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2 years ago

Explain how you can use multiplication to show that two-fourths and four-eighths are equivalent.

Mathematics

1 answer:

ANTONII [103]2 years ago

3 0

Answer:

2/4 and 4/8 are equivalent because you can use the butterfly method of multiplication. Meaning you multiply the numerator by the other fractions denominator and vis-versa.

Step-by-step explanation:

2 x 8 = 16

4 x 4 = 16

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NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! THIS IS NOT A TEST OR AN ASSESSMENT!! Please help me with these math questions

Art [367]

Answer:

See below

Step-by-step explanation:

3. What are two ways that a vector can be represented?

Considering a vector $\vec{v}$ in some vector space $\mathbb R^n$ we have

$\vec{v} = \langle a,b\rangle$

This is the component form. I don't like that way. It is probably used in high school, but

$\vec{v} = \begin{pmatrix} a\\ b\\ \end{pmatrix}$

is preferable because the inner product on $\mathbb R^n$ is defined to be

$\langle a,b\rangle := \sum_{i = 1}^n a_i b_i$

You can also write it using linear form such as $\vec{v} = 2i+2j$

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

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

and the norm of $\vec{u_1}$ is $||\vec{u_1}|| = \sqrt{(-8)^2 + 12^2} = \sqrt{64 + 144}= \sqrt{208}$

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

Thus,

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

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

3 0

2 years ago

Without looking, Luke picks necklace beads from a bag of 52 beads. Half the beads are rough. The other half are smooth. There ar

xz_007 [3.2K]

Answer: $\dfrac{1}{4}$

Step-by-step explanation:

Given

The total no of beads is 52

there 13-red,13-blue,13-green, and 13-black

favorable outcomes to select a blue bead is 13

Total outcomes are 52

Probability is given by

$P=\dfrac{\text{favorable}}{\text{Total outcomes}}\\\\\Rightarrow P=\dfrac{13}{52}=\dfrac{1}{4}$

7 0

2 years ago

Point w id located at (-2,3) on a coordinate plane. Point W is reflected over the x-axis to create point W" is then reflected ov

Anna11 [10]

Answer:

W'' = (2, -3)

Step-by-step explanation:

Reflection over the x-axis negates the y-coordinate and leaves the x-coordinate alone. The W becomes ...

... W' = (-2, -3)

Reflection over the y-axis negates the x-coordinate and leaves the y-coordinate alone. The W' becomes ...

... W'' = (2, -3)

5 0

2 years ago

Read 2 more answers

I need help with these two answers please :/

4vir4ik [10]

Rise over run is -2/4 or simplified as -1/2
The second one is
$\frac{1 - 3}{4 - 0} = \frac{ - 2}{4}$

7 0

2 years ago

What types of numbers are undefined when they are under a radical sign? If you were dealing with the number √-1, would it be def

Misha Larkins [42]

The square root of a a negative integer is imaginary.
It would still be a negative under a square root if you multiplied it by 2, therefor it will still be imaginary, or I’m assuming as your book calls it, undefined.
2•(sqrt-1) = 2sqrt-1

If you add a number to -1 itself, specifically 1 or greater it will become a positive number or 0 assuming you just add 1. In that case it would be defined.
-1 + 1 = 0
-1 + 2 = 1

If you add a number to the entire thing “sqrt-1” it will not be defined.
(sqrt-1) + 1 = 1+ (sqrt-1)

If you subtract a number it will still have a negative under a square root, meaning it would be undefined.
(sqrt-1) + 1 = 1 + (sqrt-1)

however if you subtract a negative number from -1 itself, you end up getting a positive number or zero. (Subtracting a negative number is adding because the negative signs cancel out).
-1 - -1 = 0
-1 - -2 = 1

If you squared it you would get -1, which is defined
sqrt-1 • sqrt-1 = -1

and if you cubed it, you would get a negative under a square root again, therefor it would be undefined.
sqrt-1 • sqrt-1 • sqrt-1 = -1 • sqrt-1 = -1(sqrt-1)

Sorry if this answer is confusing, I don’t have a scientific keyboard, I’ll get one soon.

8 0

2 years ago