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2 years ago

Factor the expression completely I’ve the complex numbers X^4+10x^2+25

Mathematics

1 answer:

Elza [17]2 years ago

5 0

We have

(a + b)² = a² + 2ab + b²

so that with a = x² and b = 5, we have

x⁴ + 10x² + 25 = (x² + 5)²

Next, we have

a² - b² = (a - b) (a + b)

so that with a = x and b = √5 i,

x² + 5 = x² - (-5) = (x - √5 i) (x + √5 i)

So, the complete factorization over the complexes is

(x - √5 i)² (x + √5 i)²

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Fill in the blanks to solve 48 x 8. 48 x 8 = 40 eights + 8 eights

kozerog [31]

Question is:

Fill in the blanks to solve $\frac{48}{x} =8$ .

Answer:

$x = 6$

Step-by-step explanation:

Given

$\frac{48}{x} =8$

Required

Solve

Multiply both sides by x

$x * \frac{48}{x} =8*x$

$48 =8*x$

Make x the subject

$x = \frac{48}{8}$

$x = 6$

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3 years ago

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ryzh [129]

Answer:

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Step-by-step explanation:

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3 years ago

Given: ABCD is a ∥-gram, BF ⊥ CD , BE ⊥ AD, Prove: △ABE∼△CBF

drek231 [11]

Answer:

Hence proved △ABE∼△CBF.

Step-by-step explanation:

Given,

ABCD is a parallelogram.

BF ⊥ CD and

BE ⊥ AD

To Prove : △ABE∼△CBF

We have drawn the diagram for your reference.

Proof:

Since ABCD is a parallelogram,

So according to the property of parallelogram opposite angles are equal in measure.

$\therefore m\angle A = m\angle B$ ⇒1

And given that BF ⊥ CD and BE ⊥ AD.

So we can say that;

$m\angle F=m\angle E=90\°$ ⇒2

Now In △ABE and △CBF

∠A = ∠C (from 1)

∠E = ∠F (from 2)

So by A.A. similarity postulate;

△ABE∼△CBF

7 0

3 years ago

If F(x) = x² + 5x and G(x) = 2x + 1, find F(5) + G(6). 63 48 107

Serjik [45]

Answer:

Step-by-step explanation:

Put the given value where x is in each function definition and do the arithmetic. 5 replaces x in F(x); 6 replaces x in G(x).

F(5) + G(6) = (5² +5·5) + (2·6 +1) = 25 +25 +12 +1 = 63

7 0

3 years ago

Read 2 more answers

Xyz-qrs and the scale factor from xyz to qrs is 2/5. what is the length of side rs?

raketka [301]

Answer:

RS = 10

Step-by-step explanation:

We are told that to get ∆QRS, the scale factor of ⅖ was used. To get side RS, we would multiply the side length of the side that corresponds to RS.

YZ corresponds to RS.

YZ = 25

Thus,

RS = 25*⅖

RS = 10

3 0

2 years ago