The main limiting issue with the domain this function is potentially picking an x-value that makes that denominator equal 0, because dividing by 0 is bad.
So, the domain will be all real numbers, except for those that make g(x)=0.
g(-1) = 0, g(-2)=0, and g(2) = 0, so -1, -2, and 2 must be excluded from the domain.
Your answer is {x ∈ ℝ| x ≠ −1, −2, 2}.
Answer:
[tex]\textsf{Domain}: \quad \{ x \in \mathbb{R}\;|\;x \neq -1, -2, 2\}[/tex]
Step-by-step explanation:
Given functions:
[tex]\begin{cases} f(x)=x^2+6x+5\\g(x)=x^3+x^2-4x-4\end{cases}[/tex]
Factor function f(x):
[tex]\begin{aligned}\implies f(x)&= x^2+6x+5\\&=x^2+x+5x+5\\&=x(x+1)+5(x+1)\\&=(x+5)(x+1)\end{aligned}[/tex]
Factor function g(x):
[tex]\begin{aligned}\implies g(x)&=x^3+x^2-4x-4\\&=(x+1)(x^2-4)\\&=(x+1)(x+2)(x-2)\end{aligned}[/tex]
Therefore the composite function is:
[tex]\implies \dfrac{f(x)}{g(x)}=\dfrac{(x+5)(x+1)}{(x+1)(x+2)(x-2)}[/tex]
A rational function is undefined when the denominator equals zero.
Therefore, the given composite function is undefined when (x+1)(x+2)(x-2)=0:
[tex]x+1=0 \implies x=-1[/tex][tex]x+2=0 \implies x=-2[/tex][tex]x-2=0 \implies x=2[/tex]The domain of a function is the set of all possible input values (x-values).
Therefore, as the composite function is undefined when x = -1, x = -2 and x = 2, the domain is:
[tex]\{ x \in \mathbb{R}\;|\;x \neq -1, -2, 2\}[/tex]help please thank you
the answer of this question is B
Make a tree diagram to show all the possible sequences of answers for six multiple-choice questions, each with three possible responses. Assuming that you are guessing the answers so that all outcomes listed in the tree are equally likely, what is the probability that you will guess the one sequence that contains all six correct answers? (Round your answer to five decimal places.)
Answer:
Steps and solution in the attached picture.
Step-by-step explanation:
Steps and solution in the attached picture.
Based on the information given, the probability that all three are correct will be 0.0000217.
How to calculate the probabilityFrom the information given, there are six multiple-choice questions, each with three possible responses.
If an individual is guessing the answers so that all outcomes listed in the tree are equally likely, the probability that the person will guess the one sequence that contains all six correct answers will be:
A = correct answer = 1/6
B = incorrect answer = 1 - 1/6 = 5/6
The probability of guessing the correct answer will be:
= 1/6 × 1/6 × 1/6 × 1/6 × 1/6 × 1/6
= 0.0000217
Learn more about probability on:
brainly.com/question/25870256
Mrs. Neville is baking 5 batches of cookies. She will need 2 1/3 cups of flour for each
batch of cookies. If she begins with a bag of flour that contains 20 cups, how many cups
of flour will be left in the bag? (Show work on your paper)
Answer:
8.33 cups of flour
Step-by-step explanation:
In order to find the answer to this question you need to multiply the amount of batches by the amount of flour it takes to make that batch and then just simply make sure the answer is a mixed number.
[tex]2\frac{1}{3} \times5[/tex]
Convert the mixed number into a improper fraction:
[tex]2\frac{1}{3} =2\times3=6+1=\frac{7}{3}[/tex]
[tex]\frac{7}{3} \times5[/tex]
Remember that all whole numbers have a invisible denominator:
[tex]5=\frac{5}{1}[/tex]
[tex]\frac{7}{3} \times\frac{5}{1}[/tex]
Multiply:
[tex]7\times5=35[/tex]
[tex]3\times1=3[/tex]
Now subtract from 20 cups:
[tex]\frac{20}{1} -\frac{35}{3}[/tex]
Find the common denominator
CD = 3
20 1 - 35 3 = (20 × 3) + (35 × 1) 1 × 3 = 60 - 35 3 = 25 3 = 8.33
[tex]=8.33[/tex]
Hope this helps.
Caleb rode his bike for 3.1 miles in the morning. Then he rode his
bike another 22 miles in the afternoon. How many miles did Caleb
ride all together? Draw an arrow on the number line to show how
to find the answer. Then write the answer below.
Answer:
3.1 + 22 = 25.1
Step-by-step explanation:
My question is what is -5+12+-3+-10+14
Answer:
its 8
Step-by-step explanation:
I just calculated it and got the answer
The label of a bag of trail mix says it has 180calories per 15ounces. What is the rate of calories per ounce?
Answer:
12calories per 1ounce
Step-by-step explanation:
What are the domain and range of each relation?
Drag the answer into the box to match each relation.
The domain and the range of each relation shown in the mapping and in the table of values given can be written as:
Mapping - Domain: {-2, -1, 0, 1}; Range: {-4, -2, 2}
Table - Domain: {-4, -2, 1, 4}; Range: {-2, 1, 4}
(See image attached below).
Recall:
The domain (input) of any relation consist of all the x-values.The range (output) of any relation consist of all its y-values.From the mapping shown in the image given, the domain values are:
-2, -1, 0, 1
The range values are:
-4, -2, 2
From the table of values shown in the image given, the domain values are:
-4, -2, 1, 4
The range values are:
-2, 1, 4
Therefore, the domain and the range of each relation shown in the mapping and in the table of values given can be written as:
Mapping - Domain: {-2, -1, 0, 1}; Range: {-4, -2, 2}
Table - Domain: {-4, -2, 1, 4}; Range: {-2, 1, 4}
(See image attached below).
Learn more here:
https://brainly.com/question/5687716
how do you solve m + 1 = 17
Answer:
17²Step-by-step explanation:
(1+m)1+16=17²(1+1=2)=17²
Step-by-step explanation:
(1+m) 1+16=17
(1+16=17
I need help with this please
Answer:
5
Step-by-step explanation:
4x5+12=32mm
Write an equation of the line that passes through the given point and has the given slope.
(1,-5); slope -3/2
Answer:
y – y 1 = m ( x – x 1 ) m = your slope ( x 1 , y 1 ) = your point y – ( − 5 ) = − 3 2 ( x – 1 ) y + 5 = − 3 2 ( x – 1 ) Now we need to do a little algebra to get the equation in standard form: A x + B y = C , where A, B and C are relatively prime integers. y + 5 = − 3 2 x + 3 2 3 2 x + y = 3 2 − 5 now let's multiply through with 2 to get rid if the fractions: 2 ( 3 2 x + y = 3 2 − 5 ) 3 x + 2 y = 3 − 10 3 x + 2 y = 7
Step-by-step explanation:
Pls help. Pls pls pls
Answer:
idj
Step-by-step explanation:
hope this helps
60 POINTS!!!!! IM ON QUESTION 3, PLZ GIVE ME EXPLAINATION TO BASED ON THE LONG DIVISION!!!!!!!! (circled in red) USE THE CHART TOO
PLZ ANSWERRRRRRR
people i see u hre so plz answer TmT
9514 1404 393
Answer:
3. Asia Gil
Step-by-step explanation:
You should be able to answer question 3 without any math whatsoever. The average amount of the bills will be a number between the highest and the lowest. As you found, it is $23.39.
The question is, "Who will save the most by paying the average amount?" Quite obviously it will be the person who would otherwise pay the most--the person with the highest bill amount: Asia Gil.
_____
Equally obvious, the person penalized the most by sharing the bill is the one who had the lowest bill--the amount farthest below the average: Charlie Cobs.
Solve for x.
A. 19.25
B. 14
C. 10
D. 6.5
Answer:
I think it is C
Step-by-step explanation:
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of the first angle. The third angle is eleven more than the second. Find the measures (in degrees) of the three angles. (Simplify your answers completely.)
Answer: m<2 = 62 m<3=73 m<1=45
Step-by-step explanation:
m<2+m<3 =3(m<1)
m<3 = m<2+11
m<2+m<2+11=3(m<1)
2(m<2)+11=3(m<1)
m<1=2/3(m<2)+11/3
m<1+m<2+m<3 = 180
2/3(m<2)+11/3+(m<2)+m<2+11=180
8/3(m<2)+44/3=540/3
8/3(m<2)=496/3
(496/3)*3/8=62
help asap , 40 points worth ...
Robin has a collection of dimes, nickels and quarters. He has 4 times as many dimes as
nickels. He has 20 more quarters than nickels. The ratio of the number of dimes to the
number of quarters is 3:2. Which equation can be used to calculate the number of nickels,
n, Robin has?
Answer: Robin has 50 nickels, 60 dimes, and 120 quarters
Find the future value for the ordinary annuity with the given payment and interest rate.
PMT = $2,000; 1.15% compounded monthly for 2 years.
Answer:
Step-by-step explanation:
M = C( 1+i) ²
M = 2000(1+0,0115)² = $2046,2645
A rectangle with a total of 64 square centimeters has been broken into two rectangles with
areas of 40 square centimeters and 24 square centimeters as shown. The common length of
the two smaller rectangles is a whole number that is greater than either width 1 or width 2,
which are both whole numbers. From this information, determine the length, width 1, and
width 2. Explain how you found your answers.
width 1 width 2
length
40 sq. cm
24 sq. cm
Answer:
Step-by-step explanation:
40 times 24
If varies directly as y and y = 15 when = 25. If = 155 then y is
Answer:
y = 93
Step-by-step explanation:
I assume the other variable is x.
"If x varies directly as y and y = 15 when x = 25. If x = 155 then y is"
Direct variation:
x = ky
25 = k * 15
k = 25/15
k = 5/3
The direct variation equation is
x = (5/3)y
155 = (5/3)y
y = 155 * 3/5
y = 93
Which inequality pairs with ys-2x-1 to complete the
system of linear inequalities represented by the graph?
O y<-2x+2
O y>-2x+2
O y<2x-2
O y>2x-2
Answer:
the answer is the last option, y > 2x-2
The system of linear inequalities y ≤ -2x - 1 and y > -2x + 3 is represented by the graph
InequalityInequality is an expression that shows the non equal comparison of two or more numbers and variables
Given the inequalities y ≤ -2x - 1 and y > -2x + 3, plotting the two inequalities using the geogebra online graphing tool.
The system of linear inequalities y ≤ -2x - 1 and y > -2x + 3 is represented by the graph
Find out more on Inequality at: brainly.com/question/24372553
PLEASE HELP ME 10 POINTS!
4/10
I'm not 100% sure though
What is the value of x?
34
146
56
68
34
Answer:
34 ° is the answer as vertically opposite angles are equal
1,2,2,4,3,6,4,____,____,10,____
Continue the pattern
Answer:
1,2,2,4,3,6,4,__8__,_5___,10,__12__
Step-by-step explanation:
Hope this helps :)
PLEASE HELPP I GIVE BRAINLIEST AND 30 POINTS PLEASEEEE
Answer:
30ft because that elevation is 30 feet away from sea level (meaning 0ft in elevation)
and farther away than 12 or 2 feet
Answer:
-12 feet,
30 feet
hope this helped! :)
Step-by-step explanation:
need help on this as soon as you can please
Answer:
x+5
Step-by-step explanation:
4x -3x= 1x or x
115-110= 5
x+5
Donna is going to swim 19 laps. She completed 12 laps what fraction of her swim remains?
Answer:
7/19 laps
Step-by-step explanation:
She has 19 total laps to do so you know that the denominator is 19.
She already completed 12 laps so that means she has 7 laps left out of the 19 total laps because 19-12= 7
What is the height of a triangle that has an area of 24 in.2 and a base with a length of 8 in.?
Answer:⬇️⬇️⬇️⬇️
Step-by-step explanation: Area of a triangle = ½base times height⇒ A = ½bh
Given that the area is 24 and the base is 8, we would have this equation
24 = ½(8)h
24 = 4h divide both sides by 4
6 = h So the height of the triangle is 6 feet
CHECK
A = ½bh
24 = ½(8)(6)
24 = 4(6)
24 = 24√
find f(x)•g(x)
pls helpppp
Answer:this is the answer of the question like at it
X+5=8x-6 solve for x
Hello!
x+5=8x-6
Move all the variables to the left:
x-8x=-6-5
-7x=-11
Divide both sides by -7:
x=11/7
Hope this helps! :)
~Just a joyful teen
[tex]GraceRosalia :)[/tex]
Answer:
x=11/7
Step-by-step explanation:
x+5=8x-6
- x from both sides
5=7x-6
+ 6 to both sides
11=7x
÷ both sides by 7
11/7=x
Solve for y
13.5
12
9
10.5
Answer:
y = 9
Step-by-step explanation:
1. We know that the line the angles fall on is a straight angle, meaning it's worth 180°.
2. Given the information above, 8y + 96 + 12 = 180.
3. (Solving equation above).
Step 1: Simplify both sides of the equation.
[tex](8y)+(96+12)=180[/tex] [tex]8y + 108=180[/tex]Step 2: Subtract 108 from both sides.
[tex]8y + 108 - 108 = 180 - 108[/tex] [tex]8y = 72[/tex]Step 3: Divide both sides by 8.
[tex]\frac{8y}{8}=\frac{72}{8}[/tex] [tex]y = 9[/tex]Step 4: Check if solution is correct.
[tex]8(9)+96+12=180[/tex] [tex]72+96+12=180[/tex] [tex]168+12=180[/tex] [tex]180=180[/tex]Therefore, y = 9.
A cylinder oil tank 8 foot deep hole it’s 580 gallons Winfield to capacity how many gallons remain in the tank on the depth of oil is 6 1/2 feet
Answer:
253.75
Step-by-step explanation:
Total height of the cylinder is 8 ft . Since the tank holds 580 gallons when filled to capacity so in 1 ft height there will be \frac{580}{8} gallons oil when filled to capacity .