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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Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0
The answer is x4 – 6x2 – 27 = 0 and this is a quadratic equation in the polynomials .
How to calculate and What is Quadratic equation?This is a quartic equation because the highest degree is 4
In the second option, we have 3x⁴ = 2x, this is also another quartic equation.
In the third equation, we have 2(x + 5)⁴ + 2x² + 5 = 0, this is a quartic equation because the highest degree is 4
In the fourth equation, 6(2x + 4)² = (2x + 4) + 2
This is a quadratic equation because the highest degree is 2
In the fifth equation, we have 6x⁴ = -x² + 5 which is also another quartic equation
An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. First, there must be a term other than zero in the coefficient of x2 (a 0) for an equation to be a quadratic equation. The x2 term is written first when constructing a quadratic equation in standard form, then the x term, and finally the constant term. The numerical values of a, b, and c are typically expressed as integral values rather than fractions or decimals.
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[tex]\frac{csc x -1}{cot x} = \frac{cot x}{csc x + 1}[/tex]
Answer:
The equation [tex]\frac{csc x -1}{cot x} = \frac{cot x}{csc x + 1}[/tex] can be simplified by cross-multiplying the fractions and then solving for x. This will result in the equation [tex]csc^2 x - 1 = 0[/tex], which can be simplified to [tex]csc x = 1[/tex], and thus [tex]x = \frac{\pi}{2} + n\pi[/tex], where n is any integer.
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bought a bag of candy for five dollars there were 20 pieces of candy in the bag what is the unit cost of each piece of candy in the bag
Solve pls this equation
Hey there!
If you are solving for x, then your final solutions are [tex]x=\sqrt{-y},-\sqrt{-y}[/tex].
Hope this helps!
PLEASE THIS IS DUE SOON AND I NEED HELP
To friends shop for fresh fruit. Jaxson buys a watermelon for $8.25 and 3 pounds of cherries. Tim buys a pineapple for $3.15 and 2 pounds of cherries. Use the variable P to represent the price in dollars per pound of cherries. write and simplify an expression to represent how much more Jaxson spent.
If two friends shop for fresh fruit. Jaxson buys a watermelon for $8.25 and 3 pounds of cherries. The expression to represent how much more Jaxson spent is :5.1 +p.
How to find the expression?P = price of the cherries per pound
Price of cherries bought by Jaxson= $3p
Total amount spent by Jaxson = $8.25 + $ 3p
Price of cherries bought by Tim = $2p
Total amount spent by Tim = $3.15 + $ 2p
Now let find how much more Jaxson spent.
8.25 + 3p - 3.15 + 2p
5.1 + 3p - 2p
Combine like terms
5.1 +1p
Multiply by 1
5.1 + p
Therefore the expression to represent how much more Jaxson spent is :5.1 +p.
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please help will mark BRAINLIEST
What is an equation of the line that passes through the point (2, 3) and is parallel to
the line x + y = 4?
The equation of the line that is parallel to x + y = 4 and passes through (2, 3) is expressed as: y = -x + 5.
How to Determine the Equations of Parallel Lines?Two lines are parallel if and only if their slopes are equal. The equation of the line x + y = 4 is in slope-intercept form (y = mx + b), where m is the slope. The slope of this line is m = -1, as the coefficient of x is -1.
An equation of a line that is parallel to the line x + y = 4 and passes through the point (2, 3) can be written in the form y = mx + b, where m = -1.
Substituting the point (2,3) and the slope -1 into the point-slope form of a line gives:
y - 3 = -1(x - 2)
Expanding the right hand side gives:
y - 3 = -x + 2
And rearranging the equation gives the final form of the equation of the line:
y = -x + 5
So, the equation of the line that passes through the point (2, 3) and is parallel to the line x + y = 4 is y = -x + 5.
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A fashion store is planning its end–of–season sale. It sells 40 of its signature jeans every week at $175 per pair. Last year, the store's sales increased to 60 pairs per week when the price was dropped by $25. By what amount should the store discount the price this year to maximize its revenue?
A. $112.50
B. $103.50
C. $62.50
D. $71.50
Answer:
A
Step-by-step explanation:
Every $1 decrease in price corresponds to a 0.8 increase in the number of pairs of jeans sold.
So, if [tex]x[/tex] pairs of jeans are sold, the revenue in dollars is [tex](175-x)(40+0.8x)[/tex].
The roots of this function are [tex]x=175[/tex] and [tex]x=-50[/tex]. The maximum is achieved halfway between these roots at [tex]x=62.5[/tex].
When 62.5 pairs of jeans are sold, the price is $112.50.
Based on the information, the store should discount $112.50 from the price to maximize its revenue.
How to calculate the amount of discount that the store should make?To calculate the amount of discount that the store must make to maximize its profits we must perform the following mathematical operation:
First we have to analyze the available data which are:
40 exclusive jeans/week ($175 each)60 exclusive jeans/week ($150 each)According to the above information, the problem could be answered with the following mathematical formula:
(175 - x)(40 + 0.8x)
x = 175
x = -50
x = 62.50.
According to the above, the correct answer is $112.50 (option A).
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Which ordered pair is a solution to the linear system?
2x + y = 5
x – y = 13
Choose the blanks
The linear relationship is or is not
And the graph passes or does not pass
Because the ratios between each set of numbers are equal, and the graph passes through the point, the linear relationship is proportionate (0,0).
What does the word "proportional" mean?Proportional connections are those in which the ratios of the two variables are equal. Another way to think about them is that one variable is always a constant value multiplied by the other in a proportional relationship. The "constant of proportionality" is the name given to this variable.
The origin, points (2,14.5), (4,29), and (6,43.5) are provided (0,0).
We are aware that the ratios are equivalent in a proportional connection, i.e.
So,
⇒ 14.5/2 = 29/4 = 43.5/6 = 7.25
The linear relationship is a proportionate relationship since the ratios are equal.
The given situation's graph has been drawn, and it is evident that the graph passes through its origin, or "zero," which is (0,0)
Since the ratios between each set of data are equal, the linear relationship can only be a proportional relationship because the graph passes through the point (0,0).
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the measure of the angle represented by the expression (7x+12)=1.?
The measure of the angle represented by the expression (7x+12) is 61°.
What is the measure of the angle represented by the expression (7x+12)?The measure of the angle represented by the expression (7x+12) is determined as follows:
The same-side interior angles are supplementary and their sum is 180°.
7x + 12 and 17x are same-side interior angles and are, therefore, supplementary.
7x + 12 + 17x = 180°
solving for x by summing similar terms:
24x + 12 = 180
24x = 168
Dividing both sides by 24
x = 7
Therefore,
7x + 12 = 7 * 7 + 12
7x + 12 = 61°
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$155 $267 $284 $194 $299 $284 $287 $179 What is the mean, median, and mode of this data set?
Answer:
Mean = 243.625
Median = 275.5
Mode = 284
Each value is exact without any rounding.
=================================================
Original data set:
$155 $267 $284 $194 $299 $284 $287 $179
Let's remove the dollar signs, and separate each item with a comma:
155,267,284,194,299,284,287,179
Then sort the values from lowest to highest.
155,179,194,267,284,284,287,299
---------------------
To find the mean, we add up the values and divide by n = 8 since there are 8 items in the list.
(155+179+194+267+284+284+287+299)/8 = 243.625 is the mean
----------------------
Refer to the sorted data set.
The median is the middle-most value. Because the sample size n = 8 is even, we'll have two values tied for the middle.
n/2 = 8/2 = 4
The items in slot 4 and 5 are tied for the middle.
The values in slot 4 and 5 are 267 and 284 in that exact order.
Compute the midpoint: (267+284)/2 = 275.5 is the median
----------------------
The mode is the most frequent value. Look through the sorted data set to see that 284 shows up twice. This is the most frequent compared to the other values (that show up only once).
Therefore, the mode is 284
Side note: It's possible to have multiple modes. It's also possible to not have any modes at all.
Look at the steps for solving the equation and choose a true statement.
3x-9x + 1 = 2(-3x + 1) - 1
-6x + 1 = -6x + 2-1
-6x + 1 = -6x + 1
C
There are infinitely many solutions to the equation.
There is no way to know if there is a solution to this equation.
The only solution to the equation is 1.
There are no solutions to the equation.
The only solution to the equation is -6.
Based on the steps for solving the equation, a true statement include the following: A. there are infinitely many solutions to the equation.
What is no solution?In Mathematics, no solution is sometimes referred to as zero solution, and an equation is said to have no solution when the left hand side and right hand side of the equation are not the same or equal.
What are infinitely many solutions?In Mathematics, an equation is said to have an infinitely many solution when the left hand side and right hand side of the equation are the same or equal:
3x - 9x + 1 = 2(-3x + 1) - 1
-6x + 1 = -6x + 2 - 1
-6x + 1 = -6x + 1
When x = 1, we have:
-6(1) + 1 = -6(1) + 1
-5 = -5.
When x = 2, we have:
-6(2) + 1 = -6(2) + 1
-11 = -11.
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a number n is said to be squarefree is the largest square that divides n is 1. show that any square-free integer can be uniquely written as the product of a squarefree integer and a square
Any square-free integer can be expressed as the product of a square-free integer (which has no square factors) and a perfect square (which has only square factors). This product is unique for any given square-free integer.
Any square-free integer can be expressed as the product of a square-free integer and a perfect square. This is because a square-free integer has no square factors, so the product of a square-free integer and a perfect square would have only square factors, and thus be square-free. To show that this product is unique for any given square-free integer, we can use the fact that any integer can be expressed as the product of its prime factors and that a square-free integer has no square factors. This means the prime factors of the square-free integer are all distinct, and thus the product of the square-free integer and the perfect square can be expressed as the product of the prime factors of the square-free integer and the prime factors of the perfect square. Since the prime factors of the perfect square are all the same, the product is uniquely determined by the prime factors of the square-free integer. Thus, the product of a square-free integer and a perfect square is unique for any given square-free integer.
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Ages of Dogs The ages of 20 dogs in a pet shelter are shown. Construct a frequency distribution using 7 classes.
7
9
6
8
7
6
8
6
9
5
7
7
Send data to Excel
6
89
8
8
6 4 8
9
6 3
Class limits Class boundaries Frequency
3
2.5-3.5
4
3.5-4.5
4.5-5.5
5.5-6.5
6.5-7.5
7.5-8.5
8.5-9.5
Total
5
The frequency table is added below
How to determine the frequency distributionFrom the question, we have the following parameters that can be used in our computation:
7 9 6 8 7 6 8 6 9 5 7 7
6 8 9 8 8 6 4 8
When represented on a frequency table, we have
Class limits Class boundaries Frequency
2.5 - 3.5 3.0 - 4.0 0
3.5 - 4.5 4.0 - 5.0 1
4.5 - 5.5 5.0 - 6.0 1
5.5 - 6.5 6.0 - 7.0 5
6.5 - 7.5 7.0 - 8.0 4
7.5 - 8.5 8.0 - 9.0 6
8.5 - 9.5 9.0 - 10.0 3
Total 20
The class boundary is calculated as
class boundary = Class limits ± 0.5
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When u and v are nonzero vectors, Spanlu,v) contains only the line through u and the line through v and the origin.
A. False. Span(u,v) includes linear combinations of both u and v. B. False. Span(u,v) will not contain the origin. C. True. Span(u,v) is the set of all scalar multiples of u and all scalar multiples of v
Span(u,v) is the set of all linear combinations of u and v, including scalar multiples of both. It does not include the origin.
Span(u,v) is the set of all linear combinations of u and v, meaning any combination of u and v multiplied by scalars. This includes scalar multiples of both u and v, but does not include the origin. To calculate Span(u,v), first write u and v as vectors u = (u1,u2,...,un) and v = (v1,v2,...,vn). Then, any linear combination of u and v can be written as c1u + c2v, where c1 and c2 are scalars, and the set of all such linear combinations is Span(u,v). For example, if u = (1,2) and v = (3,4), then Span(u,v) = {(1,2), (3,4), (4,6), (5,8), (7,10), ...}. In other words, Span(u,v) is the set of all scalar multiples of u and all scalar multiples of v.
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whoever can get this i will mark them brainiest
The first diagram of the triangle DEF correctly represents the transformation.
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
The preimage of the triangle is ABC and the image is DEF.
Therefore, ∠A = ∠D, ∠B = ∠E and ∠C = ∠F>
A 90° rotation counterclockwise will rotate the vertex C one-quarter left of a complete circle.
Therefore, The first triangle represents the correct transformation.
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Evaluate the expression using the given value of the variable:[pr2]; use [p = 3], and [r = 3] .
Answer:
(pr²)
given,
p=3 r=3
(3 X 3²)
(3 X 9)
27
X
%
60°
4
Z
30%
Y
Given right triangle XYZ, what is the value of tan(Y)?
02/0
O
O
O
3
√3
2
O2p
The value of tan 30 degrees is √3 / 3
How to solve for tan 30We are to solve this problem using SOH CAH TOA
We are to find the tangent of Y
Tan (Y) = opposite / adjacent
the value of y is 30 degrees
In this question, we can name opposite and adjacent as a and b respectively. No value is given for both
To get the value of a , we have to use sine
sin (y) = opposite / hypotenuse
sin 30 = opposite / 4
4 * 0.5 = opposite
opposite = 2
Cosine Y = opposite / hypotenuse
cos 30 = adjacent / 4
4 * 0.8660 = adjacent
3.464 or 2√3 = adjacent
Then tan 30 = opp / adj
tan 30 = 2 / 3.464
tan 30 = 0.5773
or tan 30 = √3 / 3
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which model can be used to find 4/5 1/10
What is the linear velocity in miles per hour for a particle moving in a circular path at 200 revolutions per minute on a circle of radius 60 feet?
Answer: 1,200. None of the above.
Step-by-step explanation:
200 revolutions per minute times 60 feet. 1,200
Rewrite 8.24 x 10 6 in standard form
A 824,000
B 8,240,000
C 8,240,000,000
D 82,400,000
Answer:
answer is B) 8 240 000
(: have a nice day
Answer:
B 8,240,000
Step-by-step explanation:
your welcome
Suppose a company has fixed costs of $40,800 and variable cost per unit of 1/3 x + 222 dollars, where x is the total number of units produced. Suppose further that the selling price of its product is 1946 − 2/3 x dollars per unit.
The break-even points at which the sum of the fixed and variable costs (40,800 + (1/3)·x + 222) is equivalent to the revenue (1946·x - (2/3)·x²) are; x = 21, 2897
What is a break-even point?The break-even point in cost accounting is the point where the total cost of production is equivalent to the total revenue from the sale of the products.
The fixed cost of the company = $40,800
The variable cost = (1/3)·x + 222 Dollars
x = The total number of units sold
The selling price of the product = 1946 - (2/3)·x Dollars
A possible question, obtained from a similar question is the value of the number of units sold at break even point
The break even point where the cost and revenue are equivalent, can be found as follows;
Revenue = Selling price × Number of units sold, therefore;
Revenue = (1946 - (2/3)·x) × x = 1946·x - (2/3)·x²
At the break even point, we get;
Sum total of the cost = Revenue
Therefore;
Fixed cost + Variable cost = Revenue
40,800 + (1/3)·x + 222 = 1946·x - (2/3)·x²
1946·x - (2/3)·x² - (40,800 + (1/3)·x + 222) = 0
(-2·x² + 5837·x - 123066)/3 = 0
x = (-5837 ± √(5837² - 4×(-2)×(-123066)))/(2×(-2))
x = (-5837 ± √(33086041))/(-4)
x ≈ 21 or x ≈ 2897
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Part B
In part A, you used the exact lengths of the sides to find the exact area of the rectangle.
Suppose this rectangle represents a piece of fabric that needs to be cut for a sewing project. Which type of measurement do you think would be more appropriate to use in this situation: the exact side lengths as given in part A or decimal approximations of the side lengths?
Use complete sentences to explain your reasoning.
Approximation of decimals is a mathematical technique for finding or measuring approximations and minimizing the number of decimal places.
What is meant by decimal approximations?A fractional representation of a real number that comes close to representing it. Any real number a can be represented by an endless number of decimal fractions.
The number of decimal places in a decimal number is the number of digits following the decimal point. A mathematical method for locating or measuring approximations and reducing the number of decimal places is known as approximation of decimals.
Any comparison that is close but not accurate to another entity is called an approximation. By rounding, one can get a good idea of a number. By rounding the values in a computation before performing the operations, a calculation can be approximated.
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City A and City B had two different temperatures on a particular day. On that day, five times the temperature of City A was 8° C more than three times the temperature of City B. The temperature of City A minus twice the temperature of City B was −4° C. The following system of equations models this scenario: 5x = 8 + 3y x − 2y = −4 What was the temperature of City A and City B on that day?
The temperature of city A is 4°C.
The temperature of city B is 4°C.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4= 6 is an equation.
We have,
5x = 8 + 3y ______(1)
x − 2y = −4 _______(2)
Where x is the temperature of city A and y is the temperature of city B.
Now,
From (2),
x = -4 + 2y
Substitution in (1).
5 (-4 + 2y) = 8 + 3y
-20 + 10y = 8 + 3y
-20 - 8 = 3y - 10y
-28 = -7y
y = 4
Now,
x = -4 + 2y
x= -4 + 2 x 4
x = -4 + 8
x = 4
Thus,
The temperature of both city A and city B is 4°C.
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Consider the following sample data.
14 9 19 18 5
8
Calculate the z-score for the following values.
a. 12
b. 6
c. 15
d. 13
a. The z-score for 12 is.
(Round to two decimal places as needed.)
The z-score for the given values is - 0280, -1.08, 0.49, 0.147 respectively.
What do z-scores mean?The z-score of a data point defines this precise distance in terms of standard deviations above or below the mean.
This formula is used to determine a z-score:
mean standard deviation for each data point
Means of the data points with a standard deviation of z
Below is the same equation in symbol form:
z= x−μ / σ
Here are some noteworthy z-score details:
When the z-score is high, the data point is.
A negative z-score indicates that a data point is below average.
If the z-score is close to 0.00, the data point is thought to be around average.
For the given data set,
14 9 19 18 5 8
Mean of the data =sum of observations / no. of observations = 73/6 = 12.16
Mean of the data is 12.16
Standard deviation = √∑(x - μ)² / n-1
= 5.70
a) The z- score of 12 is
z= x−μ / σ
z = 12 - 12.16 / 5.70
z = - 0280
b) x = 6,
z = 6 - 12.16/5.70
z = -1.08
c) x = 15
z = 15 - 12.16/5.70
z = 0.49
d) x = 13
z = 13 - 12.16 / 5.70
z = 0.147
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Two angles of a quadrilateral measure 130° and 195°. The other two angles are in a ratio of 2:5. What are the measures of those two angles?
The measure of other two angles in the given quadrilateral are 10° and 25°.
What is quadrilateral?A quadrilateral is a polygon with four sides four angles and four vertices. Whenever we name a quadrilateral, we need to keep in mind the order of the vertices.
Given that, two angles of a quadrilateral measure 130° and 195°.
The other two angles are in a ratio of 2:5.
So, the other two angles are 2x and 5x
Now, 130°+195°+2x+5x=360°
325°+7x=360°
7x=360°-325°
7x=35°
x=5
So, 2x=10° and 5x=25°
Therefore, the measure of other two angles in the given quadrilateral are 10° and 25°.
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Part B: What is the probability that a randomly chosen person is a child? (3 points)
Part C: What is the probability that a randomly chosen person prefers running and is a child? (3 points)
Part D: What is the probability that a person prefers running given that the person is a child? (3 points)
Part E Are being a child and preferring running independent events? Explain. (5 points)
The probability that a randomly chosen person is a child, that a randomly chosen person prefers running and is a child is 12/25 , 1/ 6 respectively.
What is probability ?
Probability can be defined as the ratio of number of favourable outcomes and number of total outcomes.
Given in the table ,
Probability that a randomly chosen person is a child
= 48 / 100
= 12/25
Probability that a randomly chosen person prefers running and is a child
= 6/48
= 1/8
Probability that a person prefers running given that the person is a child
= 6/48
=1/8
Therefore, The probability that a randomly chosen person is a child, that a randomly chosen person prefers running and is a child is 12/25 , 1/ 6 respectively.
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Which quadrilaterals have diagonal that bisect their angles?
Rhombus and Square are the quadrilaterals where diagonals are equal and bisect each other at 90°.
What is quadrilateral?A quadrilateral is a four-sided closed shape, where sum of the interior angles equals 180°.
Here,
For the quadrilateral there are only two quadrilaterals where diagonals bisect each other at 90° and will be of equal length of measure are square and rhombus.
Thus, Rhombus and Square are the quadrilaterals where diagonals are equal and bisect each other at 90°.
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