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3 years ago

11

The temperature at 7:00 a.m. was –5°F. By 4:00 p.m., the temperature had risen 9 degrees and by 10:00 p.m. the temperature dropp

ed 11 degrees. What was the temperature at 10:00 pm

1 answer:

ivanzaharov [21]3 years ago

5 0

Answer:

-7 degrees

Step-by-step explanation:

-5+9-11=-7

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

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<u>Answer:</u>

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<u>Solution: </u>

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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the measurements of a photo and it's frame are shown in the diagram. Write a polynomial that represents the width of the photo.

suter [353]

Answer:

The width of the photo is $4w^2+6w+4$ .

Step-by-step explanation:

From the given figure it is notices that the total width of the frame is

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3 years ago