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2 years ago

Replace the * with a monomial so that the trinomial may be represented by a square of a binomial:

Mathematics

1 answer:

pogonyaev2 years ago

8 0

Answer:

Below in bold.

Step-by-step explanation:

The identity is of the form

(a + b)^2 = a^2 + 2ab + b^2.

a) Sqrt 49 = 7 and we need + 28 as the middle coefficient . We get this with

2*7 + 2*7 so the first coefficient is 2*2 = 4.

So * = 4a^2.

(2a + 7)^2 = (2a + 7)(2a + 7) = 4x^2 + 14a + 14a + 49.

b) -6 * -6 = 36 -24 = 2*-6 + 2 *-6 so the last term is 4x^2

c) The middle term must be an 'ab' term.

sqrt 6.25 = 2.5 and sqrt 1/4 = 1/2

So the coefficient of the middle term is 2.5 * 1/2 + 2.5 * 1/2

= 2.5

So the middle term is 2.5ab.

d) The first term will be in b^2.

100 = 10* 10 and we need 2 as a middle term so coefficient of the first term

will be 1/100 or 0.01. as the 2 comes from 0.1 * 10 + 0.01 * 10 and (0.1)^2 = 0.01

So it is 0.01b^2.

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Please consider the following values for the variables X and Y. Treat each row as a pair of scores for the variables X and Y (wi

Studentka2010 [4]

Answer:

The Pearson's coefficient of correlation between the is 0.700.

Step-by-step explanation:

The correlation coefficient is a statistical degree that computes the strength of the linear relationship amid the relative movements of the two variables (i.e. dependent and independent).It ranges from -1 to +1.

The formula to compute correlation between two variables X and Y is:

$r(X, Y)=\frac{Cov(X, Y)}{\sqrt{V(X)\cdot V(Y)}}$

The formula to compute covariance is:

$Cov(X, Y)=n\cdot \sum XY-\sum X \cdot\sum Y$

The formula to compute the variances are:

$V(X)=n\cdot\sum X^{2}-(\sum X)^{2}\\V(Y)=n\cdot\sum Y^{2}-(\sum Y)^{2}$

Consider the table attached below.

Compute the covariance as follows:

$Cov(X, Y)=n\cdot \sum XY-\sum X \cdot\sum Y$

$=(5\times 165)-(30\times 25)\\=75$

Thus, the covariance is 75.

Compute the variance of X and Y as follows:

$V(X)=n\cdot\sum X^{2}-(\sum X)^{2}\\=(5\times 226)-(30)^{2}\\=230\\\\V(Y)=n\cdot\sum Y^{2}-(\sum Y)^{2}\\=(5\times 135)-(25)^{2}\\=50$

Compute the correlation coefficient as follows:

$r(X, Y)=\frac{Cov(X, Y)}{\sqrt{V(X)\cdot V(Y)}}$

$=\frac{75}{\sqrt{230\times 50}}$

$=0.69937\\\approx0.70$

Thus, the Pearson's coefficient of correlation between the is 0.700.

5 0

3 years ago

Dale works at a mattress store, and makes a salary plus commission. He has a $500 weekly salary and makes a 5% commission for sa

Anni [7]

Answer:

1. $\( f\circ g(x)=0.05x-150$

2. $\( g\circ f(x)=0.05x-3000$

3. The first one represents Dale's commission

Explanation:

1. The composition of the function

$f\circ g(x)=f(g(x))$

means that you first apply the function g(x) and then f(x) on the output of g(x).

That is:

f(x) = 0.05x
g(x) = x - 3000

$f(g(x)=0.05(x - 3000)$

$f(g(x))=0.05x-150$

2. The composition of the function

$g\circ f(x)=g(f(x))$

means that you first apply the function f(x) and then g(x) on the output of f(x).

That is:

$g(f(x))=((0.05x)-3000)=0.05x-3000$

3. Which one represents Dale's commission

To calculate Dales's commision you must subtract $3,000 from the sales, to find the sales over $3000. That is: x - 3,000, which is the function g(x).

Therefore, you first use g(x).

Then, you must multiply the output of g(x) by 0.05 to find the 5% of the sales over $3,000. That is: 0.05(g((x)) = 0.05(x - 3000) = 0.05x - 150.

Therefore, the composition that represents Dale's commission is the first one:

$f(g(x)=0.05(x - 3000)$

$f(g(x))=0.05x-150$

4 0

3 years ago

Whatis the value of x in the equation x - y = 30, when y = 15? 8

Ostrovityanka [42]

Answer:

x=45

Step-by-step explanation:

30+15=45

4 0

3 years ago

What is the answer to the equation -7x-3x+2= -8x - 8

timama [110]

Answer:

x=5

Step-by-step explanation:

-7x-3x+2= -8x - 8

Add like terms

-7x-3x=-10x

-10x+2=-8x-8

+8x +8x

-2x+2=-8

-2 -2

-2x=-10

Divide by -2 to isolate the variable

x=5

7 0

2 years ago

Read 2 more answers

What is the value of -9 + (-4 + 7) (2)?

RUDIKE [14]

Answer:

try -3

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers