Answer:
Point 5/3 is the farthest from 0
Step-by-step explanation:
Given
Points: 0.27, -1/4, 1.1, 5/3
Required
The farthest from zero
The first step is to convert all points to decimal;
Points: 0.27, -1/4, 1.1, 5/3
This becomes
Points: 0.27, -0.25, 1.1, 1.67
The next step is to calculate the absolute difference of each point from 0;
The farthest from 0 is the point with highest absolute difference
For 0.27
Absolute Difference = |0.27 - 0| = |0.27| = 0.27
For -0.25
Absolute Difference = |-0.25 - 0| = |-0.25| = 0.25
For 1.1
Absolute Difference = |1.1 - 0| = |1.1| = 1.1
For 1.67
Absolute Difference = |-1.67 - 0| = |-1.67| = 1.67
From the above calculations; point 1.67 or 5/3 is the farthest from 0
The form of the alternative hypothesis can be: A. neither one nor two-tailed B. two-tailed C. one or two-tailed D. one-tailed
Answer:
The answer is "Option C"
Step-by-step explanation:
It is the hypothesis which would be opposed to just the null hypothesis, that is used in its testing. In this, we generally believed that the results derive from a particular effect with some superimposed variance of chance. It is nothing but an option in contrast to the null and its original test starts by considering its two hypotheses, that's why the only option C is correct.Write the equations of the line with the slope=6 that passes through (4,-6)
Answer:
y=6x+18
Step-by-step explanation:
Answer:
y = 6x - 30
Step-by-step explanation:
The slope is 6.
Use the formula for the equation of a line.
y = mx + b
Where m is the slope, and b is the y-intercept.
y = 6x + b
The point is given (4, -6)
(x , y)
Put x as 4, y as -6.
-6 = 6(4) + b
-6 = 24 + b
-6 - 24 = b
-30 = b
The y-intercept is -30.
The equation of the line is y = 6x - 30.
how many are 13 x 13 ?
Answer:
169
Step-by-step explanation:
13*13=169
We can split the two 13's up:
(10+3)(10+3)
Multiply 10 with 10, 10 with 3, 3 with 10, and 3 with 3.
Basically, just multiply every single term together.
100+30+30+9
100+69
169
Hope this helps!
Answer:
169
Step-by-step explanation:
Determine the inverse of this function.
f(x) = 3 cos(2x – 3) + 1
Answer:
a) [tex]f^{-1} (x) = \frac{1}{2} Cos^{-1} (\frac{x-1}{3} ) +\frac{3}{2}[/tex]
The inverse of given function
[tex]f^{-1} (x) = \frac{1}{2} Cos^{-1} (\frac{x-1}{3} ) +\frac{3}{2}[/tex]
Step-by-step explanation:
Step(i):-
Given function f(x) = 3 cos (2 x -3) + 1
Let y = f(x) = 3 cos (2 x -3) + 1
y = 3 cos (2 x -3) + 1
⇒ y - 1 = 3 cos (2 x -3)
⇒ [tex]cos ( 2 x - 3 ) =\frac{y -1}{3}[/tex]
⇒[tex]cos ^{-1} ( cos (2 x - 3)) = Cos^{-1} (\frac{y-1}{3} )[/tex]
We know that inverse trigonometric equations
cos⁻¹(cosθ) = θ
[tex]2 x - 3 = Cos^{-1} (\frac{y-1}{3} )[/tex]
[tex]2 x = Cos^{-1} (\frac{y-1}{3} ) +3[/tex]
[tex]x = \frac{1}{2} Cos^{-1} (\frac{y-1}{3} ) +\frac{3}{2}[/tex]
Step(ii):-
we know that y= f(x)
The inverse of the given function
[tex]x = f^{-1} (y)[/tex]
[tex]f^{-1} (y) = \frac{1}{2} Cos^{-1} (\frac{y-1}{3} ) +\frac{3}{2}[/tex]
The inverse of given function in terms of 'x'
[tex]f^{-1} (x) = \frac{1}{2} Cos^{-1} (\frac{x-1}{3} ) +\frac{3}{2}[/tex]
conclusion:-
The inverse of given function
[tex]f^{-1} (x) = \frac{1}{2} Cos^{-1} (\frac{x-1}{3} ) +\frac{3}{2}[/tex]
Simplify: |2-5|-(12 ÷4-1)^2
The value of the expression when simplified is -13
How to determine the valueIt is important to note:
PEDMAS is a mathematical acronym that representing;
P for ParenthesesE for exponentsD for divisionM for multiplicationA for additionS for subtractionAlso, we should note that absolute value of a number is the non-negative value of that number. It s the value of a number irrespective of its direction from zero.
It is denoted with the symbol '| |'
Given the expression;
|2-5|-(12 ÷4-1)^2
Solve the bracket
|-3| - (12 /3)^2
Solve further
|-3| - 4^2
Find the absolute value
3 - 4^2
Find the square
3 - 16
-13
The value is - 13
Thus, the value of the expression when simplified is -13
Learn more about PEDMAS here:
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Factor completely 5x(x + 3) + 6(x + 3). (1 point)
Answer:
The answer is ( 5x + 6 ) ( x + 3 )Step-by-step explanation:
5x(x + 3) + 6(x + 3)
The final answer is
( 5x + 6 ) ( x + 3 )
Hope this helps you
The endpoints of line segment CD are C (1, -9) and D (7, 5 ). Find the coordinates of the midpoint M.
Answer:
(4, -2)
Step-by-step explanation:
To find the midpoint of two points you have to take the average of those two points. So, I can do (1+8)/2, which is 4, to find the midpoint of the x coordinates. I can then do (-9+5)/2, which is -2 to find the midpoint of the y coordinates.
Find the area of the yellow region.
Round to the nearest tenth.
15 cm
15 cm
Area = [ ? ] cm2
Answer:
48.3 cm²
Step-by-step explanation:
Let A be the area of the yellow region
A= the area of the square - the area of the quarter square
A= 15²-(15²*π)/4= 48.28≈ 48.3 cm²
Simply the expression 3.4-1/2(0.75)
Answer:
3.025
Step-by-step explanation:
3.4-1/2(0.75)
3.4-0.375
3.025
Verify the identity.
sin 2 t / cos t = t - cost
Answer:
Step-by-step explanation:
The question is incorrect. Here is the correct question.
Verify the identity sin²t / cos t = sect - cost
Given the identity sin²t / cos t = sect - cost, to verify means we are to check if both sides are equivalent. To do that we are going to start the proof from any sides of the equation and solve until we get to the function at the opposite side.
Starting with the left hand equation (LHS)
sin²t / cos t ...1
From trigonometry identity, sin²t+ cos²t = 1
sin²t = 1- cos²t ... 2
Substituting eqn 2 into 1 we have:
= 1- cos²t/cost
= 1/cost - cos²t/cost
= 1/cost - cost
Also from trig. identity, 1/cost = sect
On replacing this identity in the resulting equation we will have;
= sect - cost (which is equivalent to the RHS)
This shows that sin²t / cos t = sect - cost (Identity Proved!)
What number is 408% of 568?
Answer:
2317.44
Step-by-step explanation:
Solution for What is 408 percent of 568:
408 percent *568 =
(408:100)*568 =
(408*568):100 =
231744:100 = 2317.44
Answer:
2317.44
Step-by-step explanation:
Find
dy/dx and d2y/dx2,
and find the slope and concavity (if possible) at the given value of the parameter. (If an answer does not exist, enter DNE.)
Parametric Equations Point
x = 5t, y = 6t − 1
t = 2
Answer:
dy/dx = slope = 6/5d²y/dx² = concavity = 0.Step-by-step explanation:
Given the parametric equation points x = 5t, y = 6t − 1 when t = 2
From x = 5t, t = x/5. Substituting t = x/5 into the second equation y = 6t − 1 we will have;
y = 6(x/5) - 1
y = 6/5 x - 1
The derivative of y with respect to x i.e dy/dx = 6/5 - 0. (Note that differential of any constant is zero).
dy/dx = 6/5
d²y/dx² = d/dx(dy/dx)
d²y/dx² = d/dx(6/5)
Since 6/5 is a constant, the derivative of 6/5 with respect to x will be zero.
d²y/dx² = 0.
Since the first derivative and the second derivative are both constant then, the slope m at the given parameter will be 6/5.
m = dy/dx = 6/5
The concavity is the value of the second derivative at the given value of the parameter.
The concavity d²y/dx² = 0.
Find the first four terms of the sequence given a1=18 and an+1=2+an/2.
Answer: 18, 10, 6, 4
The first four terms of an arithmetic sequence are 18, 10, 6, 4 if the first term and the relationship between the a(n) and a(n+1) terms.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
We have given the first term and the relationship between the a(n) and a(n+1) terms.
The first term:
a(1) = 18
The relationship:
a(n+1) = [2 + a(n)]/2
Plug n = 1
a(1+1) = [2 + a(1)]/2
a(2) = [2 + 18]/2
a(2) = 20/2
a(2) = 10
Plug n = 2 in the expression:
a(2+1) = [2 + a(2)]/2
a(3) = [2 + 10]/2
a(3) = 6
Plug n = 3 in the expression:
a(3+1) = [2 + a(3)]/2
a(3) = [2 + 6]/2
a(3) = 4
Thus, the first four terms of an arithmetic sequence are 18, 10, 6, 4 if the first term and the relationship between the a(n) and a(n+1) terms.
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Solve 0=4x^2+12x+9
Simplify the expression to solve the equation
Answer:
x = -3/2
Step-by-step explanation:
0 = 4x² + 12x + 9
4x² + 12x + 9 = 0
(2x + 3)² = 0
2x + 3 = 0
2x = -3
x = -3/2
Hope this helps! :)
Orchid wants to retile her bathroom floor, which has an area of 40 square feet. She is deciding between two types of custom tiles. The square tile is One-half foot by One-half foot and costs $0.45 per tile. The rectangular tile is 2 feet by One-fourth foot and costs $0.80 per tile.
Which tile should Orchid choose to minimize costs? Explain.
She should choose the square tiles because the total cost will be $8 less.
She should choose the rectangular tiles because the total cost will be $8 less.
She should choose the square tiles because the total cost will be $14 less.
She should choose the rectangular tiles because the total cost will be $14 less.
Your answer is the second option, she should choose the rectangular tiles because the total cost will be $8 less.
To find this answer we need to first find the total cost for using square tiles, and the cost for using rectangular tiles, and compare them. We can do this by finding the area of each tile individually, calculating how many tiles we would need, and multiplying this by the cost for one tile:
Square tiles:
The area of one square tile is 1/2 × 1/2 = 1/4 ft. Therefore we need 40 ÷ 1/4 = 160 tiles. If each tile costs $0.45, this means the total cost will be $0.45 × 160 = $72
Rectangular tiles:
The area of one rectangular tile is 2 × 1/4 = 2/4 = 1/2 ft. Thus we need 40 ÷ 1/2 = 80 tiles. Each tile costs $0.80, so the total cost will be 80 × $0.80 = $64.
This shows us that the rectangular tiles will be cheaper by $8.
I hope this helps! Let me know if you have any questions :)
Answer:
B
Step-by-step explanation:
E2020 : )
A survey of 1,673 randomly selected adults showed that 545 of them have heard of a new electronic reader. The accompanying technology display results from a test of the claim that 36 % of adults have heard of the new electronic reader. Use the normal distribution as an approximation to the binomial distribution, and assume a 0.05 significance level to complete parts (a) through (e).
Requried:
a. Is the test two-tailed, left-tailed, or right-tailed?
b. What is the test statistic?
c. What is the P-value?
d. What is the null hypothesis and what do you conchide about it?
e. Identify the null hypothesis.
Answer:
Step-by-step explanation:
We would set up the hypothesis test.
For the null hypothesis,
p = 0.36
For the alternative hypothesis,
P < 0.36
a) This is a left tailed test due to the inequality sign in the alternative hypothesis.
b)Considering the population proportion, probability of success, p = 0.36
q = probability of failure = 1 - p
q = 1 - 0.36 = 0.64
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 545
n = number of samples = 1673
P = 545/1673 = 0.33
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.33 - 0.36)/√(0.36 × 0.64)/1673 = - 2.56
c)We would determine the P-value from the normal distribution table. From the normal distribution table, the area below the test z score in the left tail 0.00523
P value = 0.00523
d) Since alpha, 0.05 > than the p value, 0.00523, then we would reject the null hypothesis.
e) The null hypothesis is the claim that 36% of adults have heard of the new electronic reader.
what is u over 4-4= -20
u/4 - 4 = -20
Add 4 to both sides:
u/4 = -16
Multiply both sides by 4:
u = -64
Answer:
u=-64
Step-by-step explanation:
u/4 -4 = -20
First add 4 to both sides.
u/4=-16
Now multiply both sides by 4
u=-64
Use the given values of n to generate the 7th and 8th terms of the sequence.
f(n) = 74 + 11(n - 1)
Answer:
f(n) = 74 + 11(n - 1)
For the 7th term
n = 7
f(7) = 74 + 11(7 - 1)
= 74 + 11(6)
= 74 + 66
= 140For the 8th term
n = 8
f(8) = 74 + 11( 8 - 1)
= 74 + 11(7)
= 74 + 77
= 151Hope this helps you
Prove the following identity. Make sure to include all steps taken. [tex]\frac{1+cos\theta }{sin\theta}+\frac{sin\theta}{1+cos\theta}=2csc\theta[/tex]
Answer:
See below.
Step-by-step explanation:
[tex]\frac{1+cos(\theta)}{sin(\theta)} +\frac{sin(\theta)}{1+cos(\theta)}=2csc(\theta)[/tex]
[tex]\frac{(1+cos(\theta))(1+cos(\theta))}{sin(\theta)((1+cos(\theta))} +\frac{(sin(\theta))(sin(\theta))}{(1+cos(\theta))(sin(\theta))}=2csc(\theta)[/tex]
[tex]\frac{(1+cos(\theta))(1+cos(\theta))+(sin(\theta))(sin(\theta))}{sin(\theta)((1+cos(\theta))}=2csc(\theta)[/tex]
[tex]\frac{(1+2cos(\theta)+cos^2(\theta)+sin^2(\theta))}{sin(\theta)(1+cos(\theta))} =2csc(\theta)[/tex]
Recall the identities:
[tex]sin^2(\theta)+cos^2(\theta)=1[/tex]
[tex]\frac{1+2cos(\theta)+1}{sin(\theta)(1+cos(\theta))} =2csc(\theta)[/tex]
[tex]\frac{2+2cos(\theta)}{sin(\theta)(1+cos(\theta)}=2csc(\theta)[/tex]
[tex]\frac{2(1+cos(\theta))}{sin(\theta)(1+cos(\theta))} =2csc(\theta)[/tex]
[tex]\frac{2}{sin(\theta)} =2csc(\theta)[/tex]
[tex]2csc(\theta)=2csc(\theta)[/tex]
9. A water glass can hold 2/9 of a litre of water. How many glasses of water can be filled with a 3 litre bottle?
Solve the problem
Answer:
13 1/2 glasses of water.Step-by-step explanation:
From the question, a water glass can hold 2/9 of a litre of water, to know the number of glasses of water that can be filled with a 3-litres bottle, the following steps are crucial;
1 water of glass = 2/9 litre of water
x = 3 litre of water
cross multiplying;
2/9 * x = 3*1
2x/9 = 3
2x = 27
Dividing both sides by 2;
2x/2 = 27/2
x = 13 1/2
This means 13 1/2 glasses of water can be filled with a 3-litre bottle.
Find the product of 4 2/7 x 3 1/2
Answer:
Hey there!
The product of these two fractions would equal 15.
Hope this helps :)
Answer:
Hi! The answer to your question is 7 11/14 or rounded will be 15
Step-by-step explanation:
So first let’s take the whole numbers which is 4 and 3 if we add them up we will get 7.
Now we do LCD (least common denominator)
4/14+7/14=11/14
So the answer is 7 11/14 or 15
(In mixed number the answer is 7 11/14 and in whole the answer is 15)
Hope this helps! :)
What is the slope of the line represented by the equation y = 1/5x-3?
Answer:
1/5
Step-by-step explanation:
Your equation is written in the form y=mx+b, where m is the slope and b is the y-intercept.
m=1/5, so the slope is 1/5
A researcher wants to study the average miles run per day for marathon runners. In testing the hypotheses: H0: μ = 25 miles vs. H1: μ ≠ 25 miles, a random sample of 36 marathon runners drawn from a normal population whose standard deviation is 10, produced a mean of 22.8 miles weekly. What is the rejection region associated with 3% significance level?
Answer:
The calculated value |Z| = 1.325 < 1.881 at 0.03 level of significance
Null hypothesis is accepted
Alternative hypothesis is rejected
A researcher wants to study the average miles run per day for marathon runners is 25
Step-by-step explanation:
Step(i):-
Given sample size 'n' = 36
Given mean of the sample x⁻ = 22.8 miles
Given mean of the Population 'μ' = 25
Given standard deviation of the Population 'σ' = 10
Null hypothesis:-H₀: μ = 25
Alternative Hypothesis:H₁:μ ≠ 25
Level of significance = 3 % or 97%
The critical value Z₀.₉₇ = 1.881
Step(ii):-
Test statistic
[tex]Z = \frac{x^{-} - mean}{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{22.8 - 25}{\frac{10}{\sqrt{36} } }[/tex]
Z = -1.325
|Z| = |-1.325| = 1.325
The calculated value |Z| = 1.325 < 1.881 at 0.03 level of significance
Null hypothesis is accepted
Alternative hypothesis is rejected
conclusion:-
A researcher wants to study the average miles run per day for marathon runners is 25
Adam has $15$ of a certain type of rare coin and is interested in knowing how much this collection is worth. He discovers that $5$ of these coins are worth $12$ dollars in total. Assuming that the value of each coin is the same, how many dollars is his entire collection worth?
Answer:
$36 is the correct answer.
Step-by-step explanation:
Given that:
Adam has $15 of a certain type of rare coin.
$5 of this type of rare coins are equivalent to $12.
To find:
The total worth of $15 of rare coins = ?
If value of each coin is same.
Solution:
We are given that value of each coin is same.
So, We can simply use unitary method to find out the total worth of $15 of rare coins.
i.e. we first find out what is the worth of $1 of rare coins and then we find the worth of total required quantity.
Given that
$5 of rare coins are worthy of = $12
$1 of rare coins are worthy of = [tex]\frac{12}{5}[/tex]
$15 of rare coins are worthy of =
[tex]\\\dfrac{12}{5}\times 15\\\Rightarrow \dfrac{12\times 15}{5}\\\Rightarrow 12\times 3\\\Rightarrow \$36[/tex]
[tex]\therefore[/tex] $15 of rare coins are worth of $36.
Find the range of y=3/2cos4x-1
Answer:
Range = [- 2.5, 0.5] = [ - 5/2, 1/2]
Step-by-step explanation:
Smallest value of cos α = - 1,
largest value of cos α = 1.
When cos 4x = - 1, y=3/2cos4x-1 = 3/2*(-1) - 1 = - 5/2 = - 2 1/2 = - 2.5
When cos 4x = 1, y=3/2cos4x-1 = 3/2*1 - 1 = 1/2 = 0.5
Range = [- 2.5, 0.5] = [ - 5/2, 1/2]
Dairy cows at large commercial farms often receive injections of bST (Bovine Somatotropin), a hormone used to spur milk production. Bauman et al. (Journal of Dairy Science, 1989) reported that 12 cows given bST produced an average of 28.0 kg/d of milk. Assume that the standart deviation of milk production is 2.25 kg/d.
Requried:
a. Find a 99% confidence interval for the true mean milk production.
b. If the farms want the confidence interval to be no wider than ± 1.25 kg/d, what level of confidence would they need to use?
Answer:
a) 26.33 kg/d and 29.67 kg/d
b) 94.5%
Step-by-step explanation:
a. Find a 99% confidence interval for the true mean milk production.
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.575*\frac{2.25}{\sqrt{12}} = 1.67[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 28 - 1.67 = 26.33 kg/d
The upper end of the interval is the sample mean added to M. So it is 28 + 1.67 = 29.67 kg/d
The 99% confidence interval for the true mean milk production is between 26.33 kg/d and 29.67 kg/d
b. If the farms want the confidence interval to be no wider than ± 1.25 kg/d, what level of confidence would they need to use?
We need to find z initially, when M = 1.25.
[tex]M = z*\frac{2.25}{\sqrt{12}} = 1.67[/tex]
[tex]1.25 = z*\frac{2.25}{\sqrt{12}} = 1.67[/tex]
[tex]2.25z = 1.25\sqrt{12}[/tex]
[tex]z = \frac{1.25\sqrt{12}}{2.25}[/tex]
[tex]z = 1.92[/tex]
When [tex]z = 1.92[/tex], it has a pvalue of 0.9725.
1 - 2*(1 - 0.9725) = 0.945
So we should use a confidence level of 94.5%.
In how many different ways can each of the letters in the following words be arranged? Show your work and solutions. 25. LEARN
Answer:
120 waysStep-by-step explanation:
This problem bothers on permutation
Given the letters LEARN
The total alphabets are 5 in numbers
Since there are no repeating letters, and there are 5 total letters, there are 5!=5*4*3*2*1= 120 ways to arrange them
Multiply.
(2x2 – 3x + 1)(x2 - 4x – 3)
Answer:
2x^4−11x^3+7x^2+5x−3
Step-by-step explanation:
The ^ means exponent
Find the solution of the given initial value problem. ty' + 2y = sin t, y π 2 = 9, t > 0 y(t) =
For the ODE
[tex]ty'+2y=\sin t[/tex]
multiply both sides by t so that the left side can be condensed into the derivative of a product:
[tex]t^2y'+2ty=t\sin t[/tex]
[tex]\implies(t^2y)'=t\sin t[/tex]
Integrate both sides with respect to t :
[tex]t^2y=\displaystyle\int t\sin t\,\mathrm dt=\sin t-t\cos t+C[/tex]
Divide both sides by [tex]t^2[/tex] to solve for y :
[tex]y(t)=\dfrac{\sin t}{t^2}-\dfrac{\cos t}t+\dfrac C{t^2}[/tex]
Now use the initial condition to solve for C :
[tex]y\left(\dfrac\pi2\right)=9\implies9=\dfrac{\sin\frac\pi2}{\frac{\pi^2}4}-\dfrac{\cos\frac\pi2}{\frac\pi2}+\dfrac C{\frac{\pi^2}4}[/tex]
[tex]\implies9=\dfrac4{\pi^2}(1+C)[/tex]
[tex]\implies C=\dfrac{9\pi^2}4-1[/tex]
So the particular solution to the IVP is
[tex]y(t)=\dfrac{\sin t}{t^2}-\dfrac{\cos t}t+\dfrac{\frac{9\pi^2}4-1}{t^2}[/tex]
or
[tex]y(t)=\dfrac{4\sin t-4t\cos t+9\pi^2-4}{4t^2}[/tex]
The volume of a rectangular prism is given by the formula V = lwh, where l is the length of the prism, w is the width, and h is the height. Suppose a box in the shape of a rectangular prism has length (2a + 11), width (5a – 12), and height (a + 6). Which expression represents the volume of the box?
Answer:
Volume = 10a³ + 91a² + 54a - 792
Step-by-step explanation:
In the absence of answer choices, let's find the expression for the volume.
Given: Volume = length×width×height
V = lwh
length =(2a + 11)
width =(5a – 12)
height= (a + 6)
V = (2a + 11)(5a – 12) (a + 6)
Expand the first two brackets using distributive property
V = (10a² -24a +55a - 132)(a + 6)
Collect like terms
V = (10a² + 31a -132)(a + 6)
Expand the two brackets using distributive property
V = 10a³ + 31a² - 132a + 60a² + 186a - 792
Collect like terms
V = 10a³ + 91a² + 54a - 792
The expression that represents the volume of the box = 10a³ + 91a² + 54a - 792
Answer:
Volume = 10a³ + 91a² + 54a - 792
Step-by-step explanation: