All categories

3 years ago

The factorization of (x+y)^2+2(x+y)+1 isplease answer

Mathematics

2 answers:

Schach [20]3 years ago

8 0

Step-by-step explanation:

Using:(a+b) ² =a²+2ab+b²

Hope it is helpful to you

solong [7]3 years ago

3 0

Answer:

$(x + y+ 1)^2$

Step-by-step explanation:

$Using : (a + b)^2 = a^2 + 2ab + b^2\\\\(x+ y)^2 + 2(x +y) + 1 , \ where \ a = (x+y) , \ b = 1 \\\\= (x +y)^2 + ( 2 \times 1 \times (x+y)) + 1^2\\\\= (x +y+ 1)^2$

You might be interested in

How was the United States doing in the years

Musya8 [376]

Answer:

up down down down

Step-by-step explanation:

due to the governments high spending the employment was down because the gov. couldn't afford to pay its workers, so many were laid off and also due to the spending wages were low, and the economy was down because of the little amount of buisness.

3 0

3 years ago

Read 2 more answers

When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%. Let

sergiy2304 [10]

Answer:

(a) P(X=3) = 0.093

(b) P(X≤3) = 0.966

(c) P(X≥4) = 0.034

(d) P(1≤X≤3) = 0.688

(e) The probability that none of the 25 boards is defective is 0.277.

(f) The expected value and standard deviation of X is 1.25 and 1.089 respectively.

Step-by-step explanation:

We are given that when circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%.

Let X = the number of defective boards in a random sample of size, n = 25

So, X ∼ Bin(25,0.05)

The probability distribution for the binomial distribution is given by;

$P(X=r)= \binom{n}{r} \times p^{r}\times (1-p)^{n-r} ; x = 0,1,2,......$

where, n = number of trials (samples) taken = 25

r = number of success

p = probability of success which in our question is percentage

of defectivs, i.e. 5%

(a) P(X = 3) = $\binom{25}{3} \times 0.05^{3}\times (1-0.05)^{25-3}$

= $2300 \times 0.05^{3}\times 0.95^{22}$

= 0.093

(b) P(X $\leq$ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= $\binom{25}{0} \times 0.05^{0}\times (1-0.05)^{25-0}+\binom{25}{1} \times 0.05^{1}\times (1-0.05)^{25-1}+\binom{25}{2} \times 0.05^{2}\times (1-0.05)^{25-2}+\binom{25}{3} \times 0.05^{3}\times (1-0.05)^{25-3}$

= $1 \times 1 \times 0.95^{25}+25 \times 0.05^{1}\times 0.95^{24}+300 \times 0.05^{2}\times 0.95^{23}+2300 \times 0.05^{3}\times 0.95^{22}$

= 0.966

(c) P(X $\geq$ 4) = 1 - P(X < 4) = 1 - P(X $\leq$ 3)

= 1 - 0.966

= 0.034

(d) P(1 ≤ X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3)

= $\binom{25}{1} \times 0.05^{1}\times (1-0.05)^{25-1}+\binom{25}{2} \times 0.05^{2}\times (1-0.05)^{25-2}+\binom{25}{3} \times 0.05^{3}\times (1-0.05)^{25-3}$

= $25 \times 0.05^{1}\times 0.95^{24}+300 \times 0.05^{2}\times 0.95^{23}+2300 \times 0.05^{3}\times 0.95^{22}$

= 0.688

(e) The probability that none of the 25 boards is defective is given by = P(X = 0)

P(X = 0) = $\binom{25}{0} \times 0.05^{0}\times (1-0.05)^{25-0}$

= $1 \times 1\times 0.95^{25}$

= 0.277

(f) The expected value of X is given by;

E(X) = $n \times p$

= $25 \times 0.05$ = 1.25

The standard deviation of X is given by;

S.D.(X) = $\sqrt{n \times p \times (1-p)}$

= $\sqrt{25 \times 0.05 \times (1-0.05)}$

= 1.089

8 0

3 years ago

3. Given the following similar triangles. Find the values of variables and label all the unknown angles

astraxan [27]

Answer:

The answer to your question is x = 6 and y = 9

Step-by-step explanation:

Data

AB = x DF = 18

BC = 5 FE = 15

AC = 3 DE = y

Process

1.- Find y

Use proportions to find it

DE/FE = AC/BC

Substitution

y/15 = 3/5

Solve for y

y = 15(3/5)

y = 45/5

y = 9

2.- Find x

AB/DF = BC/FE

Substitution

x/18 = 5/15

Solve for x

x = 18(5/15)

x = 90/15

x = 6

8 0

3 years ago

Choose the appropriate table for the differential equation dy/dx=x+1/x

kenny6666 [7]

Answer: 1.

x |0|0.5|2

dy/dx |2|5 |undefined

x |0 |0.5| 2

dy/dx |undefined|5 | 2

x | 0 |0.5|2

dy/dx|undefined |4 |2

Step-by-step explanation:

7 0

2 years ago

Five WHOLE numbers are written in order

tino4ka555 [31]

x = 7

y = 8

All I did was assume x was 7 and y was 8. I added 4, 6, 7, 8, and 10 together. I got 35. Then, I divided by five (since that's how many numbers are shown) and I got 7 for the mean. 7 is the median, and the 7 is the mean gotten from 4, 6, 7, 8, and 10. Therefore, x must equal 7 and y must equal 8.

4 0

2 years ago

The factorization of (x+y)^2+2(x+y)+1 isplease answer​

The factorization of (x+y)^2+2(x+y)+1 isplease answer