The quadratic equation with the roots 1/α and 1/β using the given equation is equal to
As given in the question,
Given equation is:
2x²−5x−6=0
Roots of the given equations are α and β
Compare with standard quadratic equation:
ax² + bx + c = 0
a = 2 , b= -5 , c = -6
Sum of the roots are:
α + β = -b/a
= -( -5/2)
= 5/2
Product of the roots
αβ = c/a
= -6/2
= -3
Now ,
( α + β )/ αβ = (5/2) / -3
⇒1/ β + 1/α = -5/6
⇒ 1/α + 1/β = -5/6
And ,
1/αβ = -1/3
Quadratic equation with roots 1/α and 1/β is given by:
x² - ( 1/α + 1/β)x + 1/αβ =0
⇒x² - (-5/6)x + (-1/3) = 0
⇒x² + (5/6)x -(1/3) =0
Therefore, the quadratic equation with roots 1/α and 1/β is equal to
x² + (5/6)x -(1/3) =0
The complete question is :
Suppose the roots of the equation 2x²−5x−6=0 are α and β.Find the quadratic equation with roots 1/α and 1/β.
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Which graph shows y=2⌈x⌉−3 ???
Answer: the first 1
Step-by-step explanation:
i just did it hope it helps
compare the slopes of the linear functions f(x) and g(x) and choose the answer that best describes them. (4 points)compare the slopes of the linear functions f(x) and g(x) and choose the answer that best describes them. (4 points)
The slope of a function is defined as the change in y-coordinate with respect to the change in x-coordinate of the line.
m = Δy/Δx
∆y --> net change in the y coordinate
∆x ---> net change in x coordinate
m ---> slope of fution
The y-intercept of both functions 'f' and 'g' are equal and slope of f(x) is less than the slope of g(x). So, the correct option is option (A).
We have given a function, g (x) = 2x + 1
comparing the g(x) with standard equation
y = mx + b
where m is slope of this line
b --> y-intercept
Thus we get m = 2 , b= 1 . So, the slope of g(x) is 2 and y-intersecpt is 1 .
Now, we have a table for function f(x) that is function f(x) passing through all points as given in table. The slope of function passing through (h,k) and (a,b) is expressed as (k-b)/(h-a)
Thus, slope of function 'f' passing through (0,1) and (2,4) = (1-4)/(0-2) = -3/-2
= 3/2
=> f (x) = (3/2)x + b
where , b --> y-intercept
plug the value x= 4 and corresponding to it
f(x) = 7 we get , 7 = 3/2× 4 + b
=> b = 7-6 = 1
Therefore, slope of function g(x) is greater than slope of function f(x) and y-intercept of f(x) is equal to y-intercept g(x) .
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Complete question:
The Table represents the linear function f(x), and the equation represents the linear function g(x). Compare the y-intercepts and the slopes of the linear functions f(x) and g(x) and choose the answer that best describes them.
x / f(x)
0/1
2/4
4/7
g(x)= 2x+1
A. The slope of f(x) is less than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).
B. The slope of f(x) is less than the slope of g(x). The y-intercept of f(x) is greater than the y-intercept of g(x).
C. The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).
D. The slope of f(x) is less than the slope of g(x). The y-intercept of f(x) is greater than the y-intercept of g(x).
Write an equation for the line parallel to the given line that contains C.
C(1,5); y= -4x+7
Answer:
y=-4x+9
Step-by-step explanation:
We will find an equation in the form of y = mx + b. We know m must be -4(because the slope must be the same for parallel lines), so we need to solve for b, which is the y-intercept. To do that, we will plug in the point C, giving us [tex]5 = -4 * 1 + b[/tex]. Adding 4 to both sides gives us b = 9, so that is the y-intercept.
suppose you are testing to see if there is a difference in population mean lifetime of two brands (1,2) of batteries. random samples of batteries are taken for each brand and the following data are recorded: sample 1: n1
The test statistic of two brands of batteries is -2.177.
How to calculate test statistic?[tex]n_1[/tex] = size of sample 1 = 16
[tex]n_2[/tex] = size of sample 2 = 21
[tex]\bar{x_1}[/tex] = mean of sample 1 = 210
[tex]\bar{x_2}[/tex] = mean of sample 2 = 225
[tex]\sigma_{1}[/tex] = standard deviation of sample 1 = 20
[tex]\sigma_{2}[/tex] = standard deviation of sample 2 = 23
T test is test for statistical hypothesis that follows t-distribution table under null hypothesis. T test is used when test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known. So, for this case we use t test for test statistic,
t = [tex]\frac{\bar{x_1}-\bar{x_2}}{\sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}}[/tex]
t = [tex]\frac{210-225}{\sqrt{\frac{20^2}{16}+\frac{23^2}{21}}}[/tex]
t = [tex]\frac{-15}{\sqrt{\frac{400}{16}+\frac{529}{21}}}[/tex]
t = -15 / 7.0845
t = -2.117
Thus, the two brands of batteries have test statistic result is -2.117
Your question is incomplete, but most probably your full question was
Suppose you are testing to see if there is a difference in population mean lifetime of two brands (1,2) of batteries. Random samples of batteries are taken for each brand and the following data are recorded:
Sample 1: n1= 16, X1 = 210, s1= 20
Sample 2: n2= 21, X2 = 225, s2= 23
What is the test statistic assuming unequal population standard deviations?
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solve (x+21)+(2x+9)=90
Answer:
The answer is x=20
Step-by-step explanation:
Answer:
x = 20
Step-by-step explanation:
(x+21)+(2x+9)=90
x + 21 + 2x + 9 = 90
combine numbers on left side:
x + 30 + 2x = 90
combine x terms on left side:
3x + 30 = 90
subtract 30 from both sides:
3x + 30 -30 = 90 - 30
3x = 60
divide both sides by 3:
3x/3 = 60/3
x = 20
When we do a confidence interval for the mean, we use the following distribution to determine the number of standard deviations needed for our confidence:
t-distribution z-distribution
skewed distribution Chi Square distribution
When we do a confidence interval for the mean, we use T-distribution to determine the number of standard deviations needed for our confidence
The T-distribution is a way to describe a collection of observations in which the majority of the observations are close to the mean and the remaining observations are the tails on either side. It is a type of normal distribution that is utilized for data with unknown variance and smaller sample sizes.
We use the T-distribution to obtain the required critical value, which is nothing more than the number of standard deviations from the center taken to obtain the confidence interval, despite the fact that there is no population standard deviation and only sample metrics—the sample mean and standard deviation—are used. As a result, the solution to this problem is T-distribution.
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I need answers as soon as possible.
Answer:78 feet and 34 cubic feet
Step-by-step explanation:
One angle of a triangle measures 75°. The other two angles are in a ratio of 2:5. What are the measures of those two angles?
well, since a triangle has a total of 180° interior angles, that means 180 - 75 = 105 is leftover for the other two remaining angles.
now, they're in a 2 : 5 ratio, well, let's simply divide 105° by (2 + 5) and distribute accordingly.
[tex]2~~ : ~~5\implies 2\cdot \frac{105}{2+5}~~ : ~~5\cdot \frac{105}{2+5}\implies 2\cdot 15~~ : ~~5\cdot 15\implies \text{\LARGE 30~~ : ~~75 }[/tex]
Find the value of ccc so that the polynomial p(x)p(x)p, left parenthesis, x, right parenthesis is divisible by (x+2)(x+2)left parenthesis, x, plus, 2, right parenthesis. P(x) = 4x^3+cx^2+x+2p(x)=4x 3 +cx 2 +x+2p, left parenthesis, x, right parenthesis, equals, 4, x, cubed, plus, c, x, squared, plus, x, plus, 2 c=c=c, equals.
The value of c after solving the equation is 8.
For the polynomial to be divisible by x+2, hence x = -2
Given
p(x) = 4x³+cx²+x+2
p(-2) = 4(-2)³+c(-2)²+(-2)+2
p(-2) = 4(-8) + c(4)-2+2
p(-2) = -32+4c
If p(-2) = 0
0= -32+4c
-4c = -32
c = 32/4
c = 8
Hence we get the value of c as 8.
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Solve the inequality
2/7 > b + 5/7
Answer:
-3/7 > b
Step-by-step explanation:
subtract 5/7 on both sides
Complete the statement by filling in the blank. When constructing a confidence interval, if the level of confidence increases the margin of error will and the confidence interval will be A larger sample size will improve the accuracy of the confidence interval, therefore margin of error will and the confidence interval will be A) Decrease, wider. Increase, narrower B) Decrease, narrower. Increase, wider C) Increase, wider. Decrease, narrower. D) Increase, narrower. Decrease, wider.
Option-C is correct that is increase, wider. If the level of confidence rises when generating a confidence interval, the margin of error must increase and the confidence interval will get wider.
Given that,
By completing the blanks, the sentence is complete. When generating a confidence interval, the margin of error and the confidence interval will be larger if the level of confidence grows.
We have to find the accuracy of the confidence interval will increase with a larger sample size, so the margin of error and the confidence interval will be-----.
We know that,
If the level of confidence rises when generating a confidence interval, the margin of error must increase and the confidence interval will get wider.
The margin of error is a phrase that conveys how much sampling error there is in the data that was gathered or in the parameter estimates. Accordingly, the credibility of the poll will decrease as the margin of error increases. It displays the degree of estimation accuracy.
Three things determine the margin of error:
Confidence level: The margin of error grows in proportion to the level of confidence.
Sample size: The margin of error gets smaller as the size of the random sample gets bigger.
Population standard deviation: The population's standard deviation is: For a given level of confidence, our interval will be wider the more dispersed the population is.
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What is the value of x?
Answer: 2
Step-by-step explanation:
Since both triangles are similar you can set both side lengths to be equal
4x = 16x -24
Isolate x on one side
-12x = -24
Then solve for x
x = 2
use the appropriate normal distribution to approximate the resulting binomial distributions. a convenience store owner claims that 55% of the people buying from her store, on a certain day of the week, buy coffee during their visit. a random sample of 35 customers is made. if the store owner's claim is correct, what is the probability that fewer than 21 customers in the sample buy coffee during their visit on that certain day of the week? a) 0.7486 b) 0.6915 c) 0.7224 d) 0.5987 e) 0.6628 f) none of the above.
The probability that fewer than 21 customers in the sample buy coffee during their visit on that certain day of the week is 0.7224. Hence option C is the correct option.
What is the binomial distribution?
When each trial has the same probability of achieving a given value, the number of trials or observations is summarised using the binomial distribution. The likelihood of observing a specific number of successful outcomes in a specific number of trials is determined by the binomial distribution.
The formula for z-score is z = (x -μ)/σ
Where, μ is mean of the sample, σ is standard deviation of the sample
Given that 55% of the customers buy coffee, hence p = 55% = 0.55
Sample of 35 customers, hence n = 35.
For the binomial distribution μ = np, σ = √[np(1-p)]
The mean and the standard deviation of the approximation are:
μ = 35 ˣ 0.55 = 19.25
σ = √[35 ˣ 0.55(1-0.55)] =2.943
Now calculate the z score where μ = 19.25, σ = 2.943 and X = 21
z = (21 -19.25)/2.943
z = 0.59
The value of p is 0.2776 when z score is 0.59.
The probability is 1 - 0.2776 = 0.7224.
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Confusing! Plsss Help!!!!!!
Answer:
y = 120°
Step-by-step explanation:
Given a triangle with external angle y and remote internal angles 33° and 87°, you want the measure of y.
External angleThe external angle is the sum of the remote internal angles:
y = 33° +87°
y = 120°
__
Additional comment
Angle x is supplementary to y, so its measure is ...
x = 180° -y = 180° -120°
x = 60°
Hopefully, you notice that the value of x is ...
x = 180° -(33° +87°)
This is the same value you get when you solve the equation for the sum of angles in the triangle:
33° +87° +x = 180°
Effectively, the rule regarding the external angle being the sum of remote internal angles is another way of saying the sum of angles in a triangle is 180°.
$$1,2,2,4,8,32,256,\ldots,$$each term (starting from the third term) is the product of the two terms before it. for example, the seventh term is $256$, which is the product of the fifth term ($8$) and the sixth term ($32$). this sequence can be continued forever, though the numbers very quickly grow enormous! (for example, the $14^{\text{th}}$ term is close to some estimates of the number of particles in the observable universe.) what is the last digit of the $35^{\text{th}}$ term of the sequence?
The last digit of a₃₅ is 8 when each phrase (beginning with the third term) in the sequence $$1,2,2,4,8,32,256 is the product of the two terms that came before it.
Given that,
Each phrase (beginning with the third term) in the sequence $$1,2,2,4,8,32,256 is the product of the two terms that came before it. For instance, the seventh term, which is the sum of the fifth ($8) and sixth ($32) terms, is $256. Though the numbers very rapidly become large, this series can go on indefinitely! In terms of the number of particles in the observable universe, the $14 term, for instance, is close to some estimations.
We have to find what is the final digit of the sequence's $35 term.
We know that,
Remember the Fibonacci sequence, which goes 1, 1, 2, 3, 5, 8, 13, 21..., where each word is the total of the one before it. Continuing the above pattern, if Fn is the n-th Fibonacci number, we would arrive at
aₙ=a₂ˣₙ₋₁a₁ˣₙ₋₂=2ˣₙ₋₁
A periodic series of residues mod 10 is left behind by the sequence of positive powers of 2:
2≡2(mod 10)
2²≡4 (mod 10)
2³≡8 (mod 10)
2⁴≡16 (mod 10)
2⁵≡32 (mod 10)
2⁶≡64 (mod 10)
And so forth; this series of residues has a 4-year period.
The taken mod 4 period is 6:
34≡4 (mod 6)
F₃₄≡3 (mod6)
2³=8
So, the last digit of a₃₅ is 8.
Therefore, the last digit of a₃₅ is 8 when each phrase (beginning with the third term) in the sequence $$1,2,2,4,8,32,256 is the product of the two terms that came before it.
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Anyone know this? Kind of struggling.
Answer:
It's -5 + 3 basicaly because 2 negatives is one positive. So the answer is -2.
Victoria deposited $15,000 into a savings account that earns an annual simple interest rate of 0.2% to the nearest 10th of a year how long will it take for the account to reach 15,500
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
sus
It will take about 16.7 years to reach $15500.
What is the interest rate?The percentage that a lender adds to the amount of money lent to them is called an interest rate.
Given that, the initial deposited amount is P = $15000, the interest rate is r= 0.2% annually, and the final amount is $15500.
The interest earned is calculated by subtracting the initial amount from the final amount:
15500-15000
=500
Therefore, the interest earned is $500.
Now, the formula for the simple interest is:
interest = P × r × t
Substitute the known values:
500 = 15000 × 0.2% × t
500 = 15000 × 0.2/100 ×t
500 = 30t
t = 500/30
t = 16.7
Hence, It will take about 16.7 years to reach $15500.
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For the holidays, Kenji is driving to visit his grandparents who live 402 miles away. Kenji's car
gets 33.5 miles per gallon of gas when he is driving on the highway. In order to budget for
his trip, Kenji wants to know how much gas he will need.
Use an equation to find how much gas Kenji needs for the drive.
Kenji needs
gallons of gas.
By solving a linear equation, it can be calculated that-
Kenji needs 12 gallons of gas for the drive
What is a linear equation?
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here, a linear equation needs to be solved
Let Kenji requires x gallons of gas
Kenji's car gets 33.5 miles per gallon of gas when he is driving on the highway.
Kenji can travel 33.5x miles with x gallons of gas
Distance to be travelled = 402 miles
By the problem,
The required linear equation is
33.5x = 402
x = [tex]\frac{402}{33.5}[/tex]
x = 12 gallons
Kenji needs 12 gallons of gas for the drive
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write the expression as a sum and/or difference of logarithms. express exponents as factors.log5 a3 b
Expression of logarithms is log₅a³b = 3log₅a + log₅b.
Given expression is log₅a³b.
We have to express given expression as a sum or difference of logarithms.
We know the logarithmic formulas which is,
logₐ(PQ) = logₐP + logₐQ
logₐ([tex]P^{Q}[/tex]) = QlogₐP
we will use above formulas and solve the given equation.
log₅a³b = log₅a³ + log₅b
log₅a³b = 3log₅a + log₅b
Logarithms, like exponents, have many helpful properties that can be used to simplify logarithmic expressions ans solve logarithmic equation.
The product property states that to miltiply two powers that have the same base, add the exponents.
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a keypad at the entrance of a building has 10 buttons labeled 0 through 9. what is the probability of a person correctly guessing 8 digit entry code
The probability is it that someone will correctly guess an 8-digit entry code is 0.022.
Given that,
A keypad with 10 buttons marked 0 through 9 is located at the building's entrance.
We have to find how much probability is it that someone will correctly guess an 8-digit entry code.
We know that,
Probability is defined as the ratio of the number of required outcomes to the total number of outcomes.
Based on the details provided;
One outcome is expected if the needed number of outcomes is 8-digits.
Since there are 10 numbers and 8 numbers need to be chosen, the total number of outcomes is ¹⁰C₈.
Considering that the lock can only be opened by 8 digits;
The probability that someone will properly guess a 8-digit input code is
P=1/¹⁰C₈
P=1/10!/8!2!
P=1/10×9/2
P=1/45
P=0.022
Therefore, The probability is it that someone will correctly guess an 8-digit entry code is 0.022.
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(2+8) + 10 ^2 +60 divided 10
Answer: 17
Step-by-step explanation:
Answer:
Step-by-step explanation:
116
Dubai, United Arab Emirates set a record temperature for 49 ° C What does the number 49 mean
Answer: It means that the high in Dubai is 49
Step-by-step explanation: When saying about the weather, we always say the highest temperature first, so that mean 49 here is the high temperature in Dubai.
If you can please give me a Brainliest, I only need 1 more to become an Ace, thank you!
Answer:
The mercury is expected to cross the 49°C mark again later today.
6(x−2)=−18
due today
Answer: -1
Step-by-step explanation: 6x-12=-18
+12= +12
------------------
-6/6=-1
Nancy i making acceorie for the occer team. She ue 566. 28 inche of fabric on headband for 36 player and 3 coache. She alo ue 306. 36 inche of fabric on writband for jut the player. How much fabric wa ued on a headband and writband for each player?
Using some mathematical operations, we know that each player's headband and wristband are made from 16.18 inches of fabric and 8.63 inches of fabric.
What are mathematical operations?A mathematical function known as an operation converts zero or more input values into a precisely defined output value.
The quantity of operands affects the operation's arity.
Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are collectively referred to as PEMDAS.
So, given that we've done it:
There are 35 players.
There are two coaches.
The cloth on the headbands measures 598.66 inches in length.
Just for the players, the wristbands include 302.05 inches of fabric.
Each player's headband's fabric length is specified by:
= Total inches/Total number of persons
= 598.66/37
= 16.18 inches
Each player's wristband's fabric length is specified by:
= Total inches/Number of persons
= 302.05/35
= 8.63 inches
Therefore, using some mathematical operations, we know that each player's headband and wristband are made from 16.18 inches of fabric and 8.63 inches of fabric.
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Complete question:
Nancy is making accessories for the soccer team. She uses 598.66 inches of fabric on headbands for 35 players and 2 coaches. She also uses 302.05 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
An exponential growth function represents a quantity that has a constant
doubling time.
O A. True
OB. False
Answer:
false
Step-by-step explanation:
Hope it helps!
based on past experience, a hiring manager believes that less than one-third of applicants are actually qualified for an entry-level position. suppose that in a random sample of 144 applicants for this position, 63 are found to be qualified. do the sample data support the manager's belief? test the relevant hypotheses using a
The no. of people qualified is less than the managers belief of 0.265
What is P-value?
The likelihood of receiving outcomes from a statistical hypothesis test that are at least as severe as the actual results provided the null hypothesis is true, is known as the p-value in statistics. The p-value provides the minimal level of significance at which the null hypothesis would be rejected as an alternative to rejection points. The alternative hypothesis is more likely to be supported by greater evidence when the p-value is lower.
P-value is frequently utilised by government organisations to increase the credibility of their research or reports. The United States Census Bureau, for instance, mandates that any analysis with a p-value higher than 0.10 be accompanied by a statement stating that the difference is not statistically significant from zero.
Here [tex]H_{0}[/tex] - P =1/3=0.3333
Hi - P <0.3333
Given n =144
x = 63
P^=63/144=0.4375
Test Static = [tex]\frac{P^-P}{\sqrt{\frac{PQ}{n} } }[/tex]
= [tex]\frac{0.4375^-0.3333}{\sqrt{\frac{0.3333-(1-0.3333)}{144} } }[/tex]
=0.265
P-value =P(Z<2.65)=0.9960, Given [tex]\alpha[/tex] =0.05
here P-Value >[tex]\alpha[/tex]
So, don't reject [tex]H_{0}[/tex]
There is no evidence to support the manager's Belief That less Than 1/3 of Applications are qualified
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i need your help please!!!!!!! and no fake answers please guys
The measure of the LK us 5 units and the measure of the NL is 6 units after applying intersecting secants theorem.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle).
It is given that:
A circle:
Applying intersecting secants theorem:
4(4 + 2) = 3(3 + 2x + 5)
8 = 8 + 2x
x = 0
LK = 2x + 5 = 5 units
In the second circle:
4(4 + x - 8) = 3(3 + x - 5)
x = 10
NL = x - 8 + 4 = 10 - 8 + 4 = 6 units
Thus, the measure of the LK us 5 units and the measure of the NL is 6 units after applying intersecting secants theorem.
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If the nth term of a number sequence is n^2 + 2n,
find the first 3 terms and the 10th term.
Answer:
3, 8, 15 and 120
Step-by-step explanation:
to find the first 3 terms, substitute n = 1, 2, 3 into the nth term rule
n = 1 : 1² + 2(1) = 1 + 2 = 3
n = 2 : 2² + 2(2) = 4 + 4 = 8
n = 3 : 3² + 2(3) = 9 + 6 = 15
the first 3 terms are 3, 8, 15
to find the 10th term , substitute n = 10 into the rule
n = 10 : 10² + 2(10) = 100 + 20 = 120
Which additional piece of information would show that quadrilateral WXYZ is a rhombus?
The additional piece of information that is needed to show that the quadrilateral is a rhombus is given as follows:
The angle measures.
What is a rhombus?A rhombus is a quadrilateral, and is a special case of a parallelogram.
For the parallelogram to represent a rhombus, these following conditions need to be respected:
Parallelism of opposite sides.Congruence of opposite angles -> Same measures.All the sides are equal in length.The bisection of diagonals happen at right angles.To verify if two sides are parallel, we need to verify their slopes, which are dependent on their angle measures. Hence these angle measures are the missing piece of information to define if the quadrilateral is a rhombus.
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Wrote an equation with a vertex : (4,-5)
passes through: (2,-1)