) = 45 + 6 - 7
f(-3) = 44
(c) find x if f(x) = 0
f(x) = 5x² - 2x - 7
f(x) = 5x² - 2x - 7 = 0
(5x² + 5x)(-7x - 7)
5x(x + 1) -7(x + 1)
(5x - 7)(x + 1)
5x - 7 = 0, x + 1 = 0
+7 +7 -1 -1
--------------- ---------------
5x = 7 x = -1
÷5 ÷5
------------
x = (7/5)
5(-1)² - 2(-1) - 7 = 0
5(7/5)² - 2(7/5) - 7 = 0
----------------------------------------------------------------------------------------------------------
I hope this helps!
Use a table of trigonometric values to find the angle θ in the right triangle in the following problem. Round to the nearest degree, if necessary.
sin θ = 0.7071 O = 5 H = ?
Answers
By applying sine trigonometry, the angle θ in this right angled triangle is approximately equal to 50 degrees.
What is the law of sines?In Trigonometry, the law of sines is also referred to as sine law or sine rule and it can be defined as an equation that relates the side lengths of a triangle to the sines of its angles.
How to apply basic trigonometry?In order to determine the value of H, we would apply basic trigonometry. From the information provided about this right angled triangle, we can logically deduce the following parameters:
sinθ = 0.7071Opposite (Opp) = 5Hypotenuse (Hyp) = H.Therefore, we would use the sine trigonometry to determine the value of H as follows:
Sinθ = Opp/Hyp
0.7071 = 5/H
H = 5/0.7071
H = 7.0711.
Now, we can determine the angle θ in this right angled triangle as follows:
Sinθ = Opp/Hyp
Angle, θ = sin⁻¹(Opp/Hyp)
Angle, θ = sin⁻¹(5/7.0711)
Angle, θ = sin⁻¹(0.7071)
Angle, θ = 44.999 ≈ 50°.
Angle, θ = 50 degrees.
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can some one help meeeeee
Write an equation or inequality to model the situation:
The distance d to school is 1 1/2 miles more than the distance p to
the park.
Answers
An equation or inequality to model the situation: The distance d to school is 1 1/2 miles more than the distance p to the park is d = p + 3/2
What is an equation ?a statement that the values of two mathematical expressions are equal indicated by the sign =, is known as equation.
What is inequality ?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions is known as inequality.
For this situation, we would assume that both the distances i.e 'd' and 'p' are in miles.
It is mentioned that the distance d is more than the distance p by 3/2 miles.
It means that if we add 3/2 miles to the distance 'p' the output will be distance 'd'
The equation for this is as follows :- d = p + 3/2
It also means that if we substract 3/2 miles from distance 'd', the output will be distance 'p'
The equation for this is as follows :- p = d - 3/2
But we are asked in the situation that distance d is more than than the distance 'p'.
Therefore , an equation or inequality to model the situation: The distance d to school is 1 1/2 miles more than the distance p to the park is d = p + 3/2.
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Hello I need help with this
Answers
The graph shows a quadratic function.
The quadratic function has been shifted downwards by 2 units and to the left by 3 units.
The rules that show the translation above are given to be:
1) f (x) − b shifts the function b units downward.
2) f (x + b) shifts the function b units to the left.
Therefore, the transformation for h(x) is given to be:
[tex]h(x)\to h(x+3)-2[/tex]When a number is added to 20 and 5 is subtracted from the number, their product is 150. Find the two possible numbers
Answers
Answer:
--15 and --10 respectively
Step-by-step explanation:
Let the first no be a and second no be b
From the interpretation of the question
a + 20 (added) -- 5 (subtracted) = 0
a + 20 -- 5 = 0
a + 15 = 0
a = --15
Product = 150
a×b = 150
(--15) × b = 150
b = --150/15
b = --10
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i need help i doint think i did it right
Answers
Memory of the phones = 32 gigabytes
Now,
[tex]1\text{ gigabyte = }1073741824\text{ bytes}[/tex]Therefore ,
[tex]32\text{ gigabytes = }34359738368\text{ bytes}[/tex]Also ,
[tex]1\text{ byte = 8 bits}[/tex]Therefore,
[tex]34359738368\text{ bytes = }274877906944\text{ bits}[/tex]Thus the memory of the phone in bits is ,
[tex]274877906944\text{ bits}[/tex]can you help me please thankyou
Answers
Answer: 17
Step-by-step explanation:
The world's population grew from approximately 2.6 to 5.2 billion between 1952 and 1987.
Assuming that the population growth during this time period followed an exponential model, calculate the
average annual population growth rate of the world between 1952 and 1987 as a percentage.
Answers
Answer:
R=100%
Step-by-step explanation:
Here
Increased population (Pt) = 5.2-2.6 = 2.6
Time = 1987-1952
Rate of increase=?
By formula
Pt = P(1-R/100)^t
2.6=2.6(1-R/100)^35
1=(1-R/100)^35
0^35 = (1-R/100)^35
0=1-R/100
0= 100-R
R=100%
so the average annual population growth rate of the world between 1952and1987 is 100%
I’ve been stuck on this one for awhile now, please help. Statement: Richard takes a hang gliding lesson. He lifts off at the top of a hill and glides downward for the first 5 minutes. Then he soars at a consistent elevation for 10 minutes. The last 3 minutes he glides upward until he lands on a smaller hill. Use the information about when Richard’s elevation is increasing, decreasing, or constant to choose the graph that beat approximates Richard’s gliding lesson over time.
Answers
Answer:
c
Step-by-step explanation:
Match each phrase with its corresponding algebraic expression.
Answers
Answer/Step-by-step explanation:
Five more than a number = 5 + n
The sum of 3.6 and a number = n + 3.6
The difference of ten and a number = 10 - n
One-half less than a number = n - (1/2)
I hope this helps!
Answer:
The difference of 10 and a number: 10-n
Five more than a number: 5+n
The sum of 3.6 and a number: n+3.6
one-half less than a number: n-1/2
Which is the set of integers greater than 9 and less than or equal to -6
Answers
The set of integers as described in the task content which are greater than 9 and less than or equal to -6 can be represented using interval notation as all integer values in the set ; (9, infinity) U (-infinity, -6].
How to find the set of integers?It follows from the task content that the set of integers greater than 9 and less than or equal to -6 is to be determined.
By considering each set of possible solutions for the integer in discuss; we have;
For greater than 9; (9, infinity).For less than or equal to -6; (-infinity, -6].Therefore, the required set of Integers includes integers in union of the two sets above and hence, we have;
x = (9, infinity) U (-infinity, -6].
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Scallops eject water from their shells to provide a thrust force. A 29 g scallop accelerates from rest straight up to escape a predator, reaching a
speed of 4.10 m/s in 0.15 s. What is the ratio of the net force to the weight of the scallop (Fnet/Weight) for this motion? (Hint: Remember that
grams are a measurement of mass, not force). Round to three decimal places and express in terms of SI units.
Answers
The ratio of the net force to the weight of the scallop (F net/Weight) for this motion exists 792.657 Newtons.
What is meant by net force?The net force exists the vector sum of all the forces that act upon an object. The total of all forces exerted on an object is known as the net force. A mass can accelerate due to net force. A body is subject to another force whether it is at rest or in motion. When there are a lot of forces acting on a system, the term "net force" is employed.
Given, mass = 29g, speed = 4.10 m/s , Time = 0.15 s
Acceleration (a ) = (final speed - initial speed)/time taken
= 4.10 - 0/ 0.15 = 27.333 m/s/s
F = m × a = 29 g × 27.33 m/s
= 792.657 Newtons
Therefore, the ratio of the net force to the weight of the scallop (F net/Weight) for this motion exists 792.657 Newtons.
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Point M is the midpoint of AB¯¯¯¯¯. AM=2x+9, and AB=8x−50.
What is the length of AM¯¯¯¯¯¯?
Answers
Answer:
43
Step-by-step explanation:
→ Set up an equation
2x + 9 = 0.5 ( 8x - 50 )
→ Simplify
2x + 9 = 4x - 25
→ Minus 4x from both sides
-2x + 9 = -25
→ Minus 9 from both sides
-2x = - 34
→ Divide both sides by -2
x = 17
→ Substitute into AM
2 × 17 + 9 = 34 + 9 = 43
Need help with this one
Answers
Answer: The answer should be 10^2 or C
Step-by-step explanation: 65.108 if you move the six to left 2 times you will get 6,510.8
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answers
For the given question,
Figure A and D are the cases of reflection over y and x axis respectively.
What is termed as Translation?In mathematics, a translation is the movement of a shape to the left or right and/or upward or downward. The translated shapes appear to be the same size as that of the original shape, and thus the shapes are congruent. They were simply shifted in one or even more directions.For the given question,
Figure B and C are the cases of translation 3 right and 4 down respectively.
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what is the fraction to decimal of 2/13=
Answers
Answer:
0.1538461583
Step-by-step explanation:
2 divided by 13
explaination:
2/13=2 dived into 13 in long division form and then round 3 decimal places over that gives the answer above
15. The area of a triangle is given by
A = 1/2bh, where b is the base and h is the height of the triangle. In the triangle PQR above, PR=6, PQ=7, QR=12, and PH=3. If PH is perpendicular to QR, what is the area of the triangle PQR?
(A) 12
(B) 18
(C) 36
(D) 42
Answers
The answer is (B) 18.
In order to calculate the area of a triangle we must use the equation 1/2·base·height.
In this case, the base of the triangle would be QR, which is 12. The height would be PH, which is 3.
Using the formula above, we can do 1/2·12·3 which equals 18. This is the area of triangle PQR and our final answer.
Hope this helps.
SO GUYSS I NEED THIS TODAY if it not to much to ask for.....
how does simple interest show proportional reasoning and relate to the percent equation
Answers
Answer: Use cross-product to determine if the two ratios form a proportion.
Please help I’ll mark you as brainliest if correct!!
Answers
A puzzle, defined as "anything which baffles or perplexes," refers to an enigma or a conundrum that requires creative thinking to solve.
The answer is A = 7.
How to find A?A puzzle, defined as "anything which puzzles or perplexes," refers to a riddle or issue that defies creativity to be solved.
Retaining mental quickness and short-term memory while working on a puzzle strengthens connections between brain cells.
Dopamine, a neurotransmitter that controls mood, memory, and focus, is produced more readily as a result of solving puzzles.
Every time we complete the puzzle, dopamine is produced.
Given the puzzle condition,
The sum of any 3 consecutive digits must be 17.
Given numbers 8, 2
So the third number would be 8 + 2 + A = 17
10 + A = 17
Therefore A is 17-10 = 7
A = 7
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solve. -6 4/9 - 3 2/9 - 8 2/9
Answers
Answer:
the answer is -17 8/9
Step-by-step explanation:
when "subtracting" negative numbers you actually add all of them together and attach the negative sign
Consider the transformation shown.
6
8
Pre-image
Intro
10
3
5
Image
Use the drop-down menus to complete the sentence.
The transformation is
because the
preserved.
Done
Answers
The transformation is non rigid
What transformations ?Transformations involve the rotation, reflection, or translation of forms on a coordinate plane. Transformational geometry is a fresh viewpoint on geometry that Felix Klein suggested in the 19th century. The majority of geometric proofs rely on the transformations of objects. Any image in a coordinate plane can be changed using transformations. Applying the transformational laws will help you better understand the graphics in video games. Learn to recognize transformations, comprehend function transformation principles, and investigate the various forms of transformations.
What is non rigid transformations ?Non-Rigid Transformations actually alter the original object's structure. Scaling, for instance, allows us to make our object larger or smaller. Alternatively, shearing can be used to "push" it up or to the side. In essence, non-rigid transformations allow an object's size to change.
because the size became small as compare to pre image it is non rigid transformation
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Multiplying Binomials with Fractional Coefficients
Express the product of (2x + 3) and (x − 3) as a trinomial in simplest form
Answers
[tex] = (2x + 3)(x - 3) \\ = 2x(x - 3) +3 (x - 3) \\ = 2 {x}^{2} - 6x + 3x - 9 \\ = 2 {x}^{2} - 3x - 9[/tex]
ATTACHED IS THE SOLUTION
Event A, Event B, and Event C are provided. Event A and Event B aremutually exclusive. Event A and Event C are not mutually exclusive.P(A) = 0.45P(B) = 0.30P(C) = 0.25What is the probability of the complement of Event A [Find P(A')] ?Be sure to show your work and/or explain your reasoning.
Answers
If two events are mutually exclusive this means they cannot occur at the same time and do not over lap
If two events are mutually inclusive this means they can occur at the same time and they over lap
Event A and Event B are mutually exclusive
Event A and event C are not mutually exclusive
To find the complement of event A (A'), which is the part of the universal set of events not in A
We use the formula
[tex]1\text{ - P(A)}=P(A^{\prime})[/tex]P(A) = 0.45
substituting this into the equation yields
[tex]\begin{gathered} 1-\text{ 0.45 = P(A')} \\ P(A^{\prime})\text{ = 0.55} \end{gathered}[/tex]P(A') = 0.55
A company is reviewing a batch of 26 products to determine if any are defective. On average, 3.6% of products are defective.What is the probability that the company will find 2 or fewer defective products in this batch?What is the probability that 4 or more defective products are found in this batch?If the company finds 5 defective products in this batch, should the company stop production?
Answers
The experiment has a binomial distribution just because the product could be or not defective. In this case you have n=26 the number of product that the company will check and you also know that the probability to get a defective one is 3.6%. Now we will proceed as follows, to find the probability of getting 2 or fewer defective products is exactly the same that
[tex]\begin{gathered} P(X\leq2)=P(X=0)+P(X=1)+P(X=2)\text{ } \\ \text{ where }X\text{ is a random variable that measures the number of defective products} \end{gathered}[/tex]We also should notice that
[tex]P(X=k)=(n;k)p^k(1-p)^{(n-k)};\text{ where }(n;k)=\frac{n!}{k!(n-k)!}[/tex]Now,
[tex]P(X=0)=(26;0)(0.036)^0(1-0.036)^{26-0}=(1-0.036)^{26}\approx0.3855[/tex][tex]P(X=1)=(26;1)(0.036)(1-0.036)^{26-1}=26(0.036)(1-0.036)^{25}\approx0.3743[/tex][tex]P(X=2)=(26;2)(0.036)²(1-0.036)^{26-2}=325(0.001296)(1-0.036)^{24}\approx0.1747[/tex]Then the probability that the company takes 2 or fewer defective products in this batch is
[tex]P(X\leq2)=P(X=0)+P(X=1)+P(X=2)=0.3855+0.3743+0.1747=0.9345[/tex]Now, to get the probability that the company find 4 or more defective products we proceed as follows. Since
[tex]P(X\ge4)+P(X<4)=1,\text{ }[/tex]then
[tex]P(X\ge4)=1-P(X<4)=1-(\text{ }P(X=0)+P(X=1)+P(X=2)+P(X=3)).[/tex]Notice that we only need to find one of these probabilities to get the answer.
[tex]P(X=3)=(26;3)(0.036)³(1-0.036)^{26-3}=\frac{23!(24)(25)(26)}{3!23!}(0.036)³(1-0.036)^{23}=0.05219[/tex]Then the probability to get more than 4 defective products is
[tex]\begin{gathered} P(X\ge4)=1-(P(X=0)+P(X=1)+P(X=2)+P(X=3))= \\ =1-(0.9345+0.05219)=0.01331 \\ \\ P(X\ge4)=0.01331 \end{gathered}[/tex]So if the company finds 5 defective products in this batch the company should stop the production because the probability to get more than 4 defective products is around 1.3%. It means that if you get 5 defective products even with this small probability then we could say that is really probable to get more defective products that those who were expected.
Find S7 of the sum of the geometric series. a1 = 729, a? = 1, r = 1
Answers
Let's write out the formula for the sum of geometric series,
[tex]S_n=\frac{a(1-r^n)}{1-r}[/tex][tex]\begin{gathered} \text{where a=first term=729} \\ r=\text{common ratio=}\frac{1}{-3} \\ S_7=?,\text{ where n= number of terms=7} \end{gathered}[/tex]Let's solve for the sum of seven geometric series,
[tex]\begin{gathered} S_7=\frac{729(1-(-\frac{1}{3})^7)}{1-(-\frac{1}{3})} \\ =\frac{729(1-(-\frac{1}{2187}))}{1+\frac{1}{3}} \\ =\frac{729(1+\frac{1}{2187})}{\frac{4}{3}} \end{gathered}[/tex][tex]\begin{gathered} S_7=\frac{729(1\frac{1}{2187})}{\frac{4}{3}} \\ =\frac{729(\frac{2188}{2187})}{\frac{4}{3}}=\frac{\frac{2188}{3}}{\frac{4}{3}} \\ =\frac{2188}{3}\frac{\text{.}}{.}\frac{4}{3} \\ =\frac{2188}{3}\times\frac{3}{4}=547 \end{gathered}[/tex]Hence,
[tex]S_7=547[/tex]Therefore, option 5 is the correct answer.
Option 5 is none of these are correct.