The solutions to the functions are
a) x → –∞, y → +∞ and as x → +∞, y → –∞
b) The real solutions to the equation 4x³ - x² - 4x + 1 = 0 is x = -1 , 1 , 1/4
c) The zeros of the function f ( x ) = x³ + 6x² + 8x is x = 0, -2, -4
d) The function is odd
e) The three factors of the function are (x - 3)(x + 2)(x + 5)
f) The translation f (x - 2) + 3 means the function will shift right 2 and upward 3
g) The factor of the function is a = x - 3
What is Factorizing?Brackets should be expanded in the following ways to factorize an expression
For an expression of the form A = a ( b + c ) , the expanded version is given by A = ab + ac, i.e., multiply the term outside the bracket by everything inside the bracket
For an expression of the form A = ( a + b ) ( c + d ) , the expanded version is given by A = ac + ad + bc + bd, in other words everything in the first bracket should be multiplied by everything in the second.
Given data ,
a)
Let the function be represented as f ( x )
Now , the value of f ( x ) = -5x³ + 3x² + x - 9
The end behavior of the function is given as
As x → –∞, y → +∞ and as x → +∞, y → –∞
b)
Let the function be represented as f ( x )
Now , the value of f ( x ) = 4x³ - x² - 4x + 1
On factorizing the equation , we get
f ( x ) = x² ( 4x - 1 ) - 1 ( 4x - 1 )
f ( x ) = ( x² - 1 ) ( 4x - 1 )
Taking the common factors of the expression , we get
f ( x ) = ( x + 1 ) ( x - 1 ) ( 4x - 1 )
f ( x ) = ( x - 1 ) ( x + 1 ) ( x - 1/4 )
Therefore , the solutions of the equation are x = -1 , 1 , 1/4
c)
Let the function be represented as f ( x )
Now , the value of f ( x ) = x³ + 6x² + 8x
On factorizing the equation , we get
f ( x ) = x ( x² + 6x + 8 )
Taking the common factors of the expression , we get
f ( x ) = x ( x + 4 ) ( x + 2 )
So , the solution of the function are x = 0, -2, -4
d)
The given function f ( x ) = 3x⁵ - 9 is neither odd nor even function
e)
The fourth degree polynomial function is A = ( x + 3 ) ( x - 2 ) ( x - 5 )
f)
Let the function be f ( x )
Now , the translated function is g ( x ) = f ( x - 2 ) + 3
The translation of f (x - 2) + 3 means the function will shift right 2 and upward 3
g)
The factors of the function f ( x ) = x³ - 3x² is f ( x ) = x² ( x - 3 )
Hence , the functions are solved and factorized
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On average, Nancy has noticed that 18 trucks pass by her apartment daily (24 hours). In order to find the probability that more than 4 trucks will pass her apartment in a 5-hour time period using the Poisson distribution, find the average number of trucks per 5 hours. Round your answer to three decimal places, if necessary.
Answer:
the average number of trucks per 5 hours is 3.750 trucks per 5 hours
Step-by-step explanation:
The computation of the average number of trucks per 5 hours is given below:
= Number of trucks passed ÷ time taken × given time
= 18 trucks ÷ 24 trucks × 5
= 3.750 trucks per 5 hours
Hence, the average number of trucks per 5 hours is 3.750 trucks per 5 hours
The same is to be considered by applying the above formula
aight man can someone help me lol
Answer: 11/24
Step-by-step explanation:
whenever u see this — (
it means the opposite of. so the opposite of -5/8 is +5/8.
-1/6 + 5/8 = 11/24
lOOK AT THE SUN COME BACK THEN LOOK AT MY QUESTION.
the first one 4 x (7-3)
Answer:
Step-by-step explanation:
4×(7-3)
Solve for x.
3x-161
7x-382
Answer:
Step-by-step explanation:
7x - 382 = 3x - 161
4x - 382 = -161
4x = 221
x = 55.25
Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the interval [0, 2). (Enter your answers as a comma-separated list.)
7 csc^2 x + 3.5 cot x − 35 = 0
Answer:
Trigonometric equations are, as the name implies, equations that involve trigonometric functions. Similar in many ways to solving polynomial equations or rational equations, only specific values of the variable will be solutions, if there are solutions at all. Often we will solve a trigonometric equation over a specified interval. However, just as often, we will be asked to find all possible solutions, and as trigonometric functions are periodic, solutions are repeated within each period. In other words, trigonometric equations may have an infinite number of solutions. Additionally, like rational equations, the domain of the function must be considered before we assume that any solution is valid. The period of both the sine function and the cosine function is 2π. In other words, every 2π units, the y-values repeat. If we need to find all possible solutions, then we must add 2πk, where k is an integer, to the initial solution. Recall the rule that gives the format for stating all possible solutions for a function where the period is 2π:
sinθ=sin(θ±2kπ)
There are similar rules for indicating all possible solutions for the other trigonometric functions. Solving trigonometric equations requires the same techniques as solving algebraic equations. We read the equation from left to right, horizontally, like a sentence. We look for known patterns, factor, find common denominators, and substitute certain expressions with a variable to make solving a more straightforward process. However, with trigonometric equations, we also have the advantage of using the identities we developed in the previous sections.
Step-by-step explanation:
Trigonometric equations are, as the name implies, equations that involve trigonometric functions. Similar in many ways to solving polynomial equations or rational equations, only specific values of the variable will be solutions, if there are solutions at all. Often we will solve a trigonometric equation over a specified interval.
Find the unit rate.
Please help ty! :)
Answer:
0.008333 Servings per Calorie
Step-by-step explanation:
Im getting kicked out the house if i fail this please help
Answer:oop I put the answer in da wrong play my bad have a good day or night
Step-by-step explanation:
M=2
When using the substitution method to solve the system of equations,
what is the result of the first step?
y = 2x + 4
2x + 3y = 8
Answer:
B
Step-by-step explanation:
This is due to the fact that the first equation is saying it is equal to y so you replace the y variable with the equation
Answer:
since y=2x+4 just substitute y with 2x+4
2x + 3(2x+4) = 8
so the answer is B
how do you create a graph for linear equation? I need to graph 3x=4
Answer:
Look at the graph below, hope this helped.
Step-by-step explanation:
Use order of operations to solve:
14+15(5)-2^2
Answer: 95
Step-by-step explanation:
follow the order of operations P.E.M.D.A.S
First multiply 15 with 5 and you get 75. Next, 14+75=99
now for the last part 2^2 is 4
99-4=95
if it’s not 95 it’s 85
HELP ME PLS stock worth $60 a share dropped in value by 20% on Monday. Then it dropped again by 10$ the next Tuesday. And finally increased by 55% the following Friday. What was the final price of a share?
Answer:
58.90
Step-by-step explanation:
6x – 5 = 37 Please help I need it
98 points Please help
Answer: X = 7.
Step-by-step explanation: Move all terms that don't contain x to the right side and solve.
I'll go step-by-step.
1. Add 5 to both sides. 6x-(5+5)=37+5
2. Simplify 6x=42
3. Divide both sides by 6. [tex]\frac{6x}{6} =\frac{42}{6}[/tex]
4. Then simplify/Divide. 42 / 6 = 7
That's how you get 7!
X = 7
Hey there!
6x - 5 = 37
ADD 5 to BOTH SIDES
6x - 5 + 5 = 37 + 5
CANCEL out: -5 + 5 because it gives you 0
KEEP: 37 + 5 because it help solve for the x-value
NEW EQUATION: 6x = 5 + 37
SIMPLIFY IT!
6x = 42
DIVIDE 6 to BOTH SIDES
6x/6 = 42/6
CANCEL out: 6/6 because it give you 1
KEEP: 42/6 because it gives you the x-value
NEW EQUATION: x = 42/6
SIMPLIFY IT!
x = 7
Therefore, your answer is: x = 7
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
(05.06A)Angle ABC is formed by segments AB and BC on the coordinate grid below:
Which statement shows the measure of angle A′B′C′?
A. m∠A′B′C′ = 90 degrees
B. m∠A′B′C′ = 180 degrees
C. m∠A′B′C′ = m∠ABC
D. m∠A′B′C′ = 2 × m∠ABC
Answer:
(C) m∠A′B′C′ = m∠ABC
Step-by-step explanation:
Regardless of what translation or transformation you do to this shape, the angles will always stay the same.
Answer:
Give the other guy who answer brainlyist he is poggers.
Step-by-step explanation:
A recipe for pancake batter uses 2 cups of flour and makes 10 small pancakes. How many cups of flour are needed to make batter for 25 small pancakes?
Answer: 4.5 cups
Step-by-step explanation:
2:10
4:20
half of a cup would be 5 pancakes
so, 4.5 cups of flour will make 25 pancakes.
A bake sale sells cupcakes for $.75 and brownies for $.50 Billy spends $10 at the sale using C for cupcakes and beef or brownies write a linear equation for the amount spent by Billy for cookies and brownies
Answer:
Stuck on it
Step-by-step explanation:
what is the answer 2x5-5=
if Pentagon ABCDE was dilated to create Pentagon A'B'C'DE', what rule was used?
a- (x,y) -> (-5,7y)
b- (x,y) -> (5/2x,5/2y)
c- (x,y) -> (5x,5y)
d- (x,y) -> (5/2x,7/3y)
Answer:
B [tex](x,y) \rightarrow \left(\frac{5}{2}x,\frac{5}{2}y\right)[/tex]
Step-by-step explanation:
Dilations
Given a point A(x,y) and a scale factor k the dilated image of A, called A' is calculated as A'=(kx,ky), assuming the same scale factor is applied in both axes.
The pentagon ABCDE was dilated to create pentagon A'B'C'D'E'. To find the dilaton rule used, we must find two clear points where the coordinates of both axes can be easily read from the graph.
Point C(-2,0) maps to C'(-5,0). This gives us the scale factor for the x-axis of -5/(-2)= 5/2.
The y-coordinate of E is 2 and the y-coordinate of E' is 5. This gives us the same scale factor for the y-axis of 5/2.
Thus, the rule to dilate the pentagon is:
B [tex]\mathbf{(x,y) \rightarrow \left(\frac{5}{2}x,\frac{5}{2}y\right)}[/tex]
_____indicates the level
of uncertainty that people can
tolerate to work efficiently without
experiencing undue stress
Select one:
a. Tolerance for ambiguity
b. Risk propensity
c. Workahollism
d. Authoritaritznism
= Tolerance for ambiguity
Step-by-step explanation:
indicates the level
of uncertainty that people can
tolerate to work efficiently without
experiencing undue stress
What's the value of 280?
Question 5 options:
28
1
0
128
Answer:
28⁰ = 1
Step-by-step explanation:
If you raise a number to the power of zero, it becomes 1, regardless of the number. The only exception is 0⁰, which is undefined. Any other value to the power of zero equals one.
The easiest way to see it is like this:
Pick any value, we'll call it x
x⁴ = x⁵ / x
x³ = x⁴ / x
x² = x³ / x
x¹ = x² / x
x⁰ = x¹ / x
Because x¹ is equal to x, then x⁰ is just x/x, which is always equal to 1, unless x is equal to zero.
Answer:
280^0 is 1
Step-by-step explanation:
with exponents u have to multiply the base (280) by whatever the exponent is (0), but since the exponent is 0, use multiplicative identity to get 1. any number to ^0 is 1 because its the same as the product on no number at all (0)
its really confusing but i tried my best to explain it lol T-T
Find each difference.
A: (−5)−6
B: 35−(−8)
C: −438−(−114)
Answer:
A = -11
B = 43
C = -324
Step-by-step explanation:
-5 - 6 = -11
35 + 8 = 43
-438 + 114 = -324
I will give brainiest to whoever answers correctly !!
Which statement explains why the two systems of equations below have the same solution
Answer: "B"
The first equation B is the sum of the equations in A, while the other is obtained by multiplying the first equation in A by 2.
The first equation B is the sum of the equations in A, while the other is obtained by multiplying the first equation in A by 2 hence, the correct option is second.
What is a system of equations?An equation is an expression that shows the relationship between two or more numbers and variables.
A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
We are given the system of equation as;
A, { 6x + 8y = -10}
{2x - 5y = 12}
B, {8x + 3y = 2}
{12x + 16y = -20}
If we add the first two equations that shown in A, then;
6x + 8y + 2x - 5y = -10 + 12
8x + 3y = 2
Now the first equation in A would be multiplied by 2, So
2(6x + 8y = -10)
12x + 16y = -20
Therefore, the correct option is Option B.
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A bowl of soup at 95!C (too hot) is placed in a 22!C room. One minute later, the soup has cooled to 83!C. When will the temperature be 49!C (just right)?
Answer:
in 3 minutes and 50 seconds
Step-by-step explanation:
soup = 95c
after 1 minute = 83c
after 2 minutes = 71c
after 3 minutes = 59
soup cools down 0.2c in 1 seconds
so 10 seconds = 2c
in 3 minutes and 50 seconds = 49c
The temperature 49°C of soup bowl will be after 5.54 minutes
Newton law of coolingAccording to Newton's law of cooling, the rate of loss of heat from a body is directly proportional to the difference in the temperature of the body and its surroundingsThe formula is as follow:[tex](T-T_{s} )=(T_{0} -T_{s} )e^{-kt}[/tex]
What are the steps to solve this problem?Given[tex]T =[/tex] 83°C and 49°C
[tex]T_{s} =[/tex] 22°C
[tex]T_{0} =[/tex] 95°C
We have to find value of t for that first we will find value of k and applying all values in formula we get,(83-22)=(95-22)[tex]e^{-k}[/tex]
∴ k = -ln (61/73)
Now,
(49-22) = [tex]e^{ln(61/73)t}[/tex]
∴ t = [tex]\frac{ln (27/73)}{ln(61/73)}[/tex]
∴ t = 5.54 minutes
So, after 5.54 minutes temperature will be 49°C
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Please help! I’ll mark you as brainliest if correct
Answer:
Both answers are correct
After selecting 180 of its employees to from a new division, a company discovers that engineers outnumber analysts by a 3:1 ratio in the division. Oly analysts and engineers work in the new division. How many more analysts must the company add to the division if it wants to have a 1:1 ratio of engineers to analysts at the new division?
Answer:
I think its 90
Step-by-step explanation:
3x plus 1x is 4x divide 180 but 4 and get 45 so that meab there are 135 and 45
you need 90 more analysts to have a 1 to 1 ratio
12x12x12x10.4 in a ahedron
Answer:
it 17971.2 ;)
Step-by-step explanation:
Plz help me Plz this is 7th grade math
Answer:
d=90 e=99 f=81
Step-by-step explanation:
d is a right triangle so its a 90 degree, e is vertical angle so it would be the same as the one ajacent so its 99. F is a linear pair with e so its 81 because 180-99=81.
Consider a company that has two different divisions. The annual profits from the two divisions are independent and have distributions Profit1 ~ N(5, 3^2) and Profit2 ~ N(7, 4^2) respectively. Both the profits are in $ Million. Assume that $1 = Rs. 45
A. Specify a Rupee range (centered on the mean) such that it contains 95% probability for the annual profit of the company.
B. Specify the 5th percentile of profit (in Rupees) for the company
C. Which of the two divisions has a larger probability of making a loss in a given year?
Answer:
a) Rs 603.68
b) Rs 476.33
c) first division
Step-by-step explanation:
Total profit = profit 1 + profit 2 = P
hence P ~ N(12,74) = [tex]\frac{P-12}{\sqrt{74} } ~ N(0,1)[/tex]
A ) Specifying a Rupee range ( centered on the mean ) that contains 95% probability for annual profit of the company
$13.41 = Rs 603.68
B) specifying the 5th percentile of profit
p = $10.59 ≈ Rs 476.33
C) The division that has a larger probability of making a loss in a given year is the first division
attached below is a detailed solution of the given problem
A): Range containing 95% probability for profit of company is
(Rs. 99M, Rs. 1026M).
B): Rs. 170.1 Million.
C): First division of the company has larger probability of making a loss.
Given that:
$1 = Rs. 45
[tex]Profit_1 \sim N(5, 3^2) \\ Profit_2 \sim N(7, 4^2)[/tex]
Thus,
Company's profit:
[tex]P \sim N( 5+7, 3^2 + 4^2) = N(12, 5^2)[/tex]
A):
95% of the probability lies between 1.96 standard deviations of the mean.
Thus range is:
[tex]= (12 - 1.96\times 5, 12 + 1.96 \times 5)\\\\= (\$2.2M, \$22.8M)\\ \\= (\rm Rs. \: 99M, \rm Rs. \: 1026M)[/tex]
B): Fifth percentile is calculated as:
[tex]P(Z \leq \dfrac{p-12}{5}) = 0.05[/tex]
From p values of z score table, we get:
[tex]\dfrac{p-12}{5} = -1.644\\p = 12 - 8.22 = 3.78\\[/tex]
Thus at $3.78M dollars, or Rs. 170.1M amount, 5th percentile of profit lies.
Or 5th percentile of profit is Rs. 170.1 Million.
C): Loss is when profit < 0
Thus: p < 0
The first division of company, thus have larger probability of making a loss in a given year.
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Please help with this please
Answer:
19. w * 32
20. p / 41
Step-by-step explanation:
Product is multiplication, divided by is division.
Make sure you pay attention to what the problem says, because multiplication terms can be moved around, but division has to go a certain way.
p / 41
is not the same as
41 / p
however
w * 32
is the same thing as
32 * w
Need help ASAP swill mark Brainly
Answer:
B
Step-by-step explanation:
Hope it helps!
Answer:
-1 and 1/7
Step-by-step explanation:
hope this helps! have a great day!