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3 years ago

(-1)(-6 +3i) + (81)(-8+ 4i)

Mathematics

1 answer:

Tanya [424]3 years ago

4 0

Answer: here is the simplify version −642+321i

Step-by-step explanation:

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Drupady [299]

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4 years ago

Help with geometry hw

tiny-mole [99]

QUESTION 1

Let the third side of the right angle triangle with sides $x,6$ be $l$ .

Then, from the Pythagoras Theorem;

$l^2=x^2+6^2$

$l^2=x^2+36$

Let the hypotenuse of the right angle triangle with sides 2,6 be $m$ .

Then;

$m^2=6^2+2^2$

$m^2=36+4$

$m^2=40$

Using the bigger right angle triangle,

$(x+2)^2=m^2+l^2$

$\Rightarrow (x+2)^2=40+x^2+36$

$\Rightarrow x^2+2x+4=40+x^2+36$

Group similar terms;

$x^2-x^2+2x=40+36-4$

$\Rightarrow 2x=72$

$\Rightarrow x=36$

QUESTION 2

Let the hypotenuse of the triangle with sides (x+2),4 be $k$ .

Then, $k^2=(x+2)^2+4^2$

$\Rightarrow k^2=(x+2)^2+16$

Let the hypotenuse of the right triangle with sides 2,4 be $t$ .

Then; we have $t^2=2^2+4^2$

$t^2=4+16$

$t^2=20$

We apply the Pythagoras Theorem to the bigger right angle triangle to obtain;

$[(x+2)+2]^2=k^2+t^2$

$(x+4)^2=(x+2)^2+16+20$

$x^2+8x+16=x^2+4x+4+16+20$

$x^2-x^2+8x-4x=4+16+20-16$

$4x=24$

$x=6$

QUESTION 3

Let the hypotenuse of the triangle with sides (x+8),10 be $p$ .

Then, $p^2=(x+8)^2+10^2$

$\Rightarrow p^2=(x+8)^2+100$

Let the hypotenuse of the right triangle with sides 5,10 be $q$ .

Then; we have $q^2=5^2+10^2$

$q^2=25+100$

$q^2=125$

We apply the Pythagoras Theorem to the bigger right angle triangle to obtain;

$[(x+8)+5]^2=p^2+q^2$

$(x+13)^2=(x+8)^2+100+125$

$x^2+26x+169=x^2+16x+64+225$

$x^2-x^2+26x-16x=64+225-169$

$10x=120$

$x=12$

QUESTION 4

Let the height of the triangle be H;

Then $H^2+4^2=8^2$

$H^2=8^2-4^2$

$H^2=64-16$

$H^2=48$

Let the hypotenuse of the triangle with sides H,x be r.

Then;

$r^2=H^2+x^2$

This implies that;

$r^2=48+x^2$

We apply Pythagoras Theorem to the bigger triangle to get;

$(4+x)^2=8^2+r^2$

This implies that;

$(4+x)^2=8^2+x^2+48$

$x^2+8x+16=64+x^2+48$

$x^2-x^2+8x=64+48-16$

$8x=96$

$x=12$

QUESTION 5

Let the height of this triangle be c.

Then; $c^2+9^2=12^2$

$c^2+81=144$

$c^2=144-81$

$c^2=63$

Let the hypotenuse of the right triangle with sides x,c be j.

Then;

$j^2=c^2+x^2$

$j^2=63+x^2$

We apply Pythagoras Theorem to the bigger right triangle to obtain;

$(x+9)^2=j^2+12^2$

$(x+9)^2=63+x^2+12^2$

$x^2+18x+81=63+x^2+144$

$x^2-x^2+18x=63+144-81$

$18x=126$

$x=7$

QUESTION 6

Let the height be g.

Then;

$g^2+3^2=x^2$

$g^2=x^2-9$

Let the hypotenuse of the triangle with sides g,24, be b.

Then

$b^2=24^2+g^2$

$b^2=24^2+x^2-9$

$b^2=576+x^2-9$

$b^2=x^2+567$

We apply Pythagaoras Theorem to the bigger right triangle to get;

$x^2+b^2=27^2$

This implies that;

$x^2+x^2+567=27^2$

$x^2+x^2+567=729$

$x^2+x^2=729-567$

$2x^2=162$

$x^2=81$

Take the positive square root of both sides.

$x=\sqrt{81}$

$x=9$

QUESTION 7

Let the hypotenuse of the smaller right triangle be; n.

Then;

$n^2=x^2+2^2$

$n^2=x^2+4$

Let f be the hypotenuse of the right triangle with sides 2,(x+3), be f.

Then;

$f^2=2^2+(x+3)^2$

$f^2=4+(x+3)^2$

We apply Pythagoras Theorem to the bigger right triangle to get;

$(2x+3)^2=f^2+n^2$

$(2x+3)^2=4+(x+3)^2+x^2+4$

$4x^2+12x+9=4+x^2+6x+9+x^2+4$

$4x^2-2x^2+12x-6x=4+9+4-9$

$2x^2+6x-8=0$

$x^2+3x-4=0$

$(x-1)(x+4)=0$

$x=1,x=-4$

We are dealing with length.

$\therefore x=1$

QUESTION 8.

We apply the leg theorem to obtain;

$x(x+5)=6^2$

$x^2+5x=36$

$x^2+5x-36=0$

$(x+9)(x-4)=0$

$x=-9,x=4$

We discard the negative value;

$\therefore x=4$

QUESTION 9;

We apply the leg theorem again;

$10^2=x(x+15)$

$100=x^2+15x$

$x^2+15x-100=0$

Factor;

$(x-5)(x+20)=0$

$x=5,x=-20$

Discard the negative value;

$x=5$

QUESTION 10

According to the leg theorem;

The length of a leg of a right triangle is the geometric mean of the lengths of the hypotenuse and the portion of the hypotenuse adjacent to that leg.

We apply the leg theorem to get;

$8^2=16x$

$64=16x$

$x=4$ units.

QUESTION 11

See attachment

Question 12

See attachment

6 0

3 years ago

Each number in pascal's triangle is the ___ of the two numbers directly above it in the previous row.

mrs_skeptik [129]

Sum. To build the triangle, start with 1 at the top, then continue placing numbers below it in a triangular pattern. Each number is the numbers directly above it added together.

5 0

3 years ago

The perimeter of a rectangle is 34 m. The base is two times more than two times the height. What is the length of the base?

mafiozo [28]

Answer:

sdgfgfdggdfgfsdfdgdsd

Step-by-step explanation:

8 0

4 years ago

You select a card at random from the cards that make up the word replacement. On each card, there is one letter. Without replaci

Murrr4er [49]

In the word replacement, there are 11 letters.

4 of them are vowels : e, a, e, e

7 of them are not vowels : r, p, l, c, m, n, t

The probability of getting a vowel the first try is 4/11.

The probability of getting something that is not a vowel is 7/10. The denominator is one less because the vowel card is not replaced, meaning there is one less card to choose from.

Multiply.
4/11*7/10
=28/110
=14/55

The probability is 14/55.

Hope this helps!

5 0

3 years ago