Tìm x<br> a) (x+3)²+(x-2)²=2x²

Calculate gcd(77, 30) by using the Euclidean algorithm. Find also integers u and v such that 49u + 30v = 1. Furthermore, find su

VladimirAG [237]

Answer:

1. gcd(77,30)=1

$77=2*30+17\\30=1*17+13\\17=1*13+4\\13=3*4+1\\4=4*1+0$

Since 1 is the last non zero remainder appearing in these equations then, 1 is the gcd of 77 and 30.

2. u=-11, v=18

Using the Euclidean Algorithm we have that

$49=1*30+19\\30=1*19+11\\19=1*11+8\\11=1*8+3\\8=2*3+2\\3=1*2+1\\2=1*2+0$

Now, we express the remainder as linear combinations of 49 and 30.

$1&=3-2\\ &=3-(8-2*3)=3-8+2*3\\&=(11-8)-8+2(11-8)=3*11-4*8\\&=3*11-4(19-11)=7*11-4*19\\&=7(30-19)-4*19=7*30-11*19\\&=7*30-11(49-30)=\\&=18*30-11*49$

Then $1=(-11)49+18*30$

3. x=18

If $30x\equiv 1\text{mod 77}$ then

$30x=k*77+1$ for some $k\in \mathbb{Z}$ .

Then, if k=7,

$30x=7*77+1=540\\x=\frac{540}{30}=18$

6 0

3 years ago

In △ABC, point P∈ AC with AP:PC=1:3, point Q∈AB so that AQ:QB=3:4, Find the ratios APBQ : APBC and AAQP : AABC.

weqwewe [10]

Answer: The ratios APBQ : APBC=4:21 and AAQP : AABC= 3:28

Explanation:

Here, ABC is a triangle where, P and Q are the midpoints of the edges AC and AB respectively,

Now, according to the question ,AP:PC=1:3 let AP=x and PC=3x where x is any real number. Thus, AC=AP+AC= x+3x= 4x

Similarly, AQ:QB=3:4 let AQ=3y and QB=4y where y is also any real number. Thus, AB=AQ+QB=3y+4y=7y

Since, $\frac{AP.BQ}{AP.BC} =\frac{AP.BQ}{AB.PC} =\frac{x.4y}{7y.3x} =\frac{4xy}{21xy} =\frac{4}{21}$

And, $\frac{AA.QP}{AA.BC} =\frac{AQ.AP}{AB.AC} =\frac{3y.1x}{7y.4x} =\frac{3xy}{28xy} =\frac{3}{28}$

5 0

4 years ago

If your looking for 50 points + brainiest answer this question correctly plz. thanks

jonny [76]

Answer:

Option 3, 57+32=32+57

Step-by-step explanation:

Communitive Property of Addition is where the equation is the same except the numbers swap places. In this case, that would be 57+32=32+57.

If this answer has helped you, please mark this as brainliest

4 0

3 years ago

Read 2 more answers

A researcher is concerned that graduate students get less than the recommended 8 hours of sleep a night. She selects a random sa

dsp73

Answer:

H0 : μ = 8

H1 : μ < 8

Test statistic = - 7.51

conclude that there is statistical significance that student at the school get less than 8 hours of sleep on average.

Step-by-step explanation:

The hypothesis :

H0 : μ = 8

H1 : μ < 8

The test statistic :

(xbar - μ) ÷ (s/√(n))

Sample data :

1.75, 2, 2.25, 2.25, 2.5, 3, 3.5, 3.5, 3.5, 3.75, 4, 4.25, 4.5, 4.5, 4.5, 4.75, 5.25, 5.5, 5.75, 5.75, 5.75, 6, 6, 6, 6.25, 6.25, 6.25, 6.5, 6.5, 6.5, 6.75, 7, 7, 7, 7.5, 7.5, 7.75, 8, 8.25, 8.25, 8.25, 8.5, 8.75, 9, 9

Using calculator :

Sample mean, xbar = 5.71666

Sample standard deviation, s = 2.04

The test statistic :

(5.7166 - 8) ÷ (2.04/√(45))

-2.28 / 0.3041052

= - 7.5085

= - 7.51

Degree of freedom = 45 - 1 = 44

Pvalue(-7.51, 44) = 0.00001

α = 1% = 0.01

Since Pvalue < α ; we reject H0 and conclude that there is statistical significance that student at the school get less than 8 hours of sleep on average.

4 0

3 years ago

Find 1112+(−712)1112+(−712). Write your answer as a fraction in simplest form.

Julli [10]

I got -791344 or -791344/1

6 0

4 years ago

Read 2 more answers

Tìm x a) (x+3)²+(x-2)²=2x²