If due to gravity, an object falls 16t^2 feet in t seconds. You drop a rock from a bridge that is 75 feet above the water. The rock will hit the water in 2 seconds?
How to find seconds the rock will hit the rock?Given data:
Object falls = 16t² feet in t seconds
Rock from a bridge = 75 feet above the water
So,
72 =16t²
t² = 72/16
t²= 4.5
t = √4.5
t = 2.12 seconds to hit the water
Therefore we can conclude that the rock will hit the water in 2 seconds.
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Find the least positive integer m such that m^2 −m+11 is a product of at least four not necessarily distinct primes.
The least positive integer is m=132.
m(m−1)+11=N
It is clear that N must be odd and that can be divisible by the prime 11.
However, the following congruences have no solution as it is easy to prove directly by checking the few possibilities with m(m−1) not divisible by 3,5 and 7 respectively
{m(m-1)+2=0(mod 3)
{m(m-1)+1=0(mod 5)
{m(m-1)+4=0(mod 7)
Thus N=∏ with pi≥11
A necessary condition is that (solving the quadratic in m)
√4N-43=x² and from this, we need that
N≡1,3,7(mod10)
By chance, we find the minimum N=113⋅13 which corresponds to m=132
and that could have been calculated by direct trials but the next solution seems to be far from 132.
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Use differences to find a pattern in the sequence.
2,9,22,45,82,137,214
Assuming that the pattern continues, the eighth term should be.
If the sequence be 2, 9, 22, 45, 82, 137, 214 then the pattern be 6, 13, 23, 37, 55, 77.
What is meant by sequence ?The term "patterns" describes common, repeatable sorts of practices or regulations. To forecast what has happened or what might happen, patterns are helpful. come following a group of integers that are ordered specifically. Sequence describes this grouping of numbers.
Putting events or information in a precise order is referred to as sequencing. Higher-order thinking abilities—such as those for detecting patterns, figuring out causes and effects, and more—are necessary for sequencing. Sequencing aids students in both understanding and organizing the material they have learnt and in problem-solving.
Let the given sequence be 2, 9, 22, 45, 82, 137, 214
The differences to a pattern in the sequence be
= 9 - 2, 22 - 9, 45 - 22, 82 - 45, 137 - 82, 214 - 137
= 6, 13, 23, 37, 55, 77
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A quadrilateral has diagonal that are perpendicular but not congruent
A quadrilateral has diagonals that are perpendicular but not congruent
is a rhombus.
What is a rhombus?A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposite sides of a parallelogram are equal.
From the properties of a rhombus, we know,
A rhombus has an equal number of sides. In this case, ABCD equals DA.
At an angle of 90° divides each of the diagonals. In this instance, diagonals AC and BD split at a 90° angle.
A rhombus has parallel opposite sides. In this case, AB || CD and AD || BC.
In a rhombus, the opposite angles are equal. ∠A = ∠C, while ∠B = ∠D.
The sum of adjacent angles is 180°.
Diagonals of a rhombus bisect each other at the right angles but they are not congruent.
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a 5 ich photo was enlarged to make a poster as shown. if the dimensions of the poster are (x^2 - 6) inches by (x^ + 12) inches, what is the area of the poster
The dimensions of the poster are given as (x^2 - 6) inches by (x^2 + 12) inches.
The area of the poster is given by the product of these two dimensions:
Area = (x^2 - 6) inches * (x^2 + 12) inches
Area = x^4 - 6x^2 + 12x^2 - 72
Area = x^4 + 6x^2 - 72 inches^2
So, the area of the poster is x^4 + 6x^2 - 72 inches^2.
Below is the seating chart of 50 students in a STP226 class. You are tasked with selecting a sample of 5 students from the class in order to accurately estimate the average Exam 1 score for the entire class.
Front Desk
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Post
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
Post
Door
1) Considering the STP 226 class seating chart above, suppose you randomly selected a student from each row: students in seats 3, 18, 21, 34, and 50 were selected for your sample.
a) What was the sampling method used?
b) Is this sample going to be representative or do you see any issues with the sample? Answer briefly.
The sampling method used in this case is random sampling and the sample is representative.
What is a sample and what makes a sample to be representative?A sample is a small proportion of individuals taken from the general population to be studied. For a sample to be representative it is expected that all the individuals represent the population, for example, if the population includes people of different ages the sample should include this too.
Is the sample representative?The random sample selected is representative because the seats of the students selected are distributed within the class rather than in only one row or line.
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triangles abc and lmn are similar with measurements as shown. what is the measurement of bc, rounded to an integer?
The sides of the triangle ABC are 6, 10, and 8. The sides of the triangle LMN are 12, 20, and 16. The ratio of the respective sides is the same for the two triangles because they are comparable. Therefore, BC is 10 miles long.
Due to the equal ratio of their corresponding sides, the triangles ABC and LMN are comparable. This indicates that the lengths of the sides of LMN may be obtained by multiplying the lengths of the sides of ABC by the same factor. For instance, side AB in ABC is 6 inches long, whereas side LM in LMN is 12 inches long. The lengths are 6:12, or 1:2, apart. The ratio remains the same for all matching. We can examine the other two sides of ABC to verify this response. Ten is the length of AC, and twenty is the length of MN. These two sides must likewise be multiplied by the same factor (1/2), since the ratio of the corresponding sides is the same. This results in AC and MN having lengths of 10 and matching ABC's dimensions. This demonstrates that BC is eight miles long.
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the complete question is
triangles abc and lmn are similar with measurements as shown. what is the measurement of bc, rounded to an integer find BC?
In exercises 5–8 tell whether a correlation is likely in the situation. If so tell her there’s a casual relationship. Explain your reasoning. 6. favorite color and color of shoes 
ANSWER FAST PLEASE
WILL GIVE BRAINLIEST
Any statistical relationship between two random variables or bivariate data, whether causal or not, is referred to as dependence or correlation.
What is correlation?The correlation between two variables A and B is exactly the same as the correlation between A and B, and it describes the strength of the association between the two.
A causal relationship exists when an alteration in one variable directly affects an alteration in the other variable. A causal generalization, such as the claim that smoking causes lung cancer, does not refer specifically to any one smoker but rather to the unique connection between the characteristic of smoking and the characteristic of developing lung cancer.
An overview was given as your information is incomplete and can't be found.
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a significant number of accidents are caused by vehicle equipment failure such as the following except:
A significant number of accidents are caused by vehicle equipment failure such as the following except Operative lights.
Operative lights are also called Surgical lights which are medical equipment devices used to illuminate the operating field during surgery.
Surgical lights are referred to by many names: Operating lights, OR lights, operating room lights, surgical lamps, and surgical light heads.
The primary function of surgical lighting is to illuminate the operative site on and/or within a patient for ideal visualization by OR staff during a surgical procedure.
With proper lighting, operating room staff can achieve a higher level of efficacy during surgery and reduce the risk of complications.
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A picture measures 60 cm by 30 cm. The mat around the picture is 6 cm wide.
Find the area of the mat.
Answer:
1224 cm²
Step-by-step explanation:
The picture is a rectangle with length 60 cm and width 30 cm.
area of rectangle = length × width
area of picture = 60 cm × 30 cm = 1800 cm²
Now we add the mat to the picture. The width of the mat is 6 cm, so when you add mat to two opposite sides, the total length of the picture and mat becomes 60 cm + 6 cm + 6 cm = 72 cm. When you add mat to the other two opposite sides, the total width of the picture and mat becomes 30 cm + 6 cm + 6 cm = 42 cm. Now we have a rectangle 72 cm by 42 cm.
area of picture and mat = 72 cm × 42 cm = 3024 cm²
The area of the mat is the difference in area between the picture with mat and the picture without mat.
area of mat = 3024 cm² - 1800 cm² = 1224 cm²
Question 1 (5 points) Match the correct definition to each word or term. a number that will be used in a function rule to determine the value of the output a relation in which each input has only one ouput the result of applying a function rule to the value of an input the set of possible outputs; dependent variable the set of allowable inputs: independent variable 1. Input 2. Output 3. Domain 4. Range 5. Function
The correct description of each function term is given as follows:
1. Input: A rule to determine the value of the output.
2. Output: The result of applying a function rule to the value of an input, and is the dependent variable.
3. Domain: the set of allowable inputs.
4. Range: The set of possible outputs.
5. Function: A relation in which each input has only one output.
What is a function?A function has the notation y = f(x), in which.
x is the input.y is the output.Hence the input is applied to the function to obtain the output, and these concepts, along with domain and range, are presented in this problem.
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Help I need help with this question
The scale factor needed to form ΔA'B'C' from ΔABC is 1/2 or 0.5.
What is scale factor?
The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger.
The coordinate points of triangle ABC is -
A(2,6), B(2,2), and C(6,2)
The coordinate points of triangle A'B'C' is -
A'(1,3), B'(1,1), and C'(3,1)
Subtract the coordinate points of A'B'C' from ABC to find the scale factor -
A = (2 - 1, 6 - 3) = (1,3)
B = (2 - 1, 2 - 1) = (1,1)
B = (6 - 3, 2 - 1) = (3,1)
So, it can be seen that to form triangle ABC, the triangle A'B'C' is multiplied by the factor of 2.
A(2,6) = (x/2 , y/2) = A'(1,3)
B(2,2) = (x/2 , y/2) = B'(1,1)
C(6,2) = (x/2 , y/2) = C'(3,1)
Therefore, the scale factor is 1/2 or 0.5.
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What is the circumference of the circle? Use 3.14 for π.
circle with a segment drawn from the center of the circle to a point on the circle labeled 4 inches
A. 157.75 inches
B. 50.24 inches
C. 25.12 inches
D. 12.56 inches
Answer:
C. 25.12 inches
Step-by-step explanation:
radius = 4 inches
circumference = 2πr
circumference = 2 × 3.14 × 4 inches
circumference = 25.12 inches
Answer:c is correct 25.12
Step-by-step explanation:
Factor the expression using the GCF.
49 - 28 = ?
By calculating, The GCF of the given numbers 49 and 28 is 7.
What is Algebraic expression ?
An algebraic expression is an expression that consists of numbers, variables and operators such as addition, subtraction, multiplication and division. These expressions can be used to solve equations and other mathematical problems. Algebraic expressions can also be used to represent relationships between different variables. For example, the expression 4x + 2y can be used to represent the relationship between two variables, x and y.
So lets first find the prime factorization of 28
prime factorization of 28 = 2 × 2 × 7
So lets first find the prime factorization of 49
prime factorization of 49 = 7 × 7
To find the GCF, multiply all the prime factors common to both numbers:
Therefore, The GCF of the given numbers 49 and 28 is 7.
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10. When there are 12 observations in a small sample, the median is calculated by
a. the sixth position of an ascending sorted data
b. the average value of the sixth position and the seventh position of an ascending sorted d
c. the sixth position of the data as they were presented without sorting
d. the average value of the sixth position and the seventh position of the data as they were
sented without being sorted
When there are 12 observations in a small sample, the median is calculated by: b. the average value of the sixth position and the seventh position of an ascending sorted.
What is a median?In Mathematics, a median can be defined as the middle number (center) of a sorted data set, which is when the data set is either arranged in a descending order from the greatest to least or an ascending order the least to greatest.
How to calculate the median number of 12 observations?First of all, we would sort the 12 observations from the least to greatest as follows:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
The median for 12 observations is the average of the 6th and 7th number:
Median = (6 + 7)/2
Median = 13/2
Median = 12.5.
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1. A community garden has an area of 10 square yards. The community wants to divide it into plots that each
have an area of 1/2 square yard. How many plots can the garden be split into?
The garden can split into 20 plots.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
A community garden has an area of 10 square yards.
The community wants to divide it into plots that each have an area of 1/2 square yard.
The number of community garden,
= 10/(1/2)
= 20
Therefore, the number of required plots is 20.
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3) A mechanism used to encrypt and decrypt data
a) Data flow
b)Algorithm
c) cryptography
d)None of these
Answer:
c) cryptography
Step-by-step explanation:
Cryptography is a mechanism used to encrypt and decrypt data.
Wha is the value of the expression below (-8)^5/3
Hey there!
Solutions:Exact Form: [tex]-\frac{32768}{3}[/tex]Decimal Form: [tex]-10922.[/tex]Mixed Number Form: [tex]-10922\frac{2}{3}[/tex]
Hope this helps!
Sine/Cosine of Complementary Angles Solve for x
In a right triangle, sin (8x-9) = cos (x+6) Solve for X Round your answer to the nearest tenth
Using complementary angles, the value of x = 10.3
What are complementary angles?Complementary angles are angles in which the sum add up to 90°.
How to find the value of x in the given right triangle?Since in a right triangle, sin(8x - 9) = cos(x + 6). To solve the problem, we proceed as follows.
sin(8x - 9) = cos(x + 6).
Given that cosФ = sin(90 - Ф), we have that
cos(x + 6) = sin[90 - (x + 6)]
So, susbstituting this into the equation, we have that
sin(8x - 9) = cos(x + 6)
sin(8x - 9) = sin[90 - (x + 6)]
This implies that
8x - 9 = 90 - (x + 6)
8x - 9 = 90 - x - 6
8x - 9 = 84 - x
Adding x to both sides of the equation, we have
8x + x - 9 = 84 - x + x
9x - 9 = 84 + 0
9x - 9 = 84
Adding 9 to both sides of the equation, we have that
9x - 9 + 9 = 84 + 9
9x + 0 = 93
9x = 93
x = 93/9
x = 10.33
x ≅ 10.3
So, the value of x = 10.3
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A toy company is building dollhouse furniture. A rectangular door of a dollhouse has a height of 7 centimetres and a width of 3 centimetres. What is the perimeter of the door on a scale drawing that uses the scale 3:5?
A. 33 cm
B. 20 cm
C. 14 cm
D. 12 cm
Answer:
12 cm
Step-by-step explanation:
in the picture
Nachelle decides to estimate the volume of a grapefruit by modeling it as a sphere. She measures its diameter as 11.4 cm. Find the grapefruit's volume in cubic centimeters. Round your answer to the nearest tenth if necessary.
The grapefruit's volume in cubic centimeters to the nearest tenth is equal to 775.8 cubic centimeters.
How to calculate the volume of a sphere?Mathematically, the volume of a sphere can be calculated by using this mathematical expression:
Volume = 4/3 × πr³
Where:
r represents the radius.
Based on the information provided about the grapefruit, the diameter of the sphere is given by;
Diameter of sphere = 11.4 cm
Radius = diameter/2 = 11.4/2 = 5.7 cm.
Substituting the given points into the volume of a sphere formula, we have the following;
Volume of sphere = 4/3 × 3.142 × 5.7³
Volume of sphere = 775.8 cubic centimeters.
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Angelica buys 3 packets of
movie cards and 6 packets of cartoon cards
and adds these to the 3 packets of movie cards
she already has. Write three equivalent algebraic
expressions for the number of cards Angelica
has now.
The algebraic expression will be Y=a+9
Where Y=number of cards Angelica has now, a=added movie cards,
what are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now,
As given
Angelica buys 3 packets of movie cards and 6 packets of cartoon cards
and and adds these to the 3 packets of movie cards she already has
Now let a=packets of movies she already has
and Y=number of cards Angelica has now
Therefore, The algebraic expression will be
Y=a+3+6=a+9
Y=a+9
Where a=3
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James and kyra had a contest to see who could eat the most pizza , while kyra at 7/8 of a pizza and James ate 2 whole pizzas. How much more did James eat?
Answer:
Jessica and some friends have ordered two pizzas. One is a medium sized pizza while the other is a large
Step-by-step explanation:
Jessica and some friends have ordered two pizzas. One is a medium sized pizza while the other is a large
Which of these is a way to show that two figures are congruent
If two figures can be mapped onto one another or if all pairings of angles and side lengths are congruent, the figures are said to be congruent.
What is Triangle?
A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
What is the condition to be congruent?
If two triangles are the same size and shape, they are said to be congruent. To establish that two triangles are congruent, not all six matching elements of either triangle must be located. There are five requirements for two triangles to be congruent, according to studies and trials. The congruence properties are SSS, SAS, ASA, AAS, and RHS.
Both triangles are said to be congruent if the three angles and three sides of one triangle match the corresponding angles and sides of the other triangle.
In Δ PQR and ΔXYZ, as shown in figure,
we can identify that PQ = XY, PR = XZ,
and QR = YZ
and ∠P = ∠X,
∠Q = ∠Y and ∠R = ∠Z.
Then we can say that Δ PQR ≅ ΔXYZ.
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Describe the possible lengths of the third side of the triangle given that the lengths of the other two sides are 5 inches and 12 inches.
The possible length of the third side of a triangle, say x, with the other two sides are 5 inches and 12 inches. is
7 ≥ x ≥ 17
How to determine the possible length of third sideThe length of the third side is within the range of
sum of the two sidesdifference of the two sidesThe sum of the two ides is the highest possible length of the third side
= 12 inches + 5 inches
= 17 inches
The difference of the two ides is the lowest possible length of the third side
= 12 inches - 5 inches
= 7 inches
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Mrs moth picked 24 flowers.Six of them each had 9 petals,7 of them had 8 petals, 5 of them each had 3 petals, and the rest had 10 petals.How many flowers had 10 petals?
Using the subtraction operation, the number of flowers with 10 petals that Mrs. Moth picked was 6.
What is a subtraction operation?A subtraction operation is one of the four basic mathematical operations, including addition, division, and multiplication.
The subtraction operation involves the minuend, the subtrahend, and the difference.
The minuend is the number or value being subtracted from by the subtrahend. The result of a subtraction operation is known as the difference.
The total number of picked flowers = 24
The number of flowers with 9 petals = 6
The number of flowers with 8 petals = 7
The number of flowers with 3 petals = 5
The total number of flowers identified = 18 (6 + 7 + 5)
The number of flowers with 10 petals = x
x = 24 - 18
= 6
Thus, 6 flowers had 10 petals out of the 24 Mrs. Moth picked.
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find the slope of a line perpendicular to the line whose equation is2x+3y=-3 . Fully simply your answer.
3/2 is a slope of a line perpendicular to the line whose equation of
2x+3y=-3 .
What is meant by perpendicular ?One specific example of the more broad mathematical concept of orthogonality is the concept of perpendicularity, which is the orthogonality of traditional geometric objects.
As a result, in higher mathematics, the term "perpendicular" is occasionally used to represent considerably more intricate geometric orthogonality criteria, like the relationship between a surface and its normal vector.
If two lines cross at a right angle, they are said to be perpendicular to one another.
A first line is explicitly said to be perpendicular to a second line if the two lines meet and the straight angle on one side of the first line is cut by the second line into two congruent angles at the point of junction.
This can be done by rearranging the equation into the slope intercept form.
2x +3y = -3
3y = -2x -3
y = -2/3x - 1
Thus, the slope of the given line is -2/3.
The slope of the perpendicular line is the negative reciprocal of the given line.
Slope of perpendicular line = 3/2
The slope-intercept form was:
(i) The reciprocal of m is 1/m.
(ii) The negative reciprocal of m is -1/m.
Negative reciprocal of -2/3
= -1 ÷ (- 2/3)
= -1 × (-3/2)
= 3/2
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Which expression is equivalent to 5.25×+1246x
Answer:
The expression "5.25x + 1246x" is equivalent to "1771x"
use the pythagorean theorem to find the length of the missing side of the right triangle. then find the value of each of the six trigonometric functions of 0
The length of the missing side is 12cm.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. So if we know the lengths of two sides of a right triangle, we can use the theorem to find the length of the third side.
Given:
Base (b) = 16 cm
Hypotenuse (c) = 20 cm
We can use the Pythagorean theorem to find the length of the missing side (a), which is the side opposite the right angle and adjacent to the base.
c^2 = a^2 + b^2
20^2 = a^2 + 16^2
400 = a^2 + 256
144 = a^2
a = 12cm
once we have the length of the missing side, we can use the values of the base and hypotenuse to find the six trigonometric functions:
Sine (sin) = a/c = 12/20 = 0.6Cosine (cos) = b/c = 16/20 = 0.8Tangent (tan) = a/b = 12/16 = 0.75Cosecant (csc) = c/a = 20/12 = 1.67Secant (sec) = c/b = 20/16 = 1.25Cotangent (cot) = b/a = 16/12 = 1.33Therefore, the length of the missing side is 12cm.
The question is incomplete as it does not include the figure. Hence I have attached the figure for a complete understanding of the problem.
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Please answer this question
The weighted average for A,B and C will be 0.333.
What is weighted average?
Weighted average is a mean calculated by giving values in a data set more influence according to some attribute of the data. It is an important section in CAT quantitative aptitude. Weighted average is an average in which each quantity to be averaged is assigned a weight, and these weightings determine the relative importance of each quantity on the average. Weightings are the equivalent of having that many like items with the same value involved in the average.
Now,
Given weight for A=0.5, B=0.1 and C=0.4
Weighted average=(A+B+C)/3
=(0.5+0.1+0.4)/3
=1/3
Weighted average=0.33
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Solve the equation. 3x^2-4y-2=0 please help.
The solution for the equation 3x²-4x-2=0 is 1.72076 and 0.387426.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
3x²-4x-2=0
Now, solving the above Quadratic Equation
D= √b² - 4ac
From the given equation
a= 3, b-4, c=-2
Then, D= √(-4)² - 4(3)(-2)
D= √16 +24
D = √40
Now, x= (-b ±D)/ 2a
x= -(-4) ± √40/ (6)
x= 4+ √40/6 or x= 4-√40/6
x = 1.72076 or x=−0.387426
Hence, the value of x is 1.72076 and 0.387426.
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