How do you find the domain of a function?

Answers

Answer 1

Answer: ok so domain means the set of numbers you are alowed to use

bsaically
domain=all real numbers except for those that make strange things happen

strange things are
1. dividing by zero
2. taking square root of negative
3. might be more, dunno

example
if y ou have
f(x)=3/x, domain is all real number except 0 since if x=0, then 3/0 is undifined
f(x)=3/(2+x), domain is all real except x=-2

for the negative sqrt
f(x)=√x, x cannot be negative, it goes from zero to positive infinity
f(x)=√(x-1), x cannot be less than 1, it has to be any number more than or equal to 1 (√0=0)

basically domain=all real number except for ones that make function comlex or undefined

Answer 2

Answer: You just see what's the range of x values the function covers.

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Answers

$6x^2+19x-15=-12x+15\n6x^2+31x-30=0\n6x^2+36x-5x-30=0\n6x(x+6)-5(x+6)=0\n(6x-5)(x+6)=0\nx=(5)/(6) \vee x=-6\n\ny=-12\cdot(5)/(6) +15\vee y=-12\cdot(-6)+15\ny=-10 +15\vee y=72+15\ny=5 \vee y=87\n\nx=(5)/(6) \wedge y=5\nx=-6 \wedge y=87$

$y=6x^2+19x-15 \ny=-12x+15 \n \n6x^2+19x-15=-12x+15 \n6x^2+19x+12x-15-15=0 \n6x^2+31x-30=0 \n \n a=6 \n b=31 \n c=-30 \n \n x=(-b \pm √(b^2-4ac))/(2a)=(-31 \pm √(31^2-4 \cdot 6 \cdot (-30)))/(2 \cdot 6)=(-31 \pm √(1681))/(12)=(-31 \pm 41)/(12) \n x=(-31 -41)/(12) \ \hbox{or} \ x=(-31+41)/(12) \nx=-6 \ \hbox{or} \ x=(5)/(6)$

$y=-12 \cdot (-6)+15 \ \hbox{or} \ y=-12 \cdot (5)/(6)+15 \ny=87 \ \hbox{or} \ y=5 \n \n \hbox{the answer:} \n \boxed{x=-6, \ y=87} \ \hbox{or} \ \boxed{x=(5)/(6), \ y=5}$

1. Conduct a hypothesis test for the following scenario. SHOW ALL YOUR WORK THE WAY WE DID IN CLASS! Construction zones on highways have a much lower speed limit. To see if drivers obey these lower speed limits, a police officer uses a radar gun to measure the speed in miles per hour of a random sample of 10 drivers in a 30 mph speed zone. Here are the data: 26 28 32 21 27 31 29 22 25 34 Is there convincing evidence at the α = .05 level that the average speed is below the speed limit?

Answers

First you want to put the numbers in order 21,22,25,26,27,28,29,31,32,35

Then separate the ones above the limit from below the limit

Above-31,32,35 (a total of 3)

Below-21,22,25,26,27,28,29 (a total of 7)

.5 is equal is 1/2 and over half are below the speed limit

So the average speed is most likely below the speed level

P.S. the average speed is 24.4

Evaluate the expression 7×18+45÷3×2

Answers

Answer:

156

Step-by-step explanation:

7 * 18 = 126

126 +45 / 3 * 2

45 / 3 = 15 * 2 = 30

126 + 30 = 156

Answer:

156

Step-by-step explanation:

Which expression is a difference of cubes? 9w^33-y^12 18p^15-q^21 36a^22-b^16 64c^15- a^26

Answers

we know that

A polynomial in the form $a^(3)-b^(3)$ is called adifference of cubes. Both terms must be a perfect cubes

Let's verify each case to determine the solution to the problem

case A) $9w^(33) -y^(12)$

we know that

$9=3^(2)$ ------> the term is not a perfect cube

$w^(33)=(w^(11))^(3)$ ------> the term is a perfect cube

$y^(12)=(y^(4))^(3)$ ------> the term is a perfect cube

therefore

The expression $9w^(33) -y^(12)$ is not a difference of cubes because the term $9$ is not a perfect cube

case B) $18p^(15) -q^(21)$

we know that

$18=2*3^(2)$ ------> the term is not a perfect cube

$p^(15)=(p^(5))^(3)$ ------> the term is a perfect cube

$q^(21)=(q^(7))^(3)$ ------> the term is a perfect cube

therefore

The expression $18p^(15) -q^(21)$ is not a difference of cubes because the term $18$ is not a perfect cube

case C) $36a^(22) -b^(16)$

we know that

$36=2^(2)*3^(2)$ ------> the term is not a perfect cube

$a^(22)$ ------> the term is not a perfect cube

$b^(16)$ ------> the term is not a perfect cube

therefore

The expression $36a^(22) -b^(16)$ is not a difference of cubes because all terms are not perfect cubes

case D) $64c^(15) -a^(26)$

we know that

$64=2^(6)=(2^(2))^(3)$ ------> the term is a perfect cube

$c^(15)=(c^(5))^(3)$ ------> the term is a perfect cube

$a^(26)$ ------> the term is not a perfect cube

therefore

The expression $64c^(15) -a^(26)$ is not a difference of cubes because the term $a^(26)$ is not a perfect cube

I'm adding a new case so I can better explain the problem

case E) $64c^(15) -d^(27)$

we know that

$64=2^(6)=(2^(2))^(3)$ ------> the term is a perfect cube

$c^(15)=(c^(5))^(3)$ ------> the term is a perfect cube

$d^(27)=(d^(9))^(3)$ ------> the term is a perfect cube

Substitute

$64c^(15) -d^(27)=((2^(2))(c^(5)))^(3)-(d^(9))^(3)$

therefore

The expression $64c^(15) -d^(27)$ is a difference of cubes because all terms are perfect cubes

The expression $\boxed{64{c^(15)} - {d^(27)}}$ is a difference of cubes.

Further Explanation:

Given:

The options are as follows,

(a). $9{w^(33)} - {y^(12)}$

(b). $18{p^(15)} - {q^(21)}$

(c). $36{a^(22)} - {b^(16)}$

(d). $64{c^(15)} - {a^(26)}$

(e). $64{c^(15)} - {d^(27)}$

Calculation:

The cubic formula can be expressed as follows,

$\boxed{{a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} - ab + {b^2}} \right)}$

The expression is $9{w^(33)} - {y^(12)}.$

9 is not a perfect cube of any number, ${w^(33)}$ can be written as ${\left( {{w^(11)}} \right)^3}$ and ${y^(12)}$ can be represents as ${\left( {{y^4}} \right)^3}.$

$9{w^(33)} - {y^(12)}$ cannot be written as the difference of cube. Option (a) is not correct.

The expression is $18{p^(15)} - {q^(21)}.$

18 is not a perfect cube of any number, ${p^(15)}$ can be written as ${\left( {{p^5}} \right)^3}$ and ${q^(21)}$ can be written as ${\left( {{q^7}} \right)^3}.$

$18{p^(15)} - {q^(21)}$ cannot be written as the difference of cube. Option (b) is not correct.

The expression is $36{a^(22)} - {b^(16)}.$

36 is not a perfect cube of any number, ${a^(22)}$ is not perfect cube and ${b^(16)}$ is not a perfect cube.

$36{a^(22)} - {b^(16)}$ cannot be written as the difference of cube. Option (c) is not correct.

The expression is $64{c^(15)} - {a^(26)}.$

64 can be written as ${\left( {{2^2}} \right)^3}, {a^(26)}$ is not perfect cube and ${c^(15)}$ can be written as ${\left( {{c^5}} \right)^3}.$

$64{c^(15)} - {a^(26)}$ cannot be written as the difference of cube. Option (d) is not correct.

The expression is $64{c^(15)} - {d^(27)}.$

64 can be written as ${\left( {{2^2}} \right)^3}, {d^(27)}$ can be written as ${\left( {{d^9}} \right)^3}$ and ${c^(15)}$ can be written as ${\left( {{c^5}} \right)^3}.$

$\boxed{64{c^(15)} - {d^(27)} = {{\left( {{2^2}{c^5}} \right)}^3} - {{\left( {{d^9}} \right)}^3}}$

$64{c^(15)} - {d^(27)}$ can be written as the difference of cube. Option (e) is correct.

The expression $\boxed{64{c^(15)} - {d^(27)}}$ is a difference of cubes.

Learn more:

1. Learn more about unit conversion brainly.com/question/4837736

2. Learn more about non-collinear brainly.com/question/4165000

3. Learn more aboutbinomial and trinomial brainly.com/question/1394854

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Exponents and Powers

Keywords: Solution, factorized form, expression, difference of cubes, exponents, power, equation, power rule, exponent rule.

1) Alicia's gross monthly pay is $1,700.Alicia pays 5.7% of her monthly salary for
Social Security. How much does Alicia
pay?
A $0.96
C $96.90
B $9.69
D $969.90

Answers

Answer:

96.90

Step-by-step explanation:

1700x.0570=96.90

Tri City sells four times as many dishwashers as Solly Company. The difference between their sales is 96 dishwashers. How many dishwashers did each sell?

Answers

First of all, we have to set variables to represent the given in the problem. We have to set variables for the sales of Tri City and the sales of Solly Company. Hence,

let T be the sales of the Tri City Company and
let S be the sales of the Solly Company

Secondly, we are going to translate into mathematical terms the relationship between the two variables. Hence,

T=4S (1)
T-S=96 (2)

We have two linear equations and two unknowns so this problem is answerable. We substitute equation (1) into equation (2) to give us

4S-S=96
3S=96
S=32

Solving for T gives us

T-32=96
T=96+32
T=128

So, Tri City sold 128 dishwashers while Solly Company sold 32.

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