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valina [46]
3 years ago
13

G) 145

Mathematics
1 answer:
miskamm [114]3 years ago
4 0

Answer:

To convert binary into decimal, multiply each binary digit with a power of 2 corresponding to its position.

So for example 1010 would be 1·2³ + 0·2² + 1·2¹ + 0·2⁰ = 8+2 = 10 in decimal.

now you can calculate the answers yourself!

To convert decimal into binary, you can use the following approach:

Write down the answer from right to left

A. if your number is odd, write down a 1, if it is even, write a 0

B. divide the number by 2 and round down, ie. discard any decimals (e.g., 7 / 2 = 3)

C. repeat step A until your number is 0.

example:

18 -> write down 0

18/2 = 9 -> write down 1

9/2 = 4 -> write down 0

4/2 = 2 -> write down 0

2/2 = 1 -> write down 1

1/2 = 0 finished

The result is 10010.

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Find the length of the hypotenuse of a right triangle whose legs are 5 and √2.
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Answer:

\sqrt{27}

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let h represent the hypotenuse, then

h² = 5² + (\sqrt{2} )² = 25 + 2 = 27 ( take the square root of both sides )

h = \sqrt{27} ← exact value

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If the squared difference of the zeroes of the quadratic polynomial x2+kx+30 is equal to 169 find the value of k and the zeroes
anyanavicka [17]

ANSWER

x  =  2 \: \: or \:  \:  x  =  15

Or

x  =   - 2 \: \: or \:  \:  x  =   -  15

EXPLANATION

The given polynomial is

f(x) = {x}^{2}  + kx + 30

where a=1,b=k, c=30

Let the zeroes of this polynomial be m and n.

Then the sum of roots is

m + n =  -  \frac{b}{a}  =  -k

and the product of roots is

mn =  \frac{c}{a}  = 30

The square difference of the zeroes is given by the expression.

( {m - n})^{2} =  {(m + n)}^{2} - 4mn

From the question, this difference is 169.

This implies that:

( { - k)}^{2}  - 4(30) = 169

{  k}^{2}  -120= 169

k^{2} = 289

k=  \pm \sqrt{289}

k=  \pm17

We substitute the values of k into the equation and solve for x.

f(x) = {x}^{2}   \pm17x + 30

f(x) = (x  \pm2)(x  \pm 15)

The zeroes are given by;

(x  \pm2)(x  \pm 15) = 0

x  =  \pm2 \: \: or \:  \:  x  =  \pm 15

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