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3 years ago

Can someone help me with these

Mathematics

2 answers:

lisov135 [29]3 years ago

8 0

Answer:

number 5 The fraction 3/8 as a decimal is 0.375.

Step-by-step explanation:

vladimir1956 [14]3 years ago

5 0

Remember that: irrational numbers repeat and cannot be put into fractions.

1) C or 1/2, Since it is expressed as a fraction you know it is rational.

2) D or sqrt 61, Well, it's not -5 since it's a whole number, basic multiplication tells you the square root of 36 is 6 which is also a whole number, and 2/3 is a fraction, so using process of elimination this is the only option left.

3) quotient Since rational numbers can be written as fractions, 1/4 is the same as dividing 1 by 4.

4) repeat As explained earlier, repeating decimals cannot be made into fractions, therefore not making them rational.

5) 0.375 3 divided by 8 is equal to 0.375.

I hope this helped you and have a great rest of your day!

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Help me asap! I will give you marks

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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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Step-by-step explanation:

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3 years ago

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Answer:

Let x be the number of silver medals.

As there were two more gold medals than silver ones, gold medals are x+2

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