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2 years ago

9

Can you turn all the mixed numbers in the boxes into and improper fraction please!!!

1 answer:

zvonat [6]2 years ago

8 0

Answer:

answers are in the attached file!

Step-by-step explanation:

these are super simple to solve if you break it down! in order to turn a mixed number into an improper fraction, you first need to multiply the whole number by the <em>denominator</em> of the fraction. then, you add the numerator of the fraction to the product of the multiplication problem. that answer is then the new numerator of the fraction! the denominator will stay the same.

for example, the very first one that is given in the picture is 6 1/2. 6•2 equals 12, plus the numerator, 1, gives 13.

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4.

For this question, I think you meant

vectors

$\vec{u_1} = (-8, 12)$

$\vec{u_2} = (13, 15)$

Once

$\cos(\theta)=\dfrac{\vec{u_1} \cdot\vec{u_2}}{||\vec{u_1}||||\vec{u_2}||}$

Considering that the dot product is

$\vec{u_1}\cdot \vec{u_2} = (-8)\cdot 13 + 12\cdot 15 = -104+180= 76$

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and the norm of $\vec{u_2}$ is $||\vec{u_2}|| = \sqrt{13^2 + 15^2} = \sqrt{169 + 225}= \sqrt{394}$

Thus,

$\cos(\theta)=\dfrac{76}{\sqrt{208} \sqrt{394}} = \dfrac{19}{\sqrt{13}\sqrt{394}}=\dfrac{19}{\sqrt{5122}}$

$\therefore \theta = \arccos \left(\dfrac{19}{\sqrt{5122}} \right)$

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