The residents of downtown neighborhood designed a triangular-shaped park as part of a city beautification program. The park is bound by streets on all sides. The second angle of the triangle is 5 degrees more than the first. The third angle is 5 degrees less than four times the first. Find the measures of the angle
The triangular park has three angles: 60°, at its base, 55° at its top, and 65° at its base.
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The sum of all angle of triangle = 180
As part of a civic beautification initiative, residents in a downtown neighbourhood created a park with a triangle shape.
Let's say that the initial angle is x°.
Accordingly, the second angle is (x + 5)° and the third angle is (5x - 5)° from the information provided.
The inner angles of a triangle are known to add up to 180 degrees.
∴ x + (x + 5) + (x - 5) = 180°
3x = 180°
x = 180°/3
x =60 °.
Hence, the triangular park has three angles: The triangular park has three angles: 60°, at its base, 55° at its top, and 65° at its base.
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During lockdown down period people work very puzzled and their decided to play some game firstly they collect the 17 cards and write the numbers 1 to 17 put them in a box people make a bet from the chance of drawing the number either the prime or even number
etc.
From the universal set; N = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17}
Probability of drawing an even or prime number will be 15/17.
What is Probability?Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event. The probability of all the events in a sample space adds up to 1.
N = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17}
Prime = {1,2,5,7,11,13,17}
Even = {2,4,6,8,10,12,14,16}
Pr(Prime) = 7/17
Pr(Even) = 8/17
Pr(Prime or even) = 7/17 + 8/17
Pr(Prime or even) = 15/17
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It took Xander 31 minutes to run a 5-kilometer race last weekend. If you know that 1 kilometer equals 0.621 mile, how many minutes did it take Xander to run 1 mile during the race
So it took Xander approximately 9.96 minutes to run 1 mile during the race.
To convert the distance of the race from kilometers to miles, you can use the conversion factor 1 kilometer = 0.621 miles.
To find the time it took Xander to run 1 mile, you can divide the total time it took him to run the entire race by the number of miles he ran.
First, convert the distance of the race from 5 kilometers to miles:
5 kilometers * 0.621 miles/kilometer = 3.105 miles
Then, divide the total time it took Xander to run the race by the number of miles he ran:
31 minutes / 3.105 miles = 9.96 minutes/mile
So it took Xander approximately 9.96 minutes to run 1 mile during the race.
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Your mortgage payment is $954. 32/month. Using proportions, what is the minimum yearly amount you must have in realized income to keep your housing expenses in the acceptable range? $Fill in the blank text field 1
The mortgage payment exists $954. 32/month then the annual realized income exists 42,414.22.
What is meant by mortgage payment?Principal, interest, taxes, and insurance make up the majority of mortgage payments. Your outstanding loan balance is reduced by the amount in the principal part. Borrowing money has a cost, which is interest. Both the interest rate and the loan balance affect how much interest you pay.
You repay your mortgage loan through monthly payments. This will often be a monthly payment that aids in your gradual mortgage repayment. There will also be taxes, insurance premiums, and loan interest due.
Assume a mortgage repayment schedule that is reasonable, using 27% of gross monthly income.
The product of the monthly mortgage payment by 12 months, divided by the acceptable rate, yields the annual realized income.
[tex]$& \frac{\text { Mortgage }}{\text { Acceptable Rate\% }} * 12 \\[/tex]
substitute the values in the above equation, we get
[tex]$& =\frac{954.32}{0.27} * 12[/tex]
= 42,414.22
Therefore, the annual realized income exists 42,414.22.
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The mortgage payment exists $954. 32/month then the annual realized income exists 42,414.22.
What do you mean by mortgage payment?Generally speaking, mortgage payments are made up of principal, interest, taxes, and insurance. The sum in the principle component is deducted from your outstanding loan balance. Interest is a cost associated with borrowing money. The amount of interest you pay depends on both the interest rate and the loan balance.
Monthly payments are made to pay down your home loan. This will frequently be a monthly payment to help you slowly pay down your mortgage. Taxes, insurance premiums, and loan interest will all need to be paid.
Assume a mortgage repayment schedule that is reasonable, using 27% of gross monthly income.
The product of the monthly mortgage payment by 12 months, divided by the acceptable rate, yields the annual realized income.
[tex]\frac{Mortage}{Acceptable rate } *12[/tex]
substitute the values in the above equation, we get
[tex]\frac{954.32}{0.27} *12[/tex]
= 42,414.22
Therefore, the annual realized income exists 42,414.22.
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Which milk product will have approximately 15.36 grams of milk fat in an 80-gram serving?(Heavy Cream: 36.7%, Light Cream 19.2%, Whole Milk 3.5%, Low-Fat Milk 1.5%, Skim Milk 0.05%)
The Light cream with 19.2% content will have 15.36g of milk.
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”
Given here Light cream as 19.2% of 80g
∴ 0.192×80=15.36g
Hence, The Light cream with 19.2% content will have 15.36g of milk.
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Write the coordinates of the vertices after a translation 1 unit down.
Answer:
M(4,0)
K(0,5)
L(6,5)
go down one
A= v-u/ t
v = 37. 6 correct to 3 significant figures.
u = 11. 3 correct to 3 significant figures.
t = 8. 4 correct to 2 significant figures.
Work out the upper bound for the value of a.
Show your working clearly
The upper bound of a is 3.13.
Upper Bound
The smallest amount that would round up to the following anticipated value is the upper bound.
Significant FiguresThe number of digits that contribute to a value's level of precision is known as significant figures and is typically found in measurements. As soon as a digit is non-zero, we begin calculating significant numbers.
Given in the question
v = 37. 6
u = 11. 3
t = 8. 4
To find:- a = (v - u)/t
Solution: -
Since finding the upper boundary for a
Upper boundary = (upper v - lower u) / (lowest t)
So putting the value values of v, u, t in we get the value
a = (37.6 - 11.3) / 8.4
Therefore the value of a = 3.13
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Net of a square pyramid showing 4 triangles and the square base. The square base has side lengths of 3 inches. The height of each triangle attached to the square is 6 inches. The base of the triangle is the side of the square. What is the surface area of the solid? (1 point) a 18 square inches b 27 square inches c 36 square inches d 45 square inches
The correct option regarding the surface area of the solid is given as follows:
d. 45 square inches.
How to calculate the surface area?The surface area of a solid is composed by the sum of the areas of all the pars of the figure.
The composition of the figure in this problem is given as follows:
4 triangles of base 3 and height 6.One square of side length 3.Thea area of a triangle is given by half the multiplication of the base by the height, hence the area of the four triangles in this problem is given as follows:
At = 4 x 1/2 x 3 x 6
At = 36 square inches.
The area of a square is given by the square of the side length, hence:
As = 3³
As = 9 square inches.
Thus the surface area of the solid in this problem is given as follows:
S = At + As
S = 36 + 9
S = 45 square inches.
Meaning that option d is correct.
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If a is 200% of b, what percent of 5a is 4b?
250% (percent) of 5a is 4b.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
here, given that,
a is 200% of b
i.e. a=2b
Now, 5a=10b
So, we have,
5a/4b
=10b/4b
=5/2
=250%
Hence, 250% (percent) of 5a is 4b.
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What is called composite function?
A composite function is a type of function that is made up of two or more other functions. It is created by combining two or more functions together. The resulting function can be written as a single expression, or as a composition of multiple functions.
A composite function is a type of function that is formed by combining two or more other functions. It is created by combining two or more functions together using the mathematical operations of addition, subtraction, multiplication, division, or composition. The resulting function can be written as a single expression, or as a composition of multiple functions. A composite function is often used to simplify a complex problem, or to manipulate and analyze data. For example, if a data set contains two sets of data, a composite function could be used to combine the two sets of data into a single expression. Additionally, composite functions can be used to solve problems that involve multiple variables, as the resulting function can be used to represent the relationship between the variables. Furthermore, composite functions can be used to create graphs, which can be used to further analyze the data.
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ALGEBRA 2 - Exponential and Logarithmic Functions
Simone’s parents invested $1,500 in an account such that the value of the investment doubles every seven years. The value of the investment, V, is determined by the equation V= p · t^r/7, where p represents the amount invested and t represents the number of years since the money was deposited. How many years, to the nearest tenth of a year, will it take the value of the investment to reach $1,000,000?
It will take approximately 4687.9 years for an investment principal of $1500 to reach $1000000 at an interest rate of 14.2% per year
What is Simple InterestSimple interest is a type of interest calculated only on the principal amount of a loan or deposit, without taking into account the compound interest earned on that principal. It is calculated by multiplying the principal amount, the interest rate and the time period.
The formula of simple interest is given as;
A = P(1 + rt)
where;
A = Simple InterestP = principalr = ratet = time period.In this problem, we have to find the rate first.
The investment doubles after 7 years.
A = p(1 + rt)
2 = 1(1 + r * 7)
2 = (1 + 7r)
2 = 1 + 7r
7r = 2 - 1
7r = 1
r = 1 / 7
r = 0.142
r = 14.2%
The rate is 14.2 %
Now, we can proceed to determine how many years it will take to reach a value of 1000000
Using simple interest formula again;
A = P(1 + rt)
100000 = 1500(1 + 0.142 * t)
1000000 = 1500(1 + 0.142t)
t = 4687.8 years
It will take approximately 4687.8 years
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What is the opposite reciprocal of 0/6
Answer: The reciprocal of a number is defined as 1 divided by that number. The opposite of a number is the number with the opposite sign. Therefore, the opposite reciprocal of a number is equal to the reciprocal of the opposite of that number.
In this case, the opposite reciprocal of 0/6 is the reciprocal of the opposite of 0/6. The opposite of 0/6 is 0/-6, which is equal to -0/6. The reciprocal of -0/6 is 1/(-0/6) = -6/0.
However, division by 0 is not defined, so it is not possible to find the reciprocal of -0/6. Therefore, the opposite reciprocal of 0/6 is undefined.
Step-by-step explanation:
Answer:
there is no reciprocal for 0/6
Step-by-step explanation:
Why is it br2 and not BR?
Bromine is a diatomic molecule since it is typically found in groups of two.
What is the symbol to represent a chemical compound?
An element's one- or two-letter identification is known as a chemical symbol. O for oxygen, Zn for zinc, and Fe for iron are a few instances of chemical symbols. Symbols always start with a capital letter. Lowercase letters are used for the second letter in symbols with two letters.
A subscript appears after the atom to indicate how many of each kind there are. There is no number written if there is just one atom. The number is given as a subscript after the atom if there are multiples of a particular kind of atom.
Br represents the bromine. Bromine is a diatomic molecule and always needs to be bounded to something. Thus it is bounding to itself.
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I HAVE A F PLEASE HELP ASAP 100 POINTS
Points D, B, and E are collinear. Find the value of a so that points A, B, and C
are collinear.
Answer:
Since A, O and B are collinear,
i.e.,
∠
A
O
B
=
180
∘
or,
∠
A
O
D
+
∠
D
O
C
+
∠
B
O
C
=
180
∘
(
x
−
10
)
∘
+
(
4
x
−
25
)
∘
+
(
x
+
5
)
∘
=
180
∘
Or,
x
+
4
x
+
x
−
10
∘
−
25
∘
+
5
∘
=
180
∘
Or,
6
x
−
30
∘
=
180
∘
Or,
6
x
=
180
∘
+
30
∘
=
210
∘
Or,
x
=
210
∘
6
=
35
∘
∠
B
O
C
=
x
+
5
∘
=
35
∘
+
5
∘
=
40
∘
Julie wants to check out a book from her local library, but it is not available. Julie decides to visit the library in Lanberry, 15 kilometers away, to see if that location has a copy of the book. On a map, the two libraries are 25 centimeters apart. What is the scale of the map?
The easiest way to find this is to use the library's catalog. Depending on the integrated library system (or ILS) the library subscribes to, the process might be slightly different. Generally, you can use a catalog system on a computer to search by title, author, subject, and more.
How do you graph 3 variable lines?
Three variable lines are drawn in the three dimensional coordinate system.
What is 3 dimensional coordinate plane?
Three-dimensional coordinate system is also called rectangular coordinate system. The system has three reference axes named X, Y and Z axis which are perpendicular to each other.
The above three axes intersect at the origin.
In the analytical geometry, location of each point is represented by three coordinate system. They give mathematical statement by using three-dimensional space.
How do we graph 3 variable lines?In order to plot in the three-dimensional plane, we need to determine the value of x, y and z. At first, we start from the origin and approach to the positive x direction if our x value is positive, otherwise we need to go to the negative x direction. After identifying the x coordinate, we need to move parallel to y direction and locate the y coordinate and finally we identify the z coordinate in the same way. In the last, we will join the points.
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What is the equation of the line parallel to the line 3x + 2y = 7 passing through the point (–1 , 3)?
Answer:
idont
Step-by-step explanation:
What’s the area of a square is all sides are 6 feet long?
Answer:
36 sq ft
Step-by-step explanation:
The area of a square is equal to the length of one side squared. Therefore, if all sides of a square are 6 feet long, the area of the square is 6 feet * 6 feet = 36 square feet.
Answer:
36
Step-by-step explanation:
you multiply just two of the sides hxw and you get your answer
Write an equation using the explicit formula to represent each graph or scenario then rewrite the formula in function form
The exponential function's y-intercept is 3, while the linear function's y-intercept is 20. The y-intercept for each is obtained by substituting 0 for x in each case.
what is equation ?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
given
The first function is linear, with a y-intercept of 20, and a slope of 4:
S(x)=4x+20
The second function is exponential and has a multiplier of 2 and an initial value of 3:
J(x)=3(2)x
The game number for each function is represented by x, while the score for each game is represented by y. Each has a domain of 0, 1, 2, 3, 4, 5, 6, 7 and 8.
The exponential function's y-intercept is 3, while the linear function's y-intercept is 20. The y-intercept for each is obtained by substituting 0 for x in each case.
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write days in May to days in a year as a ratio.
Answer:
Step-by-step explanation:
Days in may = 31
Days in a year = 365
therefore, expected ratio = 31/365
2.6.2 Test (CST): Functions and Relations
Question 7 of 25
The function h(x) = -x] is a transformation of the absolute value parent
function, f(x) = [x]. Which graph shows h(x)?
Answer:
b
Step-by-step explanation:
The graph that shows the function h(x) = -x] which is a transformation of the absolute value parent function, f(x) = [x] is Option C.
The graph of the function h(x) = -x] is the reflection of the graph of f(x) = [x] about the x-axis. The graph of f(x) is piecewise defined as follows:
f(x) = x, when x ≥ 0f(x) = -x, when x < 0The graph of h(x) will have the same shape as f(x), but with all the y-values negated, so:
h(x) = -x, when x ≥ 0h(x) = x, when x < 0The graph of h(x) will thus be a downward-facing step function, with steps at x = 0, moving from -x to x as x moves from negative to non-negative values. Thus, Option C is correct.
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The ratio of cassettes tapes to compact discs is 5 to 2, and the number of cassette tapes is 10 less than 5 times the number of compact discs. How many cassette tapes are there
There are 4 cassette tapes.
Given that,
Let x be the number of compact discs
Then 5 times the number of CD's= 5x and 10 less than 5 times the number of CDs is 5x-10
Therefore the number of cassettes is 5x-10
Now we are told that the ratio of cassettes to CDs which is
((5x-10)/x) equals 5/2 so our equation to solve is:
(5x-10)/x=5/2 multiply both sides by 2x to get rid of the fractions and we get:
2(5x-10)=5x
Further solving this equation, we get:
10x-20=5x
5x=20
x= 4 (number of compact discs)
Thus, there are in total 4 cassette tapes.
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PLS HELP ASAP I DONT NNOW HOW TO DO THIS
Answer:
I think you do know how because where the point is now is correct!!
What is the probability that this year's graduation will fall on the birthday of exactly one of the 68
Seniors? What is the probability that there is more than one such Senior?
As a result, there is a 0.1863 chance, or 18.63% probability , that one of the 68 seniors who will graduate this year will graduate on their birthday.
How does probability work?fundamentals of probability A probability is a numerical representation of the likelihood or possibility of an event occurring. Probabilities can be expressed as proportions with a 0–1 range or as percentages with a 0%–100% range.
Here,
The likelihood that one of the 68 seniors graduating this year will have their birthday coincide with graduation day is given here.
As a result, this issue can be modeled using a binomial probability model with a success chance of 1/365.
Given: The likelihood of exactly 1 success after 68 attempts.
=> P(x=1) = 68!/ (68-1)! * 1/365
=> 68/365
= > 0.1863
As a result, there is a 0.1863 chance, or 18.63%, that one of the 68 seniors graduating this year will have their birthday coincide with the commencement.
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two cards are drawn from a shuffled deck of 52 cards. what is the probability that the first card is a king and the second is a heart
On solving the provided question, we can say that the required probability is = 13/204.
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
probability of 1st card = 1/4
since the card is not replaced
total number remaining cards = 51
second card 13/51
the required probability is = 13/204
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Warren is tiling his bathroom. He wants to cut three different sizes of square tiles. Tile A must be square inches, tile B must be square inches, and tile C must be square inches. He needs to know the side length of each tile. Part A In the table, note your guesses and checks to find the length of tile A, which has an area of square inches. Estimate the value to five decimal places
The length of tile A is 2.36068 inches.
The quantity of square units required to completely fill a square is known as the area of a square.
The region that lies inside the confines of a flat item or a two-dimensional figure is generally referred to as the area.
The measurement is made using square units, with square meters serving as the standard unit (m^2).
The square unit serves as the unit of area.
Let us recall that the area of a square is given by;
A = side^2
This is because, all the sides of a square are equal hence
When A = 5 square inches
5 = side^2
side = √5
side = 2.36068 inches
Therefore, The length of tile A is 2.36068 inches.
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Radicals help please
√6/3 is the value after rationalization of √2/√3
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is √2/√3
Square root two divided by square root three.
We need to rationalize the denominator
To rationalize multiply numerator and denominator by √3
√2/√3×√3/√3
√2×3/3
√6/3
Hence, √6/3 is the value after rationalization of √2/√3
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Ason is organizing the silverware drawer. He has 8 spoons. There are twice as many forks as spoons. There are 34 as many knives as forks. How many knives does Jason have
The result of two Newton's technique iterations to approximation a function's zero using the provided starting guess is 1.5262!
What is a formula that is iterative?Iteration describes carrying out a process repeatedly. To get a new value, start with an initial value and enter it into the iteration formula. To solve an equation using iteration, apply the new value for the subsequent substitution after that, and so on.
By Newton's Method, we have new guess of a zero of a function that are f(x), xn+1, and by using the previous guess, xn, like so-
xn+1 = xn - f(xn)/f'(xn)
and herethe case is [tex]f(x) = cos(x), and so f'(x) = -sin(x).[/tex]
Also, furthermore, [tex]cos(x)/(-sin(x)) = -cot(x).[/tex]
here, we have to simplify the formula to get a better guess for a zero to: xn+1 = xn + cot(xn)
[tex]x1 = 0.6, so x2 = 0.6 + cot(0.6) = 2.06170...\\And x3 = 2.06170... + cot(2.06170...) = 1.52615...\\Ans = 1.5262![/tex]
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Match each power of a power expression with its simplified expression.
(4-3)-3
(46)-3
(49)-9
(-49)²
↑
↑
1
418
49
(-4)18
40
need to know which one goes to which
Answer:
(4^6)^-3 = 1/4^18(4^0)^-9 = 4^0(4^-3)^-3 = 4^9(-4^9)^2= (-4)^18Step-by-step explanation:(4^6)^-3 = 1/4^18(4^6)^-3= 4^(6*-3)(4^6)^-3= 1/4^18(4^0)^-9 = 4^0(4^0)^-9 = 4^(0*-9)(4^0)^-9= 4^0(4^-3)^-3 = 4^9(4^-3)^-3= 4 ^ (-3*-3)(4^-3)^-3 = 4^(9)(-4^9)^2= (-4)^18(-4^9)^2= -4^(9*2)(-4^9)^2=(-4)^18
Step-by-step explanation:
Answer:
[tex](4^{-3})^{-3}=4^9[/tex]
[tex](4^6)^{-3}=\dfrac{1}{4^{18}}[/tex]
[tex](4^0)^{-9}=4^0[/tex]
[tex](-4^9)^2=(-4)^{18}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{3 cm}\underline{Exponent Rules}\\\\$(a^b)^c=a^{bc}$\\\\$a^{-n}=\dfrac{1}{a^n}$\\\end{minipage}}[/tex]
Apply the above exponent rules to simplify each expression.
[tex]\begin{aligned}\implies (4^{-3})^{-3}&=4^{-3 \times -3}\\&=4^9\end{aligned}[/tex]
[tex]\begin{aligned}\implies (4^6)^{-3}&=4^{6 \times -3}\\&=4^{-18}\\&=\dfrac{1}{4^{18}}\end{aligned}[/tex]
[tex]\begin{aligned}\implies (4^0)^{-9}&=4^{0 \times -9}\\&=4^0\end{aligned}[/tex]
[tex]\begin{aligned}\implies (-4^9)^2&=(-4)^{9 \times 2}\\&=(-4)^{18}\end{aligned}[/tex]