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3 years ago

Which object has the mass of about one kilogram?

Mathematics

1 answer:

Step2247 [10]3 years ago

7 0

Answer:

A book about a mass of 1 kilogram, but that isn't the only answer.

Explanation:

There's many objects with a mass of one kilogram like one liter of water, a pineapple, bag of sugar etc.

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Suppose h(x)=3x-2 and j(x) = ax +b. Find a relationship between a and b such that h(j(x)) = j(h(x))

sergejj [24]

Answer:

$\displaystyle a = \frac{1}{3} \text{ and } b = \frac{2}{3}$

Step-by-step explanation:

We can use the definition of inverse functions. Recall that if two functions, f and g are inverses, then:

$\displaystyle f(g(x)) = g(f(x)) = x$

So, we can let j be the inverse function of h.

Function h is given by:

$\displaystyle h(x) = y = 3x-2$

Find its inverse. Flip variables:

$x = 3y - 2$

Solve for y. Add:

$\displaystyle x + 2 = 3y$

Hence:

$\displaystyle h^{-1}(x) = j(x) = \frac{x+2}{3} = \frac{1}{3} x + \frac{2}{3}$

Therefore, a = 1/3 and b = 2/3.

We can verify our solution:

$\displaystyle \begin{aligned} h(j(x)) &= h\left( \frac{1}{3} x + \frac{2}{3}\right) \\ \\ &= 3\left(\frac{1}{3}x + \frac{2}{3}\right) -2 \\ \\ &= (x + 2) -2 \\ \\ &= x \end{aligned}$

And:

$\displaystyle \begin{aligned} j(h(x)) &= j\left(3x-2\right) \\ \\ &= \frac{1}{3}\left( 3x-2\right)+\frac{2}{3} \\ \\ &=\left( x- \frac{2}{3}\right) + \frac{2}{3} \\ \\ &= x \stackrel{\checkmark}{=} x\end{aligned}$

3 0

2 years ago

What is the least common multiple of 8 and 9? Enter your answer in the box.

Contact [7]

Answer:

Step-by-step explanation:

The LCM is when you find the lowest factor that 2 or more numbers share.

For 8 and 9,you would just need to keep multiplying each other until you find the same numbers. It would look something like this.

8,16,24,32,40,48,56,64,72..... etc.

9,18,27,36,45,54,63,72,81..... etc.

You can see how they both have the same factor (72), and since that is the lowest factor (which means I can find a lower factor then 72) then your LCM of 8 and 9 should be 72 :)

4 0

2 years ago

M∠1=119∘ and m∠2=61∘. What is m∠3?

marin [14]

Answer:

m∠3 = 119°

Step-by-step explanation:

All the angles must equal 360° when added together. You have two known angles that are right next to each other. If you add m∠1 and m∠2, 119 + 61, it is equal to 180°. This means that m∠3 and m∠4 must be equal to 180° as well and since there are only two lines, it is safe to assume that opposing angles are the same so m∠1 = m∠3 and m∠2 = m∠4.

4 0

2 years ago

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What does 9y =27 equation mean

MrRa [10]

9y=27

divide by 9 each side

9y/9y=27/9

y=3

4 0

3 years ago

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