Answers
Therefore, the domain is (-∞, ∞) and the range is (-∞, ∞) for the given function.
What is function?In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is associated with exactly one output. In other words, a function is a rule that assigns a unique output value to each input value.
Here,
To find the domain and range of the function f(x) = -1/4(x³ + 6x² + 5x - 4), we need to consider the restrictions on x and the possible values of f(x).
Domain:
Since the function involves a cubic expression in the numerator, there are no restrictions on x, and the domain of the function is all real numbers, or (-∞, ∞).
Range:
To find the range of the function, we need to consider the behavior of the cubic expression as x goes to positive infinity or negative infinity. As x becomes very large or very small, the dominant term in the expression becomes x³, and the other terms become negligible. The coefficient of x³ is negative, which means that the cubic expression approaches negative infinity as x goes to negative infinity and approaches positive infinity as x goes to positive infinity.
Therefore, as x approaches negative infinity, f(x) approaches positive infinity, and as x approaches positive infinity, f(x) approaches negative infinity. Hence, the range of the function is all real numbers, or (-∞, ∞).
To know more about function,
https://brainly.com/question/28193995
#SPJ1
Related Questions
The sum of 8 and t
help anyone??
Answers
Not sure if I’m wrong but I am also learning this.
Answer:
8 + tStep-by-step explanation:
The sum of 8 and t ⇒ 8 + t
A triangle has vertices at A(-3, 2), B(-1, -5) and C(4, 5). The triangle is transformed using the rule ro,o . What are the coordinates of A", B', and C?
Answers
Answer:
I thinck letter c.
Step-by-step explanation:
Because C.
Donna feeds her dog 3/4
pounds of dog food for each meal. Donna has just bought 36 pounds of dog food. For how many meals will the food last?
Answers
which measures form a triangle
Answers
\(\huge \rm༆ Answer ༄\)
Measure of each side of a triangle can't be greater than the sum of the other two sides and can't be smaller than the difference between the two other sides. therefore the most appropriate choice is ~
4 cm , 7 cm and 9 cmI hope it helps ~
We have:
1) 3 + 5 = 8 ⇒ wrong
2) 4 + 7 > 9 ⇒ right
3) 2 + 11 < 15 ⇒ wrong
ANSWER: 4 cm, 7 cm, 9 cm
Ok done. Thank to me :>
Heather's work to find the distance between two points, R(-3,-4) and S(5,7), is
shown:
RS = √(-4) (-3))² + (7 − 5)²
= √(-1)² + (2)²
= √1 + 4
= √5
-
What error, if any, did Heather make?
A. She substituted incorrectly into the distance formula.
B. She subtracted the coordinates instead of adding them.
C. She made a sign error when simplifying inside the radical.
OD. She made no errors.
Answers
The distance between points R and S is \(\sqrt{ (185)\). The correct answer is D. She made no errors.
Heather's work to find the distance between two points, R(-3,-4) and S(5,7), is shown:
RS = √(-4) (-3))² + (7 − 5)²
= √(-1)² + (2)²= √1 + 4
= √5
The error is with the order of subtraction in the formula for the distance between two points.
Heather did not make any errors in calculating the distance between two points. Therefore, the correct answer to the question above is (OD) She made no errors.
The formula for the distance between two points, A (x1, y1) and B (x2, y2), in the coordinate plane is given as;
dAB = \(\sqrt{ ((x^2 - x1)^2 + (y2 - y1)^2)\)
Comparing the given question with the formula above, we have;
A = R (-3, -4) and B = S (5, 7)The distance, AB = RS.
Therefore, we have;
RS = \(\sqrt{ ((5 - (-3))^2 + (7 - (-4))^2)\)
On solving the above equation;RS = \(\sqrt{ ((5 + 3)^2 + (7 + 4)^2)\)RS
= \(\sqrt{ (8^2 + 11^2)RS\)
= \(\sqrt{ (64 + 121)RS\)
= \(\sqrt{ (185)\)
Therefore, the distance between points R and S is \(\sqrt{ (185)\).
From the calculation, it is clear that Heather did not make any errors while calculating the distance between two points. The answer obtained by Heather is correct.
For more questions on distance between
https://brainly.com/question/15958176
#SPJ8
PLEASE HELP! A climber starts descending from 726 feet above sea level and keeps going until she reaches 27 feet below sea level. How many feet did she descend?
Answers
Answer:
found this online lol
The climber descends 533 feet to reach sea level. The climber then descends an additional 10 feet to reach 10 feet below sea level. So the climber descends:
533+10=543ft
Step-by-step explanation:
Answer:-753
Step-by-step explanation:726+-726+-27 = -27 which is where she's at now but she descended -726+-27= -753
4. Expand and simplify the product of
(x-a)?
Answers
Step-by-step explanation:
x-a
which of the following is equivalent to the radical expression below, when the denominator has been rationalized x is greater than or equal to 5
Answers
Let's continue
\(\frac{10}{\sqrt[]{x}\text{ - }\sqrt[]{x\text{ - 5}}}\cdot\text{ }\frac{\sqrt[]{x}\text{ + }\sqrt[]{x\text{ - 5}}}{\sqrt[]{x}\text{ + }\sqrt[]{x\text{ - 5}}}\text{ = }\frac{10\sqrt[]{x}\text{ + 10}\sqrt[]{x\text{ - 5}}}{x\text{ - x + 5}}\)\(\begin{gathered} \frac{10(\sqrt[]{x}\text{ + }\sqrt[]{x\text{ - 5}})}{5} \\ 2(\sqrt[]{x}\text{ + }\sqrt[]{x\text{ - 5}}) \end{gathered}\)Letter A is the correct answer
After training Naruto went to a ramen shop for dinner. Since Naruto eats ramen for lunch and dinner daily, the shopkeeper gives him a 33.33% discount. If ramen costs 45 cents, how much does Naruto spend in 15 days?
Points given: 20
Answers
To calculate how much Naruto spends on ramen in 15 days, we need to determine the total cost of ramen per day and then multiply it by 15.
Since Naruto receives a 33.33% discount, he pays 100% - 33.33% = 66.67% of the original price.
66.67% of 45 cents is (66.67/100) * 45 = 30 cents.
So, Naruto spends 30 cents on ramen per day.
To find out how much he spends in 15 days, we multiply the daily cost by the number of days:
30 cents * 15 = 450 cents.
Therefore, Naruto spends 450 cents, which is equivalent to $4.50, on ramen in 15 days.
Suppose Derrick is an insect enthusiast who measured the body length and weight of three insects in his backyard. His data are shown in the table.
Answers
Answer:
Step-by-step explanation:
The thermosphere layer of the atmosphere is between 90,000 and 110,000
meters above sea level. Which of the following elevations are in the
thermosphere? Select yes or no.
a. 9.8 x 10^-4 yes or no
b. 1.04 x 10^5 yes or no
c. 9.72 × 10^4 yes or no
d. 1.45 x 10^5 yes or no
Answers
Answer:
b yes c yes
Step-by-step explanation:
9.72 × 10^4 = 97200
1.04 x 10^5 = 104000
I need help:(
A) Plane UVW
B) Line VW
C) Point V
D) Point W
Answers
Answer:
Plane UVW
Step-by-step explanation:
If you draw the planes they overlap at Plane UVW :)
Hope this helps, have a great day :D
what is the negation of the statement "all summer days are muggy"
Answers
Answer:
What is the negation of the statement?
In Mathematics, the negation of a statement is the opposite of the given mathematical statement. If “P” is a statement, then the negation of statement P is represented by ~P. The symbols used to represent the negation of a statement are “~” or “¬”.
Step-by-step explanation:
Suta purrachina za waurdo
3 and (5 + 1 + 3)
What is the answer
Answers
Answer:
27
Step-by-step explanation:
3(5+1+3) distribute
15+ 3+ 9 add
27
A town’s population increases at a constant rate. In 2010 the population was 56,000. By 2012 the population had increased to 81,000. If this trend continues, predict the population in 2016.
Answers
The approximate population in 2016 is 91, 604 population
Let the time taken by the population to increase be "t"Let the number of the population be PThe exponential equation representing the statement is \(P=P_0e^t\)
If in 2010 the population was 56,000, then at t = 0, P0 = 56000Substituting into the formula will give:
P = 56000If by 2012 the population had increased to 81,000, then:
81000 = 56000e^12k
81000/56000 = e^12k
1.4464 = e^12k
ln1.4464 = 12k
0.3691 = 12k
k = 0.3690/12
k = 0.03076
Get the prediction of the population in 2016.
\(P = 56000e^{16(0.03076)}\\P=56000e^{0.49213}\\P = 56000(1.6357)\\P = 91,603.70\)
Hence the approximate population in 2016 is 91, 604 population
Learn more on exponential function here:https://brainly.com/question/2456547
I NEED HELP ASAP thank you so much!!
Answers
good luck
In which situation would it be appropriate to use square feet as a measurement?
Answers
Answer:
The correct answer is B ; Karla must determine the area of a floor in her house.
During the year 2011 season a quarterback passed for 302 yd per game he played on my 16 regular season game for that year for how many total yards did the quarterback pass
Answers
Answer:
4,832 yards
Step-by-step explanation:
302x16=
I attached the files
Answers
Answer:
What do u need the help for?
Step-by-step explanation:
Can someone help me with this problems with an explanation please? Thank you.
Answers
The values and heights obtained using the trigonometric ratios are as follows;
4. The six trigonometric ratios are;
cos(θ) = 15/17sec(θ) = \(1\frac{2}{15}\)sin(θ) = 8/17csc(θ) = \(2\frac{1}{8}\)tan(θ) = 8/15cot(θ) = \(1\frac{7}{8}\)5. The two other ways to write cot(θ) are;
cot(θ) = 1/tan(θ)cot(θ) = cos(θ)/sin(θ)6. The six trigonometric function values are;
cos(x) = -3/5sec(x) = \(-1\frac{2}{3}\)sin(x) = -4/5csc(x) = \(-1\frac{1}{4}\)tan(x) = \(1\frac{1}{3}\)cot(x) = 3/47. The function for the height of the tree is; H = 100·tan(θ)
The completed table is presented as follows;
θ \({}\) 10° 15° 20° 25°
H\({}\) 17.63 26.79 36.4 46.63
What are trigonometric ratios?Trigonometric ratios are functions that relate the ratio of two of the sides of a right triangle to an interior angle of the right triangle.
4. The length of the adjacent side to the angle θ according to the Pythagorean Theorem is; Adjacent = √(17² - 8²) = 15
The six trigonometric ratios are;
cos(θ) = 15/17, sec(θ) = 17/15 = 1 2/15
sin(θ) = 8/17, csc(θ) = 17/8 = 2 1/8
tan(θ) = 8/15, cot(θ) = 15/8 = 1 7/8
5. The 2 other ways to write cot(θ) are;
cot(θ) = 1/(tan(θ))
cot(θ) = cos(θ)/sin(θ)
6. The location of the point on the terminal side of the angle is; (-3, -4)
Length of the hypotenuse side = √((-3)² + (-4)²) = 5
Let x represent the angle, we get;
The six trig functions of the angle are;
cos(x) = -3/5sec(x) = -5/3 = -1 2/3sin(x) = -4/5csc(x) = -5/4 = -1 1/4tan(x) = -4/(-3) = 4/3 = 1 1/3cot(x) = 3/47. The length of the shadow of the tree = 100 m
Angle of elevation of the Sun = θ
Let h represent the height of the tree, we get;
tan(θ) = h/100
Therefore, the height of the tree, h = 100·tan(θ)
The values of the height of the tree at the different angle of elevation in the table are;
θ = 10°, h = 100 feet × tan(10°) ≈ 17.63 feet
θ = 15°, h = 100 feet × tan(15°) ≈ 26.79 feet
θ = 20°, h = 100 feet × tan(20°) ≈ 36.4 feet
θ = 25°, h = 100 feet × tan(25°) ≈ 46.63 feet
Learn more on trigonometric ratios here: https://brainly.com/question/30646429
#SPJ1
6 is added to three-fifths of p
Answers
Answer:
Is that the question? I don't think it is
Which fractions are equivalent to 1012?
Answers
\(50/60\)
That should be your answer
Answer:
Hello, There! I'm here to help!
QuestionWhich fractions are equivalent to 10/12?
AnswerAccording to The Question I'm guessing you mean 10/12
If so The Following Fractions are Equilvalent to 10/12
1. 20/24
2. 30/36
3. 40/48
5. 50/60
Step-by-step explanation:
To get Eqilvalent You Can Multiply Number to the fractions to find out what's Equilvalent
Therefore, I hope this helps you!
The blue dot is at what value on the number line?
12
8
Answers
Answer:
20
Step-by-step explanation:
question a factory manager selected a random sample of parts produced on an old assembly line and a random sample of parts produced on a new assembly line. the difference between the sample proportion of defective parts made on the old assembly line and the sample proportion of defective parts made on the new assembly line (old minus new) was 0.006. under the assumption that all conditions for inference were met, a hypothesis test was conducted with the alternative hypothesis being the proportion of defective parts made on the old assembly line is greater than that of the new assembly line. the pp-value of the test was 0.018.
Answers
Two methods can be used to administer the test.
A different theoryAbsent HypothesisThe justification for each of them is given below.What is hypothesis?Writing down the hypothesis throughout the proposal phase is required. Instead of a hypothesis that develops as a result of looking at the data, this will help to keep the research effort concentrated on the main goal and establish a firmer foundation for evaluating the study's outcomes. For these questions, answer option C is the best choice.Another possibility is that there are more faulty parts produced on the old assembly line than on the new assembly line.The value of the p is equal to 0.018, which is equivalent to 0.06 under the null hypothesis that the proportion of defective components produced on the old assembly line is equal to that produced on the new assembly line.Therefore, We infer that the solution to these questions is option C. The likelihood of noticing a difference of 0.006 is 0.018 if there is no difference in the proportions of all defective parts produced on the two assembly lines.
To learn more about hypothesis, refer to:
https://brainly.com/question/25263462
#SPJ4
=
Divide.
O EXPONENTS AND POLYNOMIALS
Dividing a polynomial by a monomial: Multivariate
(12y'u²-32ysu+15y¹uº) ÷ (-4y²u³)
Simplify your answer as much as possible.
0
X
010
Ś
Answers
The simplified expression when a polynomial is divided by a monomial is \(y^3 / u^3 (8u^4 - 3y^2u^4 - 3y^2).\)
What is factoring?A polynomial expression can be represented as a product of other, smaller polynomial expressions through the algebraic process of factoring. The process of factoring can be used to simplify expressions and solve problems. A polynomial equation's roots can be found by factoring, as can the common factors in an expression that can be eliminated. Factoring occasionally enables us to spot trends and connections between several expressions.
Depending on the kind of polynomial and the degree of the terms involved, there are several ways to factor. S
For the given expression \((12y^7u^2-32y^5u^6+15y^7u^6) / (-4y^2u^5)\) factor the common term.
\((12y^7u^2-32y^5u^6+15y^7u^6) / (-4y^2u^5)\\-4y^5u^2(3y^2 - 8u^4 - 3y^2u^4) / (-4y^2u^5)\)
Cancelling the -4:
\(= y^3 / u^3 (8u^4 - 3y^2u^4 - 3y^2)\)
Hence, the simplified expression is \(y^3 / u^3 (8u^4 - 3y^2u^4 - 3y^2).\)
Learn more about factors here:
https://brainly.com/question/26923098
#SPJ1
Can someone please help and explain I’ll mark brainliest
Answers
Answer:
It's asking what numbers (or integers) will equal to the number given. so it could be any four numbers that will give you 2174 exactly
Step-by-step explanation:
If this doesn't simplify it enough, let me know
Answer:
Here's your answer.......
.......
Find the expected value E(X) of the following data. Round your answer to one decimal place.AnswerHow to enter your answer (opens in new window)6P(X = x) 0.1x789100.2 0.2 0.2 0.3
Answers
\(E(X)=\Sigma xP(x)\)\(\begin{gathered} (6\times0.1)+(7\times0.2)+(8\times0.2)+(9\times0.2)+(10\times0.3) \\ \\ =8.4 \end{gathered}\)
Note ; We multiplied each of the x-values with their probabilities and obtain the sum of all. This gives the expected value.
Which relation is a function?
Answers
Answer:
A function is a relation in which each input has only one output. In the relation , y is a function of x, because for each input x (1, 2, 3, or 0), there is only one output y. x is not a function of y, because the input y = 3 has multiple outputs: x = 1 and x = 2.
Step-by-step explanation:
46÷6=? R ? What is the remainder for 46÷6= All i'm asking for is just the remainder.
Answers
Answer:
7.66666666667
Step-by-step explanation:
Envision stem the roots of plants are often the largest part of the plant. winter rye can grow combined root tissue well over 984,000 feet in length. write this number in expanded form.
Answers
984,000 = 900,000 + 80,000 + 4000
Expanded form of 984,000:
984,000 = (9 * 10⁵) + (8 * 10⁴) + (4 * 10³)
= (9 * 100,000) + (8 * 10,000) + (4 * 1,000)
Therefore, the answer is,
∴, 900,000 + 80,000 + 4,000