To determine how much silk Amanda has at the end we need to substract the amount each pice need from the original amount:
[tex]\begin{gathered} 25-\frac{18}{7}-\frac{11}{2}-\frac{7}{4}-\frac{25}{7}=25-\frac{43}{7}-\frac{11}{2}-\frac{7}{4} \\ =25-\frac{86+77}{14}-\frac{7}{4} \\ =25-\frac{163}{14}-\frac{7}{4} \\ =25-\frac{652+98}{56} \\ =25-\frac{750}{56} \\ =\frac{1400-750}{56} \\ =\frac{650}{56} \\ =\frac{325}{28} \\ =11\frac{17}{28} \end{gathered}[/tex]Therefore Amanda has 11 17/28 yards of silk left.
need help asappppppp
Here, we want to get the length of the ladder
The kind of triangle we have is a right triangle for which obeys the Pythagoras' theorem
According to the theorem, the square of the hypotenuse equals the sum of the squares of the two other sides
The length of the ladder marked as h is the hypotenuse
Thus, we have it that;
[tex]\begin{gathered} h^2=9^2+7^2 \\ h^2\text{ = 81 + 49} \\ h^2\text{ = 130} \\ h\text{ = }\sqrt[]{130} \\ h\text{ = 11.40 meters} \end{gathered}[/tex]what is the shape of a cross section that is parallel to the bases
The cross-section that is parallel to the base will have a
RECTANGULAR Shape
It's just like cutting through the shape horizontally
if I need 1/2 cup of oil but I only have 1/3 cup of oil how much oil do I need
We need 1/2 cup of oil and we are told that we already have 1/3 cup of oil, to find out how much we need we subtract this and the result will be the amount of oil we need.
[tex]\frac{1}{2}-\frac{1}{3}=\frac{3-2}{6}=\frac{1}{6}[/tex]In conclusion, the answer is 1/3 cup of oil
Use the sum and difference identities to rewrite the following expression as a trigonometric function of asingle number.sin(15°)cos(135) + cos(159) sin(135)
The value of the given trigonometric function is [tex]\sqrt{3} +1[/tex]
The given trigonometric function is sin(15°)cos(135) + cos(15) sin(135).
Evaluating the expression with the sum and difference identities.
We know, SinACosB + CosASinB = Sin(A +B)
Now, We have :
sin(15°)cos(135) + cos(15) sin(135) = Sin ( 15 +135 ) = Sin150
Now, Sin 150 = Sin(120 +30) = Sin120Cos30 + Cos120Sin30
Sin 150 =
[tex]=\frac{\sqrt{3} }{2} * \frac{\sqrt{3} }{2} + \frac{1}{2}*\frac{1}{2} = \frac{2\sqrt{3} }{2} +\frac{2}{2} \\\\= \sqrt{3} +1[/tex]
Hence, the value of the given trigonometric function is [tex]\sqrt{3} +1[/tex]
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Use the Distributive Property
solve the equation.
- 6(x + 3) = 30
Using the Distributive Property of multiplication, the equation - 6(x + 3) = 30 is solved as x = -8.
What is the distributive property of multiplication?The distributive property of multiplication shows that a mathematical expression in the form of a(b + c) is also equal to ab + ac.
The distributive property applies to either addition or subtraction in multiplication.
- 6(x + 3) = 30
-6x - 18 = 30
-6x = 48
x = -8
Thus, x = -8 is the solution to the equation - 6(x + 3) = 30.
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Solving a trigonometric equation involving an angle multiplied by a constant
In these questions, we need to follow the steps:
1 - solve for the trigonometric function
2 - Use the unit circle or a calculator to find which angles between 0 and 2π gives that results.
3 - Complete these angles with the complete round repetition, by adding
[tex]2k\pi,k\in\Z[/tex]4 - these solutions are equal to the part inside the trigonometric function, so equalize the part inside with the expression and solve for x to get the solutions.
1 - To solve, we just use algebraic operations:
[tex]\begin{gathered} \sqrt[]{3}\tan (3x)+1=0 \\ \sqrt[]{3}\tan (3x)=-1 \\ \tan (3x)=-\frac{1}{\sqrt[]{3}} \\ \tan (3x)=-\frac{\sqrt[]{3}}{3} \end{gathered}[/tex]2 - From the unit circle, we can see that we will have one solution from the 2nd quadrant and one from the 4th quadrant:
The value for the angle that give positive
[tex]+\frac{\sqrt[]{3}}{3}[/tex]is known to be 30°, which is the same as π/6, so by symmetry, we can see that the angles that have a tangent of
[tex]-\frac{\sqrt[]{3}}{3}[/tex]Are:
[tex]\begin{gathered} \theta_1=\pi-\frac{\pi}{6}=\frac{5\pi}{6} \\ \theta_2=2\pi-\frac{\pi}{6}=\frac{11\pi}{6} \end{gathered}[/tex]3 - to consider all the solutions, we need to consider the possibility of more turn around the unit circle, so:
[tex]\begin{gathered} \theta=\frac{5\pi}{6}+2k\pi,k\in\Z \\ or \\ \theta=\frac{11\pi}{6}+2k\pi,k\in\Z \end{gathered}[/tex]Since 5π/6 and 11π/6 are π radians apart, we can put them together into one expression:
[tex]\theta=\frac{5\pi}{6}+k\pi,k\in\Z[/tex]4 - Now, we need to solve for x, because these solutions are for all the interior of the tangent function, so:
[tex]\begin{gathered} 3x=\theta \\ 3x=\frac{5\pi}{6}+k\pi,k\in\Z \\ x=\frac{5\pi}{18}+\frac{k\pi}{3},k\in\Z \end{gathered}[/tex]So, the solutions are:
[tex]x=\frac{5\pi}{18}+\frac{k\pi}{3},k\in\Z[/tex]Which relation represents a function sample A or sample B
Sample A is a function because we don't have 2 values of x that are the same
Sample B is not a function, because it fails the vertical line test (x = 4 and y =1 also x=4 and y = 10) (4, 1) and (4, 10)
Hence the correct option is ; sample A
Given the definitions of f(x) and g(x) below, find the value of g(f(-2)). f(x) = 5x + 4 g(x) = x^2 - 6x - 13
f(-2) = 5(-2) + 4
= -10 + 4
= -6
g(f(-2))
= -6^2 -6*-6 -13
= 36 + 36 - 13
= 59
Is a tutor availible?
this is a conversion problem
First you must understand that 1 foot = 12inches
Given a ribbon that is 5 1/2 feet long
To convert to inches, you will simply multiply 5 1/2 by 12 as shown;
= 5 1/2 * 12
convert the mixed fraction to improper fraction
= 11/2 * 12
= 11 * 12/2
= 11 * 6
= 66 inches
Hence the ribbon is 66 inches long
If you receive 360 promotional emails per month and only 2.5% percent of those emails are of interest to you, what is the expected number of promotional emails that will be of interest to you each month?
Total email 360
percentage email of interest 2.5%
Solution[tex]\begin{gathered} \frac{2.5}{100}\times360=9 \\ \end{gathered}[/tex]The final answer9 promotional emails that will be of interest to you each monthIf pp is inversely proportional to the square of qq, and pp is 22 when qq is 8, determine pp when qq is equal to 4.
Given that p is inversely proportional to the square of q that implies:
[tex]p\propto\frac{1}{q^2}[/tex]Remove the sign of proportionality and put a proportionality constant k such that:
[tex]p=\frac{k}{q^2}[/tex]Given that when q is 8 then p is 22. So,
[tex]22=\frac{k}{8^2}\Rightarrow k=22\times64=1408[/tex]Put k = 1408 and q = 4 in the equation to find the value of p:
[tex]p=\frac{1408}{4^2}=\frac{1408}{16}=88[/tex]Thus, the answer is 88.
Don’t know how to solve with the -1 before the x
ANSWER and EXPLANATION
We are given a function and its inverse function:
[tex]\begin{gathered} f(x)=\frac{1}{2}x \\ f^{-1}(x)=2x \end{gathered}[/tex]To solve the problems, we have to substitute the values of x in the brackets into the appropriate function (or inverse function).
Therefore, we have that the value of the function for x = 2:
[tex]\begin{gathered} f(2)=\frac{1}{2}\cdot2 \\ f(2)=1 \end{gathered}[/tex]For x = 1, we have that the value of the inverse function is:
[tex]\begin{gathered} f^{-1}(1)=2(1) \\ f^{-1}(1)=2 \end{gathered}[/tex]For x = -2, we have that the value of the inverse function is:
[tex]\begin{gathered} f^{-1}(-2)=2\cdot-2 \\ f^{-1}(-2)=-4 \end{gathered}[/tex]For x = -4, we have that the value of the function is:
[tex]\begin{gathered} f(-4)=\frac{1}{2}\cdot-4 \\ f(-4)=-2 \end{gathered}[/tex]For the fifth option, substitute the value of the function at x = 2 into the inverse function.
That is:
[tex]\begin{gathered} f^{-1}(f(2))=f^{-1}(1)=2\cdot1 \\ f^{-1}(f(2))=2 \end{gathered}[/tex]For the sixth option, substitute the value of the inverse function at x = -2 into the function.
That is:
[tex]\begin{gathered} f(f^{-1}(-2))=f(-4)=\frac{1}{2}\cdot-4 \\ f(f^{-1}(-2))=-2 \end{gathered}[/tex]To find the general form of the function:
[tex]f^{-1}(f(x))=f(f^{-1}(x))[/tex]either substitute the function for x in the inverse function or substitute the inverse function for x in the function.
Therefore:
[tex]\begin{gathered} f^{-1}(f(x))=2(\frac{1}{2}x)) \\ f^{-1}(f(x))=x \end{gathered}[/tex]That is the answer.
A survey of a random sample of voters showsthat 56% plan to vote Yes to the newproposition and 44% plan to vote No. Thesurvey has a margin of error of +4%. What isthe range for the percentage of voters whoplan to vote Yes?
Answer:
G 52% to 60%
Explanation:
The percentage of voters that plan to vote Yes = 56%
The survey's margin of error = +/-4%
Therefore, the range for the percentage of voters who plan to vote Yes is:
[tex]\begin{gathered} 56\%\pm4\% \\ =56\%-4\%\text{ to }56\%+4\% \\ =52\%\text{ to }60\% \end{gathered}[/tex]The correct choice is G.
a parking lot is distracted in the shape of a parallelogram if the base is 200 feet the height is 120 ft and the Dialganal with is 140 feet what is the area of the parking lot?
a parking lot is distracted in the shape of a parallelogram if the base is 200 feet the height is 120 ft and the Dialganal with is 140 feet what is the area of the parking lot?
we know that
the area of parallelogram is equal to
A=b*h
where
b is the base
h is the height
substitute the given values
A=200*(120)
A=24,000 ft^2
the area is 24,000 square feeta rectangle has the perimeter of 116 cm and its length is 1cm more than twice its width. I got 39L and 19w but I'm having problems setting up the problems
To answer this question, we can proceed as follows:
1. We have that the perimeter of the rectangle is equal to 116cm, then, we have:
[tex]w+l+w+l=116\Rightarrow2w+2l=116[/tex]We know that a rectangle is a parallelogram. Then, its opposite sides are congruent.
2. We have that the length of the rectangle is 1 cm more than twice its width. We can translate this, algebraically, as follows:
[tex]l=2w+1[/tex]Now, to find the measures of the length and the width of the rectangle, we can substitute this last formula into the first one, as follows:
[tex]2w+2(2w+1)=116[/tex]We need to apply the distributive property to find w:
[tex]2w+4w+2=116[/tex]Adding like terms:
[tex]6w+2=116[/tex]Subtracting 2 to both sides of the equation, and then dividing by 6:
[tex]6w+2-2=116-2\Rightarrow6w=114\Rightarrow\frac{6w}{6}=\frac{114}{6}\Rightarrow w=19[/tex]Then, the width of the rectangle is equal to 19cm. The measure of the length can be calculated using either equation above. Let us use the first equation:
[tex]2w+2l=116\Rightarrow2\cdot19+2l=116\Rightarrow38+2l=116[/tex]Then, using similar properties as before, we have:
[tex]38-38+2l=116-38\Rightarrow2l=78\Rightarrow\frac{2l}{2}=\frac{78}{2}\Rightarrow l=39[/tex]In summary, we have that the measures of the length and width of this rectangle are:
• Width, ,(w) =, 19cm
,• Legth (l) = ,39cm
A resident is to receive 2 ounces of liquid . You know 30 ccs equals one ounce . How many ccs of the liquid will you give to ensure the resident receives 2 ounces
From the statement of the question, we know that 1 ounce and 30ccs are equivalent, we represent that with the following equation:
[tex]1\text{ounce}=30\text{ccs.}[/tex]Now, 2 ounces is double of 1 ounce, because 1 ounce is 30 ccs, 2 ounces must be 60ccs, the double of 30ccs.
[tex]2\text{ounces}=2\cdot1\text{ounce}=2\cdot30\text{ccs}=60\text{ccs.}[/tex]So if we want to ensure that the resident will receive 2 ounces of liquid, we must give him 60ccs.
Answer: we must give him 60ccs of liquid.
I need help with this questionthe question to this question is below is a graph of a logarithmic function, identify it key characteristics. match accordingly
The answers to the problem :
[tex]\begin{gathered} 1.\text{ Domain : x >-6} \\ 2\text{ Range : -}\infty\text{ to +}\infty \\ 3.\text{ Aymptote : x = -6} \\ 4\text{. Transformation : left 6, down 1} \\ 5.\text{ End behaviour : As x approaches }\infty,\text{ f(x) approaches }\infty.\text{ As x approaches -6, f(x) approaches -}\infty \\ 6.\text{ x-intercept : (-4,0)} \end{gathered}[/tex]Find the inverse of 1/4x^3+2x-1=y
need help with example #4 Find all missing angles and sides.
We will use the law of sines and law of cosines shown below
[tex]\begin{gathered} c=\sqrt{a^2+b^2-2ab\cos C}\rightarrow\text{ law of cosines} \\ and \\ \frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}\rightarrow\text{ law of sines} \end{gathered}[/tex]Therefore, in our case, finding side c.,
[tex]\begin{gathered} a=28,b=13,C=49\degree \\ \Rightarrow c=\sqrt{784+169-2*28*13cos(49\degree)} \\ \Rightarrow c\approx21.8 \end{gathered}[/tex]Thus, side c is approximately 21.8km.
Finding the missing angles using the law of sines,
[tex]\begin{gathered} A=\cos^{-1}(\frac{c^2+b^2-a^2}{2bc}) \\ \Rightarrow A=\cos^{-1}(\frac{21.8^2+13^2-28^2}{2*13*21.8}) \\ \Rightarrow A\approx104.3 \\ \end{gathered}[/tex]Similarly, in the case of angle B,
[tex]sinB=\frac{13}{21.8}sin(49\degree)\approx26.7\degree[/tex]Therefore, the answers are
c=21.8km,
Team A, B, and C are competing in a basketball tournament. The probability of team A winning is 0.2, the probability of team B winning is 0.45, and the probability of team C winning is 0.35. Anna can join either team A or team B. Elina can join either team B or team C. Nancy can join either team A or team C. Who is most likely to win?AnnaNancyElenaAll have an equal probability to win.
Solution
We are given that
[tex]\begin{gathered} p(A)=0.2 \\ p(B)=0.45 \\ p(C)=0.35 \end{gathered}[/tex]Note 1: Probability Formula To use
[tex]p(A\cup B)=p(A)+p(B)-p(A\cap B)[/tex]Note 2: Team A, B and C are Mutually Exclusive
[tex]\begin{gathered} p(A)+p(B)+p(C)=0.2+0.45+0.35=1 \\ Th\text{ey are mutually exclusive} \\ A\cap B=B\cap C=A\cap C=\varnothing \\ p(A\cap B)=p(B\cap C)=p(A\cap C)=0 \end{gathered}[/tex]Therefore, the formula to use now is
[tex]p(A\cup B)=p(A)+p(B)[/tex]For Anna
Anna can join either team A or team B.
We calculate the probability
[tex]\begin{gathered} p(A\cup B)=p(A)+p(B) \\ p(A\cup B)=0.2+0.45 \\ p(A\cup B)=0.65 \end{gathered}[/tex]For Elina
Elina can join either team B or team C.
We calculate the probability
[tex]\begin{gathered} p(B\cup C)=p(B)+p(C) \\ p(B\cup C)=0.45+0.35 \\ p(B\cup C)=0.8 \end{gathered}[/tex]For Nancy
Nancy can join either team A or team C.
We calculate the probability
[tex]\begin{gathered} p(A\cup C)=p(A)+p(C) \\ p(A\cup C)=0.2+0.35 \\ p(A\cup C)=0.55 \end{gathered}[/tex]The one with the highest probability is most likely to win and that is
ELINA
Correct answer is Elina
n a 45 minute basketball game, 30 girls want to play. Only 10 can play at once. If each player is to play the same length of time, how many minutes should each play?
A 45 minute basketball game, 30 girls want to play. Only 10 can play at once. If each player is to play the same length of time. 15 minutes should each play
10/30=1/3
[tex]\frac{1}{3} \times 45$$[/tex]
Convert element to fraction: [tex]$\quad 45=\frac{45}{1}$[/tex]
[tex]=\frac{1}{3} \times \frac{45}{1}$$[/tex]
Apply the fraction rule:[tex]$\frac{a}{b} \times \frac{c}{d}=\frac{a \times c}{b \times d}$[/tex]
[tex]=\frac{1 \times 45}{3 \times 1}$$[/tex]
[tex]$\frac{1 \times 45}{3 \times 1}=\frac{45}{3}$[/tex]
[tex]=\frac{45}{3}[/tex]
Divide the numbers: [tex]$\frac{45}{3}=15$[/tex]
=15
15 minutes for 3 groups of 10 each to play basketball.
To add or subtract fractions, the denominator must be the same (the bottom value). Subtraction and addition with the same denominators If the denominators are already the same, all that remains is to add or subtract the numerators (the top value).
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Use the quadratic formula to solve for X. 3x^2 = -3x +7
The solutions are:
x = -2.11 or 1.11
Explanation:Given the equation:
[tex]3x^2=-3x+7[/tex]This can be written as:
[tex]3x^2+3x-7=0[/tex]Comparing this with the general equation;
[tex]ax^2+bx+c=0[/tex]We see that;
[tex]\begin{gathered} a=3 \\ b=3 \\ c=-7 \end{gathered}[/tex]The quadratic formula is:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Substitute the values of a, b, and c
[tex]\begin{gathered} x=\frac{-3\pm\sqrt[]{3^2-4\times3\times(-7)}_{}}{2\times3} \\ \\ =\frac{-3\pm\sqrt[]{9+84}}{6} \\ \\ =\frac{-3\pm\sqrt[]{93}}{6} \\ \\ =\frac{-3\pm9.64}{6} \\ \\ x=\frac{-3+9.64}{6}=1.11 \\ \\ OR \\ x=\frac{-3-9.64}{6}=-2.11 \end{gathered}[/tex]Which of the following equations is equivalent to the given equation?
Answer:
[tex]\begin{equation*} 5(7a+5)-80=4(3a+15) \end{equation*}[/tex]Explanation:
Given the equation:
[tex]\frac{7a+5}{8}-2=\frac{3a+15}{10}[/tex]First, find the lowest common multiple of the denominators 8 and 10.
• The LCM of 8 and 10 = 40
Then, multiply all through by 40:
[tex]\begin{gathered} \frac{40(7a+5)}{8}-2(40)=\frac{40(3a+15)}{10} \\ \implies5(7a+5)-80=4(3a+15) \end{gathered}[/tex]The third option is equivalent.
Answer:
5(7a + 5) - 80 = 4(3a + 15)
Step-by-step explanation:
graph the quadrilateral with the given vertices in a coordinate plane. then show the quadrilateral in a a parallelogram
First, let's graph the polygon:
Now, let's prove it's a parallelogram by showing that the segments NP and RQ are parallel, and NR and PQ are parallel as well.
Let's prove that the angular coefficient is the same for NR and PQ
[tex]\begin{gathered} m_{NR}=\frac{0-(-4)}{-5-(-3)}=-\frac{4}{3} \\ \\ m_{PQ}=\frac{5-0}{0-3}=-\frac{4}{3} \end{gathered}[/tex]Then they're parallel, just to confirm, let's do the same for NP and RQ
[tex]\begin{gathered} m_{NP}=\frac{4-0}{0-(-5)}=\frac{4}{5} \\ \\ m_{RQ}=\frac{-4-0}{-2-(3)}=\frac{4}{5} \end{gathered}[/tex]Then it's parallel as well.
A seven digit telephone number is of theform ABC-DEFG. In one particular state,the digit ‘A’ is restricted to any numberbetween 1 and 9. The digits B and Carerestricted to any number between 2 and9. The digits D,E,F, and G have norestriction. How many seven digit phonenumbers are possible with theserestrictions?
9 x 8 x 8 x 10 x 10 x 10 x 10 = 5760000 possible phone numbers
Which of the following equations is equivalent to log(y)= 3.994
ANSWER:
[tex]y=10^{3.994}[/tex]STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]log\mleft(y\mright)=3.994[/tex]Applying property of logarithms we have:
[tex]\begin{gathered} \log _a(b)=c\rightarrow b=a^c \\ \text{ in this case:} \\ log(y)=3.994\rightarrow y=10^{3.994} \end{gathered}[/tex]210000The first five multiples for the numbers 4 and 6 are shown below.Multiples of 4: 4, 8, 12, 16, 20, ...Multiples of 6: 6, 12, 18, 24, 30,...What is the least common multiple of 4 and 6?222122423 24 25Mark this and returnSave and ExitNext
Answer: 12
Explanation
The least common multiple can be calculated by getting the factor of each number. As we are told, the multiples of 4 are 4, 8, 12, 16, 20, ..., and the multiples of 6 are 6, 12, 18, 24, 30, ....
Thus, the lowest factor that they share is 12.
lebron walked 4 1/2 miles to library in 2 1/4 hours. he walked the return trip at the same average rate , but a different route, taking my 2 1/2 hours. How many miles did lebron walk on the return trip?
Answer:
5 miles
Explanation:
First, we need to transform the mixed number into decimal numbers using as follows:
[tex]\begin{gathered} 4\frac{1}{2}=4+\frac{1}{2}=4+0.5=4.5\text{ miles} \\ 2\frac{1}{4}=2+\frac{1}{4}=2+0.25=2.25\text{ hours} \\ 2\frac{1}{2}=2+\frac{1}{2}=2+0.5=2.5\text{ hours} \end{gathered}[/tex]Now, the average rate was the same, so the ratio of the miles to the hours is always the same. Therefore, we can write the following equation:
[tex]\frac{\text{Miles}}{\text{Hours}}=\frac{4.5\text{ Miles}}{2.25\text{ Hours}}=\frac{x}{2.5\text{ Hours}}[/tex]Where x is the number of miles that Lebron walked on the return trip. So, solving for x, we get:
[tex]\begin{gathered} \frac{4.5}{2.25}=\frac{x}{2.5} \\ \frac{4.5}{2.25}\times2.5=\frac{x}{2.5}\times2.5 \\ 5=x \end{gathered}[/tex]Therefore, Lebron walked 5 miles on the return trip.
how do you do this why does it make me put so many words
Part 5
we have the points
(0,4) and (4,8)
Find the slope
m=(8-4)/(4-0)
m=4/4
m=1
Find the equation in slope intercept form
y=mx+b
we have
m=1
b=4
so
y=x+4Part 6
we have the points
(0,8) and (2,4)
m=(4-8)/(2-0)
m=-4/2
m=-2
y=mx+b
we have
m=-2
b=8
so
y=-2x+8nQuestion 6Mutiple Choice Worth 1 points)(06.04 MC)The length of a rectangle is represented by the function L(x)= 2x. The width of that same rectangle is represented by the function W(x)=8x²-4x+1. Which of the following shows the area of the rectangle interms of x?(L+ W)(x)=8x²-2x+1(L + W)(x)=8x² - 6x +1(L• W)(x)=16x-4x+1(L • W)(x)=16x³-8x²+2x
Answer:
[tex]D\text{ :}(L\text{ }\circ\text{ W\rparen\lparen x\rparen= 16x}^3-8x^2+2x[/tex]Explanation:
Here, we want to select the option that best represents the area of the rectangle in terms of x
Mathematically, the area can be calculated by:
[tex]A(x)\text{ = L\lparen x\rparen }\times\text{ W\lparen x\rparen}[/tex]We have that as:
[tex]\begin{gathered} 2x\text{ }\times\text{ 8x}^2-4x+1 \\ =\text{ 2x\lparen8x}^2-4x+1) \\ =\text{ 16x}^3-8x^2+2x \end{gathered}[/tex]