For the function f(x) = -x^3 + 2x^2 + x - 2
a. Show that (x - 1) is a factor of f(x).
b. Find other factors.
c. Sketch the graph of f(x) = -x^3 + 2x^2 x - 2
Answers
Answer:
Step-by-step explanation:
a)
[tex]f(1)=-1^3+2*1^2+1-2=-1+2+1-2=0\\\\[/tex]
b)
Rationnel roots are divisor of -2: -1,1,-2,2
[tex]f(-1)=-(-1)^3+2*(-1)^2+(-1)-2=1+2-1-2=0\\\\\begin{array}{c|cccc}&x^3&x^2&x&1\\---&---&---&---&---\\&-1&2&1&-2\\x=1&&-1&1&2\\&-1&1&2&0\\\\x=-1&&1&-2\\&-1&2&0\\---&---&---&---&---\\\end {array}\\\\\\f(x)=-x^3+2x^2+x-2=(x-1)(x+1)(-x+2)\\\\[/tex]
c) see picture
Related Questions
Y/3 -4 = 2 What does Y equal?
Answers
Answer:
y = 18
Step-by-step explanation:
y/3 - 4 = 2
y/3 = 6
y = 18
Complete the arithmetic sequence with its missing terms, then state the rate of change for the sequence.
92, _, _, _, 80
Answers
Answer:
89,86,83
Step-by-step explanation:
92-80=12
12÷4=3
80+3=83
83+3=86
86+3=89
The complete arithmetic sequence will be: 92, 89, 86, 83, and 80.
What is an arithmetic sequence?Let a₁ be the first term and d be a common difference.
Then the nth term of the arithmetic sequence is given as;
aₙ = a₁ + (n - 1)d
Given; The first term (a₁) is 92 and the fifth term (a₅) is 80.
Then the common difference between the terms will be given as;
a₅ = a₁ + (5 - 1)d
80 = 92 + 4d
-12 = 4d
d = -3
Then the missing terms will be
92, 92 - 3, 92 - 6, 92 - 9, and 92 - 12
92, 89, 86, 83, and 80
Hence, the complete arithmetic sequence will be: 92, 89, 86, 83, and 80.
More about the arithmetic sequence link given below;
brainly.com/question/12373434
#SPJ2
4= 2/9x. I need help anyone
Answers
Step-by-step explanation:
4×2= 9x
8/9=x
Transposition
Answer:
x = 8/9
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Mack beat his opponent by
SEVEn points in a game which
ends when a total of
101 points have been scored.
How many point did Mark
have
Answers
Answer:
94
Step-by-step explanation:
When a player reaches 101 points, they win. So that means that Mack reached 101 points. Since his opponent was seven points behind, we can subtract 7 from 101 to find Mark's, that is Mack's opponent's, score:
[tex]101-7=94[/tex]
Therefore, we can safely conjecture that Mark scored 94 points.
what does answer on her sceen mean? 9e+10
Answers
Answer:
19e
Step-by-step explanation:
Find the circumference of the circle. Use π ≈ 3.14 5cm
Answers
Answer:
31.4cm
Step-by-step explanation:
Use 2 pie r
Someone answer this please
Answers
Answer:
[tex] →\frac{8xy}{24y} = \frac{8}{24} . \frac{xy}{y} = \frac{1}{3}. x = \boxed{ \frac{x}{3} }✓ \\ [/tex]
x/3 is the right answer.In Exercises 9-12 solve y=f(x) for x then find the input when output is 2 9. F(x)=x+5 10. F(x)=2x-3 11. F(x)= 1/4x -1 12. F(x)= 2/3x+4
Answers
Step-by-step explanation:
Q9 . y = x + 5
x= y-5
× the input
y the output
x= -3
Q10.
y = 2x -3
y+3 = 2x
x = (y+3) ÷ 2
× = 5/2
= 2.5
Q11.
y = 1/4x - 1
y+1 = 1/4 x
4y+4 = x
x = 12
Q 12 .
y = 2/3x + 4
y-4 = 2/3x
3(y-4) = 2x
x = 3(y-4)/2
x = -3
9. Use Structure Point K is of the way from |(4,-5) to L(0, -7). a. What are the coordinates of Kif n = 4? b. What is a formula for the coordinates of K for any n?
Answers
Dividing the segments, it is found that:
a) The coordinates of K if n = 4 are [tex](5,-frac{9}{2})[/tex]b) [tex]K - J = \frac{1}{n}(J - L)[/tex]----------------------------
The endpoints are [tex]J(4,-5)[/tex] and [tex]L(0,-7)[/tex].Point K is (x,y).Since point K is [tex]\mathbf{\frac{1}{n}}[/tex] of the way from J to L, it means that:[tex]K - J = \frac{1}{n}(J - L)[/tex]
And this is the answer to option b.
----------------------------
Option a:
If [tex]\mathbf{n = 4}[/tex], it has that:
[tex]K - J = \frac{1}{4}(J - L)[/tex]
This is applied to find both the x-coordinate and the y-coordinate of K.
----------------------------
The x-coordinate of K is x.The x-coordinate of J is 4.The x-coordinate of L is 0.Thus:
[tex]K - J = \frac{1}{4}(J - L)[/tex]
[tex]x - 4 = \frac{1}{4}(4 - 0)[/tex]
[tex]x - 4 = 1[/tex]
[tex]x = 5[/tex]
----------------------------
The y-coordinate of K is y.The y-coordinate of J is -5.The y-coordinate of L is -7.Thus:
[tex]K - J = \frac{1}{4}(J - L)[/tex]
[tex]y - (-5) = \frac{1}{4}(-5 - (-7))[/tex]
[tex]y + 5 = \frac{2}{4}[/tex]
[tex]y = \frac{1}{2} - 5[/tex]
[tex]y = \frac{1}{2} - \frac{10}[2}[/tex]
[tex]y = -\frac{9}{2}[/tex]
The coordinates of K if n = 4 are [tex](5,-frac{9}{2})[/tex]
A similar problem is given at https://brainly.com/question/20847604
If mean of first 3 digits is 19 and next 2 digits is 18, what would be the mean of all 5 digits?
Answers
Mean of total 5 digits is 18.6
Given:
Mean of first 3 digit = 19
Mean of next 2 digit = 18
Find:
Mean of total 5 digits
Computation:
Sum of first 3 digit = Mean of first 3 digit × Number of digits
Sum of first 3 digit = 19 × 3
Sum of first 3 digit = 57
Sum of next 2 digit = Mean of first 3 digit × Number of digits
Sum of next 2 digit = 18 × 2
Sum of next 2 digit = 36
Total of 5 digit = Sum of first 3 digit + Sum of next 2 digit
Total of 5 digit = 57 + 36
Total of 5 digit = 93
Mean of total 5 digits = Total of 5 digit / 5
Mean of total 5 digits = 93 / 5
Mean of total 5 digits = 18.6
Learn more:
https://brainly.com/question/16645147?referrer=searchResults
The answer is "mean of all 5 digits is 18.6" and the further calculation can be defined as follows:
The mean would be the total number divided by the number of numbers. To obtain the mean, we add all the numbers and divide by number.It is also known as the "average" value, which was established by summing all data points then divided by the information gain amount.Its most popular statistics used to measure the center of a collection of data and analysis are the statistics sometimes referred to it as average by statistics.In this question, let the value are a,b,c..., and e So,Mean of 3 digits:
[tex]\to \bold{\frac{a+b+c}{3}}=19[/tex]
Mean of 2 digits:
[tex]\to \bold{\frac{d+e}{2}}=18[/tex]
Find:
Mean of all 5 digits =?
Calculating the sum of 3 digits:
[tex]\to \bold{\frac{a+b+c}{3}}=19\\\\\to \bold{a+b+c}=19 \times 3\\\\\to \bold{a+b+c}=57\\\\[/tex]
Calculating the sum of 2 digits:
[tex]\to \bold{\frac{d+e}{2}}=18\\\\\to \bold{d+e}=18\times 2\\\\\to \bold{d+e}=36\\\\[/tex]
Calculating the Mean of all 5 digits:
[tex]\to \bold{\frac{a+b+c+d+e}{5}}= \bold{\frac{57+36}{5}}[/tex]
[tex]= \bold{\frac{93}{5}}\\\\=\bold{18.6}[/tex]
So, the mean of all 5 digits is "18.6".
Learn more:
brainly.com/question/2003309
Given that
()=2(−3)2−8
f
(
x
)
=
2
(
x
−
3
)
2
−
8
, determine the true statement.
The x intercepts of the graph of f(x) are (1,0) and (5,0).
Group of answer choices
The range of f(x) is
≥−8
y
≥
−
8
.
The graph of f(x) is decreasing from
(3,∞)
(
3
,
∞
)
.
The graph of f(x) has a maximum point at (3, -8).
The domain of f(x) is
≥3
x
≥
3
Answers
Equations are used to show the relationship between variables (usually x and y). The true statement about f(x) is that the range of f(x) is [tex]y \ge -8[/tex]
Given that:
[tex]f(x) = 2(x - 2)^2 - 8[/tex]
To identify the true statement, I will make use of graphical method.
See attachment for the graph of [tex]f(x) = 2(x - 2)^2 - 8[/tex]
From the attached graph, we can see that the graph as a minimum at:
[tex](x,y) = (2,-8)[/tex]
And it opens upward.
This implies that the minimum y-value of f(x) is at -8, and it has no maximum.
In other words, the range of the function is:
[tex]f(x) \ge -8[/tex]
Hence, the true statement is option (a):
The range of f(x) is [tex]y \ge -8[/tex]
Read more about equations at:
https://brainly.com/question/17995541
Solve 2x + 4 = 12.
O A. x = -4 and x = -8
O B. x = -4 and x = 8
O C. x = 4 and x = -8
O D. x = 4 and x = -4
Answers
If ; | 2x+4|=12 —> x = 4 , x = – 8 —> The choose C.
If ; | 2x | +4=12 —> x =4 , x = – 4 —> The choose D.
I hope I helped you^_^
12-4= 8 and you will be left with 2x & 8 you divide both sides by 2 the 2 from 2x will cancel leaving you with x and 8 divided by 2 gives you 4
then if you say 4-12 that will give you -8 and you left with 2x & -8 you divide both sides by 2 leaving you with -4
Which equation corresponds to the following word problem?
Cory spends $6.50 on snacks at a gas station. He also buys gas, which costs $2.78 per gallon. If he spends a total of $24.00 at the gas station, how many
gallons of gas did he buy? Let g equal the number of gallons of gas.
(1 point)
O 6.509 +2.78 = 24.00
O 2.789 -6.50 = 24.00
O 6.50g - 2.78 = 24.00
2.789 +6.50 = 24.00
Answers
Answer:
Cory bought 6.30 gallons of gas at the gas station.
Step-by-step explanation:
total amount = cost of snacks + amount spent on gas
[tex]$\$ 24.00=\$ 6.50+\$ 2.78 \mathrm{~g}$[/tex]
[tex]$\$ 2.78 \mathrm{~g}=\$ 24.00-\$ 6.50$[/tex]
[tex]$\$ 2.78 \mathrm{~g}=\$ 17.50$[/tex]
[tex]$g=\frac{\$ 17.50}{\$ 2.78}$[/tex]
[tex]$g=6.30$[/tex]
Learn more about gallon refer:
https://brainly.com/question/18591352What is the HCF of 25, 45
Answers
Answer:
5
Step-by-step explanation:
25 = 5 x 5
45 = 5 x 9
Hey there!
25: 1, 5, & 25
because: 5 * 5 = 25 & 1 * 25 = 25
45: 1, 3, 5, 9, 15, 45
because: 1 * 45 = 45, 3 * 15 = 45, & 5 * 9 = 45
Common factors: 1 & 5
The bigger number of those two is 5
Therefore, your possible answer is: 5
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
when is x2 greater than x3?
Answers
×2 is greater than ×3 when the numbers are in negative form.
Can someone please help me please?
Answers
[2+(12×3÷9)-6]÷4
with explanation
Answers
Answer:
PEMDAS:
ZERO 0
Left to right "p" parenthesis, "e" exponents,
"md" multiplication OR division , "as" addition or subtraction
Step-by-step explanation:
[2+(12×3÷9)-6]÷4
[2+(36÷9)-6]÷4
[2+(4)-6]÷4
[6-6]÷4
[0]÷4
0
Answer:
Ans: 0
Step-by-step explanation:
[2+(12×3÷9)-6]÷4
= [2+(36÷9)-6]÷4
= [2+4-6]÷4
= [6-6]÷4
= 0÷4
= 0
Sandy can read 25 words in 5 seconds. At that
rate
Answers
Answer:
5 words a second because 5÷25 is 5 so in 1 second she reads 5 words
if a + 1 by a is equal to 3 find the value of bracket a minus 1 by a bracket square
Answers
a+1 = 3
To find:(a - 1)^2
[tex] {a}^{2} - 2.a.b + {b}^{2} \\ \\ a - 2a + 1 \\ \\ 1 + 1 = 2[/tex]
So, the answer is 2Hope it help youpls someone edit it and send
Answers
Step-by-step explanation:
1 & 2 are on the attachment
3 --------------
4)4x+5=17
5x+5=20
5)2x+15+85+x+20=180
3x+120 =180-120
3x=60
x=20 degrees
6)son's age=x
3x+x=48
4x=48
x=12
Therefore; son's age=12 years old
Mr.Robert age=12*3
=36 years old
Hope this helps you
If you have any question just ask me
If you think this is the best answer please mark me as brainiest
Erin is buying produce at a store. She buys c cucumbers at $0.69 each and a apples at $0.89 each. What does the expression 0.69c + 0.89a represent?
The expression represents the
(select)
.
Answers
Answer:
It represents the total amount that Erin is going to spend at the store.
Step-by-step explanation:
PLEASE HELPPPPPPPPPPPPP
Answers
Answer:
G
Step-by-step explanation:
three line segments : HI, EF, and JG,
intersect in one point => G
Three axis given
[tex]\\ \sf\longmapsto \overleftrightarrow{HI}[/tex]
[tex]\\ \sf\longmapsto \overleftrightarrow{EF}[/tex]
[tex]\\ \sf\longmapsto \overleftrightarrow{GJ}[/tex]
Now
All are intersected at one point G
What is 22 divided by 2,715
Answers
Answer:
0.0081031308
Step-by-step explanation:
The average yearly cumulative rainfall in Tucson by month is shown in the graph below. Does this
graph represent cumulative rainfall as a function of the day? Why or why not? What is the average
annual cumulative rainfall in Tucson? What is the approximate average rainfall in December? During
which month is average rainfall the greatest? How do you know?
Answers
Answer:
The average annual cumulative rainfall is [tex]1[/tex] inch per month.
During month of August average rain fall is greatest because slope in this month is maximum.
Step-by-step explanation:
The graph does not represent cumulative rainfall as a function of day.
Because they have average all values for month Total cumulative rainfall is [tex]12[/tex] inches.
Total period is [tex]12[/tex] month
So average annual cumulative rainfall is
[tex]$12 / 12=1$[/tex] inch per month
Average rain fall in month of December= (average cumulative rainfall in December[tex])-([/tex]average cumulative rainfall in November)
[tex]=12-11[/tex]
[tex]$=1$[/tex] inch
During month of August average rain fall is greatest because slope in this month is maximum.
Learn more about average, refer :
https://brainly.com/question/22390452
If x is an odd integer and y is a negative, odd integer, the product of x and y must be
Answers
Please Help! I will give you the brainiest and a lot of points (If you give me an unreasonable answer or something this is obviously not related to the question I will report you and all of your posts (whether their related to my questions or not).
-You have to use the Hindu-Arabic number system
Answers
[tex]\qquad[/tex]2010_(nine)
[tex]\qquad[/tex]7716_(nine)
[tex]\qquad[/tex]+_________
[tex]\qquad[/tex]9726_(nine)
Keep nine stable and add the bases
Please Help! I will give you a lot of points! You don't have to show your work unless you want to. Just the answer.
Answers
Answer:
52
Step-by-step explanation:
15+7+19+11+0=52
may help.
Convert into numbers
[tex]\\ \sf\longmapsto 15+7+19+13+11+0[/tex]
[tex]\\ \sf\longmapsto 22+32+11[/tex]
[tex]\\ \sf\longmapsto 55+11[/tex]
[tex]\\ \sf\longmapsto 66[/tex]
What is the Gcf of 10 and 6?
Answers
The GCF of 10 and 6 is 2. May this will help you.
Will three sides of any length create a triangle?
Answers
A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s2 for g. Use 1000 kg/m3as the weight density of water.)
(A water tank shaped like a triangular prism is given. The base of the prism is at the top and a spout is located at the top of the tank. The dimensions of the tank are 9 meters long, 4 meters wide, and 4 meters deep. The spout is 3 meters long.)
Answers
Answer:
W = 1.06 MJ
Step-by-step explanation:
- We will use differential calculus to solve this problem.
- Make a differential volume of water in the tank with thickness dx. We see as we traverse up or down the differential volume of water the side length is always constant, hence, its always 8.
- As for the width of the part w we see that it varies as we move up and down the differential element. We will draw a rectangle whose base axis is x and vertical axis is y. we will find the equation of the slant line that comes out to be y = 0.5*x. And the width spans towards both of the sides its going to be 2*y = x.
