Simplify: 9^-3<br><br><br> Please help!

Question 10 The hypotenuse of a right triangle is I m longer than the longer leg. The other leg is 7 m shorter than the longer l

bonufazy [111]

Answer:

5, 12, 13

Step-by-step explanation:

let x be the longer leg then x + 1 is the hypotenuse and x - 7 the shorter leg

Using Pythagoras' identity in the right triangle

x² + (x - 7)² = (x + 1)² ← expand using FOIL

x² + x² - 14x + 49 = x² + 2x + 1

2x² - 14x + 49 = x² + 2x + 1 ( subtract x² + 2x + 1 from both sides )

x² - 16x + 48 = 0 ← in standard form

(x - 4)(x - 12) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x - 12 = 0 ⇒ x = 12

x = 4 , then x - 7 = 4 - 7 = - 3 ← not possible

x = 12, then x - 7 = 12 - 7 = 5 and x + 1 = 12 + 1 = 13

The lengths of the 3 sides are

longer leg = 12 m , shorter leg = 5 m and hypotenuse = 13 m

5 0

3 years ago

Match each power of i with its multiplicative inverse.

erastovalidia [21]

By definition we have to:
In mathematics, the inverse multiplicative, reciprocal or inverse of a non-zero number x, is the number, denoted as 1/x or x -1, which multiplied by x gives 1.
We have then:

1) i
The multiplicative inverse is:
$\frac{1}{i}$
Rewriting we have:
$\frac{1}{i} \frac{i}{i}$
$\frac{i}{i^2}$
$\frac{i}{-1}$
$-i$
Answer 3) -i

2) i^2
The multiplicative inverse is:
$\frac{1}{i^2}$
Rewriting we have:
$\frac{1}{-1}$
$-1$
Answer 4) -1

3) i^3
The multiplicative inverse is:
$\frac{1}{i^3}$
Rewriting we have:
$\frac{1}{i*i^2}$
$\frac{1}{i^2}*\frac{1}{i}$
$\frac{1}{-1}*\frac{1}{i}*\frac{i}{i}$
$(-1)*\frac{i}{i^2}$
$(-1)* \frac{i}{-1}$
$i$
Answer 1) i

4) i^4
The multiplicative inverse is:
$\frac{1}{i^4}$
Rewriting we have:
$\frac{1}{i^2i^2}$
$\frac{1}{(-1)(-1)}$
$\frac{1}{1}$
$1$
Answer 2) 1

3 0

3 years ago

Read 2 more answers

What is 86÷724.12 in decimal form?

zheka24 [161]

Answer:

.118764846

Step-by-step explanation:

86/ (724.12) = .118764846

3 0

3 years ago

Factorise the expression:21x+3xy+6x²