Question 8. I need help !!

Select all the statements that describe the expression 5+2x.

ivanzaharov [21]

Answer:

The expression represents the sum of 5 and 2x.
The expression represents 5 plus x plus x.
The expression represents 5 plus 2 times x.

5 0

3 years ago

In the expansion of ( x^3 - 2/x^2 ) ^10 , find the coefficient of 1/x^5

Lilit [14]

Answer:

240

Step-by-step explanation:

We need to find the coeffeicent of the binomial expansion of

$( {x}^{3} - 2 {x}^{ - 2} ) {}^{10}$

Note that

$- 2 {x}^{ - 2} = - \frac{2}{ {x}^{2} }$

The binomial theorem states that

$(x + y) {}^{n} = x {}^{n} y {}^{0} + \binom{n}{1} x {}^{n - 1} y + \binom{n}{2} x {}^{n - 2} y {}^{2} ....... + x {}^{0} y {}^{n} ( \binom{n}{n} )$

Using this, we let expand our series

$( {x}^{3} - 2 {x}^{ - 2} ) {}^{10} = x {}^{30} + \binom{10}{1} ( {x}^{27} 2 {x}^{ - 2} ) + \binom{10}{2} {x}^{24} 2x {}^{ - 4} + \binom{10}{3} {x}^{21} 2x {}^{ - 6} + \binom{10}{4} {x}^{18} 2x { }^{ - 8} + \binom{10}{5} x {}^{15} 2x {}^{ - 10} + \binom{10}{6} x {}^{12}2 x {}^{ - 12} + \binom{10}{7} x {}^{ 9} 2x {}^{ - 14} + \binom{10}{8} x {}^{ 6} 2x {}^{ - 16} + \binom{10}{9} ( {x}^{3} )2x {}^{ - 18} + 2x {}^{ - 20}$

$\frac{1}{ {x}^{5} } = x {}^{ - 5}$

So what term in the series eqaul x^-5.

That term is the 10 choose 7 term.

$\binom{10}{7} {x}^{9} 2x {}^{ - 14}$

Because

$= \binom{10}{7} 2x {}^{ - 14} {x}^{9} = \binom{10}{7} 2 {x}^{ - 5}$

So we need to compute 10 choose 7.

That equals

10!/3!(7!)= 10×9×8/6= 720/6=120.

So we get

$120(2) {x}^{ - 5}$

$240 {x}^{ - 5}$

So the coeffceint u

is 240

3 0

3 years ago

15 POINTS please help!

BlackZzzverrR [31]

Answer: is the day you are going to be a little while now and then you

Step-by-step explanation:

is it a little while to get to the bar graph and then I will be home in a little while I am going to

8 0

3 years ago

Find the equation of a straight line that is perpendicular to 5x–y=1 and is such that the area of the triangle formed by the x-

nexus9112 [7]

Answer: $y = -\frac{1}{5}x+\sqrt{2}$

This is approximately the same as $y = -\frac{1}{5}x+1.41$

===============================================

Explanation:

Solve the given equation for y

5x-y = 1

-y = -5x+1

y = 5x-1

slope of this line is m = 5 since it is in the form y = mx+b

Write m = 5 as m = 5/1

Flip the fraction: 5/1 ----> 1/5

Flip the sign: 1/5 ----> -1/5

The perpendicular slope is -1/5

---------------------------

Let p and q be the x and y intercepts

So the equation we're after goes through the points (p,0) and (0,q)

The slope of the line through these points is

m = (y2-y1)/(x2-x1)

m = (q-0)/(0-p)

m = q/(-p)

m = -q/p

We want this slope to be -1/5 as this is the perpendicular slope we found earlier

-q/p = -1/5

q/p = 1/5

5q = 1p

p = 5q ... we will use this later

---------------------------

The base of the triangle is p while the height is q

We want the area of the triangle to be 5 square units

area = 0.5*base*height

5 = 0.5*p*q

5 = 0.5*(5q)*q ... plug in p = 5q

5 = 2.5q^2

2.5q^2 = 5

q^2 = 5/2.5

q^2 = 2

q = sqrt(2)

p = 5*q

p = 5*sqrt(2)

The y intercept is b = q = sqrt(2), so

y = mx+b

$y = -\frac{1}{5}x+\sqrt{2}$

See the diagram below.

5 0

3 years ago

I would really appreciate some help

Len [333]

Answer:

A or x = 1

Step-by-step explanation:

So we can see from the most right column that the sum of the three number is 9 (2 + 4 + 3) so we know that every row or column has to add up to 9. We want to find x so we must make sure that, 8 + 0 + x should be 9 and 2 + 6 + x should be 9. From 8 + 0 + x, we know that 8 + 1 is 9 so x is 1. We can also see that 2 + 6 is 8 and 8 + 1 is 9 so x = 1.

3 0

3 years ago