State the missing factors. there may be more than one correct solution

I need help with this math problem

den301095 [7]

Answer:

1). $\frac{2}{x^{2}-x-12 }=\frac{2}{(x+3)(x-4)}$

2). $\frac{1}{x^{2}-16 }=\frac{1}{(x-4)(x+4)}$

Step-by-step explanation:

In this question we have to write the fractions in the factored form.

Rational expressions are $\frac{2}{x^{2}-x-12 }$ and $\frac{1}{x^{2}-16 }$ .

1). $\frac{2}{x^{2}-x-12 }$

Factored form of the denominator (x² - x - 12) = x² - 4x + 3x - 12

= x(x - 4) + 3(x - 4)

= (x + 3)(x - 4)

Therefore. $\frac{2}{x^{2}-x-12 }=\frac{2}{(x+3)(x-4)}$

2). $\frac{1}{x^{2}-16 }$

Factored form of the denominator (x² - 16) = (x - 4)(x + 4)

[Since (a²- b²) = (a - b)(a + b)]

Therefore, $\frac{1}{x^{2}-16 }=\frac{1}{(x-4)(x+4)}$

8 0

3 years ago

Help! plz plz plz plz plz plz plz

Helga [31]

Answer:

how to help. what is the question.

8 0

3 years ago

Describe the steps to dividing imaginary numbers and complex numbers with two terms in the denominator?

zlopas [31]

Answer:

Let be a rational complex number of the form $z = \frac{a + i\,b}{c + i\,d}$ , we proceed to show the procedure of resolution by algebraic means:

1) $\frac{a + i\,b}{c + i\,d}$ Given.

2) $\frac{a + i\,b}{c + i\,d} \cdot 1$ Modulative property.

3) $\left(\frac{a+i\,b}{c + i\,d} \right)\cdot \left(\frac{c-i\,d}{c-i\,d} \right)$ Existence of additive inverse/Definition of division.

4) $\frac{(a+i\,b)\cdot (c - i\,d)}{(c+i\,d)\cdot (c - i\,d)}$ $\frac{x}{y}\cdot \frac{w}{z} = \frac{x\cdot w}{y\cdot z}$

5) $\frac{a\cdot (c-i\,d) + (i\,b)\cdot (c-i\,d)}{c\cdot (c-i\,d)+(i\,d)\cdot (c-i\,d)}$ Distributive and commutative properties.

6) $\frac{a\cdot c + a\cdot (-i\,d) + (i\,b)\cdot c +(i\,b) \cdot (-i\,d)}{c^{2}-c\cdot (i\,d)+(i\,d)\cdot c+(i\,d)\cdot (-i\,d)}$ Distributive property.

7) $\frac{a\cdot c +i\,(-a\cdot d) + i\,(b\cdot c) +(-i^{2})\cdot (b\cdot d)}{c^{2}+i\,(c\cdot d)+[-i\,(c\cdot d)] +(-i^{2})\cdot d^{2}}$ Definition of power/Associative and commutative properties/ $x\cdot (-y) = -x\cdot y$ /Definition of subtraction.

8) $\frac{(a\cdot c + b\cdot d) +i\cdot (b\cdot c -a\cdot d)}{c^{2}+d^{2}}$ Definition of imaginary number/ $x\cdot (-y) = -x\cdot y$ /Definition of subtraction/Distributive, commutative, modulative and associative properties/Existence of additive inverse/Result.

Step-by-step explanation:

Let be a rational complex number of the form $z = \frac{a + i\,b}{c + i\,d}$ , we proceed to show the procedure of resolution by algebraic means:

1) $\frac{a + i\,b}{c + i\,d}$ Given.

2) $\frac{a + i\,b}{c + i\,d} \cdot 1$ Modulative property.

3) $\left(\frac{a+i\,b}{c + i\,d} \right)\cdot \left(\frac{c-i\,d}{c-i\,d} \right)$ Existence of additive inverse/Definition of division.

4) $\frac{(a+i\,b)\cdot (c - i\,d)}{(c+i\,d)\cdot (c - i\,d)}$ $\frac{x}{y}\cdot \frac{w}{z} = \frac{x\cdot w}{y\cdot z}$

5) $\frac{a\cdot (c-i\,d) + (i\,b)\cdot (c-i\,d)}{c\cdot (c-i\,d)+(i\,d)\cdot (c-i\,d)}$ Distributive and commutative properties.

6) $\frac{a\cdot c + a\cdot (-i\,d) + (i\,b)\cdot c +(i\,b) \cdot (-i\,d)}{c^{2}-c\cdot (i\,d)+(i\,d)\cdot c+(i\,d)\cdot (-i\,d)}$ Distributive property.

7) $\frac{a\cdot c +i\,(-a\cdot d) + i\,(b\cdot c) +(-i^{2})\cdot (b\cdot d)}{c^{2}+i\,(c\cdot d)+[-i\,(c\cdot d)] +(-i^{2})\cdot d^{2}}$ Definition of power/Associative and commutative properties/ $x\cdot (-y) = -x\cdot y$ /Definition of subtraction.

8) $\frac{(a\cdot c + b\cdot d) +i\cdot (b\cdot c -a\cdot d)}{c^{2}+d^{2}}$ Definition of imaginary number/ $x\cdot (-y) = -x\cdot y$ /Definition of subtraction/Distributive, commutative, modulative and associative properties/Existence of additive inverse/Result.

3 0

2 years ago

Angle 1 and Angle 2 are complementary angles.

Andrej [43]

Answer:

p = 35

Step-by-step explanation:

Complementary angles sum to 90°

Sum the 2 given angles and equate to 90, that is

20 + 2p = 90 ( subtract 20 from both sides )

2p = 70 ( divide both sides by 2 )

p = 35

7 0

3 years ago

A desk is on sale for $380 which is 20% of the original price. Which equation can be used to determine the amount of money saved

elena-s [515]

Answer:

S = 380 - 380*80%

Step-by-step explanation:

Given:

The original price of the desk: $380
Discount: 20%

So, the new price of the desk after discounting is:

380(100% - 20%)

= 380*80%

= 304$

The amount of money saved: 380 - 304 = 76$

Hence, the equation can be used to determine the amount of money saved is:

Saving = 380 - 380*80%

Hope it will find you well.

8 0

3 years ago

Read 2 more answers