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2 years ago

How to find domain of (1/x-3)(x^2-x-12)

Mathematics

1 answer:

Taya2010 [7]2 years ago

5 0

Set denominator to zero and solve for x.

x^2 - x - 12 = 0

Factor.

(x - 4)(x + 3) = 0

Solve each factor for x.

x - 4 = 0

x = 4

x + 3 = 0

x = -3

Answer:

The domain is ALL REAL NUMBERS except for x = 4 and x = -3.

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Evaluate 1/4c+3d when c=6 and d=7

labwork [276]

$\dfrac{1}{4}c+3d$

Put the values of c = 6 and d = 7 to the expression:

$\dfrac{1}{4}\cdot6+3\cdot7=\dfrac{1}{2}\cdot3+21=1.5+21=22.5$

5 0

3 years ago

Angle pwm is equal to angle pkm

Len [333]

<h3>Answer: 24 (choice C)</h3>

Assuming M is a midpoint of KW, this means that WM and KM are congruent

WM = KM

x+3 = 2(x-3) ... substitution

x+3 = 2x-6

2x-6 = x+3

2x-6-x = x+3-x .... subtract x from both sides

x-6 = 3

x-6+6 = 3+6 ... add 6 to both sides

x = 9

Use x = 9 to find the length of WM

WM = x+3 = 9+3 = 12

Which can be used to find the length of KM as well

KM = 2(x-3) = 2(9-3) = 2(6) = 12

both lengths are the same (12) as expected

This makes WK to be

WK = WM + KM

WK = 12 + 12

WK = 24

3 0

3 years ago

Read 2 more answers

What is the length of the arc when the degree measure is 60° and the radius is 7?

shepuryov [24]

Inscribed angle =1/2 arc

4 0

3 years ago

An atrium is being designed to house an exhibit of tropical birds. The atrium must enclose 250,000 cubic feet of space, and the

9966 [12]

The proposed design of the atrium (V < V') is possible since its volume is less than the maximum possible atrium.

<h3>Can this atrium be built in the rectangular plot of land?</h3>

The atrium with the maximum allowable radius (R), in feet, is represented in the image attached. The real atrium is possible if and only if the real radius (r) is less than the maximum allowable radius and therefore, the real volume (V), in cubic feet, must be less than than maximum possible volume (V'), in cubic feet.

First, we calculate the volume occupied by the maximum allowable radius:

V' = (8 · π / 3) · (45 ft)³

V' ≈ 763407.015 ft³

The proposed design of the atrium (V < V') is possible since its volume is less than the maximum possible atrium. $\blacksquare$

To learn more on volumes, we kindly invite to check this verified question: brainly.com/question/13338592

3 0

2 years ago

Determine whether these statements are true or false. a) ∅ ∈ {∅} b) ∅ ∈ {∅,{∅}} c) {∅} ∈ {∅} d) {∅} ∈ {{∅}} e) {∅} ⊂ {∅,{∅}} f )

Pavel [41]

Answer:

a) ∅ ∈ {∅} TRUE

b) ∅ ∈ {∅,{∅}} TRUE

c) {∅} ∈ {∅} FALSE

d) {∅} ∈ {{∅}} TRUE

e) {∅} ⊂ {∅,{∅}} TRUE

f ) {{∅}} ⊂ {∅,{∅}} TRUE

g) {{∅}} ⊂ {{∅},{∅}}FALSE

Step-by-step explanation:

To assess whether these statements are true or false, first observe the symbol:

"∈" means that element, as it is and as it is, belongs to the set. To belong to the set it must be within the symbols "{}"

On the other hand, the symbol "⊂" means "subset", that is, it is a subset that is included in the main set.

So:

c) is false because "{∅}" is not included in the set

g) is false because " {{∅}}" is not included in the set

7 0

3 years ago