If you were given the equation f ( x ) = 3x⁵+6x, what behavior would the ends of the graph have?
a. Both ends will point up
b. Both ends will point down
c. the left end will start down at a large negative and the right end will go upwards
d. the left end will start up at a large positive and the right end will go downwards EXPLAIN ANSWER
Answers
You can know the behavior of the function f(x)=3x⁵+6x by given values to the variable x and plot each point obtained. For example:
If x=-1⇒ f(-1)=3(-1)⁵+6(-1)=9
If x=0⇒ f(0)==3(0)⁵+6(0)=0
If x=1⇒ f(1)=3(1)⁵+6(1)=9
Therefore, as you can see in the graph attached, the correct answer is:
c. The left end will start down at a large negative and the right end will go upwards.
The ends of the graph of the function f(x) = 3x^5 + 6x will display the behavior described in option c. This is due to the highest power of x in the equation being an odd number and the coefficient being positive. As such, the left end of the graph will start down at a large negative and the right end will go upwards.
Explanation:The behavior of the ends of the graph of the function f(x) = 3x^5 + 6x is determined by the highest power of x in the equation, which is 5 in this case. The coefficient of x^5 is positive, so as x approaches positive infinity, f(x) also approaches positive infinity. Conversely, as x approaches negative infinity, the value of f(x) would approach negative infinity. We can describe this behavior as the left end of the graph starting at a large negative and the right end going upwards. Thus, answer c. 'the left end will start down at a large negative and the right end will go upwards' is correct.
Learn more about End behavior of polynomial functions here:https://brainly.com/question/19809669
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Related Questions
What are the roots of the polynomial equation?
x2−14x−32=0
Answers
We can easily factor that into:
(x +2) * (x -16) = 0
x1 = -2
x2 = 16
We are given the quadratic equation :
[tex] x^{2} -14x-32=0 [/tex]
Now let us use AC method to factorise it.
Step 1:
Find product of A and C
A=1 and C =-32
A*C =-32
Step 2:
Find factors of -32 such that they add up to give -14.
Factors of -32 that add up to give -14 are -16 and 2.
Step 3:
Rewrite the equation using factors found in step 2.
[tex] x^{2} -16x +2x -32 =0 [/tex]
Step 4:
Factoring by grouping.
[tex] x(x-16) +2(x -16) =0 [/tex]
[tex] (x-16) (x+2) =0 [/tex]
Step 5:
Find roots.
x-16=0 gives x=16
x+2=0 gives x=-2
Answer : Roots of the given Polynomial equation are 16 and -2.
We are given the quadratic equation :
[tex] x^{2} -14x-32=0 [/tex]
Now let us use AC method to factorise it.
Step 1:
Find product of A and C
A=1 and C =-32
A*C =-32
Step 2:
Find factors of -32 such that they add up to give -14.
Factors of -32 that add up to give -14 are -16 and 2.
Step 3:
Rewrite the equation using factors found in step 2.
[tex] x^{2} -16x +2x -32 =0 [/tex]
Step 4:
Factoring by grouping.
[tex] x(x-16) +2(x -16) =0 [/tex]
[tex] (x-16) (x+2) =0 [/tex]
Step 5:
Find roots.
x-16=0 gives x=16
x+2=0 gives x=-2
Answer : Roots of the given Polynomial equation are 16 and -2.
PLEASE HELP
8.04b
1. Eliminate the parameter.
x = 5t, y = t + 8
A) y = 5x + 8
B) y = x divided by five + 8
C) y = 5x - 8
D) y = x divided by five - 8
2. Eliminate the parameter.
x = square root of x , y = 3t + 7
A) y = 3x2 + 7
B) y = 3 square root of x + 7, x ≥0
C) y = 3 square root of x - 7, x ≥0
D) y = 3x2 - 7
3. Eliminate the parameter.
x = t2 + 2, y = t2 - 4
A) y = x - 6, x ≥ 1
B) y = x + 6, x ≥ 1
C) y = x2 - 6, x ≥1
D) y = x2 + 6, x ≥1
4. Eliminate the parameter.
x = 4 cos t, y = 4 sin t
Answers
Question 1. Eliminate the parameter. x = 5t, y = t + 8
Answer: option B: y = (x / 5) + 8 ↔ x divided by 5 + 8
Explanation:
1) From x = 5t => t = x / 5
2) Substitute t in y = t + 8 => y = (x / 5) + 8
Which is the option B) y = the division of x by 5, added to 8.
Question 2. Eliminate the parameter.
There is an error in the question, because it says x = √x
If the righ question is x = √t , y = 3t + 7 , then the answer is the option A) y = 3x^2 + 7
Explanation:
1) Given: x = √t , y = 3t + 7
2) from x = √t => t = x^2
3) Substitute t = x^2 in y = 3t + 7
=> y = 3 x^2 + 7 ↔ option A) y = x^2 + 7
Question 3. Eliminate the parameter.
x = t^2 + 2, y = t^2 - 4
Answer: option A) y = x - 6
Explanation:
1) From x = t^2 + 2 => t^2 = x - 2
2) Substitute t^2 in y = t^2 - 4
=> y = x - 2 - 4
=> y = x - 6, since t^2 is ≥ 0, then x ≥ 0
=> option A) y = x - 6, x ≥ 1
Question 4. Eliminate the parameter.
x = 4 cos t, y = 4 sin t
Answer: x^2 + y^2 = 16
Explanation:
1) Square both sides of x = 4 cost
=> x^2 = (4 cos t)^2
x^2 = 16 (cos t)^2
2) Square both sides of y = 4 sin t
y^2 = 16 (sin t)^2
3) Add x^2 and y^2
x^2 + y^2 = 16(cos t)^2 + 16 (sin t)^2
=> x^2 + y^2 = 16 [ (cos t)^2 + (sin t)^2 ]
4) since (cos t)^2 + (sin t)^2 = 1
x^2 + y^2 = 16
Mrs. Rodriguez has 18 packages of pens in stock at her store on monday. On tuesday, she has 5/6 the number of pens she had on monday. On Wednesday, she has 2/5 of the number of pens she had on tuesday. How many packages of pens does she hve on Wednesday?
Answers
Mrs. Rodriguez has 18 packages of pens in stock at her store on Monday.
[tex] Number \; of\; packages\; of \; Pens\; on\; Monday=18\\ \\ [/tex]
On Tuesday, she has 5/6 the number of pens she had on Monday, which means...
[tex] Number \; of\; packages\; of \; Pens\; on\; Tuesday=\frac{5}{6} \; of \ 18 = \frac{5}{6} \times 18=\frac{90}{6}=15\\ [/tex]
On Wednesday, she has 2/5 of the number of pens she had on Tuesday, which means...
\\ Number \; of\; packages\; of \; Pens\; on\; Wednesday = \frac{2}{5} \; of \ 15=\frac{2}{5} \times 15=\frac{30}{5}=6
Conclusion:
Number of packages of pens does she have on Wednesday is 6 Packages
Picture included!
What is the slope of the line shown in the graph?
A.) -1
B.) -2
C.) 1/2
D.) 2
Answers
:D
[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 0 &,& 3~) % (c,d) &&(~ 1 &,& 1~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-3}{1-0}\implies \cfrac{-2}{1}\implies -2[/tex]
helppppppppppppppppppppppppppppppp
Answers
Now lets apply this to our expression:
[tex](y^{3} +3x)^{4} = y^{12} +12x y^{9}+54 x^{2} y^{6}+108 x^{3} y^{3} +81 x^{4} [/tex]
The third term in our binomial expansion is [tex]54 x^{2} y^{6} [/tex]; therefore, the correct answer is the fourth one.
Choose the graph which represents the solution to the inequality.
Answers
To solve the inequality:
3-2x >= -17
-2x >= -20
x <= 10 when you divide by a negative, the inequality sign switches
Graph D covers all numbers less than or equal to 10
PS. Open circle is without the bottom equal sign, Closed circle always has to bottom line. I always get confused with those.
find the arithmetic mean an of an-1 = 3.9 and an+1 = 7.1
a. 11
b. 5.5
c. 3.7
d. 1.6
Answers
Answer:
Step-by-step explanation:
Alright, lets get started.
We are asked to find arithmetic mean of two terms given.
For finding arithmetic mean, we add up the values and divide the sum by the number of values.
Here we have given two numbers , below
[tex]a_{n-1}=3.9[/tex]
[tex]a_{n+1}=7.1[/tex]
So, mean of these two numbers will be = [tex]\frac{3.9+7.1}{2}[/tex]
So, mean of these two numbers will be = [tex]\frac{11}{2}=5.5[/tex]
So, arithmetic mean for given two numbers are 5.5 : Answer (b)
Hope it will help :)
b. 5.5
Step-by-step explanation:FOR LEARNING ONLY.. not necessary to read, but I hope it helps!
you start with:
[tex]a_{n-1}=3.9\\a_{n-1}=7.1[/tex]
arithmetic questions like this are like finding an average.
so you add the values while dividing by the total of values there are.
in this case:
[tex]\frac{7.1+3.9}{2}[/tex]
which is simplified to:
[tex]\frac{11}{2}[/tex]
then decimal:
[tex]5.5[/tex]
Sylvia is going to pick out a souvenir hat while she is on vacation. She knows the price of the hat will increase by 5% when she pays sales tax. She writes the expression h + 0.05h to find the total amount she will pay for the hat if it costs h dollars. Jin correctly writes another expression, 1.05h, that will also find the the total amount Sylvia will pay for the hat if it costs h dollars. Use the drop-down menus to explain what each part of Sylvia's and Jin's expressions mean.
Answers
Sylvia's espression:
h + 0.05h
h: Original hat price.
0.05h: Increase of 5% due to sales tax.
Jin's expressions:
1.05h
h: Original hat price.
1.05: Factor for which you must multiply the original price to add 5% due to sales tax.
Answer:
Step-by-step explanation:
Sylvia's expression
H: Price of hat
0.05: percent sales tax
0.05 h: amount of sales tax Sylvia will pay
h+0.5 h: total amount Sylvia will pay
Jin's Expression
1.05: One whole plus percent sales tax
H: price of hat
1.05 h: total amount Sylvia will pay
Using the completing-the-square method, rewrite f(x) = x2 + 10x + 7 in vertex form.
Answers
f(x) - 7 = x² + 10x
Next let's add (half of 10)² to both sides of the equation: btw that is 25 but on the right side we will leave it as 5² because it will make the factoring easier
f(x) - 7 + 25 = x² + 10x + 5²
Lets simplify the left side a bit and factor the perfect square trinomial on the right.
f(x) + 18 = (x + 5)²
Finally move the constant back to the side with the binomial
f(x) = (x + 5)² - 18
The vertex is (-5, -18)
Using the completing-the-square method the vertex form of the function
f(x) = x² + 10x + 7 is f(x) = (x + 5)² - 18
The given function is:
f(x) = x² + 10x + 7
Comparing f(x) = x² + 10x + 7 with f(x) = ax² + bx + c
a = 1, b = 10, c = 7
(b/2)² = (10/2)² = 5²
Add and subtract 5² to the right hand side of the equation
f(x) = x² + 10x + 5² + 7 - 5²
f(x) = x² + 10x + 5² + 7 - 25
f(x) = x² + 10x + 5² - 18
f(x) = (x + 5)² - 18
f(x) = (x + 5)² - 18 is of the form f(x) = a(x - h)² + k which is the vertex form of a quadratic equation
Therefore, the vertex form of the function f(x) = x² + 10x + 7 is
f(x) = (x + 5)² - 18
Learn more here: https://brainly.com/question/19105786
think of 2 numbers that subtract to 5 and multiply to 24
Answers
write out all the numbers that multiply to get to 24 and subtract and see which will be 5
1 * 24 <--- -23
2* 12 <--- -10
3*8 <--- -5
4*6 <--- -2
6*4 <--- 2
8*3<--- 5
12*2<--- 10
24*1<---23
We can see that 8 and 3 multiply to get 24 and subtract to get 5
8*3 = 24
8 - 3 = 5
Hope this helps :)
The data set represents a bimonthly progression of gasoline prices over the course of several months in an unspecified city. Use a graphing calculator to determine the quadratic regression equation for this data set. x 0 2 4 6 8 y 2.86 2.89 2.93 3.04 3.11 a. c. b. d.
Answers
Answer:
y = 0.0027*x^2 + 0.0111*x + 2.8574
Step-by-step explanation:
Using Excel the procedure is:
First, insert x and y values in a table format, as can be seen in the figure
Then, select data
Next, go to insert tab and inside charts options select scatter plot without any lines
Finally, select a point in the plot, right-click, add trend line, polynomial order 2 and check display equation option
50 POINTS!
A high school coach wants to buy new shirts for the 25 members of the track team. The coach must spend less than $300 on the shirts and needs to figure out how much he can spend per shirt, s. Which of the following must be true about the inequality and the resulting graph? Check all that apply
A)The inequality should be written as 25s<300.
B)The inequality should be written as 25s>300.
C)The circle is open.
D)The circle is closed.
E)The arrow points left.
F)The arrow points right
Answers
Answer:
Step-by-step explanation:
A,C,E
What is the area of this polygon?
Answers
The polygon has a rectangle and a triangle
Area of triangle FSCW
= Length × width
= 9 × 2
= 18 square units
area of triangle FNS
= 1/2 × base× height
= 1/2 × 9 × 6
= 27 square units
Therefore the area of the polygon is
= 27 + 18
= 45 square units
Find the constant of variation k for the inverse variation. Then write an equation for the inverse variation. Y=4.5 when x = 3
Answers
Choose the option that correctly completes the statement.
A triangle must have _____ one acute angle.
at most
at least
Answers
A jar contains 17 orange,7 pink, and 4 black marbles. A marble is drawn at random.What is the probability that the marble is pink or orange
Answers
P(pink) = 7/28
P(orange) = 17/28
P(pink or orange) = P(pink) + P(orange)
P(pink or orange) = 7/28 + 17/28
P(pink or orange) = 24/28
P(pink or orange) = 6/7 or 0.857143 or 85.7%
helppppppppppppppppppppppp
Answers
10.3 units
Explanation:
Triangle ABC is a right-angled triangle. This means that we can apply special trig functions.
We are given that:
angle B = 25 degrees and AB = 4 units
Therefore:
cos(B) = adjacent / hypotenuse
cos(25) = 4 / BC
BC = 4.414 units
tan(B) = opposite / adjacent
tan(25) = AC / 4
AC = 1.865
Finally, we can get the perimeter as follows:
perimeter = AB + BC + AC
perimeter = 4 + 4.414 + 1.865
perimeter = 10.279 which is approximately 10.3 units
Hope this helps :)
Side c = 4
Angle B = 25°
Step #1: Find angle C by subtracting the other 2 angles from 180°.
C = 180° - A° - B°
C = 180° - 90° - 25°
C = 65°
Step #2: Use the Law of Sines to find side a.
a / sin(A) = c / sin(C)
a / sin(90°) = 4 / sin(65°)
a = (sin(90°) x 4) / sin(65°)
a = 4.414
Step #3: Use the Law of Sines to find side b.
b / sin(B) = c / sin(C)
b / sin(25°) = 4 / sin(65°)
b = (sin(25°) x 4) / sin(65°)
b = 1.865
So you have the sides
c = 4
b = 1.865
a = 4.414
The perimeter is all the sides added up
P = 4 + 1.865 + 4.414
P = 10.279
That can be rounded to 10.3 units
Hope this helps!
The measure of Angle E, the angle of elevation from point A to point B, is ( 3 x plus 1 ). The measure of Angle D, the angle of depression from point B to point A, is 2 ( x plus 8 ) Find the measure of each angle.
Answers
E----------------> angle of elevation
D----------------> angle of depression
we know that
E=(3x+1)
D=2(x+8)
remember that
angle of elevation is equals to angle of depression------> by alternate angles
then
E=D
(3x+1)=2(x+8)-----------> 3x+1=2x+16----------> 3x-2x=16-1-----> x=15
E=3*15+1-------> 46°
D=2*15+16-----> 46°
the answer is
the measure of angle of elevation and angle of depression is 46°
.help please and thank you
Answers
helpppppppppppppppppppppppppppppp
Answers
-------------------------------
-x³+5x² (x²+4x+3)----------- > the quotient q(x)
4x²-17x-15
-4x²+20x
3x-15
-3x+15
the quotient q(x) is x²+4x+3
the answer is the option x²+4x+3
Graph the following inequality and then select the correct graph below.
y ≤ x - 2
Answers
Hope it helps.
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]y\leq x-2[/tex]
The solution of the inequality is the shaded area below the solid line
The equation of the line is [tex]y= x-2[/tex]
The slope of the line is positive [tex]m=1[/tex]
The y-intercept of the line is the point [tex](0,-2)[/tex]
The x-intercept of the line is the point [tex](2,0)[/tex]
therefore
the graph in the attached figure
Eugene knows the circumference of a circle is 125.6 meters. Does he have enough information to find the area?
Answers
Answer:
the answer is aStep-by-step explanation:
i did the test
How to find two consecutive positive even integers such that their sum is 48?
Answers
22 + 24 = 46
24 + 26 = 50
Which statement about this product is true?
0.44 ×(−5 3/4)
It is equal to 0 because 0.44 rounded to the nearest whole number is 0, and 0 times any number is 0.
It is equal to −5 3/4 because 4/4 is equal to 1, and 1 times any number equals that number.
It is greater than −3 because 0.44 × 5 3/4 is less than 1/2 × 6
It is less than −5 3/4 because multiplying by a number less than 1 gives a smaller number.
Answers
Answer:
It is greater than −3 because 0.44 × 5 3/4 is less than 1/2 × 6
Step-by-step explanation:
i guessed it and it was right so ye.
Given that (-4,1) is on the graph of f(x), find the corresponding point for the function 4f(x)
Answers
4f(-4) = 4
The point of interest is (-4, 4).
Find the range of ƒ(x) = –2x – 5 for the domain {–2, –1, 1, 2}.
Answers
By substituting each value of the domain of x in the function and solving it we will get the range of the function for respective domain
The given function is :
f(x) = -2x - 5
For x = -2 , f(x) is:
f(-2) = (-2*-2) - 5 = 4 - 5 = -1
For x = -1, f(x) is :
f(-1) = (-2*-1) - 5 = 2 - 5 = -3
For x = 1 , f(x) is
f(1) = (-2*1) - 5 = -2 -5 = -7
For x = 2, f(x) is
f(2) = (-2*2) - 5 = -4 -5 = -9
The range is -1 , -3 , -7 , -9
Hope this helps ..!!
Thank you :)
A car rental company's standard charge includes an initial fee plus an additional fee for each mile driven. The standard charge S (in dollars) is given by the function =S+0.60M18.95, where M is the number of miles driven.
The company also offers an option to insure the car against damage. The insurance charge I (in dollars) is given by the function =I+0.15M3.70
.
Let C be the total charge (in dollars) for a rental that includes insurance. Write an equation relating C to M. Simplify your answer as much as possible.
Answers
~ Natalia
can someone help me with this?
Answers
6+7 = 13 individuals under age 12
7+4 = 11 individuals 13 to 30 years old
13+11 = 24 people total from the two groups
There are 6+7+7+4+4+1 = 29 people total from the entire survey
So the final answer is 24/29. It cannot be reduced further.
Zach uses his car for business and must keep accurate driving records so that his company will reimburse him for car expenses. When he started his trip, the odometer read 26.645, When he returned home, the odometer read 28,017. Zach's car gets about 48 miles per gallon. If the tank was full at the beginning of the trip and it cost $62.28 to fill the tank at the end of the trip, what price did Zach pay per gallon?
Answers
We can divide that by his average mpg to figure out how many gallons of gas he bought:
1372/48 = 28.583 gallons.
Now divide the amount he paid by this to get the price per gallon:
62.28/28.583 = $2.179 per gallon of gas.
You work at an ice-cream shop. One of your jobs is to order new ice-cream cones. You pick the cone that is 5 inches high and has a diameter of 3.5 inches. What is the volume of each cone? Use 3.14 to approximate pi. Round your answer to the nearest whole number.
Answers
the Volume of cone=(1/3)*B*h
B=the area of the base
h= the height of the cone
D=3.5 in-----------------> r=D/2=1.75 in
h=5 in
B=pi*r²---------> 3.14*1.75²=9.616 in²
V=(1/3)*9.616*5=48.08 in³--------> 48 in³
the answer is 48 in³
Answer:
The answer is about 16
Step-by-step explanation: