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3 years ago

Right Thangles & Pythagorean Theorem

Mathematics

1 answer:

weqwewe [10]3 years ago

6 0

The ship Y traveled 240 miles which is option C).

<u>Step-by-step explanation:</u>

It is instructed to use Right Triangles & Pythagorean Theorem in order to find the solution.

So, the right angle has three sides namely, the base, the height and the hypotenuse.

The given data are,

Two ships leave port at the same time.

Ship X is heading due north ⇒ Take it as "height" of the right triangle.
Ship Y is heading due east ⇒ Take it as "base" of the right triangle.

They were 400 miles apart after 8 hours which forms the "hypotenuse" of the right triangle.

Hypotenuse = 400 miles.

Ship X had traveled 320 miles from the port in 8 hours. Therefore,

Height = 320 miles.

<u>To find the miles ship Y traveled in 8 hours :</u>

You can easily find the base of triangle which gives the number of miles traveled by ship Y in 8 hours.

<u>Using Pythagorean Theorem, you can find the base : </u>

The Pythagorean triplets is (3,4,5).

We know that, in a right triangle, hypotenuse is the largest side of all the three sides.

The hypotenuse is 400 miles ⇒ 5×(80) = 400

The height is 320 miles ⇒ 4×(80) = 320

Then, the base will be 3×(80) = 240 miles.

Therefore, the ship Y traveled 240 miles in 8 hours.

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Take a deck of playing cards form following sets out of those

swat32

The information given about the probability shows that the cardinality of D is 18.

<h3>How to calculate the probability?</h3>

From the complete information, the number of red-colored cards is 26.

Also, the number of red-colored number cards will be 18.

The cardinality of a set is a measure of a set's size, meaning the number of elements in the set.

Here, the cardinality of set D is 18.

Here is the complete question:

Take a deck of playing cards. Form following sets out of those:

A = Set of Face Cards

B = Set of Red Coloured Face cards

C = Set of Black Coloured Face Cards

D = Set of Red Coloured Number Cards

Find the Cardinality of set D

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brainly.com/question/24756209

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7 0

2 years ago

It is given that y is directly proportional to x. When x = 3, y = 18. (a) Find the equation connecting x and y. (b) Hence, find

guapka [62]

Answer:

see explanation

Step-by-step explanation:

(a)

Given y is directly proportional to x then the equation relating them is

y = kx ← k is the constant of proportion

To find k use the condition when x = 3, y = 18 , then

18 = 3k ( divide both sides by 3 )

6 = k

y = 6x ← equation of proportion

(b)

(i)

when x = 12 , then

y = 6 × 12 = 72

(ii)

when y = 42

42 = 6x ( divide both sides by 6 )

7 = x

8 0

3 years ago

Find thhe remainder when 7^203 is divided by 4

Aleksandr [31]

Using the square-and-multiply approach, we have

$7^{203}=7\times(7^{101})^2$
$7^{101}=7\times(7^{50})^2$
$7^{50}=(7^{25})^2$
$7^{25}=7\times(7^{12})^2$
$7^{12}=(7^6)^2$
$7^6=(7^3)^2$
$7^3=7\times7^2$

and so, using the property that, if $a_1\equiv b_1\mod n$ and $a_2\equiv b_2\mod n$ , then $a_1a_2\equiv b_1b_2\mod n$ , we get

$7\equiv3\mod4$
$7^2\equiv9\equiv1\mod4$
$7^3\equiv7\times1\equiv7\equiv3\mod4$
$7^6\equiv9\equiv1\mod4$
$7^{12}\equiv1\mod4$
$7^{25}\equiv7\times1\equiv7\equiv3\mod4$
$7^{50}\equiv9\equiv1\mod4$
$7^{101}\equiv7\times1\equiv7\equiv3\mod4$
$7^{203}\equiv7\times9\equiv3\times1\equiv3\mod4$

4 0

3 years ago

Jake rewrites the expression 81x2 – 1 as a difference of squares so he can factor it. Which answer choice shows how Jake could r

patriot [66]

Letter B
Different of 2 squares
(9x-1)(9x+1)

3 0

3 years ago

Is (4, 1) a solution to this system of inequalities?<br><br> x ≥ 4<br> x + 7y ≤ 11

Naya [18.7K]

Yess!!!!!!!!!!!!!!!!!!!!

6 0

3 years ago

Read 2 more answers