The solutions for the given equation are [tex]2+\sqrt{31}[/tex] and [tex]2-\sqrt{31}[/tex]. These are calculated by applying the quadratic formula since the given equation is a quadratic equation.
What is the quadratic formula?The quadratic formula is used for finding the roots of a quadratic equation in the form of ax² + bx + c = 0.
The formula is,
x = [tex]\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
Calculation:The given equation is
x² - 27 = 4x
On rewriting the equation, we get
x² - 4x - 27 = 0
thus, it is in the form of ax² + bx + c = 0. So, this is a quadratic equation.
Then, applying the quadratic formula for finding roots is nothing but its solutions.
Where a = 1; b = -4; c = -27
⇒ x = [tex]\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
= [tex]\frac{-(-4)\pm\sqrt{(-4)^2-4(1)(-27)} }{2(1)}[/tex]
= (4 ± [tex]\sqrt{16+108}[/tex])/2
= (4 ± [tex]\sqrt{124}[/tex])/2
= (4 ± 2[tex]\sqrt{31}[/tex])/2
= 2 ± [tex]\sqrt{31}[/tex]
So, the roots of the given equation are 2 + [tex]\sqrt{31}[/tex] and 2 - [tex]\sqrt{31}[/tex].
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Pre-image ABCD was dilated to produce image A'B'C'D'.
What is the scale factor from the pre-image to the image?
Enter your answer in the box as a fraction in simplest form.
The scale factor from the pre-image to the image is 2/5.
What is dilation?Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape.
let the scale factor be m, so that the scale factor multiplied by the dimension of pre-image should give dimension of image.
so that we have,
20 x m = 8
20m = 8
divide both sides by 20
m = 8/20
m = 2/5
In conclusion the dilation factor is 2/5
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A set of magical wand prices are normally distributed with a mean of 505050 dollars and a standard deviation of 444 dollars. A blackthorn wand has a price of 45. 2045. 2045, point, 20 dollars. What proportion of wand prices are lower than the price of the blackthorn wand?.
The proportion of wand prices as per normal distribution are lower than the price of the blackthorn wand is equal to 0.1151.
As given in the question,
Mean of the set of magical wand price 'μ' = 50dollars
Standard deviation 'σ' for normal distribution = 4 dollars
Price of blackthorn wand 'X' = 45.20 dollars
z-score = (x - μ)/σ
Proportion of wand prices be 'x'
P(x < X)
=P( x< 45.20)
=P [(x - μ)/σ < (X - μ )/σ]
=P[ z < (45.20 - 50)/4]
=P( z < -1.2 )
= 0.11507
=0.1151
Therefore, the proportion of the wand prices which are lower than the price of blackthorn wand using normal distribution is equal to 0.1151.
The complete question is:
A set of magical wand prices are normally distributed with a mean of 50 dollars and a standard deviation of 4 dollars. A blackthor wand has a price of 45.20 dollars. What proportion of wand prices are lower than the price of the blackthorn wand? You may round your answer to four decimal places.
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What is quadrilateral with two distinct pairs of congruent and adjacent side?? a quadrilateral with two pairs of adjacent, congruent sides. it has perpendicular diagonals and one pair of opposite interior angles that are congruent. if you draw midsegments between adjacent sides of this quadrilateral, you form a parallelogram.
A quadrilateral with two distinct pairs of congruent and adjacent side is a kite.
A quadrilateral is a figure that has 4 sides and edges. Parallelogram, rectangle, square are all examples of quadrilateral.
Different quadrilaterals have different properties. A quadrilateral in which two distinct pairs of adjacent sides are congruent is termed as a kite.
Only kite is a quadrilateral which has the given property.
Some other properties of kite include-
1. diagonals of a kite are perpendicular to each other
2. along its main diagonal, a kite is symmetrical
3. one of the diagonals of the kite bisects the other
Thus, a quadrilateral with two distinct pairs of congruent and adjacent side is a kite.
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What is the y-coordinate of the solution to the following system of equations?
y=2x + 1
x+y = 1
Answer : y coordinate is 1
y = 2x + 1
x + y = 1
solve for y : x + y = 1
-x -x
y = -x + 1
Graph them,
(0,1) (x,y) y value is 1
ou are offered a free play at the following game: ten balls are numbered 1 through 10. three are selected at random (each combination equally likely). before balls are drawn, players try to guess which three numbers are drawn by filling out a ticket. neither the order that the player selects the numbers nor the order in which the balls are drawn matters. how many outcomes are in the sample space for this experim
The outcome in sample space is equal to the no. of ways of selecting 3 balls at random from 10 distinct balls. So, number of outcomes in sample space = ¹⁰C₃.
Permutation:
Permutations are different ways of arranging objects in a particular order. This can also be expressed as rearranging the elements in linear order of an already ordered set. The symbol are used to denote the number of permutations of n distinct objects obtained for each r. Block bus, train and plane timetables, postcode and phone number assignments. These are some situations where permutations are used.
Example: There are 5 chairs and 3 people need to sit on them. There are 5 ways to place the first person. 2nd person 4 seats, 3rd person 3 seats. So to find the number of ways to place her 3 on 5 chairs, multiply these ways. Make 5×4×3 streets. So we can do it 60 ways. 5 × 4 × 3 is written as (5!) / (2!) (or) (5!) / (5 - 3).
Combination:A combination is a selection of elements from a set with different members, so the order of selection does not matter (unlike a permutation). For example, if he is given three fruits, such as apples, oranges, and pears, he has three binary combinations that he can draw from this set. An apple and a pear. apples and oranges. Or pear and orange. More formally, a k-combination of a set S is a subset of the k distinct elements of S. Two combinations are identical only if each combination has the same members.
According to the Question:
The outcome in sample space is equal to the no. of ways of selecting 3 balls at random from 10 distinct balls. So, number of outcomes in sample space = ¹⁰C₃.
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Which of these relations is a function?
last question!!!!!!!!
Answer: the top left is a function
the tunnel under the english channel that connects england and france is actually three separate tunnels built end to end. each is a half-cylinder that is 50,000 meters long and 4 meters high. how many cubic meters of dirt had to be removed to build the tunnel?
Answer: im not exactly sure but i think 600,000m³
Step-by-step explanation: multiply 50,000m by 4 to get 200,000m and then multiply that by 3 (because 200,000 is only one section of the tunnel)
and by doing that you get 600,000m and then add cubed onto the end because it says cubic meters
Evaluate the expression for the given value of the variables.
0.7g - 2.7h
g= 17, h =2
Answer:
6.5
Step-by-step explanation:
Step 1: Plug in g = 17, h = 2
0.7 * 17 - 2.7 * 2
Step 2: Solve Using PEMDAS
11.9 - 2.7 * 2
11.9 - 5.4
6.5
Which of these fractions is equivalent to the fraction in this image?
1 of 3 slices of pizza
1) 4/12
2) 3/12
3) 2/12
4) None of these is correct.
Answer:
4/12
Step-by-step explanation:
create a birthday polynomial with 10-12-2247
The birthday polynomial with 10-12-2247 is given as follows:
f(x) = x^7 - x^5 - 2x^4 + 2x³ + 2x² - 4x + 7.
How to create a birthday polynomial?A birthday polynomial is created attributing each digit of the birthday as a coefficient of the polynomial.
The birthday in this problem is given as follows:
10-12-2247.
Thus the coefficients of each term of the polynomial, in order, are given as follows:
1.0.1.2.2.2.4.7.There are eight coefficients, hence the polynomial is of the seventh degree.
The signs of each coefficient is not important, they can be chosen at random, and thus the birthday polynomial for the date of 10-12-2247 can be defined as follows:
f(x) = x^7 - x^5 - 2x^4 + 2x³ + 2x² - 4x + 7.
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50x=10 please help!!!
Answer:
[tex]\boxed{\boxed{\tt x=\frac{1}{5}}\: \bf Or\:\boxed{\tt x=0.2}}[/tex]
Step-by-step explanation:
[tex]\tt 50x=10[/tex]
Divide both sides by 50:-
[tex]\tt \cfrac{50x}{50}=\cfrac{10}{50}[/tex]
Simplify:-
[tex]\tt x=\cfrac{1}{5}[/tex]
_____________________
Hope this helps!
Have a great day!
Phil and Meredith work for a book publisher editing mathematics textbooks. Phil has less experience and takes three times as long as Meredith to edit a textbook. Together, it takes them 15 hours to edit a textbook.
How long does it take Phil to edit a textbook if he works alone?
hours
How long does it take Meredith to edit a textbook if she works alone?
The number of hours taken by Meredith to edit a textbook if she works alone is 20 hours and time taken by Phil alone to edit text book is 60 hours..
Given that, Phil and Meredith work for a book publisher editing mathematics textbooks.
What is time and work?The basic concept of Time and Work is similar to that across all Arithmetic topics, i.e. the concept of Proportionality. Efficiency is inversely proportional to the Time taken when the amount of work done is constant.
Let the time taken by Meredith be x.
Phil has less experience and takes three times as long as Meredith to edit a textbook.
So, time taken by Phil be 3x.
Now, 1/x +1/3x =1/15
⇒ (3+1)/3x =1/15
⇒ 4/3x =1/15
⇒ 4/x =1/5
⇒ x=20 hours
So, time taken by Phil =3x =60 hours
Therefore, the number of hours are 60 hours.
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a biologist had mice and rats run through a maze and recorded the number that finished the maze successfully and the number that did not. the table below shows the results of the study: mice rats finished: 22 25 did not finish: 26 12 suppose we use this data along with a .05 significance level to test the claim that the rodent type and the success of finishing the maze are not related. what can we conclude?
Answer:3.53% probability that the rat fails the maze 6 times in a row, and then succeeds on his 7th attempt
Step-by-step explanation:For each time that the rat goes through the maze, there are only two possible outcomes. Either he fails it, or he succeds. The trials are independent. So we use the binomial probability distribution to solve this question.
Binomial probability distribution:The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.In which is the number of different combinations of x objects from a set of n elements, given by the following formula.And p is the probability of X happening.
What is the probability that the rat fails the maze 6 times in a row, and then succeeds on his 7th attempt?Missing on the first six, each with 70% probability(P(X = 6) when p = 0.7, n = 6).Succeeding on the 7th attempt, with p = 0.3. So 3.53% probability that the rat fails the maze 6 times in a row, and then succeeds on his 7th attempt
help.
Find the area of the figure.
the area of the triangle is 7.5
Interest Earned over One Year
Answer: $300,000
Step-by-step explanation:
Does dilation change the position?
Yes , Dilation do changes the position
Dilation is the process of changing the size or shape of an object. With the aid of the specified scale factor, it is a transformation that makes the objects smaller or larger.
The pre-image is the original figure before dilation, while the new figure is referred to as the image.
Dilation can be of two types:
Expansion - When the size of an object is increased.Contraction - When the size of an object is decreased.Dilation does not change the shape of the object from preimage to image only size and position are changed.
The shape can be a point, a line segment, a polygon, etc. It should be noted that the shape can be enlarged or shrunk but the proportion of each dimension of the shape and the angles remain the same.
Hence , It is true that dilation changes the position
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In the month of March, the temperature at the
South Pole varies over the day in a periodic way
that can be modeled approximately by a
trigonometric function.
The highest temperature is about -50°C, and it is
reached around 2 p.m. The lowest temperature is
about -54°C and it is reached half a day a apart
from the highest temperature, at 2 a.m.
Find the formula of the trigonometric function
that models the temperature T in the South Pole
in March t hours after midnight. Define the
function using radians.
T(3) = - 50.59 is time period
What is Function using Radian ?A specific quantity is converted from degrees to radians using the RADIANS function. The supplied angle, which is in degrees, is translated into a roughly equivalent angle, which is in radians.
According to given information
Since maximum term is -50°C at 2 pm
So
We can start with cosine curve with maximum temperature -50°C at t = 0
Assuming 2 pm as starting point t = 0
Period = [tex]\frac{2\pi }{b}[/tex]
24 = [tex]\frac{2\pi }{b}[/tex]
b = [tex]\frac{\pi }{12}[/tex]
By using Formula
y = a cos(bx) + d
y = a cos([tex]\frac{\pi }{12}[/tex]t) - 52
At 5 pm , t = 3
T(3) = 2 cos([tex]\frac{\pi }{12}[/tex]×3) - 52
= 2 ×[tex]\frac{\sqrt{3} }{2}[/tex] - 52
T(3) = - 50.59 is time period
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Given the points (-15, 30) and (5, 50). The slope of the line between the two points would be?
Answer:
The slope of the line is 1
Step-by-step explanation:
gradient = difference of y-coordinates / difference of x-coordinates
gradient = (y2-y1) / (x2-x1)
gradient = 50-30 / 5-(-15)
gradient = 20/20
gradient = 1
Gabriel's salary is £24500.
Next year he is due to get a 9% increase.
What will his new salary be?
Answer:
26,705
Step-by-step explanation:
First find 9% of 24500
24500 x 0.09 = 2205
Second add 2205 + 24500
2205 + 24500 = 26,705
You are running a concession stand at a basketball game. You are selling pizza slices and sodas. Each pizza slice sells for $2.50 and each soda sells for $1.25. At the end of the night you made a total of $696.25. You sold a total of 384 pizza slices and sodas combined. You must report the number of pizza slices sold and the number of sodas sold. What equations did you use to solve this where P = the number of pizza slices sold and S = the number of sodas sold?
The circumference of a circular garden is 84 feet. What is the diameter of the garden
Round your answer to the nearest hundredth.
Diameter is 25.46 feet as circumference is 2πr and 2r is d so we just simply divide the circumference with π and get the value as 25.46
Step-by-step explanation:
Answer:
26.727feet
Step-by-step explanation:
Circumference = 22 x diameter
7
7x 84= 22d
d= 588
22
= 26.727feet
On the first day of a song's release, it had 20 million streams. If the number of streams increases by 10% per day, how many streams will there be on the seventh day? round to the nearest million.
Nearest Twenty-one million streams will be available on the seventh day of song's release day. So, the correct option is option(A).
As we know the formula for the increase of population for compond increasing rate
A = P(1 + r)ᵗ---(1)
where P --> the intial population
r --> rate in decimal
t --> the time
A --> final population after t years
We have given that,
On the first day the song's release , it streams around 20 million population.
Rate of increase= 10% per day
We have to find the number of streams on seventh day.
so, time is 6 for it.
we have , P= 20 million ; t= 6
r = 10% = 10/100 = 0.1
putting all values we get,
A = 20 ( 1 + 0.1 )⁶
=> A = 20(1.01)⁶
=> A = 21.23
so the numnber of stream is 21.23 million ~ 21 million on seventh day.
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Complete question:
On the first day of a song's release, it had 20 million streams. If the number of streams increases by 10% per day, how many streams will there be on the seventh day? Round to the nearest million.
a)21 million
b)35 million
c)37 million
d) 38 million
8th grade math help plsssss
members of the fitness club hosted a benefit. They charged $4 for adults and $3 for students. if they earned a total $435 and 120 people attended, how many students were there?
Answer:
101.25
Step-by-step explanation:
To find the number of students, we need to first determine the total amount earned from the students. We can do this by multiplying the number of people by the cost per student: $3/student * 120 people = $<<3*120=360>>360.
Since the total amount earned was $435 and we know that $360 of that came from students, we can find the number of students by subtracting the total earned from students from the total amount earned: $435 total - $360 from students = $75 from adults.
Since the cost per adult was $4, we can divide the total amount earned from adults by the cost per adult to find the number of adults: $75 / $4/adult = <<75/4=18.75>>18.75 adults.
Since there were 120 people in total and 18.75 of them were adults, there must have been 120 people - 18.75 people = <<120-18.75=101.25>>101.25 students
What is the end behavior of the graph of the polynomial function y 7x12 3x8 9x4?
The end behavior for this polynomial function is like;
f(x)--> +∞, as x--> −∞
f(x)--> +∞, as x--?>+∞
Given,
The polynomial function; y = 7x12 – 3x8 – 9x4
We have to find the nd behavior of the graph of the polynomial function;
End behavior of polynomial function;
The behavior of the function graph at the "ends" of the x-axis is known as the end behavior of a function, or f. In other words, if we look at the right end of the x-axis (as x approaches +) and the left end of the x-axis (as x approaches ), the end behavior of a function represents the trend of the graph.
Here,
We examine the polynomial's degree and the sign of the coefficient of the variable with the highest exponent to determine the graph's final behavior.
The degree is even 12.The coefficient, 7, is a positive number.That is,
The end behavior for this polynomial function is like;
f(x)--> +∞, as x--> −∞
f(x)--> +∞, as x--?>+∞
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Find the value of x.
x=
Select all the statements that are true of the relation.
Answer: A C and D
Step-by-step explanation:
The italian mathematician fibonacci is known for introducing what mathematical concept?
A group of friends were hanging out discussing the movies. They discovered that altogether, they went to the movies 30 times last year. Clio went 5 times as often as alex. Bernice went 2 more times than alex. How many times did clio go to the movies last year?.
Clio went 20 times to the movies last year. This can be calculated using linear equations.
Given,
Number of times all together they went to movies = 30
Clio = 5 times more than Alex
Bernie = is 2 times more than Alex.
Let 'a' be the number of times Alex has gone to the movie:
Clio = 5a
Bernie = a + 2
So, we can calculate the number of times Clio went to the movies if we find out how many times Alex went. This can be calculated using the following linear equation:
Clio + Bernie + Alex = 30
5a + (a +2) + a = 30
7a + 2 = 30
7a = 30 - 2
7a = 28
a = 28 ÷ 7
a = 4 times
From solving the above equation, we got that Alex (a) went to the theatre 4 times last year. Now, substituting the value of 'a' we get:
Clio = 5a
Clio = 5*4 = 20 times
Bernie = a+2 = 4+2 = 6 times
So, we can conclude by saying that, Clio went 20 times to the movies last year.
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I need help can someone help pls?
Answer: B
Step-by-step explanation:
Can someone pls tell me how many boxes he can afford it’s due at 11:59 tonight!!
Answer:
You have chosen the correct answer
Step-by-step explanation:
He cannot spend more than 55. So the cost of the groceries has to be 55 or less.
He is only buying one package of eggs and the x represents how many packages of sugar he can purchase knowing that each box costs 11.50.