What is 78 million in scientific notation?

Please answer the question above.

kenny6666 [7]

Answer:

5.3!

Step-by-step explanation:

( in case you need work ) the angles are congruent so you set them equal to each other!

6x+12=9x-4

you then get 16=3x then divided its 5.3!

8 0

3 years ago

What is the coefficient of the x^5y^5- term in the biomial expansion of (2x-3y)^10

jasenka [17]

Answer:

The coefficient of $x^{5} \times y^{5} \text { is }=\left(252 \times 2^{5} \times(-3)^{5}\right)=252 \times 32 \times 243=1959552$

Solution:

The given expression is $(2 x-3 y)^{10}$

As per binomial theorem, we know,

$(x+y)^{n}=\sum n C_{k} x^{n-k} y^{k}$

Now here a = 2x, b = (- 3y) and n = 10 and k = 0,1,2,….10

Now $x^{5}\times y^5$ will be the 6 term where k =5

Now, $\mathrm{T}_{6}=10 \mathrm{C}_{5} \times(2 \mathrm{x})^{(10-5)} \times(-3 \mathrm{y})^{5}=10 \mathrm{C}_{5} 2^{5} \times \mathrm{x}^{5} \times(-3)^{5} \times \mathrm{y}^{5}$

So, the coefficient of $x^{5} \times y^{5} \text { is }=10\left(5 \times 2^{5} \times(-3)^{5}\right$ .

$10 \mathrm{C}_{5}=\frac{10 !}{5 ! \times(10-5) !}=\frac{10 !}{5 !+5 !}=\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 !}{5 ! \times 5 !}=\frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2 \times 1}=\left(\frac{30240}{120}\right)=252$

The coefficient of $x^{5} \times y^{5} \text { is }=\left(252 \times 2^{5} \times(-3)^{5}\right)=252 \times 32 \times 243=1959552$

6 0

3 years ago

Determine whether 81a2 − 25z6 is a difference of two squares. If so, factor it. If not, explain why.

aev [14]

81 a² - 25 $z^{6}$ is a difference of two squares and its factors are (9a + 5z³) and (9a - 5z³)

Step-by-step explanation:

The difference of two squares is a binomial of two terms each term is a square and the sign between the two terms is (-), its factorization is the product of two identical binomials with different middle signs