Points, lines and planes can be used in different fields like Navigation, Architecture, Art, Engineering, etc.
What are points, lines, and planes?
Point: A point is a basic geometric object that represents a specific location in space.
Line: A line is a straight path that extends infinitely in both directions. It is made up of an infinite number of points that are all collinear, or lie on the same straight path.
Plane: A plane is a two-dimensional flat surface that extends infinitely in all directions.
Navigation: Points and lines are essential for navigation, both on land and in the air. For example, on a map, points represent specific locations, while lines represent roads, highways, and other paths that can be taken to get from one point to another.
Architecture and Design: Points, lines, and planes are critical for architecture and design. Architects use points to specify the locations of walls, columns, and other structural elements, while lines are used to create the edges of rooms and buildings. Planes are used to define the surfaces of walls, floors, and ceilings.
Art: Artists often use points, lines, and planes to create visual effects in their work. Points can be used to create texture, while lines can be used to create movement and depth. Planes can be used to create shapes and form.
Engineering: Points, lines, and planes are fundamental to engineering, which involves the design and construction of structures and machines. Engineers use points to specify the locations of components, while lines are used to create the edges of parts. Planes are used to define the surfaces of structures, such as the wings of an airplane.
Hence, points, lines and planes can be used in different fields like Navigation, Architecture, Art, Engineering, etc.
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The number of students enrolled at a college 18,000 and grows 5% each year. What is the initial amount
Answer:
900
Step-by-step explanation:
5% of 18,000
Tara stayed at the Merry Mountain campgrounds last weekend. She paid a rental fee to use a kayak for 4 days. She also paid $18 for a guided waterfall tour. Tara paid $94 in all. What was the rental cost of each day Tara used the kayak?
Answer:
$19
Step-by-step explanation:
calculate 94-18/4 = 19
if you randomly select a mechanical component, what is the probability that it weighs more than 11.5lbf
The probability that randomly selected mechanical component weighs: more than 11.5 lbf is 0.0099, less than 8.7 lbf is 0.3208, less than 5.0 lbf is 0.0228, between 6.2 lbf and 7.0 lbf is 0.1314, between 10.3 lbf and 14.0 lbf is 0.0436, between 6.8 lbf and 8.9 lbf is 0.3464.
We can use the standard normal distribution and z-scores to answer these questions:
P(X > 11.5) = P(Z > (11.5 - 8) / 1.5) = P(Z > 2.33) = 0.0099
Therefore, the probability that a randomly selected mechanical component weighs more than 11.5 lbf is 0.0099, or about 1%.
P(X < 8.7) = P(Z < (8.7 - 8) / 1.5) = P(Z < 0.47) = 0.3208
Therefore, the probability that a randomly selected mechanical component weighs less than 8.7 lbf is 0.3208, or about 32%.
P(X < 5.0) = P(Z < (5 - 8) / 1.5) = P(Z < -2) = 0.0228
Therefore, the probability that a randomly selected mechanical component weighs less than 5.0 lbf is 0.0228, or about 2%.
P(6.2 < X < 7.0) = P((6.2 - 8) / 1.5 < Z < (7 - 8) / 1.5) = P(-1.2 < Z < -0.67) = 0.1314
Therefore, the probability that a randomly selected mechanical component weighs between 6.2 lbf and 7.0 lbf is 0.1314, or about 13%.
P(10.3 < X < 14.0) = P((10.3 - 8) / 1.5 < Z < (14 - 8) / 1.5) = P(1.53 < Z < 2.67) = 0.0436
Therefore, the probability that a randomly selected mechanical component weighs between 10.3 lbf and 14.0 lbf is 0.0436, or about 4%.
P(6.8 < X < 8.9) = P((6.8 - 8) / 1.5 < Z < (8.9 - 8) / 1.5) = P(-0.47 < Z < 0.60) = 0.3464
Therefore, the probability that a randomly selected mechanical component weighs between 6.8 lbf and 8.9 lbf is 0.3464, or about 35%.
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____The given question is incomplete, the complete question is given below:
Suppose that the weight of a mechanical component is normally distributed with mean p = 8.0 Ibf and standard deviation = 1.5 lbf. Answer the following questions: 1. If you randomly select a mechanical component, what is the probability that it weighs more than 11.5 lbf? 2. If you randomly select a mechanical component, what is the probability that it weighs less than 8.7 lbf? 3. If you randomly select a mechanical component, what is the probability that it weighs less than 5.0 lbf? 5. If you randomly select a mechanical component, what is the probability that it weighs between 6.2 lbf and 7.0 lbf? 6. If you randomly select a mechanical component, what is the probability that it weighs between 10.3 lbf and 14.0 lbf? 7. If you randomly select a mechanical component, what is the probability that it weighs between 6.8 lbf and 8.9 lbf?
−4x+7=2y−3 how do i solve for x
get rid of y. that's all you have to do.
32 Ounces of Juice for $7.04. How much per ounce
Answer:
$0.22.
Step-by-step explanation:
To find the cost per ounce of juice, divide the total cost of 32 ounces of juice by the number of ounces:
7.04 ÷ 32 ounces = 0.22 per ounce
So, the cost per ounce of juice is approximately $0.22.
Answer:
0.22
Step-by-step explanation:
help plsplspls
Find the value of the following expression and round to the nearest integer:
34
Σ 400(0.93)n-2
n=2
The value of the expression is 5193.
How to find the value of the expression?From the question, we have the following parameters that can be used in our computation:
From the notation, we have the following values:
The first term, a = 400
The common ratio, r = 0.93
The number of terms, n = 34 - 1 = 33
The sum of the geometric progression is represented as:
Sum = a(1-rⁿ)/(1-r)
Sum = 400(1-0.93³³)/(1-0.93)
Sum = 5193
Therefore, the value of the expression is 5193
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Colton is flying a kite, holding his hands a distance of 3 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be 32 . If the string from the kite to his hand is 90 feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary.
Answer:
The height of the kite above the ground is; approximately 50.69 feet.
What are trigonometric identities?
Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
The height of his hands above the ground, h is given by 3 feet
Angle of elevation of the string (above the horizontal), θ = 32°
Length of the string, l is given as 90 feet
The height of the kite above the ground is given by trigonometric ratios as ;
Sin∅ =h /90
Sin 32°= h/90
0.52 =h /90 (Sin32°= 0.52)
so h= 47.69 feet
Then height from ground is (H) = 3 +47.69
H = 50.69 feet
The height of the kite above the ground , ≈ 50.69 feet
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Step-by-step explanation:
amit took part in an cycle race .he started at 1:25 pm and reached the finishing line at 1:50 . what was the duration of the race ?
amit took a part in cycle race .he started at 1:25 and he reached finishing lline at 1:50 pm what was the duration of the race .
Answer:
25 minutes
Step-by-step explanation:
Subtract the two times to find the duration.
Find the greatest whole number which divides 372 & 324 without leaving remainder
The greatest whole number that divides both 372 and 324 without a remainder is 4.
To find the greatest whole number that divides both 372 and 324 without a remainder, we can use the concept of the greatest common divisor (GCD).
One method to find the GCD is to factor each number into its prime factors and then find the product of the common prime factors.
372 can be factorized as 2 * 186, and 324 can be factorized as [tex]2^2 * 3^4[/tex]
The greatest common divisor is [tex]2^2[/tex], which is equal to 4.
So, the greatest whole number that divides both 372 and 324 without a remainder is 4. This means that 4 is the largest number that can divide both 372 and 324 evenly, leaving no remainder.
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f(x)=x^2-4x+3 find the quadratic function
Answer:
Step-by-step explanation:
3. Find the height of the tree below to the nearest foot.
The height of the tree to the nearest foot is 27 feet.
How to find the height of a tree?The height of the tree can be found as follows:
The height of the tree can be found using trigonometric ratios. Therefore,
let
tan ∅ = opposite / adjacent
Therefore,
opposite side = adjacent tan ∅
Hence,
height of the tree = 20 + x tan 45° = x tan 75°
20 + x tan 45° = x tan 75°
20 tan 45 + x tan 45° = x tan 75°
20 tan 45 = x tan 75° - x tan 45°
20 tan 45 = x(tan 75 - tan 45)
20 tan 45 = x(3.73205080757 - 1)
2.73205x = 20
x = 20 / 2.73
x = 7.32600732601
x = 7.34
Therefore,
height of the tree = x tan 75°
height of the tree = 7.34 × tan 75°
height of the tree = 27.3186119114
height of the tree = 27 ft
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please help im kinda failing in math
Answer:
Step-by-step explanation:
c
a
Hiro painted his room. After 333 hours of painting at a rate of 888 square meters per hour, he had 282828 square meters left to paint.
The solution is, the situation can be modeled as y = 52 - 8x.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
Hiro painted his room. After 3 hours of painting at a rate of 8 square meters per hour, he had 28 square meters left to paint.
So, the total area to be painted is (28 + 3 × 8) = 52 square meters.
Let y represent the area (in square meters) left to paint after x hours of painting then the situation can be modeled as
y = 52 - 8x ................ (1) (Answer)
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Which is the graph of f(x) = 100(0.772)
It is not possible to graph f(x) = 100(0.772) without additional information. A function needs at least two points to graph a line. The expression f(x) = 100(0.772) represents a constant value, not a function of x, so it cannot be graphed on its own.
Answer: knvsvvs
Step-by-step explanation:
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 3\le x \le 43≤x≤4.
The average rate of change of f(x) over the interval 3≤x≤4 is 15
What is the average rate of change of f(x) over the intervalFrom the question, we have the following parameters that can be used in our computation:
The table of values
On the table, we have
f(3) = -4
f(4) = 11
The average rate is then calculated as
Average rate = [f(4) - f(3)]/[4 - 3]
Substitute the known values in the above equation, so, we have the following representation
Average rate = (11 + 4)/(4 - 3)
Evaluate
Average rate = 15
Hence, the average rate is 15
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Complete question
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 3\le x \le 43≤x≤4.
X f(x)
3 -4
4 11
5 8
6 10
7 11
8 14
To increase sales, a local donut shop began putting an extra donut in some of the boxes. Customers are unaware of which boxes
had the extra donut, and the shop owner claimed that one in seven boxes had an extra donut. Nine customers each bought one box
of donuts at the shop. Let X = the number of customers that bought a box containing an extra donut. What are the mean and
standard deviation of X? Provide an interpretation for each value in context.
Opx = 1.143 and ox= 0.990; If the shop were to sell many boxes of donuts, the average number of boxes with an extra
donut is 1.143 out of 9, and they will typically sell between 0.153 and 2.133 boxes out of 9 with extra donuts.
O μx = 1.286 and ox= 1.050; If the shop were to sell many boxes of donuts, the average number of boxes with an extra
donut is 1.286 out of 9, and they will typically sell between 0.236 and 2.336 boxes out of 9 with extra donuts.
Opx 1.286 and ox= 1.050; If the shop were to sell many boxes of donuts, the average number of extra donuts is 1.286
out of 9, and they will typically sell between 0.236 and 2.336 extra donuts.
Opx 1.143 and ox=0.990; If the shop were to sell many boxes of donuts, the average number of extra donuts is 1.143
out of 9, and they will typically sell between 0.153 and 2.133 extra donuts.
The answer is given below:
What is binomial distribution?Binomial distribution is a discrete probability distribution in which it gives two values that is either success or failure.
A local donut shop began putting an extra donut in some of the boxes.
The shop owner claimed that one in seven boxes had an extra donut.
Nine customers each bought one box of donuts at the shop.
Probability of success fixed is, [tex]p=\frac{1}{7}[/tex]
A value of n fixed, n=9.
We can use binomial distribution to solve this problem,
The probability mass function for the Binomial distribution is given as:
Assume X is a binomial distribution, [tex]B(n=9,p=\frac{1}{7}=1.143)[/tex].
[tex]P(X)=(nCx)(p)^{x} (1-p)^{n-x}[/tex]
The mean is given by:
[tex]E(X)=np=9*\frac{1}{7}=1.29\\[/tex]
The variance is given by,
[tex]Var(X)=np(1-p)=9*\frac{1}{7}(1-\frac{1}{7} )[/tex]=1.1094
From variance, the standard deviation is given by, [tex]std(X)=\sqrt{1.1094}[/tex]=1.05.
Two of the nine customers buy a box of donuts with an extra donut. Compute P(X ≥ 2) and use the result to justify your answer.
[tex]P(X\ge2)=1-P(X=2)\\1-P(X\le1)=1-[P(X=0)+P(X=1)][/tex]
And if we find the individual probabilities we got,
[tex]P(X=0)=(9C0)(0.143)^{0} (1-0.143)^{9-0}=0.249\\P(X=1)= (9C1)(0.143)^{1} (1-0.143)^{9-1}=0.374[/tex]
[tex]P(X\ge2)=1-P(X=2)\\1-P(X\le1)=1-[P(X=0)+P(X=1)]\\[/tex]
= 1-[0.249+0.374]
= 0.377
Hence, [tex]P(X\ge2)=[/tex] 0.377.
This case makes sense the claim since the probability is higher or equal than the expected with the claim.
Corrected question:
To increase sales, a local donut shop began putting an extra donut in some of the boxes. Customers are unaware of which boxes had the extra donut and the shop owner claimed that one in seven boxes had an extra donut. Nine customers each bought one box of donuts at the shop. Let X = the number of customers that bought a box containing an extra donut.A. Is X a binomial random variable? Explain.B. What is the mean and standard deviation of X? Provide an interpretation for each value in context.C. Two of the nine customers buy a box of donuts with an extra donut. Is the shop's claim accurate? Compute P(X ≥ 2) and use the result to justify your answer.
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working alone, Ted can install a new deck in 15 hours. Jimmy can install the same deck in 16 hours. How long would it take them to install the deck if they worked together
The time taken to complete the work when Ted and Jimmy work together is found using the unitary method and it is 7.7 hours.
What is the unitary method?
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, and then multiplying that value to determine the required value.
Let W be the total work to be done, which is installing a new deck.
Given Ted alone can complete the work W in 15 hours.
Using unitary method,
So in one hour, work done by Ted = W/15
Also given Jimmy alone can complete the work W in 16 hours.
So in one hour, work done by Jimmy = W/16
Using unitary method,
In one hour the work done by Jimmy and Ted together = W/15 + W/16 = 31W/240
ie 31W/240 = 1 hour
So W = 240/31 = 7.7 hours
Therefore the time taken to complete the work when Ted and Jimmy work together is found using the unitary method and it is 7.7 hours.
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If 3 garbage trucks can collect the trash of 24 homes in a day, how many trucks are needed to collect in 72 houses?
Answer:
9
Step-by-step explanation:
72/24 = 3
72 is 3 times 24, so you need 3 times as many garbage trucks.
Answer: 9
A group consisting of 32 aggressive zombies quadruples in size every hour. Which equation matches the number of zombies after 6 hours?
Answer:
131,072 Zombies:
the equation: 32 x 4^6 = 131,072
the equation in scientific notation form: 3.2 x 4^7 = 131,072
Step-by-step explanation:
The amount of zombies starts at 32. It quadruples per hour, so we need to multiply the amount by 4 six times(once for every hour).
We can use an exponent to represent this in an equation:
32 x 4^6 = 131,072
Or, if we put it in scientific notation,
3.2 X 4^7 = 131,072.
The equation which represents the number of zombies is;
= [tex]1.31072[/tex]×[tex]10^{5}[/tex]
What is an equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.
Given that
The amount of zombies = 32.
And It quadruples per hour,
Therefore,
Multiply the amount by 4 six times (as it occurs once for every hour).
The the exponent form to represent this equation:
32 x 4^6 = 131,072
Hence, in scientific notation the equation is,
= [tex]1.31072[/tex]×[tex]10^{5}[/tex]
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Two factory plants are making TV panels. Yesterday, Plant A produced 4000 fewer panels than Plant B did. Four percent of the panels from Plant A and 2% of
the panels from Plant B were defective. How many panels did Plant B produce, if the two plants together produced 500 defective panels?
14
The number of panels that Plant B produced is; 11000 panels
How to solve algebra word problems?We are told that Plant A produced 4000 fewer panels than Plant B did.
Thus;
A = B - 4000 -----(1)
Four percent of the panels from Plant A and 2% of the panels from Plant B were defective. Thus;
0.04A + 0.02B = 500 ------(2)
Put eq 1 in eq 2 to get;
0.04(B - 4000) + 0.02B = 500
0.04B - 160 + 0.02B = 500
0.06B = 660
B = 660/0.06
B = 11000 panels
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pls help i dont understand
The linear function giving the amount remaining after buying x cups of coffee is given as follows:
A(x) = -3x + 15.
How to obtain a linear function?
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.Each cup of coffee costs $3, hence the slope m is given as follows:
m = -3.
(for each cup purchased, the balance decays by $3).
Hence:
A(x) = -3x + b.
Buying 4 cups of coffee, the balance is of $3, hence the intercept b is obtained as follows:
3 = -3(4) + b
b = 15.
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It says its wrong is it?
Answer: Yes, it's wrong.
Step-by-step explanation:
In the equation, it was [tex]A=\pi r^{2}[/tex]3 ft is the circle's diameter, and d is not the r.
r = d/2 = 3/2 = 1.5 ft
[tex]A=\pi r^{2}\\[/tex]
≈ 3.14 x 1.5
= 4.71
Solve -28r = 4r.
r = , r =
Step-by-step explanation:
this is very simple, we only have to divide each side by four to single out our unknown.
[tex]-28=4r[/tex][tex]-14=2r[/tex][tex]-7=r[/tex]
Answer:
the solution to the equation -28r = 4r is r = 0.
Step-by-step explanation:
To solve the equation -28r = 4r, we can isolate the variable "r" on one side of the equation and find its value. To do this, we can start by subtracting 4r from both sides of the equation:
-28r - 4r = 4r - 4r
-32r = 0
Next, we can divide both sides of the equation by -32 to find the value of "r":
(-32r) / -32 = 0 / -32
r = 0
So the solution to the equation -28r = 4r is r = 0.
What is the area of ∆AOB?
The Area of Rhombus is 97.5 cm².
What is area of Rhombus?The area of a rhombus is equal to half the product of the lengths of the diagonals. The formula to calculate the area of a rhombus using diagonals is given as, Area = (a × b )/2 where, a and b are the diagonals of the rhombus.
Given:
As, diagonals of rhombus bisect perpendicularly.
so, In triangle OAD using Pythagoras theorem
AD² = OD² + OA²
10² = 7.8² + OD²
OD= 6.25 cm
So, length of BD = 2 x 6.25 = 12.5 cm
Now, area of Rhombus = 1/2 x a x b
= 1/2 x 15.6 x 12.5
= 97.5 cm².
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A plumber cut a pipe into 5 equal pieces and had 27 cm of the pipe left. For a second
pipe 15m long, he cut 11 pieces of the same length as that of each piece cut from the
first pipe and had 15 cm of the second pipe left. What was the length, in cm, of each
shorter piece of the second pipe? What was the length of the first pipe originally?
Please input your answer:
Answer:
Step-by-step explanation:
Let's call the length of each shorter piece of the first pipe x. Then the total length of the first pipe would be 5x + 27 cm.
Similarly, the length of each shorter piece of the second pipe would be x and the total length of the second pipe would be 11x + 15 cm.
Since both pipes were cut into the same length pieces, we can set the two equations equal to each other:
5x + 27 = 11x + 15
Solving for x, we can find the length of each shorter piece:
6x = -12
x = -2
This means that each shorter piece of both pipes was -2 cm long, which is not physically possible. So, this solution is not valid. This means that the problem is underdetermined and that we cannot determine the length of each piece.
Factor the polynomial.
3x³-300x
The result to the factorization of the polynomial is 3x (x + 10) (x - 10).
Polynomial FactorizationFactoring polynomials involves utilizing prime factorization to break the given polynomial down into a product of two or more polynomials. Polynomials can be readily simplified by factoring them.
Writing each term of the longer expression as the product of its elements is the initial step to factorization polynomials.
= 3x³ - 300x
= 3x(x²) - 300x
= 3x(x²) - 3x(100)
= 3x(x² - 100)
= 3x(x² - 10²)
Since both terms are perfect squares, factor using the difference of squares formula, a² − b² = ( a + b ) ( a − b );
where
a = x and b = 10= 3x (x+10) (x−10)
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who has a better chance of winning the super bowl 2023
The Kansas City Chiefs has a better chance of winning the super bowl 2023.
In 1967's Super Bowl I, Las Vegas sportsbooks gave the Green Bay Packers a 14-point advantage against the Kansas City Chiefs. Nevada was the only state up until 2018 to allow legal Super Bowl sports betting.
The reigning champion Kansas City Chiefs are the early favorited in the Super Bowl 58 odds, according to the top NFL betting companies. At BetMGM, the Super Bowl 58 odds for the Kansas City Chiefs are +600. You can evaluate the odds on a team you prefer to discover the best price because competing sportsbooks provide different odds for each team to win the Super Bowl.
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a knitted hat pattern comes in styles with stitch options and sizes, and there are yarns appropriate for the hat. disregarding size, how many different hats can be made?
A knitted hat pattern comes in 4 styles with 4 stitch options and 3 sizes, and there are 7 yarns appropriate for the hat. There are 112 different hats that can be made using the knitted hat pattern, disregarding size.
To find the total number of different hats that can be made using the knitted hat pattern, we need to multiply the number of choices for each feature.
There are 4 styles to choose from and 4 stitch options, so there are 4 x 4 = 16 different combinations of style and stitch.
For each of these style and stitch combinations, there are 7 yarns that can be used, so the number of possible yarn choices is 7.
Therefore, the total number of different hats that can be made, disregarding size, is:
16 (style and stitch combinations) x 7 (yarn choices) = 112
This calculation shows how the multiplication principle of counting can be used to find the total number of outcomes in a multi-stage process where the number of choices at each stage is known. In this case, we multiplied the number of style and stitch combinations by the number of yarn choices to find the total number of different hats that can be made.
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Complete question is:
A knitted hat pattern comes in 4 styles with 4 stitch options and 3 sizes, and there are 7 yarns appropriate for the hat. Disregarding size, how many different hats can be made?
find the quadratic equation whose roots are 5 and -9
The equation of the quadratic equation whose root are 5 and -9 is x² +4x -45
What is quadratic equation?quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The equation of a quadratic is given as :
x²-(alpha+beta)x + alpha×beta = 0
where alpha and beta are the roots of the quadratic equation.
alpha+beta = 5-9 = -4
alpha × beta = -9× 5 = -45
therefore the equation will be;
x²-(-4)x + ( -45) = 0
x² + 4x -45 = 0
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2 + cscsecx/cscsecx = (sinx+cos)
Answerk bzijnjlngljntgojengojnetgihnrtgkte4wg
