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2 years ago

The slope in decimal form ?

Mathematics

2 answers:

Jet001 [13]2 years ago

5 0

Answer:

-2

Step-by-step explanation:

Let's get two coordinate points and plug into the slope equation.

(1,2) and (.5,1)

$(y_{2} - y_{1}) / (x_{2} - x_{1} )$

(1-2) / (.5 - 1)

1 / (-.5)

-2

bogdanovich [222]2 years ago

4 0

Answer:

Step-by-step explanation:

Look at two points on the graph that are easy to read.

(0, 0) and (1, 2) are on the graph and are easy to read.

slope = (y2 - y1)/(x2 - x1) = (2 - 0)/(1 - 0) = 2/1 = 2

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Factor 3/4 out of 3/4z+6.

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Step-by-step explanation:

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2 years ago

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

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

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