Answer: x>3
Step-by-step explanation:
x-5>2
x>+5-2
x>3
What is the value of x for the given equation?
4 – 2(x + 7) = 3(x + 5)
X=
Answer:
-5
Step-by-step explanation:
A study was conducted to explore the effects of ethanol on sleep time. Fifteen rats were randomized to one of three treatments. Treatment 1 got only water (control). Treatment 2 got 1g of ethanol per kg of body weight, and treatment 3 got 2g/kg. The amount of REM sleep in a 24hr period was recorded, in minutes. Data are below:
Treatment 1: 63, 54, 69, 50, 72
Treatment 2: 45, 60, 40, 56
Treatment 3: 31, 40, 45, 25, 23, 28
Required:
a. Calculate 90% confidence intervals for all pairwise comparisons of treatment means using the uncorrected method. Create a letter code table to summarize your results, then interpret the results in context.
b. Now calculate 90% confidence intervals for all pairwise comparisons using the Bonferroni correction. Create a letter code table, and interpret your results in context. Do any of the results differ from part (a)?
Answer:
the answer is A
Step-by-step explanation: i have calculated this problom
NEED HELP ASAP!! Trigonometry!! Need to find x
Answer:
Hey there!
We have tangent x=8/10
This simplifies to tangent x=0.8
Arctan=0.8, x=38.7 degrees.
Let me know if this helps :)
Answer:
38.7
Step-by-step explanation:
You are given the lengths of the legs of the triangle.
The trig ratio that relates the lengths of the legs is the tangent.
tan x = opp/adj
tan x = 8/10
tan x = 0.8
Use the inverse tangent function to find x.
tan^(-1) 0.8 = 38.7 deg
Answer: x = 38.7 deg
You run a souvenir store that sells key rings. You can get 50 key rings from your first supplier for $.50 cents each. You can get the same 50 key rings from your second supplier for $30 total, or you can get them from your third supplier for $27.50. How much will you pay if you get the best deal?
Answer:
$25
Step-by-step explanation:
.5 * 50 = 25
25<27.5<30
The cheapest supplier is the first one.
show that an integer is divisible by 11 if and only if the alternating sum (add first digit, subtract the second, add the third, subtract the fourth etc) of its digits is divisible by 11
Need an answer by tomorrow if possible please
Answer and Step-by-step explanation:
Suppose that we have a number y which is a positive integer and that:
y = [tex]x_n...x_5x_4x_3x_2x_1x_0[/tex]
Where;
[tex]x_{0}[/tex] = digit at 10⁰ => one's place (units place)
[tex]x_1[/tex] = digit at 10¹ => 10's place (tens place)
[tex]x_{2}[/tex] = digit at 10² => 100's place (hundreds place)
[tex]x_{3}[/tex] = digit at 10³ => 1000's place (thousands place)
.
.
.
[tex]x_{n}[/tex] = digit at 10ⁿ place
Then;
y = [tex]x_{0}[/tex] * 10⁰ + [tex]x_1[/tex] * 10¹ + [tex]x_{2}[/tex] * 10² + [tex]x_{3}[/tex] * 10³ + [tex]x_{4}[/tex] * 10⁴ + [tex]x_5[/tex] * 10⁵ + . . . + [tex]x_{n}[/tex] * 10ⁿ
Since 10⁰ = 1, let's rewrite y as follows;
y = [tex]x_{0}[/tex] + [tex]x_1[/tex] * 10¹ + [tex]x_{2}[/tex] * 10² + [tex]x_{3}[/tex] * 10³ + [tex]x_{4}[/tex] * 10⁴ + [tex]x_5[/tex] * 10⁵ + . . . + [tex]x_{n}[/tex] * 10ⁿ
Now, to test if y is divisible by 11, replace 10 in the equation above by -1. Since 10 divided by 11 gives -1 (mod 11) [mod means modulus]
y = [tex]x_{0}[/tex] + [tex]x_1[/tex] * (-1)¹ + [tex]x_{2}[/tex] * (-1)² + [tex]x_{3}[/tex] * (-1)³ + [tex]x_{4}[/tex] * (-1)⁴ + [tex]x_5[/tex] * (-1)⁵ + . . . + [tex]x_{n}[/tex] * (-1)ⁿ
=> y = [tex]x_{0}[/tex] - [tex]x_1[/tex] + [tex]x_{2}[/tex] - [tex]x_{3}[/tex] + [tex]x_{4}[/tex] - [tex]x_5[/tex] + . . . + [tex]x_{n}[/tex] (-1)ⁿ (mod 11)
Therefore, it can be seen that, y is divisible by 11 if and only if alternating sum of its digits [tex]x_{0}[/tex] - [tex]x_1[/tex] + [tex]x_{2}[/tex] - [tex]x_{3}[/tex] + [tex]x_{4}[/tex] - [tex]x_5[/tex] + . . . + [tex]x_{n}[/tex] (-1)ⁿ is divisible by 11
Let's take an example
Check if the following is divisible by 11.
i. 1859
Solution
1859 is divisible by 11 if and only if the alternating sum of its digit is divisible by 11. i.e if (1 - 8 + 5 - 9) is divisible by 11.
1 - 8 + 5 - 9 = -11.
Since -11 is divisible by 11 so is 1859
ii. 31415
Solution
31415 is divisible by 11 if and only if the alternating sum of its digit is divisible by 11. i.e if (3 - 1 + 4 - 1 + 5) is divisible by 11.
3 - 1 + 4 - 1 + 5 = 10.
Since 10 is not divisible by 11 so is 31415 not divisible.
Refer to △ABC. Find the length of side AB .
Step-by-step explanation:
Hello, there!!!!
It's simple lets get started with simple solution.....
Given,
AC= 7cm
BC= 25cm
let AB be x.
Now, As it is a Right angled triangle, taking angle B as a refrence angle. we get,
h= BC= 25cm
p= AC= 7cm
b= AB= x
now, by Pythagoras relation we get,
[tex]b = \sqrt{ {h}^{2} - {p}^{2} } [/tex]
[tex]or \: b = \sqrt{ {25}^{2} - {7}^{2} } [/tex]
By simplifying it we get,
b= 24cm
Therefore, the value of AB is 24 cm.
Hope it helps...
For the lengths AB, BC, and AC to equal 7,6, and 13 respectively, what is the
value of x?
Answer:
x = 5
Step-by-step explanation:
We know that AB = 2x - 3 and AB = 7, therefore:
2x - 3 = 7
2x - 3 + 3 = 7 + 3
2x = 10
2x / 2 = 10 / 2
x = 5
What is $121 divided into ratio of 7:4
Answer:
77:44
Step-by-step explanation:
Since 7:4 is equal to 11 and 121/11, each ratio can be multiplied by 11.
Expand $(x+1)(x^{2}+1)(x-1)$. What is the sum of the coefficients of the resulting expression?
Answer:
0
Step-by-step explanation:
Hello, please consider the following.
For any a and b real numbers we can write.
[tex](a-b)(a+b)=a^2-b^2[/tex]
We apply this formula two times here, as below.
[tex](x+1)(x^{2}+1)(x-1)=(x+1)(x-1)(x^{2}+1)\\\\=(x^2-1^2)(x^2+1)=(x^2-1)(x^2+1)\\\\=(x^2)^2-1^2=x^4-1[/tex]
We have the coefficient of 1 for [tex]x^4[/tex] and the constant term is -1, so the sum of the coefficients is 0.
Thank you.
Answer:
1
Step-by-step explanation:
(x + 1)(x² + 1)(x - 1)
= (x³ + x + x² + 1)(x - 1)
= x^4 - x³ + x² - x - x³ - x² + x - 1
= x^4 - 1
Coefficient of x^4 = 1
Trials in an experiment with a polygraph include results that include cases of wrong results and cases of correct results. Use a significance level to test the claim that such polygraph results are correct less than % of the time. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution.
Answer and Step-by-step explanation:
This is a complete question
Trials in an experiment with a polygraph include 97 results that include 23 cases of wrong results and 74 cases of correct results. Use a 0.01 significance level to test the claim that such polygraph results are correct less than 80% of the time. Identify the nullhypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution.
The computation is shown below:
The null and alternative hypothesis is
[tex]H_0 : p = 0.80[/tex]
[tex]Ha : p < 0.80[/tex]
[tex]\hat p = \frac{x}{ n} \\\\= \frac{74}{97}[/tex]
= 0.7629
Now Test statistic = z
[tex]= \hat p - P0 / [\sqrtP0 \times (1 - P0 ) / n][/tex]
[tex]= 0.7629 - 0.80 / [\sqrt(0.80 \times 0.20) / 97][/tex]
= -0.91
Now
P-value = 0.1804
[tex]\alpha = 0.01[/tex]
[tex]P-value > \alpha[/tex]
So, it is Fail to reject the null hypothesis.
There is ample evidence to demonstrate that less than 80 percent of the time reports that these polygraph findings are accurate.
Evaluate the expression for y=-1? 14+5y=
Answer:
The answer is 9Step-by-step explanation:
14 + 5y
To solve the expression substitute the value of y that's - 1 into the expression
That's
14 + 5(-1)
= 14 - 5
= 9
Hope this helps you
Help me please I need answers
Answer:
[tex]\huge \boxed{\mathrm{\$ \ 7,533.33}}[/tex]
Step-by-step explanation:
There are 12 months in one whole year.
In one year, the person earns $96,600 with bonus.
The person gets a bonus of $6,200 during Christmas.
96,600 - 6,200 = 90,400
The person earns $90,400 yearly.
[tex]\frac{90,400}{12}[/tex] = 7,533.3333
Each month, the person earns $7,533.33, to the nearest cent.
Two math classes took the same quiz. The scores of 10 randomly selected students from each class are listed below. • Sample of Class A: 75, 80, 60, 90, 85, 80, 70, 90, 70, 65 • Sample of Class B: 95, 90, 85, 90, 100, 75, 90, 85, 90, 85 Based on the medians of the scores for each class, what inference would you make about the quiz scores of all the students in Class A compared to all the students in Class B? Explain your reasoning to justify your answer.
Answer:
Step-by-step explanation:
First you have to find the medians which is when you put the numbers in number order and find the one in the middle.
Class A: 60,65,70,70,75,80,80,85,90,90
=77.5
Class B: 75,85,85,85,90,90,90,90,95,100
=90
That the class B is more advanced, and they probably studied.
Apply the distributive property to factor out the greatest common factor. 18d+12 =18d+12=18, d, plus, 12, equals
Answer:
[tex]\huge\boxed{6 ( 3d + 2 )}[/tex]
Step-by-step explanation:
18d + 12
The greatest common factor is 6, So we need to factor out 6
=> 6 ( 3d + 2 ) [Distributive property has been applied and this is the simplest form]
Answer:
6(3d+2)
Step-by-step explanation:
6 is the gcd of the two terms.
50q + 43 > −11q + 70
Answer:
q > 27/61
Step-by-step explanation:
50q + 43 > −11q + 70
Add 11 q to each side
50q+11q + 43 > −11q+11q + 70
61q+43> 70
Subtract 43 from each side
61q> 27
Divide each side by 61
61q/61> 27/61
q > 27/61
The data show the number of hours of television watched per day by a sample of 28 people. Use technology to answer parts (a) and (b) below. 1 1 2 8 8 4 8 7 8 3 1 2 8 2 4 7 4 0 5 7 7 8 9 3 6 2 2 7 a. Find the data set's first, second, and third quartiles. Upper Q 1 equals nothing Upper Q 2 equals nothing Upper Q 3 equals nothing
Answer:
Q1= 2, Q2 = 4.5, Q3 = 7.5
Step-by-step explanation:
firstly, put the data is other;
0 1 1 1 2 2 2, 2 2 3 3 4 4 4, 5 6 7 7 7 7 7, 8 8 8 8 8 8 9
the Q1 = (2+2)/2 = 2
Q2 = (4 + 5)/ 2 = 4.5
Q3 = (7 + 8)/2 = 7.5
the height of a soccer ball that is kicked from the ground can be approximated by the function:
y = -12x^2 + 48x
where y is the height of the soccer ball in feet x seconds after it is kicked. What is the soccer ball's maximum height in feet?
Answer: 4 seconds
Step-by-step explanation:
x refers to time. Since we want to know how long it is in the air, we need to find the time (x) when the ball lands on the ground (y = 0)
0 = -12x² + 48x
0 = -12x(x - 4)
0 = -12x 0 = x - 4
0 = x 4 = x
x = 0 seconds is when the ball was kicked
x = 4 seconds is when the ball landed on the ground
Consider the following two questions designed to assess quantitative literacy: a. What is 15% of 1000? b. A store is offering a 1596 off sale on all TVs. The most popular television is normally priced at $1000. How much money would a customer save on the television during this sale? Suppose the first question is asked of 200 randomly selected college students, with 165 answering correctly; the second one is asked of a different random sample of 200 college students, resulting in 142 correct responses. Carry out a test of hypotheses at significance level 0.05 to decide if the true proportion of correct responses to the question without context exceeds that for the one with context. (Use p1 for the true proportion students who answered the question without context correctly and p2 for the true proportion of students who answered the question with context correctly.) Carry out a test of hypotheses at significance level 0.05 to decide if the true proportion of correct responses to the question without context exceeds that for the one with context.
Answer:
The calculated value of z= 2.7225 falls in the critical region therefore we reject the null hypothesis and conclude that at the 5% significance level, true proportion of correct responses to the question without context exceeds that for the one with context.
Step-by-step explanation:
a: 15 % of 1000= 150
b. 15.96 % of $ 1000= $ 159.6
The customer would pay = $ 1000- $ 159.6= $ 840.4 and save $ 159.6
Formulate the hypotheses as
H0: p1= p2 true proportion of correct responses to the question without context is equal that for the one with context.
Ha : p1≠ p2
We choose the significance level ∝= 0.05
The critical value for two tailed test at alpha=0.05 is ± 1.96
The test statistic is
Z = p1-p2/ √pq (1/n1+ 1/n2)
p1= true proportion students who answered the question without context correctly = 165/200=0.825
p2= true proportion of students who answered the question with context correctly = 142/200= 0.71
p = an estimate of the common rate on the assumption that the two proportions are same.
p = n1p1+ n2p2/ n1 + n2
p =200 (0.825) + 200 (0.71) / 400
p= 165+ 142/400= 307 /400 =0.7675
now q = 1-p= 1- 0.7675= 0.2325
Thus
z= 0.825- 0.71/ √0.7675*0.2325( 1/200 + 1/200)
z= 0.115/√ 0.17844( 2/200)
z= 0.115/0.04224
z= 2.7225
The calculated value of z falls in the critical region therefore we reject the null hypothesis and conclude that at the 5% significance level, true proportion of correct responses to the question without context exceeds that for the one with context.
Statistics professors believe the average number of headaches per semester for all students is more than 18. From a random sample of 15 students, the professors find the mean number of headaches is 19 and the standard deviation is 1.7. Assume the population distribution of number of headaches is normal.
Complete Question
Statistics professors believe the average number of headaches per semester for all students is more than 18. From a random sample of 15 students, the professors find the mean number of headaches is 19 and the standard deviation is 1.7. Assume the population distribution of number of headaches is normal.the correct conclusion at [tex]\alpha =0.001[/tex] is?
Answer:
There is no sufficient evidence to support the professor believe
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 18[/tex]
The sample size is [tex]n = 15[/tex]
The sample mean is [tex]\= x = 19[/tex]
The standard deviation is [tex]\sigma = 1.7[/tex]
The level of significance is [tex]\alpha = 0.001[/tex]
The null hypothesis is [tex]H_o: \mu = 18[/tex]
The alternative hypothesis is [tex]H_a : \mu > 18[/tex]
The critical value of the level of significance from the normal distribution table is
[tex]Z_{\alpha } = 3.290527[/tex]
The test hypothesis is mathematically represented as
[tex]t = \frac{\= x - \mu }{ \frac{\sigma}{ \sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 19 - 18}{ \frac{1.7}{ \sqrt{15} } }[/tex]
[tex]t = 2.28[/tex]
Looking at the value of t and [tex]Z_{\alpha }[/tex] we can see that [tex]t < Z_{\alpha }[/tex] so we fail to reject the null hypothesis.
This mean that there is no sufficient evidence to support the professor believe
price.
A shopkeeper marks the price of his her goods 40 % above the cost price and
allows 20% discount. If his her purchase price of an item is Rs 6.000. how much
should a customer pay for it levying 13 % VAT!
e 990 the honorariter
Answer:
73%
Step-by-step explanation:
please help! algebra 2 work
-5y + 8 = -7
I need to know how to do that
Answer:
y=3
Step-by-step explanation:
-5y+8=-7
Minus 8 from each side.
-5y=-15
Divide -5 from each side.
y=3
Determine whether each equation has one solution, no solution or infinitely many solutions. 4x + 10 = 2(2x + 5) 4x - 5 = 4x + 10 4x - 5 = -5
Answer:
see below
Step-by-step explanation:
4x + 10 = 2(2x + 5)
Distribute
4x+10 = 4x+10
Since the left side is identical to the right side, there are infinite solutions
4x - 5 = 4x + 10
Subtract 4x from each side
-5 = 10
This is never true, so there are no solutions
4x-5 = -5
Add 5 to each side
4x = 0
x=0
There is one solutions
A researcher at the University of Washington medical school believes that energy drink consumption may increase heart rate. Suppose it is known that heart rate (in beats per minute) is normally distributed with an average of 70 bpm for adults. A random sample of 25 adults was selected and it was found that their average heartbeat was 73 bpm after energy drink consumption, with a standard deviation of 7 bpm. In order to test belief at the 10% significance level, determine P-value for the test.
Answer:
Step-by-step explanation:
Given that:
mean μ = 70
sample size = 25
sample mean = 73
standard deviation = 7
level of significance = 0.10
The null hypothesis and the alternative hypothesis can be computed as follows:
[tex]\mathtt{H_o : \mu = 70} \\ \\ \mathtt{H_1 : \mu > 70 }[/tex]
The z score for this statistics can be calculated by using the formula:
[tex]z = \dfrac{X- \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \dfrac{73- 70}{\dfrac{7}{\sqrt{25}}}[/tex]
[tex]z = \dfrac{3}{\dfrac{7}{5}}[/tex]
[tex]z = \dfrac{3 \times 5}{{7}{}}[/tex]
z = 2.143
At level of significance of 0.10
degree of freedom = n -1
degree of freedom = 25 - 1
degree of freedom = 24
The p - value from the z score at level of significance of 0.10 and degree of freedom of 24 is:
P - value = 1 - (Z < 2.143)
P - value = 1 - 0.9839
P - value = 0.0161
Decision Rule: since P value is lesser than the level of significance, we reject the null hypothesis.
Conclusion: We conclude that energy drink consumption increases heart rate.
Can somebody help me with parametric equations?
I do not have a TI-84 at the moment! Thanks!
1. Graph the following set of parametric equations on your calculator and select the matching graph.
2. Transform the given parametric equations into rectangular form. Then identify the conic.
Answer:
Attachment 1 : Graph B
Attachment 2 : Option B
Step-by-step explanation:
( 1 ) The equation x = t² - 3 is represented by exponential growth, ( t² ) so it's graph will be similar to the first graph, graph 1, in our options. Then again we have to consider the equation y = √t - 2, which will be similar to graph 4, but with a greater slope. This leaves us with a solution of graph b.
( 2 ) We have the following system of equations at hand here.
{ x = 5 cot(t), y = - 3csc(t) + 4 }
Now instead of isolating the t from either equation, let's isolate cot(t) and csc(t) --- Step #1,
x = 5 cot(t) ⇒ x - 5 = cot(t),
y = - 3csc(t) + 4 ⇒ y - 4 = - 3csc(t) ⇒ y - 4 / - 3 = csc(t)
Now let's square these two equations, adding them --- Step #2
We know that csc²θ - cot²θ = 1, so let's subtract the equations
( y - 4 / - 3 )² = (csc(t))²
- ( x - 5 / 1 )² = (cot(t))²
___________________
(y - 4)² / 9 - x² / 25 = 1
And as we are subtracting the two expressions, this is an example of a hyperbola. Therefore your solution is option b.
8 less than one-fourteenth of some number, w
Answer:
The answer is 1/14w-8
For a given confidence level, t ? df is larger than z ? . Explain how t ∗ df being slightly larger than z ∗ affects the width of the confidence interval.
Answer:
Answer is below
Step-by-step explanation:
The width of the CI is directly proportional to critical value. When t* is greater than z value, the t value would then cause the margin of error to be larger and this will in turn cause the width of the confidence interval to be larger.
Greater t*df than z* gives us a bigger margin of error. This would in turn give bigger width of confidence interval. t distribution has greater width confidence interval compared to z distribution.
The width of confidence interval is a function of the margin of error. If the critical value of t(t*) is slightly larger than the critical value of z(z*), then the width of the confidence interval will be larger.
The margin of error is the product of the critical value and the standard error. Therefore, given the same standard error value, the value of the margin of error will increases based on the value of the critical value.
Since, t* is slightly larger than z*, then the confidence interval, t will be wider.
Learn more : https://brainly.com/question/18405415
solve the following system of equations
1/2x+1/4y=-2
-2/3x+1/2y=6
x=
y=
Answer:
x = -6
y = 4
Step-by-step explanation:
Rewriting the equations :
2x + y = -84x - 3y = -36Now, solving the two equations using substitution method, we get :
x = -6
y = 4
Answer:
y = 4
x = -6
Step-by-step explanation:
1/2 x + 1/4 y= -2 first equation
-2/3 x + 1/2 y = 6 second equation
solution:
from the first equation:
8(1/2 x + 1/4 y) = -2*8
8x*1/2 + 8y*1/4 = -16
8x/2 + 8y/4 = -16
4x + 2y = -16 third equation
from the second equation
6(-2/3 x + 1/2 y) = 6*6
6x*-2/3 + 6y*1/2 = 36
-12x/3 + 6y/2 = 36
-4x + 3y = 36 fourth equation
from the third & fourth equation:
4x + 2y = -16
-4x + 3y = 36
0 + 5y = 20
5y = 20
y = 20/5
y = 4
from the fourth equation:
-4x + 3y = 36
-4x + 3*4 = 36
-4x + 12 = 36
-4x = 36 - 12
-4x = 24
x = 24/-4
x = -6
Check:
from the first equation:
1/2 x + 1/4 y = -2
1/2 *-6 + 1/4 * 4 = -2
-3 + 1 0 -2
from the second equation:
-2/3 x + 1/2 y = 6
-2/3 * -6 + 1/2 * 4 = 6
4 + 2 = 6
In an experiment to determine whether there is a systematic difference between the weights obtained with two different mass balances, six specimens were weighed, in grams, on each balance. The following data were obtained:
Specimen A B
1 13.76 13.74
2 12.47 12.45
3 10.09 10.08
4 8.91 8.92
5 13.57 13.54
6 12.74 12.75
Can you conclude that the mean weight differs between the two balances?
i). State the null and alternative hypotheses.
ii). Compute the test statistic.
iii). State a conclusion using the a =0.05 level of significance.
Answer:
H0: μd=0 Ha: μd≠0
t= 0.07607
On the basis of this we conclude that the mean weight differs between the two balances.
Step-by-step explanation:
The null and alternative hypotheses as
H0: μd=0 Ha: μd≠0
Significance level is set at ∝= 0.05
The critical region is t ( base alpha by 2 with df=5) ≥ ± 2.571
The test statistic under H0 is
t = d/ sd/ √n
Which has t distribution with n-1 degrees of freedom
Specimen A B d = a - b d²
1 13.76 13.74 0.02 0.004
2 12.47 12.45 0.02 0.004
3 10.09 10.08 0.01 0.001
4 8.91 8.92 -0.01 0.001
5 13.57 13.54 0.03 0.009
6 12.74 12.75 -0.01 0.001
∑ 0.06 0.0173
d`= ∑d/n= 0.006/6= 0.001
sd²= 1/6( 0.0173- 0.006²/6) = 1/6 ( 0.017294) = 0.002882
sd= 0.05368
t= 0.001/ 0.05368/ √6
t= 0.18629/2.449
t= 0.07607
Since the calculated value of t= 0.07607 does not falls in the rejection region we therefore accept the null hypothesis at 5 % significance level . On the basis of this we conclude that the mean weight differs between the two balances.
If x and y are two positive real numbers such that x 2 +4y 2 =17 and xy =2, then find the value of x- 2y. a. 3 b. 4 c. 8 d. 9
Answer: The value of x- 2y is a. [tex]\pm 3[/tex].
Step-by-step explanation:
Given: x and y are two positive real numbers such that [tex]x^2+4y^2=17[/tex] and [tex]xy= 2[/tex] .
Consider [tex](x-2y)^2=x^2-2(x)(2y)+(2y)^2\ \ \ [(a+b)^2=(a^2-2ab+b^2)][/tex]
[tex]=x^2-4xy+4y^2[/tex]
[tex]=x^2+4y^2-4(xy)[/tex]
Put [tex]x^2+4y^2=17[/tex] and [tex]xy= 2[/tex] , we get
[tex](x-2y)^2=17-4(2)=17-8=9[/tex]
[tex]\Rightarrow\ (x-2y)^2=9[/tex]
Taking square root on both sides , we get'
[tex]x-2y= \pm3[/tex]
Hence, the value of x- 2y is a. [tex]\pm 3[/tex].
