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4 years ago

Determine the quotient: 2 4/7 ÷ 1 3/6

Mathematics

1 answer:

Scilla [17]4 years ago

4 0

First we must change these numbers to improper fractions:

$2\frac{4}{7}=\frac{18}{7}$

$1\frac{3}{6}=\frac{9}{6}$

So then we set it up:

$\frac{18}{7}$ ÷ $\frac{9}{6}$

When we divide fractions like this, we must flip the second fraction and change the sign from division to multiplication like so:

$\frac{18}{7}*\frac{6}{9}$

Then we solve:

$\frac{108}{63}$

Then if we divide the numerator and the denominator by 9, we get:

$\frac{12}{7}$ or, in mixed-number form, $1\frac{5}{7}$ .

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Find the length of the arc. round your answer to nearest tenth

tigry1 [53]

41.9 mi

Step-by-step explanation:

First, we convert the angle from degree measure to radian measure:

$\theta = 240°×\left(\dfrac{\pi}{180°}\right)= \dfrac{4\pi}{3}\:\text{rad}$

Using the definition of an arc length $s$

$s = r\theta$

$\:\:\:\:=(10\:\text{mi})\left(\dfrac{4\pi}{3}\:\text{rad}\right)$

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3 years ago

Help asap plspls !! :)

Kay [80]

Answer:

-5 1/3

Step-by-step explanation:

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3 years ago

What transformations are represented by the following coordinate graphing? (geometry)

Minchanka [31]

Answer:

(a,b) → (a,-b) : Reflection about x axis.

(a,b) → (a, b+5) : Translation of the point by 5 units up.

(a,b) → (b,-a) : Rotation by 90 degree clockwise.

Step-by-step explanation:

Given:

The transformation of points are given as:

(a,b) → (a,-b)

(a,b) → (a, b+5)

(a,b) → (b,-a)

Now, let us consider each transformation one by one.

(1) (a,b) → (a,-b)

Here, the order of the coordinates has not changed. But, the y coordinate of the point has changed. The y coordinate was 'b' and it has changed only its sign but not value. So, it is a transformation related to reflection.

In reflection, only the sign changes. Since, the 'y' coordinate sing is reversed, so, it is a reflection about x axis.

(2) (a,b) → (a, b+5)

Here, the 'y' coordinate of the point has changed. The change is from 'b' to 'b+5'. So, 5 is added to the y coordinate. As per transformation rules, if a positive number 'C' is added to the y coordinate, then the point shifts vertically up by 'C' units. Hence, there is a translation of 5 units up here.

(3) (a,b) → (b,-a)

Here, the 'x' and 'y' coordinates interchange their values and also the new y coordinate has its sign reversed. This happens in rotation.

We know that, (x, y) → (y, –x) is true when there is rotation by 90 degree clockwise.

So, the point (a,b) → (b,-a) is rotated by 90 degree clockwise.

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3 years ago

Help please give brainliest

Nezavi [6.7K]

You need to explain to us what to do or else nobody will understand what your trying to ask for.

4 0

3 years ago

Hi there! Sorry to bother you, but can someone help me out with this?

Rudik [331]

Problem 6

<h3>Answer: A) Conjecture</h3>

Explanation:

We can rule out choices B through D because they are valid items to use in any proof. A definition is a statement (or set of statements) set up in a logical fashion that is very clear and unambiguous. This means there cannot be any contradiction to the definition. An example of a definition is a line is defined by 2 points (aka a line goes through 2 points).

A postulate is a term that refers to a basic concept that doesn't need much proof to see why it's true. An example would be the segment addition postulate which says we can break up a segment into smaller pieces only to glue those pieces back together and get the original segment back.

A theorem is more rigorous involving items B and C to make a chain of statements leading from a hypothesis to a conclusion. You usually would see theorems in the form "if this, then that". Where "this" and "that" are logical statements of some kind. One theorem example is the SSS congruence theorem that says "if two triangles have three pairs of congruent corresponding sides, then the triangles are congruent". Chaining previously proven/established theorems is often done to form new theorems. So math builds on itself.

A conjecture is basically a guess. You cannot just blindly guess and have it be valid in a proof. You can have a hypothesis and have it lead to a conclusion (whether true or false) but simply blindly guessing isn't going to cut it. So that's why conjectures aren't a good idea in a proof.

==========================================================

Problem 7

<h3>Answer: Choice A) A theorem does not require proof</h3>

Explanation:

As mentioned in the section above (paragraph 3), a theorem does require proof. It's like having a friend come up to you and make a claim, only to not back it up at all. Do you trust your friend? What if they might be lying? Now consider that instead of a friend, but now it's some random stranger you just met.

Of course, they may not realize they are lying but it's always a good idea to verify any claim no matter how trivial. Math tries to be as impartial as possible to have every theorem require proof. Some proofs are a few lines long (we consider these trivial) while others take up many pages, if not an entire book, depending on the complexity of the theorem.

So that's why we can rule out choice B since it's a true statement. Choices C and D sort of repeat the ideas mentioned, just phrased in different ways. As mentioned earlier, a theorem is built from fundamental building blocks of various definitions and postulates and theorems. The term "axiom" is more or less the same as "postulate" (though with slight differences).

If you wanted to go for a statement that doesn't require proof, then you'd go for an axiom or postulate. Another example of such would be something like "if two straight lines intersect, then they intersect at exactly one point".

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3 years ago