[tex]x^2+2x-3=0\\\\\implies x^2 +3x -x -3 =0\\\\\implies x(x+3) -(x+3)=0\\\\\implies (x-1)(x+3)=0\\\\\implies x =1 ~ \text{or}~ x = -3[/tex]
y=5/2x-9 find the y intercept
Answer:
(0,-9) You have to substitute 0 for x and solve for y
What is the total height of the plants that measured 1
1/8 and
1/4?
How can you tell that (496 + 77 + 189) x 10 is twice as large as (496 + 77 +189) x 5 without doing complicated calculations?
Answer:
Because 10 is twice as large as 5.
Step-by-step explanation:
[tex]\large \rm \sum \limits_{n = 0}^ \infty \frac{( { - 1)}^{1 + 2 + 3 + \dots + n} }{(2n + 1 {)}^{2} }[/tex]
The sum we want is
[tex]\displaystyle \sum_{n=0}^\infty \frac{(-1)^{T_n}}{(2n+1)^2} = 1 - \frac1{3^2} - \frac1{5^2} + \frac1{7^2} + \cdots[/tex]
where [tex]T_n=\frac{n(n+1)}2[/tex] is the n-th triangular number, with a repeating sign pattern (+, -, -, +). We can rewrite this sum as
[tex]\displaystyle \sum_{k=0}^\infty \left(\frac1{(8k+1)^2} - \frac1{(8k+3)^2} - \frac1{(8k+7)^2} + \frac1{(8k+7)^2}\right)[/tex]
For convenience, I'll use the abbreviations
[tex]S_m = \displaystyle \sum_{k=0}^\infty \frac1{(8k+m)^2}[/tex]
[tex]{S_m}' = \displaystyle \sum_{k=0}^\infty \frac{(-1)^k}{(8k+m)^2}[/tex]
for m ∈ {1, 2, 3, …, 7}, as well as the well-known series
[tex]\displaystyle \sum_{k=1}^\infty \frac{(-1)^k}{k^2} = -\frac{\pi^2}{12}[/tex]
We want to find [tex]S_1-S_3-S_5+S_7[/tex].
Consider the periodic function [tex]f(x) = \left(x-\frac12\right)^2[/tex] on the interval [0, 1], which has the Fourier expansion
[tex]f(x) = \frac1{12} + \frac1{\pi^2} \sum_{n=1}^\infty \frac{\cos(2\pi nx)}{n^2}[/tex]
That is, since f(x) is even,
[tex]f(x) = a_0 + \displaystyle \sum_{n=1}^\infty a_n \cos(2\pi nx)[/tex]
where
[tex]a_0 = \displaystyle \int_0^1 f(x) \, dx = \frac1{12}[/tex]
[tex]a_n = \displaystyle 2 \int_0^1 f(x) \cos(2\pi nx) \, dx = \frac1{n^2\pi^2}[/tex]
(See attached for a plot of f(x) along with its Fourier expansion up to order n = 10.)
Expand the Fourier series to get sums resembling the [tex]S'[/tex]-s :
[tex]\displaystyle f(x) = \frac1{12} + \frac1{\pi^2} \left(\sum_{k=0}^\infty \frac{\cos(2\pi(8k+1) x)}{(8k+1)^2} + \sum_{k=0}^\infty \frac{\cos(2\pi(8k+2) x)}{(8k+2)^2} + \cdots \right. \\ \,\,\,\, \left. + \sum_{k=0}^\infty \frac{\cos(2\pi(8k+7) x)}{(8k+7)^2} + \sum_{k=1}^\infty \frac{\cos(2\pi(8k) x)}{(8k)^2}\right)[/tex]
which reduces to the identity
[tex]\pi^2\left(\left(x-\dfrac12\right)^2-\dfrac{21}{256}\right) = \\\\ \cos(2\pi x) {S_1}' + \cos(4\pi x) {S_2}' + \cos(6\pi x) {S_3}' + \cos(8\pi x) {S_4}' \\\\ \,\,\,\, + \cos(10\pi x) {S_5}' + \cos(12\pi x) {S_6}' + \cos(14\pi x) {S_7}'[/tex]
Evaluating both sides at x for x ∈ {1/8, 3/8, 5/8, 7/8} and solving the system of equations yields the dependent solution
[tex]\begin{cases}{S_4}' = \dfrac{\pi^2}{256} \\\\ {S_1}' - {S_3}' - {S_5}' + {S_7}' = \dfrac{\pi^2}{8\sqrt 2}\end{cases}[/tex]
It turns out that
[tex]{S_1}' - {S_3}' - {S_5}' + {S_7}' = S_1 - S_3 - S_5 + S_7[/tex]
so we're done, and the sum's value is [tex]\boxed{\dfrac{\pi^2}{8\sqrt2}}[/tex].
A card is picked from a standard deck of 52 cards. Determine the odds against and the odds in favor of selecting a red face card (king, queen, or jack).
6 red face cards
->in favour:
6/52
= 3/26
-> against:
52-6= 46
46/52
=23/26
Sita saves Rs. 1 today, Rs. 2 the next day, Rs. 4 the succeeding day and so on (each saving being twice of the preceding one). What will be total saving in two weeks time?
a
Answer:
Rs. 32767
Step-by-step explanation:
Because the amount is doubling every day, we can use the expression 1*2^15-1 because there is 1 to start with. Also cool trick! if you need to do 2^1+2^2+2^3+....+2^x, it will be equal to 2^(x+1)-1. So:
2^15-1
32768-1
32767
the equation is :
answer x:
Answer:
A) x would be 21 if i interpreted it right
Step-by-step explanation:
4x - 11 = 73
i think anyways
4x = 73 + 11
4x = 84
x = 21
i d k what B means?
Help help math math math math math
Answer:
A
Step-by-step explanation:
You can think about it as an equation without the inequality:
y = 5 - x OR y = -x + 5
Slope = -1
Y-intercept = 5
Graph B is a horizontal line with a slope of zero and y-intercept of 2. Graph A is the only one that fits the above parameters.
Hope this helps!
Answer:
a
Step-by-step explanation:
find the value of x
Answer:
See below, please
Step-by-step explanation:
[tex](2x + 9) + (4x - 3) = 90[/tex]
[tex]6x + 6 = 90[/tex]
[tex]6x = 90 - 6 = 84[/tex]
Hence
[tex]x = 14[/tex]
Can somebody please help with this, I have been stuck on it for a while
Answer:
$2821.50
Step-by-step explanation:
value = 2700 (deposit) x 0.003 (rate) x 15 (time) + 2700
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$2700\\ r=rate\to 0.3\%\to \frac{0.3}{100}\dotfill &0.003\\ t=years\dotfill &15 \end{cases} \\\\\\ A=2700[1+(0.003)(15)]\implies A=2700(1.045)\implies A=2821.5[/tex]
?A bag contains red, blue, and green candies. Benjamin pour
out a handful and counted 10 red, 6 blue, and 14 green
candies. According to these ratios, if the bag contains a total of
400 candies, about how many of them are blue?
Find the area of the following shape. (8 points)
what is the answer?
Answer:
72 square units
Step-by-step explanation:
Identify the heightIdentify the lengthMultiply those two togetherThat is your answerH = 9 units
L = 8 units
A = H × L
A = 9 × 8
A = 72 square units
1. For each diagram below, find the value of x
The square root of 7^16 is equal to 7^n for some positive integer n. Find n.
[tex]\sqrt{7^{16}} = 7^n\\\\\implies \left(7^{16}\right)^{\tfrac 12} = 7^n\\\\\implies 7^{\left(\tfrac 12 \times 16\right)}=7^n\\\\\implies 7^8 = 7^n\\\\\implies \ln 7^8 = \ln 7^n\\\\\implies 8\ln 7 = n \ln 7\\\\\implies n =8[/tex]
Can somebody help me pls!
Answer: C
Step-by-step explanation:
Just look at a z-score table and multiply by 100.
-> (0.308538)(100) is about 30.85%
Please the answer ... Integral
Answer:
[tex]\frac{dx^{2} (x+1)S^{2} }{2(x^{2} +6x+3)^{2} }+ C[/tex]
Step-by-step explanation:
WILL GIVE EXTRA POINTS FOR ANSWER ⭐️⭐️!! PLEASE EXPLAIN IF POSSIBLE
Answer:
B. (-3, 10)
Step-by-step explanation:
I am going to graph the given equation. I then will see which of the points given are within the required area.
-> See attached.
-> I have explained in the image more in-depth as well.
What is the approximate volume of a cone with a height of 9 ft and radius of 3 ft? Use 3.14 to approximate pi, and express your final answer to the nearest hundredth Enter your answer as a decimal in the box. ft3
Find the area of sector RST Enter your answer in terms of a fraction of it and rounded to the nearest
hundredth.
Fort nite battle pass is 8 dollars
A perfect score on a test with 25 questions is 100. Each question is worth the same number of points. How many points is each question on the test worth
Answer:
4
Step-by-step explanation:
100 divided by 25 equals 4.
Which function has a maximum with the same maximum value as
f(x) = – |x + 3| – 2? f(x) = (x + 3)2 – 2 f(x) = –(x – 6)2 – 3
Answer:
The answer is c on edge or f(x) = 1 sqt x + 6 -2
Step-by-step explanation:
From the given two options, none of them has a function that has the same maximum value as f(x) = -|x+3|-2.
What is a function?A function is a correspondence between input numbers (x-values) and output numbers (y-values). It is used to describe an equation.
Given that:
f(x) = -|x + 3| - 2Suppose that x = c is a critical point of (x) then,
If f'(x) > 0 to the left of x = c and f'(x) < 0 to the right of x = c;
then x = c is a local maximum.If f'(x) < 0 to the left of x = c and f'(x) > 0 to the right of x = c;
then x = c is a local minimum.If f'(x) is the same sign on both sides of x = c;
then x = c and is neither a local maximum nor a local minimum.From the given equation, the critical points: x = -3
The intervals is: Increasing at -∞ < x < -3 and decreasing at -3<x<∞If we put the point x = -3 into - |x+3|-2
Then, y = -2 and it is Maximum at (-3, -2) Only f(x) = (x+3)^2 - 2 has a minimum at (-3,-2)We can therefore conclude that none of them has a function that has the same maximum value as f(x) = -|x+3|-2.
Learn more about the maximum and minimum of a function here:
https://brainly.com/question/6787214
#SPJ9
Find the missing information for the triangle.
*not drawn to scale
• Make sure to find the missing angle measure and the 2 missing side
lengths.
missing angle:
180° - 90° - 30°
180° - 120°
60°
missing sides:
(a)
[tex]\rightarrow \sf tan(x)= \dfrac{opposite}{adjacent}[/tex]
[tex]\rightarrow \sf tan(30)= \dfrac{4}{adjacent}[/tex]
[tex]\rightarrow \sf adjacent= \dfrac{4}{tan(30)}[/tex]
[tex]\rightarrow \sf adjacent= 4\sqrt{3}[/tex]
[tex]\rightarrow \sf adjacent= 6.93 \ cm[/tex]
(b)
[tex]\sf \rightarrow sin(x)= \dfrac{opposite}{hypotensue}[/tex]
[tex]\sf \rightarrow sin(30)= \dfrac{4}{hypotensue}[/tex]
[tex]\sf \rightarrow hypotensue= \dfrac{4}{ sin(30)}[/tex]
[tex]\sf \rightarrow hypotensue= 8 \ cm[/tex]
Answer:
m∠X = 60°
BX = 8 cm
BM = 4√3 cm
Step-by-step explanation:
The sum of the interior angles of a triangle is 180°
Given:
m∠B = 30°m∠M = 90°⇒ m∠B + m∠M + m∠X = 180°
⇒ 30° + 90° + m∠X = 180°
⇒ 120° + m∠X = 180°
⇒ m∠X = 180° - 120°
⇒ m∠X = 60°
Using the sine rule to find the side lengths:
[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
(where A, B and C are the angles, and a, b and c are the sides opposites the angles)
Given:
m∠X = 60°m∠B = 30°m∠M = 90°MX = 4 cm[tex]\implies \dfrac{4}{\sin 30\textdegree}=\dfrac{BX}{\sin 90\textdegree}=\dfrac{BM}{\sin 60\textdegree}[/tex]
[tex]\implies BX=\sin 90\textdegree \cdot\dfrac{4}{\sin 30\textdegree}[/tex]
[tex]=1 \cdot \dfrac{4}{\frac12}[/tex]
[tex]=1 \cdot 4 \cdot 2[/tex]
[tex]=8 \textsf{ cm}[/tex]
[tex]\implies BM=\sin 60\textdegree \cdot\dfrac{4}{\sin 30\textdegree}[/tex]
[tex]=\dfrac{\sqrt{3}}{2}\cdot \dfrac{4}{\frac12}[/tex]
[tex]=\dfrac{\sqrt{3}}{2}\cdot 4 \cdot 2[/tex]
[tex]=4\sqrt{3} \textsf{ cm}[/tex]
Find the mean of the data.
8,14,22,7,2,11,25,7,5,9
Answer:
11
Step-by-step explanation:
Given:
8,14,22,7,2,11,25,7,5,9
Solve:
Put in order:
2, 5, 7, 7, 8, 9, 11, 14, 22, 25
Note:
Mean-
Add up all data values to get the sumCount the number of values in your data setDivide the sum by the count2+ 5+7+7+8+9+11+ 14+22+25=110
110/10 = 11
Hence, the mean of the data is 11.
[RevyBreeze]
Answer:
The mean of the data given is 11
What is mean?
The mean is the arithmetic average of a set of given numbers. The median is the middle score in a set of given numbers. The mode is the most frequently occurring score in a set of given numbers.
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
(pls give the person who answered before me braineist)
Question 2:
If the following frequency distribution shows the average number of students per teacher in the 50 major cities of Pakistan
Class Limits Frequency
9-11 3
12 – 14 5
15 – 17 12
18 – 20 18
21 – 23 8
24 – 26 4
Table 1
Determine
• Range
• Mean
• Median
• Mode
• Standard Deviation
• Relative Dispersion
• Variance
• Kurtosis
With the frequecy distribution shown in the 50 cities of pakistan,
range = 18mean = 18.1median = 19.8333mode = 19.125kurtosis = 2.7508Standard deviation = 3.75How to find the Range= highest value - lowest value
= 26.5 - 8.5
= 18
How to find the mean= ∑ f x / ∑ f
= ∑ f x / N
= 905 / 50
= 18.1
median
= lower limit + ( N/2 - C ) * h / ( frequency of the class interval )
C = cumulative frequency preceeding to the median class frequency
h = class interval
= 18.5 + ( 50 / 2 - ( 5 + 12 ) ) * 3 / 18
= 18.5 + 1.3333
= 19.8333
How to find the modeThe mode is the value with the highest frequency occurence. This is under class 18 - 20
mode = lower limit + ( ( f1 - f0 ) / (2*f1 - f0 - f2 ) ) * h
f1 = fequency of the modal class
f0 = freqency of the preceeding modal class
f2 = frequency of the next modal class
h = class interval
= 18.5 + ( ( 18 - 12 ) / (2 * 18 - 12 - 8 ) ) * 3
= 18 + ( 0.375 ) * 3
= 19.125
How to find the standard deviation= sqrt ( 1 / N ∑ f ( x - x' )^2 )
= sqrt (1 / 50 * 706.5
= 3.7589
How to solve for relative dispersion= standard deviation / mean
= 3.7589 / 3
= 1.2530
What is the variance?= ( standard deviation )^2
= ( 3.7589 )^2
= 14.1293
How to solve for kurtosis= ∑ f ( x - x' )^4 / ( N * ( standard deviation )^4 )
= 27459.405 / ( 50 * 3.7589^4 )
= 2.7509
Read more on frequency distribution here: https://brainly.com/question/1094036
Find the area if the pentagon. I’ll mark the brainiest :)
Answer:
688.19 inches
Step-by-step explanation:
You randomly draw twice from this deck of cards
0 с G|F. D C G
What is the probability of not drawing a C, then not drawing a C,
without replacing the first card? Write your answer as a decimal
rounded to the nearest hundredth.
The probability of not drawing C in neither draw is P = 0.5
How to get the probability?
All the cards have the same probability of being drawn, in this case, our set of cards is {F, D, C, G}
The probability of not drawing C is equal to the probability of drawing F, D or G. So we have 3 options out of 4, then the probability is:
p = 3/4.
Now we draw another, this time there are 3 cards, one of these is C, and the other two cards are not C. Then the probability of not drawing C again is equal to 2 over 3.
q = 2/3.
The joint probability (for both of these events to happen) is equal to the product of the individual probabilities:
P = p*q = (3/4)*(2/3) = 0.5
If you want to learn more about probability, you can read:
https://brainly.com/question/251701
jack had m math problems to complete during his vacation. he solved the same number of problems every day and finished them all in 5 days. how many problems did jack solve per day.
If Jack finish them all in 5 days, then he can solve m/5 math problem in just one day.
Word problems leading to quadratic equationFrom the given question, jack can only solve m math problems in 5 days, this can be expressed as:
m problems = 5 days
The number of questions he can solve per day is expressed as:
x = 1 day
Take the ratio
m/x = 5/1
5x = m
x = m/5 math problems
This shows that jack can solve m/5 math problem in just one day
Learn more on ratio here: https://brainly.com/question/2328454
How can i prove this property to be true for all values of n, using mathematical induction.
ps: spam/wrong answers will be reported and blocked.
Proof -
So, in the first part we'll verify by taking n = 1.
[tex] \implies \: 1 = {1}^{2} = \frac{1(1 + 1)(2 + 1)}{6} [/tex]
[tex] \implies{ \frac{1(2)(3)}{6} }[/tex]
[tex]\implies{ 1}[/tex]
Therefore, it is true for the first part.
In the second part we will assume that,
[tex] \: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} = \frac{k(k + 1)(2k + 1)}{6} }[/tex]
and we will prove that,
[tex]\sf{ \: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 1 + 1) \{2(k + 1) + 1\}}{6}}}[/tex]
[tex] \: {{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 2) (2k + 3)}{6}}[/tex]
[tex]{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{k (k + 1) (2k + 1) }{6} + \frac{(k + 1) ^{2} }{6} [/tex]
[tex]{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{k(k+1)(2k+1)+6(k+1)^ 2 }{6} [/tex]
[tex]{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)\{k(2k+1)+6(k+1)\} }{6}[/tex]
[tex]{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(2k^2 +k+6k+6) }{6} [/tex]
[tex]{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(2k^2+7k+6) }{6} [/tex]
[tex]{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(k+2)(2k+3) }{6} [/tex]
Henceforth, by using the principle of mathematical induction 1²+2² +3²+....+n² = n(n+1)(2n+1)/ 6 for all positive integers n.
_______________________________
Please scroll left - right to view the full solution.
The loudness (L) of sound in decibels is related to intensity (I)measured in watts per square centimeter by the equation: L = 10log( I 10-16 ). Find the loudness of a whisper at 10-12 W/cm2. A) 35 decibels B) 40 decibels C) 45 decibels D) 50 decibels
The function L= 10 log(I/10^-16) is a logarithmic equation
The loudness of the whisper is 40 decibels
How to determine the loudness?The function of the loudness is given as:
L= 10 log(I/10^-16)
When the intensity is 10^-12, the equation becomes
L= 10 log(10^-12/10^-16)
Evaluate the quotient
L= 10 log(10^4)
Apply the rule of logarithm
L= 10 * 4
Evaluate the product
L = 40
Hence, the loudness of the whisper is 40 decibels
Read more about decibels at:
https://brainly.com/question/25480493
According to the line plot how many apples weigh 5/8 of a pound
Answer:
Answer:4 apples weigh 5/8 pound.
Step-by-step explanation:
Answer:
2(−5) − 10 = 2(0)
Step-by-step explanation:
If you substitute the values x = 0 and y = −5 into the second equation, you get a false statement