Answers
The composition of the two functions evaluated in x = 2 is:
(f o g)(2) = 33
How to find the composition?Here we have the next two functions:
f(x) = x² - 3x + 5
g(x) = -2x
And we want to find the composition:
(f o g)(2) = f( g(2))
So we need to evaluate f(x) in g(2).
First, we need to evaluate g(x) in x = 2.
g(2) = -2*2 = -4
Then we have:
(f o g)(2) = f( g(2)) = f(-4)
f(-4) = (-4)² - 3*(-4) + 5 = 16 + 12 + 5 = 28 + 5 = 33
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Related Questions
Find the 52nd term.16, 36, 56, 76,…
Answers
Answer:
[tex]\text{ a}_{52}\text{ = 1,036}[/tex]Explanation:
Here, we want to find the 52nd term of the sequence
What we have to do here is to check if the sequence is geometric or arithmetic
We can see that:
[tex]\text{ 36-16 = 56-36=76-56 = 20}[/tex]Since the difference between the terms is constant, we can say that the terms have a common difference and that makes the sequence arithmetic
The nth term of an arithmetic sequence can be written as:
[tex]\text{ a}_n\text{ = a +(n-1)d}[/tex]where a is the first term which is given as 16 and d is the common difference which is 20 from the calculation above. n is the term number
We proceed to substitute these values into the formula above
Mathematically, we have this as:
[tex]\begin{gathered} a_{52}\text{ = 16 +(52-1)20} \\ a_{52}\text{ = 16 + (51}\times20) \\ a_{52}\text{ = 16 + 1020 = 1,036} \end{gathered}[/tex]Someone help me please
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Approximately 5 meters long.
957.55x8042x6/4x6=??
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6930553.9
1) Let's rewrite and solve the expression, note that since Multiplication and Division are on the same level of priority according to PEMDAS acronym for the order of operations:
[tex]\begin{gathered} 957.55\times8042\times\frac{6}{4}\times6= \\ 957.55\times8042\times\frac{3}{2}\times6= \\ 957.55\times8042\times\frac{3}{1}\times3= \\ 69305553.90= \end{gathered}[/tex]Notice that we simplified 6/4 to 3/2 and then 6 by 2. In addition to this, note that the 2 decimal places were kept, we can write 69305553.90 or simply 69305553.9
2) Hence, the answer is = 6930553.9
If d - 243 = 542, what does d-245 equal? CARA GOIECT CH 1UJAINRIகபட்ட RE Lien Answer: Your answer
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Given the following expression:
[tex]d-243=542[/tex]if we add 243 on both sides of the equation we get the following:
[tex]\begin{gathered} d-243+243=542+243=785 \\ \Rightarrow d=785 \end{gathered}[/tex]thus, d = 785
Graph the line that passes through the points (9,4) and (9,1) and determine the equation of the line.
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Both points of the given points have the same x-coordinate. This is only possible if we have a vertical line. The vertical line have the format
[tex]x=k[/tex]Where k represents the x-coordinate of all points of the line. The x-coordinate of our points is 9, therefore, the equation of the line is
[tex]x=9[/tex]And its graph is
If a rectangle has a perimeter of 70, a length of x and a width of x-9, find the value of the length of the rectangle040 3113O 22
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The formula for the perimeter of rectangle is,
[tex]P=2(l+w)[/tex]Substitute 70 for P, x for l and (x - 9) for w in the formula to determine the value of x.
[tex]\begin{gathered} 70=2(x+x-9) \\ 35=2x-9 \\ 2x=35+9 \\ x=\frac{44}{2} \\ =22 \end{gathered}[/tex]So value of x is 22.
Point M is the midpoint of AB. If AM = b² + 5b and
MB = 3b + 35, what is the length of AM?
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Step-by-step explanation:
since M is the midpoint, it means that AM = MB.
so,
b² + 5b = 3b + 35
b² + 2b - 35 = 0
the general solution to such a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case (x is called b, don't get confused, as this is not the factor of x) this gives us
b = (-2 ± sqrt(2² - 4×1×-35))/(2×1) =
= (-2 ± sqrt(4 + 140))/2 = (-2 ± sqrt(144))/2 =
= (-2 ± 12)/2 = -1 ± 6
b1 = -1 + 6 = 5
b2 = -1 - 6 = -7
therefore, we have 2 solutions
b = 5
AM = 5² + 5×5 = 25 + 25 = 50
b = -7
AM = (-7)² + 5×-7 = 49 - 35 = 14
control, as AM = MB
MB = 3×5 + 35 = 15 + 35 = 50
or
MB = 3×-7 + 35 = -21 + 35 = 14
AM = MB in both cases, so, all is correct.
Which ordered pair is in the solution set fit the system of inequalities shown below?2x-y<3x+2y>-1A. (-2,-1)B. (0,1)C. (1,-2)D.(6,1)
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Given the System of Inequalities:
[tex]\begin{cases}2x-y<3 \\ x+2y>-1\end{cases}[/tex]1. Take the first inequality and solve for "y":
[tex]\begin{gathered} -y<2x+3 \\ (-1)(-y)<(-2x+3)(-1) \\ y>2x-3 \\ \end{gathered}[/tex]Notice that direction of the symbol changes, because you had to multiply both sides of the inequality by a negative number.
Now you can identify that the boundary line is:
[tex]y=2x-3[/tex]Since it is written in Slope-Intercept Form, you can identify that its slope is:
[tex]m_1=2[/tex]And its y-intercept is:
[tex]b_1=-3[/tex]Notice that the symbol of the inequality is:
[tex]>[/tex]That indicates that the line is dashed and the shaded region is above the line.
Knowing all this information, you can graph the first inequality on the Coordinate Plane.
2. Apply the same procedure to graph the second inequality. Solving for "y", you get:
[tex]\begin{gathered} 2y>-x-1 \\ \\ y>-\frac{1}{2}x-\frac{1}{2} \end{gathered}[/tex]Notice that the boundary line is:
[tex]y=-\frac{1}{2}x-\frac{1}{2}[/tex]Where:
[tex]\begin{gathered} m_2=-\frac{1}{2} \\ \\ b_2=-\frac{1}{2} \end{gathered}[/tex]Since the symbol is:
[tex]>[/tex]The line is dashed and the shaded region is above the line.
Knowing this, you can graph the second inequality.
3. Look at the graph of the System of Inequalities:
Notice that:
-The black line is the boundary line of the first inequality and the green line is the boundary line of the second inequality.
- The solution of the system is the intersection region. It is the region where the shaded region of the first inequality and the shaded region of the second inequality, intersect.
4. Plot the points given in the options on the graph of the Systems:
5. You can identify that this point is in the intersection region:
[tex](0,1)[/tex]Therefore, it is a solution.
Hence, the answer is: Option B.
Translate each English phrase in the following problem into an algebraic expression and set up the related equation. Let z be the unknown number. The sum of a number and -41 is equal to the quotient of the number and 11. Step 2 of 3: Translate "the quotient of the number and 11". Answer
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An algebraic expression which represents the translation of "The sum of a number and -41 is equal to the quotient of the number and 11" is z - 1 = z/11.
How to translate an English phrase into an algebraic expression?In order to translate a word problem into an algebraic expression, we would have to assign a variable to the unknown number:
Let z represent the unknown number.
The sum of a number and -41 is given by:
z + (-1) = z - 1 ....equation 1.
The quotient of the number and 11 is given by:
z/11 .....equation 2.
Next, we would equate equation 1 and equation 2 as follows:
Translation; z - 1 = z/11
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Find the surface area of a right cone with diameter 30 in. and slant height 8 in.Your answerEXTRA CREDIT: Find the surface area of the figure below. Round to the nearesttenth, if necessary.10 in?
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Answer:
Surface area = 1084 in²
Step-by-step explanation:
To find the surface area of a right cone, we can use the following formula:
[tex]\boxed{{Area = \pi r^2 + \pi rl}}[/tex],
where:
• r = radius
• l = slant height.
In the question, we are told that the diameter of the cone is 30 in. Therefore its radius is (30 ÷ 2 = ) 15 in. We are also told that its height is 8 in.
Using this information and the formula above, we can calculate the surface area of the cone:
Surface area = [tex]\pi \times (15)^2 + \pi \times 15 \times 8[/tex]
= [tex]345 \pi[/tex]
[tex]\approx[/tex] 1084 in²
need help asap look in file attached
Answers
Answer:
length: 21 cm
width: 16 cm
Step-by-step explanation:
. A rectangle has two lengths and two widths, or two sides that are vertical (up and down) and two sides that are horizontal (left and right)
. In order to find the perimeter we must add up all four side lengths.
. You can find the perimeter of a rectangle by adding the length and the width then multiplying by 2, because there are two of each side length.
P = 2(l+w)
In the question the perimeter is given, which is 74.
We can divide 74 by 2 so that we can find the sum of the length and width.
74/2 = 37
l + w = 37
In the question is states that the length is 5 inches longer than the width.
l = (5 + w)
There are two widths and two lengths in a rectangle, the measurement of the two lengths is 5 inches longer than the two widths.
5 + w + w = 37
5 + 2w = 37
Now that we have our equation we can solve for w, or the width.
1. Move the term containing the variable to the left
5 + 2w = 37
2w + 5 = 37
2. Subtract 5 from both sides of the equation, the opposite of adding 5
2w + 5 = 37
2w + 5 - 5 = 37 - 5
2w = 32
3. Divide by 2 in both sides of the equation, the opposite of multiplying 2
2w = 32
2w/2 = 32/2
4. Cancel out the 2s on the left, but leave the x
2w/2 = 32/2
w = 16
So, now that w, or the width = 16, we can find the length:
l = 5 + w
l = 5 + 16
l = 21
You can check your answer by plugging in our values into the original perimeter formula:
P = 2(l+w)
P = 2(21 + 16)
P = 2(37)
P = 74, so my answer is correct, because 74 is the perimeter given in the question.
the value of y is directly proportional to the value of x. if y = 45 when x = 180 what is the value of y = 90
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We have a direct proportionality between y and x.
If "k" is the constant of proportionality, the equation for this situation is:
[tex]y=kx[/tex]To find the constant of proportionality, we solve that equation for k:
[tex]k=\frac{y}{x}[/tex]And since when y=45, x=180, substituting these values to find k:
[tex]\begin{gathered} k=\frac{45}{180} \\ k=0.25 \end{gathered}[/tex]Now, we substitute the value of k into the equation of proportionality:
[tex]y=0.25x[/tex]And in this equation, we can substitute any value of the variables, and find the value of the other variable.
In this case, we have y=90, so we substitute that value and solve for x:
[tex]\begin{gathered} 90=0.25x \\ \frac{90}{0.25}=x \\ 360=x \end{gathered}[/tex]Answer: when y=90, x=360
use geometric relationship to develop the sequence represented in the table
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The first figure has 3 tiles
The second figure has 8 tiles
The third figure has 15 tiles
The 4th figure has 24 tiles
The 5th figure has 35 tiles
The 6th figure has 48 tiles
Each time we increased row and column
So the rule is
a(n) = n(n + 2)
Let us use the rule to find figure 46
n = 46
[tex]a_{46}=46(46+2)=2208[/tex]The number of tiles in figure 46 is 2208
Find the value of m and n that prove the two triangles are congruent by the HL theorem.
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If both triangles are congruent by the HL theorem, then their hypotenuses are equal and at least one of the corresponding legs is equal too.
Hypothenuses:
[tex]13=4m+1[/tex]From this expression, you can calculate the value of m
[tex]\begin{gathered} 13=4m+1 \\ 13-1=4m \\ 12=4m \\ \frac{12}{4}=\frac{4m}{4} \\ 3=m \end{gathered}[/tex]Legs:
[tex]2m+n=8m-2n[/tex]Replace the expression with the calculated value of m
[tex]\begin{gathered} 2\cdot3+n=8\cdot3-2n \\ 6+n=24-2n \end{gathered}[/tex]Now pass the n-related term to the left side of the equation and the numbers to the right side:
[tex]\begin{gathered} 6-6+n=24-6-2n \\ n=18-2n \\ n+2n=18-2n+2n \\ 3n=18 \end{gathered}[/tex]And divide both sides of the expression by 3
[tex]\begin{gathered} \frac{3n}{3}=\frac{18}{3} \\ n=6 \end{gathered}[/tex]So, for m=3 and n=6 the triangles are congruent by HL
Reflects the given the coordinates points across the y - axis
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Answer:
Explanation:
The reflection over the line y = x gives the following transformation of coordinates
[tex](x,y)\to(y,x)[/tex]therefore, for our case the transformation gives
[tex]\begin{gathered} S(-2,5)\to S^{\prime}(5,-2) \\ T(-3,0)\to T^{\prime}(0,-3) \\ U(1,-1)\to U^{\prime}(-1,1)_{} \end{gathered}[/tex]which are our answers!
The graphical representation of a point and its reflection about the line y =x is the following:
8.Find the range,A. (-0,00)B. (-0,0)C. (- 0, 1)D. Cannot be determined4/5
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From the graph, the range of the graph, the y values range from zero down; so the range is given by;
[tex](-\infty,0\rbrack[/tex]Option
James types 50 words per minute. He spends 20 minutes typing his homework. What is the domain of this situation?
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Answer:
You answer is B, from 0 to 20 and including 0 and 20.
Step-by-step explanation:
NO LINKS!! Show all work where necessary to get full credit
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16. Circle F
You name a circle using the center.17. BF
A radius connects the center to a point on the circumference of the circle.18. CD
A chord is a segment connecting two points on the circumference of the circle.19. BE
A diameter is a segment that passes through the center while also connecting two points on the circumference of the circle.20. FA
See 17 and 19.Answer:
16. F
17. FA
18. CD
19. BE
20. FA
Step-by-step explanation:
Question 16
A circle is named by its center.
The center of the given circle is F, therefore the name of the given circle is F.
Question 17
The radius of a circle is a straight line segment from the center to the circumference.
Therefore, the radii of the given circle are:
FA, FB and FE.Question 18
A chord is a straight line segment joining two points on the circumference of the circle.
Therefore, the chords of the given circle are:
BE and CD.Question 19
The diameter of a circle is the width of the circle at its widest part. It is a straight line segment that passes through the center of the circle and whose endpoints lie on the circumference.
Therefore, the diameter of the given circle is:
BE.Question 20
As the diameter is BE, it contains the radii FB and FE.
Therefore, the radius that is not contained in the diameter is:
FA.O GRAPHS AND FUNCTIONSIdentifying solutions to a linear equation in two variables
Answers
Given:
Function is:
[tex]9x+2y=13[/tex]Find-:
Check for solution
Explanation-:
The value of "y" is:
[tex]\begin{gathered} 9x+2y=13 \\ \\ 2y=13-9x \\ \\ y=\frac{13-9x}{2} \end{gathered}[/tex]For (0,8)
Check value of "y" at x = 0 then,
[tex]\begin{gathered} x=0 \\ \\ y=\frac{13-9x}{2} \\ \\ y=\frac{13-9(0)}{2} \\ \\ y=\frac{13-0}{2} \\ \\ y=\frac{13}{2} \\ \\ y=6.5 \end{gathered}[/tex]So (0,8) it is not a solution.
Check (3,-7) the value of "x" is 3
[tex]\begin{gathered} x=3 \\ \\ y=\frac{13-9x}{2} \\ \\ y=\frac{13-9(3)}{2} \\ \\ y=\frac{13-27}{2} \\ \\ y=-\frac{14}{2} \\ \\ y=-7 \end{gathered}[/tex]So (3,-7) is the solution of function.
Check for (1 , 2) value of "x" is 1.
[tex]\begin{gathered} x=1 \\ \\ y=\frac{13-9x}{2} \\ \\ y=\frac{13-9}{2} \\ \\ y=\frac{4}{2} \\ \\ y=2 \end{gathered}[/tex]So, (1,2) is the solution.
Check for (4,-5) the value of "x" is 4.
[tex]\begin{gathered} x=4 \\ \\ y=\frac{13-9x}{2} \\ \\ y=\frac{13-9(4)}{2} \\ \\ y=\frac{13-36}{2} \\ \\ y=-\frac{23}{2} \\ \\ y=-11.5 \end{gathered}[/tex]So, (4,-5) is not a solution
[tex]4(3w-2)=8(2w+3)[/tex]
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The most appropriate choice for linear equation will be given by -
w = -8 is the required answer
What is linear equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here
[tex]4(3w - 2) = 8(2w+3)\\12w - 8 = 16w+24\\16w - 12w = -8-24\\4w = -32\\w = -\frac{32}{4}\\w = -8[/tex]
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Find the domain. Then use the drop down menu to select the correct symbols to indicate your answer in interval notation. If a number is not an integer then round it to the nearest hundredth. To indicate positive infinifty ( \infty ) type the three letters "inf". To indicate negative infinity(-\infty ) type "-inf" with no spaces between characters. \frac{ \sqrt[]{x-4} }{\sqrt[]{x-6}} AnswerAnswer,AnswerAnswer
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The domain of a function is all values of x the function can have.
Since this function has radicals, and the value inside a radical needs to be positive or zero, and also the denominator of a fraction can't be zero, we have the following conditions:
[tex]\begin{gathered} x-4\ge0 \\ x\ge4 \\ \\ x-6>0 \\ x>6 \end{gathered}[/tex]Since the first condition contains the second, so the domain set is represented by the second condition:
[tex](6,\text{inf)}[/tex]Suppose a certain company sells regular keyboards for $82 and wireless keyboards for $115. Last week the store sold three times as many regular keyboards as wireless. If total keyboard sales were $5,415, how many of each type were sold?how many regular keyboards?how many wireless keyboards?
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Given:
A set 3 regular and 1 wireless keyboard,
Regular keyboards = $ 82
Wireless keyboards = $ 115
Total keyboards sales = $ 5415
Find-:
(a) how many regular keyboards?
(b) how many wireless keyboards?
Explanation-:
A set of 3 regular and 1 wireless keyboard would sell for:
[tex]\begin{gathered} =3\times82+115 \\ \\ =246+115 \\ \\ =361 \end{gathered}[/tex]For, the given sales, the number of sets sold:
Total keyboard sales = $5415
[tex]\begin{gathered} =\frac{5415}{361} \\ \\ =15 \end{gathered}[/tex]Since there are 3 regular keyboards in each set,
The regular keyboard is:
[tex]\begin{gathered} =3\times15 \\ \\ =45\text{ Regular Keyboards} \end{gathered}[/tex]The regular keyboard is 45.
Wireless keyboard is 15.
I'm trying to solve this problem. I went wrong somwhere.
Answers
martin earns $23.89 per hour proofreading ads at a local newspaper.His weekly wage w can be describe by the equation w= 23.89h, where h is the number of hours worked (a). write the equation in function notation (b). find f(23) f(35) and f(41)
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SOLUTION
(a) The equation in function notation is
[tex]\begin{gathered} w=23.89h=f(h) \\ w=f(h)=23.89h \end{gathered}[/tex]Hence the answer is
[tex]w=f(h)=23.89h[/tex](b). f(23) becomes
[tex]\begin{gathered} f(h)=23.89h \\ f(23)=23.89\times23 \\ f(23)=549.47 \end{gathered}[/tex]f(35) becomes
[tex]\begin{gathered} f(h)=23.89h \\ f(35)=23.89\times35 \\ f(35)=836.15 \end{gathered}[/tex]f(41) becomes
[tex]\begin{gathered} f(h)=23.89h \\ f(41)=23.89\times41 \\ f(h)=979.49 \end{gathered}[/tex]! WHAT IS 3 3/8 - 1 3/4=
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The given expression is
[tex]3\frac{3}{8}-1\frac{3}{4}[/tex][tex]\text{Use a}\frac{b}{c}=\frac{a\times c+b}{c}\text{.}[/tex][tex]3\frac{3}{8}-1\frac{3}{4}=\frac{3\times8+4}{8}-\frac{1\times4+3}{4}[/tex][tex]=\frac{28}{8}-\frac{7}{4}[/tex]LCM of 8 and 4 is 8, making the denominator 8.
[tex]=\frac{28}{8}-\frac{7\times2}{4\times2}[/tex][tex]=\frac{28}{8}-\frac{14}{8}[/tex][tex]=\frac{28-14}{8}[/tex][tex]=\frac{14}{8}[/tex][tex]=\frac{2\times7}{2\times4}[/tex][tex]=\frac{7}{4}[/tex][tex]=\frac{1\times4+3}{4}[/tex][tex]=1\frac{3}{4}[/tex]Hence the answer is
[tex]3\frac{3}{8}-1\frac{3}{4}=1\frac{3}{4}[/tex]given a quadratic equation in standard form f(x) = ax^2 + bx + c. explain how to determine if there is one real solution, two real solutions, or no real solutions (use the discriminant b^2 - 4ac)
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As per given by the question,
There are given that a general form od quadratic equation.
The equation is,
[tex]f(x)=ax^2+bx+c[/tex]Now,
For determine the one real solution, two real solution, and no real solution;
There are apply the condition for all these three.
So,
First for one real solution.
If
[tex]b^2-4ac=0,\text{ then}[/tex]The given quadratic equation has one real solution.
If,
[tex]b^2-4ac>0,\text{ then;}[/tex]The given quadratic equation has two real solution.
And,
If,
[tex]b^2-4ac<0,\text{ then;}[/tex]The given quadratic equation has no real solution.
I am trying to solve this equation using Synthetic Division. I got the answer wrong, I would like to see where I made a mistake.
Answers
The result for the division is:
[tex]2x^2+43x+865+\frac{17309}{x-20}[/tex]Explanation:Step 1: Write the coefficients of the numerator on the right-hand side, and the opposite of the constant term in the denominator on the left-hand side.
20..............2 || 3 || 5 || 9
..................2
Step 2: Multiply 20 by 2 and add the result to 3
20..............2.......................|| 3 || 5 || 9
..................2*20 = 40
....................2 || 3 + 40 = 43
Step 3: Multiply 43 by 20, and add the result to 5
20..............2 || 3 .........................|| 5 || 9
...................... 40.......20*43 = 860
....................2||43 .......5+860=865
Step 4: Multiply 865 by 20, and add the result to 9
20..............2 || 3 || 5 ..........................|| 9
...................... 40 ||860......20*865=17300
....................2||43||865...9 + 17300=17309
The coefficients are 2, 43, 865, 17309
The quotient is:
[tex]2x^2+43x+865[/tex]and the remainder is 17309
So, we can write:
[tex]2x^2+43x+865+\frac{17309}{x-20}[/tex]What is the measure of m?n20m5m = [?]✓=Give your answer in simplest form.Enter
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STEP - BY - STEP EXPLANATION
What to find?
The value of m.
To find the value of m, we take the proportion of the sides of the triangles.
That is;
adjacent of the bigger triangle/hypotenuse of the bigger triangle = adjacent of the smaller triangle / hypotenuse of the smaller triangle.
That is;
[tex]\frac{m}{20+5}=\frac{5}{m}[/tex][tex]\frac{m}{25}=\frac{5}{m}[/tex]Cross-multiply
[tex]m^2=25\times5[/tex]Take the square root of both-side of the equation.
[tex]m=\sqrt[]{25\times5}[/tex][tex]m=5\sqrt[]{5}[/tex]Eight less than a number n is at least 10
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Answer:
n - 8 ≥ 10
n ≥ 18
Step-by-step explanation:
Hello!
8 less than the number n can be represented as n - 8.
To be atleast 10, we can have values greater than 10 and equal to 10, but cannot be less than 10 . We can use the ≥ symbol to represent this.
The inequality would be n - 8 ≥ 10
Solving for n:n - 8 ≥ 10n ≥ 18n has to be greater than or equal to 18
5.Given the sample triangle below and the conditions a=3, c = _51, find:cot(A).
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Depending on the angle we are analyzing on the right triangle, each side of it takes a different name. In this case, we are going to name them depending on the angle A. Then,
a: opposite side (to A)
b: adjacent side
c: hypotenuse
STEP 2: formula for cot(A)We know that the formula for cot(A) is:
[tex]\cot (A)=\frac{\text{adjacent}}{\text{opposite}}[/tex]Replacing it with a and b:
[tex]\begin{gathered} \cot (A)=\frac{\text{adjacent}}{\text{opposite}} \\ \downarrow \\ \cot (A)=\frac{b}{a} \end{gathered}[/tex]Since a = 3:
[tex]\cot (A)=\frac{b}{3}[/tex]STEP 3: finding bWe have an expression for cot(A) but we do not know its exact value yet. First we have to find the value of b to find it out.
We do this using the Pythagorean Theorem. Its formula is given by the equation:
[tex]c^2=a^2+b^2[/tex]Since
a = 3
and
c = √51
Then,
[tex]\begin{gathered} c^2=a^2+b^2 \\ \downarrow \\ \sqrt[]{51}^2=3^2+b^2 \\ 51=9+b^2 \end{gathered}[/tex]solving the equation for b:
[tex]\begin{gathered} 51=9+b^2 \\ \downarrow\text{ taking 9 to the left} \\ 51-9=b^2 \\ 42=b^2 \\ \downarrow square\text{ root of both sides} \\ \sqrt{42}=\sqrt{b^2}=b \\ \sqrt[]{42}=b \end{gathered}[/tex]Then,
b= √42
Therefore, the equation for cot(A) is:
[tex]\begin{gathered} \cot (A)=\frac{b}{3} \\ \downarrow \\ \cot (A)=\frac{\sqrt[]{42}}{3} \end{gathered}[/tex]Answer: D