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3 years ago

-2/5 - 4/5 + -9/10 = ??? Please help, will mark brainliest for answer with an explanation

Mathematics

1 answer:

NeX [460]3 years ago

5 0

Answer:

Step-by-step explanation:

-2/5 - 4/5 + -9/10

= -2/5 - 4/5 - 9/10

= {-2(2) -4(2) - 9)/10

= (-4 - 8 - 9)/10

= -21/10

= -2 1/10

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Factor trinomial x^2n+10x^n+16

iragen [17]

Answer:

$\large\boxed{x^{2n}+10x^n+16=(x^n+2)(x^n+8)}$

Step-by-step explanation:

$\text{Use}\ (a^n)^m=a^{nm}.\\\\x^{2n}+10x^n+16=(x^n)^2+10x^n+16=x^n\cdot x^n+2x^n+8x^n+16\\\\=x^n(x^n+2)+8(x^n+2)=(x^n+2)(x^n+8)$

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2 years ago

What is the coefficient of x2y3 in the expansion of (2x + y)5?

Zigmanuir [339]

Option C:

The coefficient of $x^{2} y^{3}$ is 40.

Solution:

Given expression:

$(2 x+y)^{5}$

Using binomial theorem:

$(a+b)^{n}=\sum_{i=0}^{n}\left(\begin{array}{l}n \\i\end{array}\right) a^{(n-i)} b^{i}$

Here $a=2 x, b=y$

Substitute in the binomial formula, we get

$(2x+y)^5=\sum_{i=0}^{5}\left(\begin{array}{l}5 \\i\end{array}\right)(2 x)^{(5-i)} y^{i}$

Now to expand the summation, substitute i = 0, 1, 2, 3, 4 and 5.

$$=\frac{5 !}{0 !(5-0) !}(2 x)^{5} y^{0}+\frac{5 !}{1 !(5-1) !}(2 x)^{4} y^{1}+\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}+\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}$

$$+\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}+\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}$

Let us solve the term one by one.

$$\frac{5 !}{0 !(5-0) !}(2 x)^{5} y^{0}=32 x^{5}$

$$\frac{5 !}{1 !(5-1) !}(2 x)^{4} y^{1} = 80 x^{4} y$

$$\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}= 80 x^{3} y^{2}$

$$\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}= 40 x^{2} y^{3}$

$$\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}= 10 x y^{4}$

$$\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}=y^{5}$

Substitute these into the above expansion.

$(2x+y)^5=32 x^{5}+80 x^{4} y+80 x^{3} y^{2}+40 x^{2} y^{3}+10 x y^{4}+y^{5}$

The coefficient of $x^{2} y^{3}$ is 40.

Option C is the correct answer.

5 0

2 years ago

Find the value of x

olya-2409 [2.1K]

Answer:

A) 33

Step-by-step explanation:

180 - 105= 75

75 + 72 + x = 180

147 + x = 180

x= 33

3 0

2 years ago

Let p =Vector F G where F(0, 5) and G(–4, –3). What is the direction angle of Negative three-halves p?

Harlamova29_29 [7]

Answer:

63 Degrees

Step-by-step explanation:

Edge 2020

3 0

2 years ago

Read 2 more answers

Which of the following is a correct equation for the line passing through the point (-2,1) and having slope m= 1/2?

Taya2010 [7]

Incomplete Question the complete Qs is

Which of the following is a correct equation for the line passing through the point (-2,1) and having slope m = 1/2?

a: y=1/2x+2

b: y=-2x+1/2

c: x-2y=-4

d: y-1=1/2(x+2)

Answer:

The Correct option is c. x-2y=-4

Therefore the correct equation for the line passing through the point (-2,1) and having slope m= 1/2 is

$x-2y=-4$

Step-by-step explanation:

Given:

$Slope = m =\dfrac{1}{2}$

point A(x₁, y₁)=(-2,1)

To Find:

Equation of Line =?

Solution:

Equation of a line passing through a points A( x₁ , y₁) and having slope m is given by the formula,

i.e equation in point - slope form

$(y-y_{1})=m(x-x_{1})$

Now on substituting the slope and point A( x₁ , y₁) ≡ ( -2 , 1) we get

$(y-1)=\dfrac{1}{2}(x-(-2))\\\\2y-2=x+2\\x-2y=-2-2=-4\\x-2y=-4$ As required

Therefore the correct equation for the line passing through the point (-2,1) and having slope m= 1/2 is

$x-2y=-4$

6 0

2 years ago