I'm not understanding what they're wanting me to do here?? Can someone pls help?
Answers
From the given figure,
[tex]\begin{gathered} In\text{ }\Delta ABD,\text{ BD }\perp\text{ AC} \\ \end{gathered}[/tex]By using right angled triangle theorem,
According to right angled triangle theorem, perpendicular drawn on the hypotenuse is equal to the square root of the product of parts in which hypotenuse is divided.
[tex]\begin{gathered} x\text{ = }\sqrt[]{10\text{ }\times\text{ 4}} \\ x\text{ = }\sqrt[]{40} \\ x\text{ = 2}\sqrt[]{10} \end{gathered}[/tex]By using Pythagoras theorem,
[tex]\begin{gathered} AB^2=AD^2+DB^2 \\ z^2=10^2+x^2\text{ } \\ z^2=10^2\text{ + (2}\sqrt[]{10})^2 \\ \end{gathered}[/tex]Further,
[tex]\begin{gathered} z^2=\text{ 100 + 40} \\ z^2\text{ = 140} \\ z\text{ = 2}\sqrt[]{35\text{ }}\text{ } \end{gathered}[/tex]Also,
[tex]In\text{ }\Delta ABC,[/tex]By using Pythagoras theorem,
According to Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the remaining sides.
[tex]\begin{gathered} AC^2=AB^2+BC^2 \\ 14^2=z^2+y^2_{_{_{}\text{ }_{}}} \\ z^2=14^2-y^2_{_{_{}}}\text{ } \end{gathered}[/tex]Further,
[tex]\begin{gathered} y^2=14^2-z^2 \\ y^2\text{ = 196 - (2}\sqrt[]{35})^2 \\ y^2\text{ = 196 - 140} \\ \end{gathered}[/tex]Therefore ,
[tex]\begin{gathered} y^2\text{ = 56} \\ y\text{ = 2}\sqrt[]{14} \end{gathered}[/tex]Thus the required values of x , y and z are
[tex]\begin{gathered} x\text{ = 2}\sqrt[]{10}\text{ units} \\ y\text{ = 2}\sqrt[]{14}\text{ units} \\ z\text{ = 2}\sqrt[]{35\text{ }}\text{ units} \end{gathered}[/tex]
Related Questions
Don Stone obtained an $8.500 installment loan at 14% for 42 months. The loan's balance after 26 payments is 3.733.55. What is the interest for payment 27?
Answers
Given:
The unpaid balance after the 26 payments is $3,733.55.
Therefore, the interest for payment 27 will be
[tex]14\text{ \% of \$3733.55}[/tex]Evaluating
[tex]\frac{14}{100}\times3733.55=0.14\times3733.55=522.697\approx522.70(nearest\text{ cent)}[/tex]Hence, the interest for payment 27 is $522.70.
Determine if the following statement is true or false regarding sets A and B.A = {3, 5, 7, 9, 11, 13}B = {3, 5, 11, 13}Every element of A is also an element of B.Choose the correct answer below.FalseTrue
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We have the following sets:
A = {3, 5, 7, 9, 11, 13}
B = {3, 5, 11, 13}
If we look closely, all the elements of B are in A. But each element of A does not belong to B, therefore the statement is totally false.
can you answer 3 please show a table graph and work
Answers
To solve the question, choose values for x to find its corresponding image y. Then, plot the points and connect them.
Step 01: Choosing x = -2.
Substituting x by -2 in the equation:
[tex]\begin{gathered} y=2\cdot3^{-2} \\ y=2\cdot(\frac{1}{3})^2 \\ y=2\cdot\frac{1}{9} \\ y=\frac{2}{9} \end{gathered}[/tex]So, the first point is (-2, 2/9).
Step 02: Choosing x = -1.
Substituting x by -1 in the equation:
[tex]\begin{gathered} y=2\cdot3^{-1} \\ y=2\cdot(\frac{1}{3})^1 \\ y=2\cdot\frac{1}{3} \\ y=\frac{2}{3} \end{gathered}[/tex]So, the second point is (-1, 2/3).
Step 03: Choosing x = 0.
Substituting x by 0 in the equation:
[tex]\begin{gathered} y=2\cdot3^0 \\ y=2\cdot1 \\ y=2 \end{gathered}[/tex]So, the third point is (0, 2).
Step 04: Choosing x = 1.
Substituting x by 1 in the equation:
[tex]\begin{gathered} y=2\cdot3^1 \\ y=2\cdot3 \\ y=6 \end{gathered}[/tex]So, the fourth point is (1, 6).
Step 05: Write the points in a table.
x y (x, y)
-2 2/9 (-2, 2/9)
-1 2/3 (-1, 2/3)
0 2 (0, 2)
1 6 (1, 6)
Step 06: Plot the points and connect them.
The figure below shows the points and the graph.
Done! Your question is solved!
I need help with 4 problems
Answers
1)
[tex]c^2=5^2+5^2[/tex]then the solution is
[tex]c=\sqrt[]{25+25}=\sqrt[]{50}=5\sqrt[]{2}\approx7.1[/tex]Question 3 of 102 PointsWhat is the midpoint of the segment shown below?(-1,2)(73)O A. (6,3)O B. (3,3)O C. (3.)O D. (6,5)10
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If Ellen's gross pay for a two-week period is $1680.00, what is her net pay?O $1606.92O $168.00O $1341.48O $1478.40
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It's important to know that the gross pay refers to money before taxes, while the net pay refers to money after deductions.
Hence, the net payment must be less than $1,680.
Hence, the answer is $1,606.92.A box contains four red marbles three green marbles and to blue marbles one marble is removed from the box and it's not replaced another marble is drawn from the box does the following represent in and a independent event
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The correct option is Yes, which is option A
Why?
The reason is that the probability that marble is removed from the box does not affect the probability that a marble is drawn from the same box. i.e the two events do not affect each other
Section 1- Question 1Ryan is solving the equation - 6x = 12 by completing the square. What number should be added to both sides of the equation to complete the square?
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Solution:
Given the equation below
[tex]x^2-6x=12[/tex]Applying the completing the square method
Where the general form of a quadratic equation is
[tex]ax^2+bx+c=0[/tex]For the completing square method,
[tex]Add\text{ }(\frac{b}{2})^2\text{ to both sides of the equation}[/tex]Where
[tex]b=-6[/tex]The number that should be added to both sides of the equation to complete the square is
[tex]=(\frac{-6}{2})^2=(-3)^2=9[/tex]Hence, the number is 9 (option B)
Write 12.5% as a decimal.
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12.5% as a decimal is 0.125.
To convert a percentage in to a decimal, we divide the percentage by 100:
[tex]12.5\div100=0.125[/tex]Differentiatey = -8 In x
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Given:
[tex]y=-8lnx[/tex]Let's differentiate the equation.
To differentiate since -8 is constant with resppect to x, the derivative will be:
[tex]\begin{gathered} \frac{d}{dx}(-8lnx) \\ \\ =-8\frac{d}{dx}(ln(x)) \end{gathered}[/tex]Where:
derivative of ln(x) with respect to x = 1/x
Thus, we have:
[tex]\begin{gathered} -8\frac{1}{x} \\ \\ =-\frac{8}{x} \end{gathered}[/tex]ANSWER:
[tex]-\frac{8}{x}[/tex]a sea turtle can swim at rate of 20 miles per hour. How many feet per hour can a sea turtle swim
Answers
The rate at which turtle can swim is 20 miles per hour or 20 miles in one hour.
For conversion, 1 mile is equal to 5280 foot.
Convert 20 miles per hour in foot per hour.
[tex]\begin{gathered} 20\text{ mile per hour=20 miles per hour}\times\frac{5280\text{ foot per hour}}{1\text{ mile per hour}} \\ =20\cdot5280\text{ foot per hour} \\ =105600\text{ foot per hour} \end{gathered}[/tex]So answer is 105600 foot per hour.
Question 1 Business Analytics
Answers
The responses to the linear optimization questions are;
Question 1
The optimal daily profit is $380
Question 2
The combination of x and y that yield the optimal value is the option;
x = 0, y = 3
What is linear optimization or optimization?Linear programming is a method by which the optimal solution can be obtained from a model represented mathematically and in which the constraints of the model have linear relationships.
Question 1
Let B represent the number of bear claws, C the almond-filled croissant, F represent the flour, Y represent the amount of yeast and A represent the number of almonds.
The amount of ingredient per each produce is therefore;
B = 6·F + 1·Y + 2·A
C = 3·F + 1·Y + 4A
The amount of ingredient available for the days production is as follows;
Ingredient available; 6600·F + 1400·Y + 4800·A
The constraints are therefore
6·B + 3·C ≤ 6,600
B + C ≤ 1,400
2·B + 4·C ≤ 4800
The maximizing function is therefore;
Profit = 0.2·B + 0.3·F
The equations of the lines are therefore;
B = 1,100 - 0.5·C
B = 1400 - C
B = 2400 - 2·C
The vertices of the feasible region are;
(0, 1100), (600, 800), (1000, 400), 1200, 0)
The values of the maximizing function at the vertices of the feasible region are;
Profit, P = 0.2×1100 + 3×0 = 220
At point (600, 800), P = 0.2×800 + 0.3×600 = 340
At point (1000, 400), P = 0.2×400 + 0.3×1000 = 380
At point (1200, 0), P = 0.2×0 + 0.3×1200 = 360
The maximum profit is $380, obtained when 400 Bear claws and 1000 almond filled croissants are producedQuestion 2
Maximize $3·x + $15·y
Subject to the following constraints;
2·x + 4·y ≤ 12
5·x + 2·y ≤ 10
x, y ≥ 10
The equations are therefore;
4·y ≤ 12 - 2·x
y ≤ 3 - 0.5·x...(1)
5·x + 2·y ≤ 10
2·y ≤ 10 - 5·x
y ≤ 5 - 2.5·x...(2)
x ≥ 10, y ≥ 10
The coordinates of the vertices of the feasible region are;
(0, 3), (1, 2.5), and (2, 0)
The values of the maximizing function are therefore;
At (0, 3), M = $3 × 0 + $15 × 3 = $45
At (1, 2.5), M = $3 × 1 + $15 × 2.5 = $40.5
At (2, 0), M = $3 × 2 + $15 × 0 = $6
The combination of x and y that yield the optimum is therefore;
(x, y) = (0, 3)
x = 0, and y = 3
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2. The total sales for June at Jim's Candy Store were $7,785. The total sales for June and Julywere $12,603, what were the total sales for July?ExplorerPlanSolve:Examine:Answer:
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A student bought a calculator and a textbook for a course in algebra. He told his friend that the total cost was $165 (without tax) and thatthe calculator cost $25 more than thrice the cost of the textbook. Whatwas the cost of each item? Let x = the cost of a calculator andy = the cost of the textbook. The corresponding modeling system is { x = 3y + 25x + y =Solve the system by using the method of= 165substitution
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We know that the calculator price (x) was 25 more than 3 times the price of the textbook (y).
This can be represented as:
[tex]x=3y+25[/tex]We also know that the sum of the prices of the two items is equal to $165:
[tex]x+y=165[/tex]We have to solve this system of equations with the method of substitution.
We can use the first equation, as we have already clear the value of x, to substitute x in the second equation and then solve for y:
[tex]\begin{gathered} x+y=165 \\ (3y+25)+y=165 \\ 4y+25=165 \\ 4y=165-25 \\ 4y=140 \\ y=\frac{140}{4} \\ y=35 \end{gathered}[/tex]With the value of y we can calculate x using the first equation:
[tex]\begin{gathered} x=3y+25 \\ x=3\cdot35+25 \\ x=105+25 \\ x=130 \end{gathered}[/tex]Answer: the solution as ordered pair is (x,y) = (130, 35)
I NEED HELP WITH THIS ASAP 100 POINTS IF SOMEONE GETS THIS RIGHT.
Question 12(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
For triangle XYZ, m∠X = (4g + 13)° and the exterior angle to ∠X measures (3g + 48)°. Find the measure of ∠X and its exterior angle.
Interior angle = 48°; exterior angle = 74.25°
Interior angle = 74.25°; exterior angle = 48°
Interior angle = 81°; exterior angle = 99°
Interior angle = 99°; exterior angle = 81°
Answers
Answer:
Interior angle = 81°; exterior angle = 99°.
Step-by-step explanation:
For triangle XYZ:
m∠X = (4g + 13)° exterior angle to ∠X = (3g + 48)°Angle X and its exterior angle form a straight line.
Angles on a straight line sum to 180°.
Therefore:
⇒ (4g + 13)° + (3g + 48)° = 180°
⇒ 4g + 13 + 3g + 48 = 180
⇒ 7g + 61 = 180
⇒ 7g + 61 - 61 = 180 - 61
⇒ 7g = 119
⇒ 7g ÷ 7 = 119 ÷ 7
⇒ g = 17
To find the measure of ∠X and its exterior angle, substitute the found value of g into the angle expressions:
⇒ m∠X = (4(17) + 13)°
⇒ m∠X = (68 + 13)°
⇒ m∠X = 81°
⇒ exterior angle to ∠X = (3(17) + 48)°
⇒ exterior angle to ∠X = (51 + 48)°
⇒ exterior angle to ∠X = 99°
Therefore:
Interior angle = 81°Exterior angle = 99°Answer: C
Step-by-step explanation: did the practice test!
Rewrite each equation in slope intercept form, if necessary. Then determine whether the lines are parallel. Explain3x+4y = 86x+3y = 6Are these lines parallel?A.B.C.D.(look at image for answer choices)
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We can rewrite the next equations in the slope-intercept form:
The first equation:
[tex]3x+4y=8\Rightarrow4y=8-3x\Rightarrow y=\frac{8}{4}-\frac{3}{4}x\Rightarrow y=2-\frac{3}{4}x\Rightarrow y=-\frac{3}{4}x+2[/tex]The second equation:
[tex]6x+3y=6\Rightarrow3y=6-6x\Rightarrow y=\frac{6}{3}-\frac{6}{3}x\Rightarrow y=2-2x\Rightarrow y=-2x+2_{}[/tex]As we can see, the slope of the first line is m = -3/4, and the slope of the second line is m = -2. Then, since the slope is different, these lines are not parallel (Option C).
I have an advanced trig equation it's a word problem about non-right triangles it's just for practice not for a graded homework or a quiz. it is a word problem and a picture is included.
Answers
Using trigonometric equations we calculate the length of the guy wire from the tower is approximately 1306.5 feet .
The given information about the Tower are :
ED = 175 feet
∠DAB = 57°
∠CED = 30°
Now in the triangle ADB we have ∠ABD = 90° (refer to diagram below)
Therefore ∠ADB = 180° - (57° + 90°) = 33°
Now ∠ EDC = 180° - 33° = 147 °
Hence in triangle EDC ,
∠ECD = 180° - (147°+ 30°) = 3°
Now we will use the law of sines to find the height of the tower.
We know from the law of sines that in ΔEDC
[tex]\frac{ED}{sin\angle C} =\frac{CD}{sin\angle E} =\frac{CE}{sin\angle D}[/tex]
now we will use this to find the height of the tower which is CD
∴ CD = sin °30 × 175 ÷ sin 3°
CD = 1671.8907...
CD ≈ 1671.9 feet.
length of the guy wire = CE
∴CE = sin 157° × 175 ÷ sin 3°
CE = 1306.5195...
CE ≈ 1306.5 feet
Hence the height of the tower is 1671.9 feet and the length of the guy wire is 1306.5 feet.
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Given a triangle ABC at points A = ( - 6, 3 ) B = ( - 4, 7 ) C = ( - 2, 3 ), and a first transformation of up 2 and right 3, and a second transformation of down 1 and left 6, what would be the location of the final point B'' ?
Answers
B'' = (-7, 8)
Explanation:The points of the triangle are:
A = ( - 6, 3 ) B = ( - 4, 7 ) C = ( - 2, 3 )
The first transformation:
2 units up and 3 units right
B' = (-4+3, 7+2)
B' = (-1, 9)
Second transformation:
1 unit down, 6 units left
B'' = (-1-6, 9-1)
B'' = (-7, 8)
write (2 to the power of -1) to the power of 3 with the same base but one exponent
Answers
Explanation
Step 1
[tex](2^{-1})^3[/tex]remember
[tex]\begin{gathered} a^{-n}=\frac{1}{a^n} \\ (a^n)^m=a^{n\cdot m} \\ (\frac{a}{b})^m=\frac{a^m}{b^m} \end{gathered}[/tex]Step 2
solve
[tex]\begin{gathered} (2^{-1})^3 \\ (2^{-1})^3=(\frac{1}{2^1})^3=(\frac{1^3}{2^3})=\frac{1}{8} \end{gathered}[/tex]The engine of a car has a displacement of 460 cubic inches. What is the displacement in cubic feet? Round your answer to 2 places.
Answers
Explanation
To find the displacement in cubic feet, divide the volume value by 1728.
[tex]\frac{460}{1728}=0.27[/tex]Answer: 0.27 cubic feet
A line is graphed on the coordinate plane below.Line y = -2 +2 will be graphed on the same coordinate plane to create a system of equations.What is the solution to that system of equations?4A (-2,4)B (0-4)C (2,-4)0 (4,-2)Rod End TeeFlagOptionsBackNext
Answers
Solution:
Step 1: Find the equation of the line in the graph.
Two points the line pass through are (0, -4) and (2, -3)
Thus,
[tex]\begin{gathered} x_1=0,y_1=-4 \\ x_2=2,y_2=-3 \end{gathered}[/tex][tex]\begin{gathered} The\text{ equation of the line can be calculated with the formula} \\ \frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1} \\ \\ \frac{-3-(-4)}{2-0}=\frac{y-(-4)}{x-0} \\ \\ \frac{-3+4}{2}=\frac{y+4}{x} \\ \frac{1}{2}=\frac{y+4}{x} \end{gathered}[/tex][tex]\begin{gathered} 2(y+4)=x \\ 2y+8=x \\ 2y=x-8 \end{gathered}[/tex]The equation of the graph is 2y = x - 8
Step 2:
Solve the two equations simultaneously to detemine the solution to the systems of equations
2y = x - 8 ------------------------equation (1)
y = -x + 2 ----------------------equation (2)
Add both equations to eliminate x
2y + y = x - 8 + (-x) + 2
3y = x -8-x+2
3y = -8 + 2
3y = -6
y = -6/3
y = -2
Substitute y = -2 into equation (2)
y = -x + 2
-2 = -x + 2
-2 -2 = -x
-4 = -x
-x = -4
Divide both sides by -1
x = 4
Hence, the solution to the system of equations is (4, -2)
The correct option is option D
the amount of money a worker earns is directly proportional to the number of hours worked.at this rate.thag worker makes $104 in an 8 hour shift.weite a direct variation equation that relates the earnings (e) of the worker to the number of hours (n) worked. use the correct lowercase variables given ,and use no spaces
Answers
the amount of money a worker earns is directly proportional to the number of hours worked.at this rate.thag worker makes $104 in an 8 hour shift.weite a direct variation equation that relates the earnings (e) of the worker to the number of hours (n) worked. use the correct lowercase variables given ,and use no spaces
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form e=kn
In this problem we have
e -----> amount of money a worker earns
n -----> number of hours worked
k is the constant of proportionality
k=e/n
Find the value of k
we have
For n=8 hours, e=$104
sibstitute
k=104/8
k=$13 per hour
The linear equation is
e=13nSimplify the expression. 2m - 8 - 2m - 1
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At the independent record company where Gwen works, the vinyl format has been experiencing a resurgence in popularity. Record sales are increasing by 11% each year. If 19,360 records were sold this year, what will annual sales be in 2 years?If necessary, round your answer to the nearest whole number.
Answers
Step 1:
Write the given data
r = 11% = 0.11
P = 19360
t = 2
Step 2:
Apply exponential increase or growth formula
[tex]\begin{gathered} A=P(1+r)^t \\ A\text{ = future value} \\ P\text{ = present value} \\ r\text{ = rate} \\ t\text{ = time} \end{gathered}[/tex]Step 3:
Substitute in the formula
[tex]\begin{gathered} A\text{ = 19360 }\times(1+0.11)^2 \\ A\text{ = 19360 }\times1.11^2 \\ A\text{ = }23853.456 \end{gathered}[/tex]Final answer
23853
7:20 A.M to 9:49 A.M
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We can add the minutes from 7:20 AM to the next hour (8:00 AM), that is 40 minutes.
Then, from 8:00 AM to 9:00 AM we have 60 more minutes.
Then, from 9:00 AM to 9:49 AM we have 49 additional minutes.
We add all three segments as:
[tex]40+60+49=149[/tex]As 60 minutes is 1 hour, 120 minutes is 2 hours. Then, 149 minutes are 2 hours and 29 minutes.
Answer: the time elapsed us 149 minutes (or 2 hours and 29 minutes)
Using the data in the image could you help with this question State some possible causes of the error in your measured value. What techniques could be used to correct it?
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Answer:
Step-by-step explanation:
1 + z/3 + 2w. Which part of the expression is a product of two factors? Describe it's part e form quotient of two factors? Describe its parts.
Answers
2w is the part of two factors.
The part of the expression is a product of two factors.
The expression we have is:
[tex]1 + \frac{z}{3}+2w[/tex]
Let's analyze the parts of this expression.
The first term of the expression is a constant term: 1.
1 is not a product of two factors, so this is not the answer.
The second term of the expression is: z/3.
This part of the expression is a division or quotient between z and 3. Thus, since it is a division and not a product, this is also not the answer we are looking for.
The third term of the expression is: 2w
In this case, the term 2w is a product between "2" and "w". Thus, 2w is a product of two factors. The parts of this product are 2 and which when multiplied result in 2w.
Hence the answer is 2w is the part of two factors.
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A dairy produced 8.1 liters of milk in 2 hours. How much milk, on average, did the dairyproduce per hour?
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To answer this question, we need to find the unit rate in this case. For this, we need to divide the given liters by the hours. Then, we have:
[tex]\frac{8.1l}{2h}=4.05\frac{l}{h}[/tex]Then, the dairy produces 4.05 liters per hour.
WZ = 32, YZ = 6, and X is the midpoint of WY. Find WX.
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We are given the length of two segments:
WZ = 32
YZ = 6
and we are told that x is the midpoint of the segment WY
We are asked to find the length of the segment WX
Notice that the total length of the segment WZ is 32. from the point Y to the point Z we have 6 units. therefore, between W and Y there is 32 - 6 = 26 units.
SInce X is the midpoint of the distance between W and Y, then it has to cut the segment WY (26 units long) in two equal parts, each of length 13 units (half of 26).
Therefore, WX must be of length 13 units.
Complete each equation in order to obtain the indicated solution
Answers
Question 13.
Part (a).
Given the solution:
All real numbers
We have the expression:
3(4x + 2) = ________
Let's complete the equation in order to obtain the indicated solution.
For a solution to be all real numbers, the equation must be true.
hence, we have:
[tex]\begin{gathered} 3(4x+2)=3(4x+2) \\ \end{gathered}[/tex]After solving we have:
0 = 0
This means the system has infinitely many solutions, therefore, the solution is all real numbers.
ANSWER:
3(4x + 2) = 3(4x + 2)