Answers
Solution :
2x² - 2x - 9 = 0
ax² + bx + c = 0 is the standard form of quadratic equation.
where,
a = 2 b = -2c = 9Formula :
[tex]x = \dfrac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \\[/tex]
Substituting the values,,
[tex] \sf x = \dfrac{ - ( - 2) \pm \sqrt{ {( - 2)}^{2} + 4 \times ( - 2) \times ( - 9) }}{2 \times 2 } \\ \\ \sf x = \dfrac{2 \pm \sqrt{4 + 4 \times 18 } }{4} \\ \\ \sf x = \dfrac{2 \pm \sqrt{4 + 72}}{4} \\ \\ \sf x = \frac{2 \pm \sqrt{ 76} }{4} \\ \\ [/tex]
Now, We can simplify √76.
Prime factorisation of √76 is [tex]\sqrt{2 \pm 2 \times 19}[/tex]
√19 can be written as 4.359.
Now,
[tex]\sf x = \dfrac{ 2 \pm 2 \times 4.359}{4} \\ \\ \sf x = \frac{2 \pm \sqrt{76} }{4} \\ \\ \sf { \boxed{ \red {x = \frac{1 \pm \sqrt{19} }{2} }}}\\ [/tex]
Therefore, Option (C) is the required answer.
Related Questions
A company makes 140 bags. 47 of the bags have buttons but no zips. 48 of the bags have zips but no buttons. 22 of the bags have neither zips nor buttons. How many bags have zips on them?
Answers
Required number of bags which have zips on them are 71.
Here given, A company makes 140 bags.
So, total number of bags = 140
It is also given, 47 of the bags have buttons but no zips 48 of the bags have zips but no buttons.
So, number bags which have buttons but no zips = 47 and number bags which have zips but no buttons = 48
and numbers of bags which have neither zips nor buttons = 22.
If we subtract number of bags which have no zips from total number of bags then we will get total number of bags which have zips
So, number of bags have zips on them
[tex] = 140 - 47 - 22 = 71[/tex]
Therefore, 71 bags have zips on them.
This is a problem of Subtraction.
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Find the value of X
Answers
The measure or value of x = 55°. This is solved using the Tangent, Secant and Arc theorems.
What is the explanation for the above response?Note that the Measure of and x (m∠x) = (Far Arc - Near Arc)/2
Where
Far Arc = 360 - 65 - 120 = 175°
Near Arc = 65°
thus, m∠x = (175-65)/2
m∠x = 55°
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How do you write the standard form for 2 hundreds 9 tens and 18 ones
Answers
The standard form as: 298
What is standard form?
Standard form is a way of writing numbers a little differently for instance
The number "2 hundreds 9 tens and 18 ones" can be written in standard form as:
298
In standard form, we write the digits in the place value of their corresponding powers of 10. In this case, the digit 2 is in the hundreds place (10)², the digit 9 is in the tens place (10), and the digit 8 is in the ones place (10^0).
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In a survey of women in a certain country (ages 20−29), the mean height was 63.7 inches with a standard deviation of 2.75 inches. Answer the following questions about the specified normal distribution.
(a) What height represents the 95th percentile?
(b) What height represents the first quartile?
Answers
a) The height that represents the 95th percentile is approximately 68.1 inches.
b) the height that represents the first quartile is approximately 65.5 inches.
Percentile and Quartile Heights(a) To find the height that represents the 95th percentile, we need to find the z-score that corresponds to this percentile and then use that to find the corresponding height.
The z-score for the 95th percentile can be found using a standard normal distribution table or calculator. The area to the left of the z-score is 0.95, so the area to the right is 0.05. From the standard normal distribution table, the z-score corresponding to an area of 0.05 is approximately 1.645.
Now we can use the formula for z-scores to find the corresponding height:
z = (x - mu) / sigma
where x is the height we want to find, mu is the mean height (63.7 inches), sigma is the standard deviation (2.75 inches), and z is the z-score we just calculated (1.645).
Rearranging the formula, we get:
x = mu + z * sigma
Plugging in the values, we get:
x = 63.7 + 1.645 * 2.75 ≈ 68.1
Therefore, the height that represents the 95th percentile is approximately 68.1 inches.
(b) To find the height that represents the first quartile, we need to find the z-score that corresponds to the 25th percentile and then use that to find the corresponding height.
The z-score for the 25th percentile can be found using a standard normal distribution table or calculator. The area to the left of the z-score is 0.25, so the area to the right is 0.75. From the standard normal distribution table, the z-score corresponding to an area of 0.75 is approximately 0.67.
Using the formula for z-scores and the same values for mu and sigma, we get:
x = mu + z * sigma = 63.7 + 0.67 * 2.75 ≈ 65.5
Therefore, the height that represents the first quartile is approximately 65.5 inches.
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Susan placed an order for a drum set priced at $71.28, cluding the taxes. The drum set is 30% off. 30% of $71.28, which means .3 x 71.28, is $21.39 off. How much does Susan have to pay in total?
Answers
Answer:
Step-by-step explanation:
take 71.28-21.39
Answer:
If the drum set is 30% off, this means that Susan only needs to pay 70% of the original price. We can calculate this using the following formula:
Total price = Original price x (1 - Discount rate)
where the discount rate is the percentage discount expressed as a decimal. In this case, the discount rate is 30% or 0.3. Substituting in the given values, we get:
Total price = $71.28 x (1 - 0.3)
Total price = $71.28 x 0.7
Simplifying, we get:
Total price = $49.896
However, we also know that Susan got a discount of $21.39. This means that she only needs to pay:
Total price - Discount = $49.896 - $21.39
Total price - Discount = $28.506
Therefore, Susan has to pay $28.506 in total.
The number 325 is equal to a square number multiplied by a prime number.
a) What are these two numbers?
Answers
13 is a prime number.
325 divided by 13= 25
25 is a square number.
So your answer is 13 and 25
what is required for a current to flow?
A. Electrons, protons, and an energy source
B. An insulator, battery, and recipient
C. A recipient, a connection, and something made out of rubber
D. An Energy source, a recipient, and a connection
Answers
Answer:
D. An Energy source, a recipient, and a connection
Point GG is located at (-3,6)(-3,6) on the coordinate plane. Point GG is reflected over the xx-axis to create point G'G ′ . Point G'G ′ is then reflected over the yy-axis to create point G''G ′′ . What ordered pair describes the location of G''?G ′′ ?
Answers
For given coordinates, the ordered pair describing the location of G'' is (3,-6).
What are coordinates?
Coordinates are a set of numbers that specify the position or location of a point or object in space, relative to a reference point or system. In two-dimensional space, coordinates are usually represented by a pair of numbers (x, y), where the first number represents the horizontal position of the point along the x-axis, and the second number represents the vertical position of the point along the y-axis. In three-dimensional space, coordinates are usually represented by a triple of numbers (x, y, z), where the first number represents the horizontal position of the point along the x-axis, the second number represents the vertical position of the point along the y-axis, and the third number represents the position of the point along the z-axis, which is perpendicular to the x-y plane.
Now,
When a point is reflected over the x-axis, the y-coordinate is negated. So the image of G(-3,6) over the x-axis is G'(-3,-6).
When a point is reflected over the y-axis, the x-coordinate is negated. So the image of G'(-3,-6) over the y-axis is G''(3,-6).
Therefore, the ordered pair describing the location of G'' is (3,-6).
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Nicole bought
6
CDs that were each the same price. Including sales tax, she paid a total of
$
69.60
. Of that total,
$
4.20
was tax. What was the price of each CD before tax?
Answers
Answer: $11.60
Step-by-step explanation: Since ur finding the cost of one cd and she bought 6 and since is before tax you do 36.90/(divided by) 6 and boom #!
If 9x+10=20
, what is the value of 18x+1
?
Answers
Answer:
21
Step-by-step explanation:
9x + 10 = 20
9x = 10
x = 10/9
What is the value of 18x + 1?
18(10/9) + 1
= 20 + 1
= 21
So, the value of 18x + 1 is 21
Find the value of x and y. Not drawn to scale
Answers
Using the definitions for the types of triangles in the image, we can see that the interior angles are:
x = 37°
y = 14°
How to find the value of x and y?First, on the right side we can see an equilateral triangle, then all its interior angles are of 60°.
Amd the triangle in the left side is isoceles, then the angle in the right side has the same measure than x, and now with that we can write the equation:
x + 83° + 60° = 180°
Solving for x, we will get:
x = 180° - 83° - 60°
x = 37°
Now let's find the value of y, we cansee that the triangle in the middle is also isoceles, and remember that for any triangle the sum of the interior angles must be 180°, so here we can write:
83° + 83° + y = 180°
y = 180° - 2*83°
y = 14°
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Simultaneous Equations
y=x-2
y=3x+5
Answers
Hello and regards kiann09.
So the solution of the equation is:
x = - 7/2y = - 11/2Step-by-step explanation:y = x - 2
y = 3x + 5
We substitute the given value of y into the equation y = 3x + 5.
x - 2 = 3x + 5
We solve the equation for x.
x - 2 - 3x = 5
We move the variable to the left side and change its sign.
The sign of the variable must be changed because, in the process of "moving the variable", we are adding its opposite to both sides.
x - 2 - 3x = 5
Now we move the constant to the right hand side and change its sign.
x - 3x = 5 + 2
We group like terms.
-2x = 5 + 2 ⇒ We add the numbers ⇒ -2x + 7
We must divide both sides by -2.
x = - 7/2
We substitute the given value of x into the equation y = x - 2.
y = (-7/2)-2
We solve the equation for y. We write all the numerators above the common denominator.
y = -(7 + 4)/2
y = - 11/2
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A cabinet was ordered from a carpenter with a volume of 1.08 m³. He wrote down the following measurements: 1.2 m wide and 1.8 m high, but forgot to write down the depth. Therefore, the depth measurement is
Answers
The depth of this cabinet is equal to 0.5 m³.
VolumeVolume is a three-dimensional measure that indicates the space occupied by an object. It is a physical quantity that expresses the amount of space an object occupies in three dimensions - length, width and height.
Note that this cabinet has the shape of a parallelepiped, and its volume is found by multiplying its dimensions. Calculating the depth measurement, we have:
1,08 m³ = 1,2 m * 1,8 m * p
p = 1,08 m³/(1,2 m * 1,8 m)
p = 1,08 m³ / 2,16 m³
p = 0,5 m
the sum of
44+45+46+47+...+131
Answers
Answer:313:)
Step-by-step explanation:
Lee watches TV for 4 hours per day. During that time, the TV consumes 200 watts per hour. Electricity costs (12 cents)/(1 kilowatt-hour). How much does Lee’s TV cost to operate for a month of 30 days?
Answers
The cost to operate Lee's Tv is 2.88 dollars.
How to find the cost to operate for a month?Lee watches TV for 4 hours per day. During that time, the TV consumes 200 watts per hour. Electricity costs (12 cents)/(1 kilowatt-hour).
Therefore, the cost for Lee to operate in 30 days can be calculated as follows:
200 watt = 0.2 kilowatt
Therefore,
1 day = 4 hours
30 days = ?
cross multiply
number of hours = 120 hours.
Therefore, in 30 days he watches television for 120 hours.
Let's find the cost
0.12 dollars = 12 cent
1 hour = 0.2 kilowatt
120 hours =
kilowatt use in 30 days = 0.2 × 120 = 24 kilowatts
Therefore,
1 kilowatts = 0.12 dollars
24 kilowatts = ?
cost of Tv for a month of 30 days = 24 × 0.12
cost of Tv for a month of 30 days = 2.88 dollars
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Un camino recto que continua para siempre en ambas direcciones es un
Answers
Answer: una linea
Step-by-step explanation:
A diner has 645 napkins. 325 napkins are used at lunch. 113 napkins are used at dinner.Melanie says that 325−113=n325-113= napkins are used in all, and that 645−212=r645-212= napkins are left.Is her answer reasonable? Explain why or why not.
Answers
Melanie's answer that 212 napkins were used in all and 433 napkins were left is reasonable and can be verified by using simple algebraic equations.
Yes, Melanie's answer is reasonable. She correctly determined that the total number of napkins used in lunch and dinner was 325-113 = 212. From this, we can also confirm that the total number of napkins left was 645 - 212 = 433. We can verify these answers by using simple algebraic equations to solve the problem. Using the equation 645 = 325 + x, where x is the number of napkins used at dinner, we can solve for x by subtracting 325 from both sides to get x = 320. Similarly, using the equation 645 = 433 + y, where y is the number of napkins used in all, we can solve for y by subtracting 433 from both sides to get y = 212. This confirms Melanie's answer that 212 napkins were used in all and 433 napkins were left.
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Which of the following is a way your bank can make money? A Your bank can charge you a fee for using an ATM from another bank. B Your bank can charge an annual or monthly fee just for having an account. C Your bank can charge fees if your balance goes below a certain amount. D all of the above
Answers
Answer:
D. All of the above
Step-by-step explanation:
Your bank can incur additional revenue by charging you for all of those things
Weathering and erosion are two processes that shape Earth’s surface. Which of the
following sets of factors cause both weathering and erosion?
a) acid rain, tree roots, waves
b) glaciers, waves, wind
c) moving water, plants, wind
d) acid rain, plants, ice
Answers
Points D, B, and E are collinear. Find
the value of a so that points A, B, and
C are collinear.
A
(4x)
O
E
B
148°
D
C
Answers
Using the supplementary angle theorem, the value for x so that points A, B, and C are collinear is 8.
What is a supplementary angle?
The definition of "supplementary" in mathematics relates to angles that combine to form a straight angle. It indicates that when two angles sum up to 180 degrees, they are said to be supplementary angles.
A line segment AC is drawn.
Point B is in between A and C.
A transversal DE is drawn passing through point B.
Points D, B, and E are collinear.
The measure of angle CBE is 148° and the measure of angle EBA is 4x°.
The angles ∠CBE and ∠EBA forms a pair of supplementary angles.
Their sum result in value of 180°.
Mathematically, this can be represented as -
∠CBE + ∠EBA = 180°
Substituting the values into the equation -
148° + 4x° = 180°
Solving for x, we get -
4x° = 180° - 148°
4x° = 32°
x = 32 / 4
x = 8
Therefore, the value for x is obtained as 8.
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129. (1+x)y' = (x + 2)(y − 1)
Calculus vol 2 need help solving this!!!!
Answers
By answering the question using the information provided, we can conclude that in order to arrive at the general solution, we must take into account the scenario in which [tex]y-1\neq 0 , y \neq 1[/tex], by constructing equations.
What do you mean by equations?Two equations are said to be equivalent when their bases and solutions line up. To create an equivalent equation, the same quantity, symbol, or expression must be added to or removed from both of the equation's two sides.
We can also create an analogous equation by multiplying or dividing both sides of an equation by a nonzero integer.
Solving differntial calculus
[tex](1+x)y'=( x+2) (y-1)[/tex]
We will first employ varying separation. The variables y and x will be placed on the opposite sides of the equation, and both sides will be integrated.
[tex](1+x)y'/(y-1) = (x+2)dx[/tex]
We will integrate both sides using the substitution[tex]u= y-1,\frac{du}{dy} =y'[/tex]
∫[tex](x+2)dx[/tex] =∫[tex](1+x)\frac{du}{u}[/tex]
㏑l[tex]u[/tex]l +[tex]x[/tex]㏑l[tex]u[/tex]l= [tex]\frac{1}{2} x^{2}+2x+c[/tex]
Substituting [tex]u= y-1[/tex]
㏑l[tex]y-1[/tex]l+ [tex]x[/tex]㏑l[tex]y-1[/tex]l= [tex]\frac{1}{2x^{2} } +2x+c[/tex]
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The complete question is: Find the general solution to the differential equation (1+x)y' = (x + 2)(y − 1).
Please Help ASAP (sequence question)
The sequence goes like this: 1, .5, .33, .25, ____, _____, ______
Please fill out the next three terms and write a function for the sequence
f(x)=_____
Answers
Answer: .2, .14, .125
Step-by-step explanation:f(x)=1/x or 1/n
A photographer is arranging 3 puppies in a row for a photo. There is one black puppy (B), one tan puppy (T) and one white puppy (W). Which list shows all the possible arrangements of the puppies?
Answers
Thus, the list BTW, BWT, TBW, TWB, WBT, and WTB is the correct response.
What is a number arrangement?The number of possible arrangements or orders for a set of items is known as the arrangement number, sometimes known as the permutation number or simply as the permutation.
The following is the accurate list of all conceivable pup arrangements:
BTW, BWT, TBW, TWB, WBT, WTB
This is due to the fact that the puppies' order is important, thus we may utilize permutations to discover every potential configuration. There are 3 pups to place in a row, which results in a total of 3! = 6 combinations. We can categories them as follows:
1. BTW
2. BWT
3. TBW
4. TWB
5. WBT
6. WTB
Thus, the list BTW, BWT, TBW, TWB, WBT, and WTB is the correct response.
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Write a paragraph proof of the Quadrilateral Sum Theorem.
Given: Quadrilateral ABCD
Prove: m
Answers
Step-by-step explanation:
Quadrilateral Sum Theorem. The total sum of the interior angles of a quadrilateral is 360°. A quadrilateral is formed by joining four non-collinear points. A quadrilateral has four sides, four vertices and four angles. Therefore, that is the Quadrilateral Sum Theorem.
What is an equation for the linear relationship in slope-intercept form?
y = ? x + ?
Answers
Answer:
y = -4x + 5
Step-by-step explanation:
y = mx + b
From the graph, we see the line intersects the y-axis at 5, so the y-intercept, b, is 5.
y = mx + 5
slope = m = rise/run
rise = up and down
run = left and right
We go up 4 units from the lower point to the upper point. That is a rise of 4 units. Then we go left 1 unit. That is a run of -1.
slope = m = 4/(-1) = -4
y = mx + 5
y = -4x + 5
PLEASE HELP! URGENT AND WORTH 50 POINTS!!!
Answers
Answer: 3.5
Step-by-step explanation: sry if im wrong ):
Write a quadratic function in standard form to represent the data in the table.
Answers
Therefore, the quadratic function in standard form that represents the data in the table is: y = 1/2 x² - 5/2 x + 5.
What is function?A function is a mathematical concept that describes the relationship between two sets of numbers. It is a rule that assigns to each input (or element in the domain) exactly one output (or element in the range). In simpler terms, a function is like a machine that takes in a number and produces another number as output, according to some specific rules. The input is usually denoted by x, and the output by f(x), which is read as "f of x". Functions can take many forms, such as linear, quadratic, trigonometric, exponential, logarithmic, and more. They are widely used in mathematics, science, engineering, and many other fields to model and analyze various phenomena.
Here,
To write a quadratic function in standard form, we need to use the general form of the quadratic equation:
y = ax²+ bx + c
where a, b, and c are constants. We can use the values in the table to find these constants.
When x = 2, y = 3
When x = 4, y = 1
When x = 6, y = 3
When x = 8, y = 9
When x = 10, y = 19
Substituting these values into the quadratic equation, we get:
3 = 4a + 2b + c
1 = 16a + 4b + c
3 = 36a + 6b + c
9 = 64a + 8b + c
19 = 100a + 10b + c
We can now use these equations to solve for a, b, and c. One way to do this is to use a matrix equation:
|16 4 1| |a| |1|
|36 6 1| |b| = |3|
|64 8 1| |c| |9|
Using a calculator or matrix software, we can solve for a, b, and c:
a = 1/2
b = -5/2
c = 5
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Rhonda just got promoted in her job as a physical therapy assistant. She will now earn $20.70 per hour. This is 115% of her hourly salary before her promotion. What was her hourly salary before her promotion?
Answers
As a result, Rhonda was paid $18 per hour before to being promoted; nevertheless, she will now be paid $20.70 per hour.
what is unitary method ?Finding a single unit value and applying it to ratio and proportional problem solving is known as the unitary method in mathematics. It is frequently employed in order to resolve issues involving either direct proportion, inverse proportion, or both. In the unitary technique, the ratio of the quantities' corresponding unit values is used to indicate the relationship between the quantities. The desired value is then achieved by multiplying or dividing the unit value, as necessary.
given
Let x be the hourly wage Rhonda received prior to her promotion.
The issue states that her new hourly wage is equal to 115% of her previous wage:
20.70 = 1.15x
We can divide both sides by 1.15 to find x:
x = 20.70 / 1.15
x = 18
As a result, Rhonda was paid $18 per hour before to being promoted; nevertheless, she will now be paid $20.70 per hour.
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there are 3 containers of chocolate ice cream for every 2 containers of vanilla ice cream. What is the constant of proportionality in terms of vanilla to chocolate.
Answers
Answer: 2:3
Step-by-step explanation:
Rosa is in the 25% tax bracket and How much will her tax bill be reduced if she makes a $600 contribution to charity?
Answers
Answer:
Her contribution to charity reduces her taxable income by $600, Thus, her tax liability will be reduced by 28% of $ 600, and she comes under 28%
Step-by-step explanation: