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3 years ago

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A) The hypotenuse of a right angled triangle is 15 cm. Taking the

1 answer:

Anastasy [175]3 years ago

3 0

a) By Pythagoras theorem , h^2 is = a^2 + b^2 where a is the hypotenuse and a and b are the legs.

=) 15^2 = x^2 + y^2

That is the relation

b) area of triangle = 1/2 x height x base

=) 1/2 * x * y = 30

=) xy = 15cm

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If y varies directly as the x^2 and y = 200 when x = 5, what is the value of y when x = -3?

gayaneshka [121]

As the variation is direct we have:
$y = kx ^ 2
$
We must find the value of k.
For this, we use the following data:
y = 200 when x = 5
Substituting values we have:
$200 = k5 ^ 2
$
Clearing k:
$k = 200/5 ^ 2

k = 200/25

k = 8$
Then, the function is:
$y = 8x ^ 2
$
We evaluate the function for x = -3
$y = 8 (-3) ^ 2

y = 8 (9)

y = 72$
Answer:
the value of y when x = -3 is:
c.
72

6 0

3 years ago

Who became president after the 1876 presidential election?<br> Nfnf

REY [17]

Answer:

Rutherford B. Hayes

Step-by-step explanation:

It was controversial, however Hayes was declared the winner of the election.

7 0

3 years ago

Given that F( x ) = x 2 + 2, evaluate F(1) + F(5).

stealth61 [152]

Hi there! :)

Answer:

$\huge\boxed{f(1) + f(5) = 30}$

Given:

$f(x) = x^{2} + 2$

Evaluate $f(1) + f(5)$

Solve for each:

$f(1) = (1)^{2} + 2 = 3$

$f(5) = (5)^{2} + 2 = 27$

$27 + 3 = 30$

3 0

3 years ago

Read 2 more answers

Let FS R be a finite set. (a) Prove that F is closed (b) Prove that every point in F is an isolated point.

Lorico [155]

Answer:

a) Suppose that F is ordered in ascending order: $F = \{x_1,\ldots, x_n\}$ . Then, the complement of F can be written as

$F^c = (-\infty,x_1)\cup (x_1,x_2)\cup (x_2,x_3)\cup \cdots \cup (x_{n-1}, x_{n})\cup (x_n,+\infty)$

which is the union of a finite number of open intervals, then $F^c$ is an open set. Thus, F is a closed subset of the real numbers.

b) Take an arbitrary element of F, let us say $x_k$ . Now, choose a real number $\epsilon$ such that

$0$ there are not other element of F, because $\epsilon$ is less that the minimum distance between $x_k$ and its neighbors.

In case that $k=1$ we only consider $0$ , and if $k=n$ we only consider $0$ .

Then, all points of F are isolated.

Step-by-step explanation:

8 0

3 years ago

A certain mathematics contest has a peculiar way of giving prizes. Five people are named as Grand Prize winners, but their finis

bixtya [17]

Answer:

The number of complete award announcements possible are 19,554,575,040.

Step-by-step explanation:

Combination is the number of ways to select <em>k</em> items from <em>n</em> distinct items when the order of selection does not matters.

Whereas permutation is the number of ways to select <em>k</em> item from <em>n</em> items when order of selection matters.

The number of people entering this year is 22.

The number of ways to select 5 people for Grand Prize is, ${22\choose 5}=\frac{22!}{5!(22-5)!} =26334$ .

The remaining number of people is, 22 - 5 = 17.

It is provided that the other 5 are selected according to an order.

The number of ways to select other 5 winners is,

$^{17}P_{5}=\frac{17!}{(17-5)!} =742560$

The total number of ways to select 10 winners of 22 is:

Total number of ways = 26334 × 742560 = 19,554,575,040.

6 0

3 years ago