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3 years ago

What are the values of a and b?

Mathematics

1 answer:

krok68 [10]3 years ago

7 0

Answer:a=8; b=40

Step-by-step explanation:answer d is correct

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Help me asap! I will give you marks

Law Incorporation [45]

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 $k=2$ :

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

6 0

1 year ago

Which statements are true about these lines? Check all that apply. Line RS has a slope of 6. Line SW has an undefined slope. Lin

brilliants [131]

Line SW is perpendicular to line RS, but not to line TV

3 0

3 years ago

Read 2 more answers

Can someone please help me?

Pachacha [2.7K]

Hello there!

So, remember that m = the slope, and slope intercept form is represented as y = mx + b. To find the y intercept, place the values of x, y, and the slope into the equation.

The first step, ____ = (____)____ + b should look like 3 = (2/5)10 + b once you plug the values for your x and y values and slope.

The second step, ___ = ____ + b should look like 3 = 4 + b since you should multiply 2/5 x 10.

The final step, -1 = b should look like since you subtracted 4 from both sides of the equation.

Y = 2/5x - 1 is your final equation. I hope this helps, have a great rest of your day!

7 0

2 years ago

Find the difference. Enter your answer in simplest terms, using the slash (/) as the fraction bar.

Kitty [74]

So, difference as in subtract? so, if it is, it would be 15. if it means percent difference, it's about 60%.

3 0

3 years ago

What is 2 1/6 * 1 1/4 equal too

timofeeve [1]

Hmmm idk if you want fractions but, 65/24 or 2 17/24 I think

6 0

3 years ago