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Vedmedyk [2.9K]
1 year ago
6

Help me asap! I will give you marks

Mathematics
1 answer:
Law Incorporation [45]1 year ago
6 0

Recall the binomial theorem.

(a+b)^n = \displaystyle \sum_{k=0}^n \binom nk a^{n-k} b^k

1. The binomial expansion of \left(1+\frac x3\right)^7 is

\left(1 + \dfrac x3\right)^7 = \displaystyle\sum_{k=0}^7 \binom 7k 1^{7-k} \left(\frac x3\right)^k = \sum_{k=0}^7 \binom 7k \frac{x^k}{3^k}

Observe that

k = 1 \implies \dbinom 71 \left(\dfrac x3\right)^1 = \dfrac73 x

k = 2 \implies \dbinom 72 \left(\dfrac x3\right)^2 = \dfrac73 x^2

When we multiply these by 8-9x,

• 8 and \frac73 x^2 combine to make \frac{56}3 x^2

• -9x and \frac73 x combine to make -\frac{63}3 x^2 = -21x^2

and the sum of these terms is

\dfrac{56}3 x^2 - 21x^2 = \boxed{-\dfrac73 x^2}

2. The binomial expansion is

\left(2a - \dfrac b2\right)^8 = \displaystyle \sum_{k=0}^8 \binom 8k (2a)^{8-k} \left(-\frac b2\right)^k = \sum_{k=0}^8 \binom 8k 2^{8-2k} a^{8-k} b^k

We get the a^6b^2 term when k=2 :

k=2 \implies \dbinom 82 2^{8-2\cdot2} a^{8-2} b^2 = 28 \cdot2^4 a^6 b^2 = \boxed{448} \, a^6b^2

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paul bought a soft and a sandwich for 9.90. what equation may be used to find the price of each item if the sandwich cost 3.5 ti
irina [24]

So, let's say the soft drink equals y and the sandwich equals x.

x + y = 9.9

The sandwich costs 3.5 times as much as the soft drink

x = 3.5y

Therefore, we can replace x with 3.5y since they're the same thing

3.5y + y = 9.9  <-- That's the equation :)


3 0
3 years ago
The vertices of a triangle are labeled clockwise A(–5, 3), B(6, 1), and C(–2, –3). How could you show that the figure is a right
mafiozo [28]

Explanation:

When the points are plotted on a graph, it is easy to see that the slope of AC is -2 and the slope of BC is 1/2. These slope values have a product of -1, so the corresponding line segments are perpendicular to each other.

___

If you have studied vectors, you can find the dot product of AC with BC:

  AC = (-5, 3) -(-2, -3) = (-3, 6)

  BC = (6, 1) -(-2, -3) = (8, 4)

The dot product is ...

  (-3, 6)·(8, 4) = (-3)(8) + (6)(4) = -24+24 = 0

When the dot product of vectors is zero, they are perpendicular.

5 0
3 years ago
Which multiplication expression is equivalent to<br>6+ (6) + 16)​
IrinaK [193]

Answer:

isn't it 28

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
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Answer: V = 1512 cm3

Step-by-step explanation:

3 0
3 years ago
Use completing the square to solve the equation x^2 0 10x = 08.
wariber [46]
Ok so assuming the 0 means minus from typing problems

x^2-10x=-8

to completet  the square
make sure the term in front of x^2 is 1
that is correct
then take 1/2 of the term in front of the x term and square it
-10/2=-5, (-5)^2=25
add that to both sides
x^2-10x+25=17


answer is the first equation
4 0
3 years ago
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