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2 years ago

9

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the corre

ct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Perform the indicated operation.

1 answer:

Len [333]2 years ago

6 0

Answer:

In the operation, simplify

9-a² = (3-a)(3+a)

Factorize

4a²-4a-24-------------------divide each term by 4

a²-a-6-------------------------factorize

a²-3a+2a-6

a(a-3)+2(a-3)

(a+2)(a-3)

Factorize

a²-6a+9

a²-3a-3a+9

a(a-3)-3(a-3)

(a-3)(a-3)

Rewrite operation as

$\frac{8}{(3-a)(3+a)} /\frac{(a+2)(a-3)}{(a-3)(a-3)}$

Multiply by the recipricol

$\frac{8}{(3-a)(3+a)} *\frac{(a-3)(a-3)}{(a+2)(a-3)}$

cancel the similar terms

$\frac{8}{(3-a)(3+a)} *\frac{(a-3)}{(a+2)}$

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Use the diagram to find lengths. BP is the perpendicular bisector of AC. QC is the

faust18 [17]

Answer:

The length of the side PC is 34 cm.

Step-by-step explanation:

We are given that BP is the perpendicular bisector of AC. QC is the perpendicular bisector of BD. AB = BC = CD.

Suppose BP = 16 cm and AD = 90 cm.

As, it is given that AD = 90 cm and the three sides AB = BC = CD.

From the figure it is clear that AD = AB + BC + CD

So, AB = $\frac{90}{3}$ = 30 cm

BC = $\frac{90}{3}$ = 30 cm

CD = $\frac{90}{3}$ = 30 cm

Since the triangle, BPC is a right-angled triangle as $\angle$ PBC = 90°, so we can use Pythagoras theorem in this triangle to find the length of the side PC.

Now, the Pythagoras theorem states that;

$\text{Hypotenuse}^{2} = \text{Perpendicular}^{2} +\text{Base}^{2}$

$\text{PC}^{2} = \text{BP}^{2} +\text{BC}^{2}$

$\text{PC}^{2} = \text{16}^{2} +\text{30}^{2}$

$\text{PC}^{2} = 256+900$ = 1156

$\text{PC}=\sqrt{1156}$

PC = 34 cm

Hence, the length of the side PC is 34 cm.

4 0

2 years ago

What is the area of the triangle shown on the picture?

aivan3 [116]

Answer:

37 times 45 divide by 2

Step-by-step explanation:

Hope that helps

3 0

3 years ago

Compare 2.3 and 2.03

Andru [333]

2.3= 2.03 so there for it is equal

8 0

3 years ago

Solve linear equation 1/4 x + 18 = X

Anton [14]

Answer:

24

Step-by-step explanation:

1 / 4 x + 18 = x

x / 4 + 18 = x

x = x / 4 + 18

x - x / 4 = 18

( 4x / 4 ) - ( x/4 ) = 18

( 4x - x ) / 4 = 18

3x / 4 = 18

3x = 18 * 4

x = ( 18 * 4 ) / 3

= 6 * 4

x = 24

3 0

2 years ago

Find the quotient of these Complex Numbers. <br><br><br> (5-i) / (3+2i)

JulsSmile [24]

Let the given complex number

z = x + ix = $\dfrac{5-i}{3+2i}$

We have to find the standard form of complex number.

Solution:

∴ x + iy = $\dfrac{5-i}{3+2i}$

Rationalising numerator part of complex number, we get

x + iy = $\dfrac{5-i}{3+2i}\times \dfrac{3-2i}{3-2i}$

⇒ x + iy = $\dfrac{(5-i)(3-2i)}{3^2-(2i)^2}$

Using the algebraic identity:

(a + b)(a - b) = $a^{2}$ - $b^{2}$

⇒ x + iy = $\dfrac{15-10i-3i+2i^2}{9-4i^2}$

⇒ x + iy = $\dfrac{15-13i+2(-1)}{9-4(-1)}$ [ ∵ $i^{2} =-1$ ]

⇒ x + iy = $\dfrac{15-2-13i}{9+4}$

⇒ x + iy = $\dfrac{13-13i}{13}$

⇒ x + iy = $\dfrac{13(1-i)}{13}$

⇒ x + iy = 1 - i

Thus, the given complex number in standard form as "1 - i".

5 0

2 years ago