PLEASE HELP FAST 100 POINTS!
Construct the graph of the following function and identify its zeros on the same document. f(x) = (-x + 2)(x + 1)(x +2). Upload your document in the box below.
Answers
Answer:
Given function:
f(x) = (-x + 2)(x + 1)(x +2)We can rewrite it as:
f(x) = - (x - 2)(x + 1)(x +2)Zeros are:
- (x - 2)(x + 1)(x +2) = 0x - 2 = 0 ⇒ x = 2x + 1 = 0 ⇒ x = -1x + 2 = 0 ⇒ x = -2As leading coefficient is negative the function is decreasing.
As the function is of degree 3, it is odd.
Considering the above two factors we can define the shape of the graph:
It is decreasing function with one local minimum and one local maximum.See the graph and zero's reflected.
Analyze the function:
[tex]f(x) = \\ ( - x + 2)(x + 1)(x + 2)[/tex]
Write properties of function:
Solution:
x-intercept/zero
[tex] {x}^{1} = - 2 \\ {x}^{2} = - 1 \\ {x}^{3} = 2[/tex]
y-intercept:
[tex]y = 4[/tex]
domain:
[tex]( - \infty \: . \: + \infty )[/tex]
type of function:
[tex]cubic \: function[/tex]
standard form:
[tex]f(x) = - {x}^{3} - {x}^{2} + 4x + 4[/tex]
factorized form:
[tex]f(x) = - ( - (x + 1)( x + 2) ( - 2x + 2))[/tex]
even/odd:
[tex]neither[/tex]
bounce/cross x-axis:
[tex]x = - 2 \: . \: cross \: . \: x = - 1 \: . \: cross \: . \: x = 2 \: . \: cross[/tex]
increasing interval:
[tex]{ - \frac{1}{3} - \frac{ \sqrt{13} }{3} - \frac{1}{3} + \frac{ \sqrt{13} }{3} }[/tex]
decreasing interval:
[tex]( - \infty - \frac{1}{3} - \frac{ \sqrt{13} }{3} )( - \frac{1}{3} + \frac{ \sqrt{13} }{3} \infty )[/tex]
number of possibles real zero:
[tex]3[/tex]
number of possible turning points:
[tex]2[/tex]
order/degree:
[tex]3[/tex]
leading term:
[tex] - {x}^{3} [/tex]
leading coefficient:
[tex] - 1[/tex]
constant terms:
[tex] - 1[/tex]
end behavior:
[tex]as \: x + \infty \: f(x) - \infty \\ as \: x - \infty f(x) \infty [/tex]
Related Questions
Helppp!
What is the solution to the equation 1x + 8 = 12?
x=1
x = 5
x= 16
x = 20
Answers
A ship is 7 ft from the dock. One sailor who is standing at the front of the boat 10 ft above dock level tosses rope to another sailor who is standing on the dock to tie the boat to the dock. How is the angle of elevation for the sailor standing on the dock related to the angle of depression for the sailor standing at the front of the boat?
Answers
Answer:
ım not speak english because i'm turkish
The angle of the depression is equal to the angle of elevation for the same place.
The angle of elevation for the sailor standing on the dock is equal to the angle of depression for the sailor standing at the front of the boat which is 55 degrees.
What is angle of elevation?The angle of elevation is the angle between the horizontal line and the line of sight which is above the horizontal line.
What is angle of depression?The angle of depression is the angle between the horizontal line and the line of sight which is below the horizontal line.
Given information-
The distance between the ship and dock is 7 ft.
The one sailor is standing 10 ft above the dock level.
The another sailor is standing on the dock.
The angle of depression and elevation is shown in the image.
Here the angle made by the sailor who is 10 ft above from the dock level on the ship is,
[tex]\tan \theta=\dfrac{10}{7}[/tex]
Find the value of angle as,
[tex]\theta=\tan ^-(\dfrac{10}{7})\\\theta=55[/tex]
Hence the angle of depression is 55 degree.
As the angle of the depression is equal to the angle of depression for the same place.
Thus the angle of elevation is 55 degrees.
Hence, The angle of elevation for the sailor standing on the dock is equal to the angle of depression for the sailor standing at the front of the boat which is 55 degrees.
Learn more about the angle of depression here;
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PLEASE HELP THIS IS THE LAST QUESTION I NEED FOR AN ASSIGNMENT!!
Please show steps!!
An aquarium is being filled with water. The graph shows the height of the water over time as the aquarium is being filled.
Which statement best describes the rate of change for this situation?
a. The height of the water increases 20 inches per second
B. The height of the water increases 1 inch per second
C. The height of the water increases 5 inches per second
D. The height of the water increases 2.5 inches per second
Answers
Answer:
D
Step-by-step explanation:
Divide 5/2 and you'll get 2.5/1 or 2.5
Identity the slope and y intercept
Answers
Answer:
3,-2
Step-by-step explanation:
From the attached graph we need to find the slope and the y Intercept . The data that can beextracted from the graph is ,
The line passes through (0,3) and (1.5,0) .Hence the y Intercept here is 3 , since the graph cuts y axis at 3 units above the x axis.
Slope :-
→ m = 3 - 0 / 0 - 1.5
→ m = 3/-1.5
→ m = -2
• Hence the y Intercept is 3 and the slope is (-2) .Dado que sen =9/10 y cos =8/10, encuentre los valores restantes de las cuatro funciones trigonométricas.
Answers
Answer:
tgα = 9/8
secα = 10/8
cscα = 10/9
ctgα = 8/9
Step-by-step explanation:
PAra resolver esto, es necesario conocer como se determinan las funciones trigonométricas en general. Ya tenemos el valor del seno y coseno de un angulo dado (supongamos un angulo α)
Si senα = 9/10 y cosα = 8/10, para calcular la tangente se aplica la siguiente expresión:
tgα = senα / cosα (1)
Reemplazando tenemos:
tgα = (9/10) / (8/10) Aqui se simplifican los 10, y nos queda
tgα = 9/8Nos quedan 3 funciones, y son las inversas de estas 3 funciones anteriores, y se determinan de la siguiente forma:
secα = 1 / cosα (2)
cscα = 1 / senα (3)
ctgα = 1 / tgα = cscα / secα (4)
Aplicando estas 3 expresiones tenemos:
secα = 1 / (8/10) Se aplica inversión de numerador y denominador
secα = 10/8cscα = 1 / (9/10)
cscα = 10/9ctgα = 1 / (9/8)
ctgα = 8/9Espero te sirva
If 3 meters of a pinya cloth cost P200, how much will 9 meters of the same cloth cost? *
Answers
9 meters cost P600
Step-by-step explanation:
3×3 = 9
p200×3 =P600
A bag contains 5 green marbles, 7 yellow marbles, 4 blue marbles, 6 pink marbles, and 3 purple marbles. If two marbles are chosen without replacement, find the probability of choosing a yellow marble, then another yellow marble. Give your answer as a fraction in simplest form.
Answers
Answer:
The probability of choosing a yellow marble then choosing another one without replacement is 1/30.
Step-by-step explanation:
First, get the total amount of marbles.
5 + 7 + 4 + 6 + 3 = 25 total marbles.
Now find the probability of finding a yellow marble.
P = 5 yellow marbles / 25 total marbles.
Now find the probability of finding a yellow marble after pulling one without replacement.
P = 4 yellow marbles / 24 total marbles.
To find the probability of both events happening, multiply the probabilities together.
(5/25) * (4/24)
Multiply the numerators and denominators.
20/600
Simplify.
1/30.
Please help as soon as possible
Answers
Answer:
d, b + b + 3c and 2b + 3c
Step-by-step explanation:
what is the mean of 12,24,24 and 52?
Answers
Answer: 28
Step-by-step explanation: Mean will be the average of all your numbers divided by the amount of numbers you have. So
24+24+12+52=112
Now since you have 4 numbers divide 112 by 4
So your mean is 28
Have a wonderful day!
Mezclas de alimentos. Un chef repostero creó una solución de azúcar de 50 onzas constituida por 34% de azúcar con una solución de azúcar al 20% y otra solución al 40%. ¿Qué cantidad utilizó de la solución de azúcar al 20% y de la solución al 40%?
Answers
Answer:
Las cantidades empleadas para su preparación son: 15 onzas de solución al 20 % y 35 onzas de solución al 40 %.
Step-by-step explanation:
Podemos estimar la proporción de ingredientes mediante el siguiente promedio ponderado:
[tex]0.34= \frac{0.2\cdot m_{A} + 0.4\cdot m_{B}}{m_{A}+m_{B}}[/tex] (1)
Donde:
[tex]m_{A}[/tex] - Masa de la solución al 20 %, en onzas.
[tex]m_{B}[/tex] - Masa de la solución al 40 %, en onzas.
Podemos simplificar la formula como sigue:
[tex]0.2\cdot x + 0.4\cdot (1-x) = 0.34[/tex] (2)
Donde [tex]x[/tex] es la proporción de la solución al 20 % dentro de la solución final, sin unidades.
Ahora resolvemos para [tex]x[/tex] en (2):
[tex]0.4-0.2\cdot x = 0.34[/tex]
[tex]0.2\cdot x = 0.06[/tex]
[tex]x = \frac{0.06}{0.2}[/tex]
[tex]x = 0.3[/tex]
Este resultado quiere decir que la solución al 34 % es el resultado de 30 % de la solución al 20 % y 70 % de la solución al 40 %. Si conocemos que la solución final tiene una masa de 50 onzas, entonces las cantidades empleadas para su preparación son: 15 onzas de solución al 20 % y 35 onzas de solución al 40 %.
What is the probability of flipping a coin 85 times and getting tails 50 times or
fewer? Round your answer to the nearest tenth of a percent.
A. 33.2%
B. 0.4%
C. 95.9%
D. 99.8%
Answers
Answer:
C: 95.9%
Step-by-step explanation:
To find this, we shall be using the cumulative binomial probability calculator
As we know, the probability of getting a head or a tail in a throw of a coin is same with a value of 0.5
So, we want to find the probability of getting tails 50 times or fewer which means the probability of getting at most 50 tails
So we have the parameters as follows;
P( x ≤ 50)
n = number of trials = 85
p = probability of success = 0.5
r = number of success = 50
Using the parameters in the cumulative binomial probability calculator, we have the value as ;
0.9589 = 95.9%
Answer:
answering so the guy above gets brainliest
HELP IM BEING TIMEDDDDDDDDDDDDDDDDDDDDDDDDD
Answers
Answer:
B
Step-by-step explanation:
Answer:
B. The sign is buried 0.6 of a meter below the ground
Step-by-step explanation:
-1.8 = how far underground the capsule is
+1.2 = how much dirt was added on top of the capsule
-0.6 = where the sign was placed, on top of the 1.2 meters of dirt
Hope this helps! :)
A pair of shoes that normally sells for $85.00 goes on sale for 35% off.
Sean thinks that the sale price should be $50.00 but Melanie disagrees and says the price should be $55.25. Aiyanna says they are both wrong and decides the price should be $29.75.
Who is correct and why?
a. Melanie is correct.
b. Sean is correct.
c. Aiyanna is correct.
Answers
Answer:
A
Step-by-step explanation:
Melanie is correct
85 x 0.35 = 29.75
85 - 29.75 = 55.25
Answer:
a. Melanie is correct
Step-by-step explanation:
35% of 85= 29.75
*Find this by finding 10% (move decimal place over) and five percent (half of ten percent) and add triple of 10% plus the 5% or look it up*
Subtract this from 85
85-29.75=
$55.25
Hope this helps! Have a nice day :)
Help!!‼️‼️
How old am lif 500 reduced by 4 times my age is 256?
Answers
Answer:
Question 1172264: How old am I if 500 reduced by 4 times my age is 256? How old am I if 500 reduced by 4 times my age is 256? A is our age. 500 - 4A = 256.
Step-by-step explanation:
thank me later
5) The coordinates of A are (1, 0) and the coordinates of B are (2, 6), what are the coordinates of the midpoint of AB?
Answers
Answer:
The coordinate of the midpoint of AB is (1.5, 3).
Step-by-step explanation:
The midpoint of AB is the point that is the same distance between both points A and B. In order to find the midpoint, add the x and y values of points A and B respectively, and divide the sum by 2 to find the midpoint of AB. [tex]\frac{1+2}{2} = 1.5[/tex], so the x value of the midpoint is 1.5. [tex]\frac{0+6}{2} = 3[/tex], so the y value of the midpoint is 3. You'll get that the coordinate of the midpoint of AB is (1.5, 3).
You shuffle a deck of 26 cards representing the letters of the alphabet. You randomly select a card from the deck. What is the theoretical probability that the card represents one of the letters in the word "skateboard"?
Answers
Answer:
0.38461538461
Step-by-step explanation:
skateboard has 10 letters. there are 26 cards
[tex]p(a)=\frac{number of favorable outcomes}{possible outcomes}[/tex]
10/26=
Dylan wants to buy both the tablet and
the camcorder. How much will he pay
if he buys them during the sale?
Answers
Answer:
108$
Step-by-step explanation:
⚠️10 points⚠️
⚠️no links ir i will report ⚠️
Find the distance between the two points rounding to the nearest tenth (if necessary).
Answers
Answer:
8.9
Step-by-step explanation:
The distance between each point is 8.9, hope this helps!
Maya invests $3,500 into an ETF which earns 7% per year. In
30 years, how much will Maya's investment be worth if
interest is compounded semiannually (twice a year)? Round to
the nearest dollar.
Answers
Solve the following right triangle. Round your answers to the nearest tenth. B = 28.3°, C = 90°, and c= 62.4 in.
Answers
Answer:
181º isnt a triangle.
Step-by-step explanation:
need help on math please
Answers
The length of missing leg is √40 = 6..32
Answer:
This one should match according to the pythagoras theorem
Find the sum: 50 + 48 + 46 ....+10
Answers
Answer:
630
Step-by-step explanation:
Which equation can be used to find the volume of this solid? 6 in 8 in. 1 7 in. O V. 758 xa ov-+6+8 o v-7x6x8
Answers
Answer:
Option 1: V = pi(6)2(8)
Step-by-step explanation:
This is because when we plug in the value given in the picture.
Formula
The way we write this is by using our "r" which is 6. We plug in the 6 for "r" so the equation will look something like this:
Then we will plug in our height "h", which is 8. So the equation will look something like this:
So that's it. Very simple. Just remember to keep the formula in mind and you will get the hang of it.
I hope this help! :D
Equation to calculate volume of solid is V = 6 × 8 × 7
What is equation?An equation is a formula that expresses equality by connecting two expressions with an equal sign =. Equation consists of variables, constants and coefficients. Right side and left side of an equation are in equality.
There are different types of equations as linear equations, quadratic equation etc.
example: 2x + 5y + 7 = 0 is an equation
here, 2, 5 are coefficients of variables x and y, 7 is a constant value
2x² + 5x + 3 = 0 is a quadratic equation.
Given,
measurement of the sides of solid
length = 6in
Width = 8 in
Height = 7 in
Volume = Length×Width×Height
V = 6 × 8 × 7
Volume = 336 in³
Hence, V = 6 × 8 × 7 is the equation to calculate volume of solid.
Learn more about equation here:
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HELP DUE IN 10 MINS!
Circle R is defined by the equation ( x - 3)2 + ( y - 5)2 = 4. Select all of the points that lie on circle R.
A. (3,5)
B. (5,5)
C. (3,3)
D. (1,5)
E. (-1,5)
F. (3,7)
Answers
Answer:
B. (5,5)
C. (3,3)
D. (1,5)
F. (3,7)
Step-by-step explanation:
The equation of a circle with radius [tex]r[/tex] and center [tex](h, k)[/tex] is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
From this, we can find that the radius of the circle is [tex]\sqrt{4}=2[/tex] and the center of the circle is at [tex](3, 5)[/tex]. Therefore, the coordinates of all points exactly 2 units away from this center point will lie on the circle.
Out of all options given, the desired answers are:
B. (5,5)
C. (3,3)
D. (1,5)
F. (3,7)
real life example of plane in geometry
Answers
Answer: piece of paper or a door
Step-by-step explanation:
PLEASE HELP ME WITH GEOMETRY!!! Please
Answers
Answer:
100
Step-by-step explanation:
What you need to do is multiply all of the numbers together so the three sides equal 12 so you need to do 12x3 which equals to 36 and 8x8 is 64 and then add 64 and 36 which gives you 100
Solution :
The given figure consists of two shapes that are a triangle and a square . To find the total area of the figure we will first find the area of the triangle then that of the square and add them .
Let's work on this ,
Area of triangle [tex]\sf\implies\::\dfrac{1}{2}\:\times\:base\:\times\:height[/tex]In the given figure the base of the triangle is 12 inches and it's height is 8 inches .
[tex]\sf\implies\::\dfrac{1}{2}\:\times\:12\:\times\:8[/tex]6 × 8 48 inches²Now lets find the area of the square ,
Area of square = Side × Side12 × 12144 inches²Total area of the figure
Area of triangle + Area of square 48 + 144192 inches²Answer this question to get marked as brainliest!!!!
Answers
Answer:
7
Step-by-step explanation:
Ann is twice as old as mary and three times as old as donald. Together their ages total 99. How old is ann?
Answers
Answer:
54 years
Step-by-step explanation:
Given that :
Let :
Ann's age = x
Mary's age = x/2
Donald's age = x/3
x + x/2 + x/3 = 99
Take the L. C. M
(6x + 3x + 2x) / 6 = 99
11x / 6 = 99
11x = 99 * 6
11x = 594
x = 594 / 11
x = 54
Hence, Ann is 54 years
Triangle FGH is similar to triangle IJK. Find the measure of side KI. Round your
answer to the nearest tenth if necessary.
43
8
H Η
G
K
J
31
F
Answers
Answer:
[tex]5.8[/tex]
Step-by-step explanation:
Similar shapes also maintain a constant proportion of sides. Therefore, we can set up the following equation:
[tex]\frac{31}{43}=\frac{\text{KI}}{8}[/tex]
Solving, we get:
[tex]\text{KI}=\frac{8\cdot 31}{43}\approx \boxed{5.8}[/tex]
Evaluate:
26 (2n + 5) = [?]
Can someone please help me ASAP !
Answers
Answer:
it's 823 problem solved