Then all factors of the function f(x) = x³ – 2x² – 68x – 120 is (x + 2), (x + 6), and (x – 10).
What is a factorization?It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.
If f(–2) = 0, that mean one root is –2.
The function f(x) = x³ – 2x² – 68x – 120
We have the one factor is (x + 2)
Then the function can be written as
f(x) = (x + 2)(x² – 4x – 60)
f(x) = (x + 2)(x² – 10x + 6x – 60)
f(x) = (x + 2)[(x(x – 10) + 6(x – 10)]
f(x) = (x + 2)(x – 10)(x + 6)
More about the factorization link is given below.
https://brainly.com/question/6810544
Answer:
C
Step-by-step explanation:
edge2022
Mike received 79 dollars and 9 movie tickets for his birthday. He went to
a sporting goods store and bought a baseball glove, baseball, and bat. He had
22 dollars left over, how much did he spent on the baseball gear?
Answer:
57
Step-by-step explanation:
79-22=57
simplified?
0.018 + (3.1 × 10^-3)
Answer:
the answer is easy.. I'm glad to help you out. it is 0.018+ 3.1 × 10^-3. just simply remove the bracket
How many distinct permutations can be formed using the letters of the word believable?
Answer:
✒️Answer:No. of Permutations=3360.
Step-by-step explanation:
#CarryOnLearning[tex]watch.some.anime[/tex]
The number of distinct permutations that can be formed using the letters of the word believable is 15,1200.
What are permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
It is given that:
The word is:
"believable"
Total number of letters = 10
b repeated two(2) times
e repeated three(3) times
l repeated two(2) times
No. of Permutations = 10!/(2!3!2!)
No. of Permutations = 15,1200
Thus, the number of distinct permutations that can be formed using the letters of the word believable is 15,1200.
Learn more about permutation and combination here:
https://brainly.com/question/2295036
#SPJ5
What is the value of p?
140°
90°
p
Answer:
230 or 50
Step-by-step explanation:
but i think it os 230
Answer:
50
Step-by-step explanation:
Which expression can you use to find 16÷45?
Answer:
☆<《HOPE IT WILL HELP YOU 》>☆
Step-by-step explanation:
Exprassion is 16/45--x=0
Answer:
16 x 5/4
Step-by-step explanation:
u change division to multiplication then flip the fraction.
tada!
:)
What is the value of x in the equation −x = 6 − 4x + 18? (1 point) 24 8 −8 −24
Answer:
-8
Step-by-step explanation:
-24=6-(4x24)+18= 6-96+18=-90+18=-72
-8=6-(4x8)+18= 6-32+18=-26+18=-8
what is 0.6x + 4.8 = 7.2
Answer:
2.88x=7.2
x=7.2/2.88
x=2.5
=)
Answer:
x=4
Step-by-step explanation:
btw that's what M a t h w a y.
Rewrite the equation without absolute value.
y=|x-3|+|x-2|-|x-5|
Answer:
y = {-x, x < 2; x-4, 2 ≤ x < 3; 3x -10, 3 ≤ x < 5; x, 5 ≤ x}
Step-by-step explanation:
The absolute value function is a piecewise linear function that changes its definition when its argument changes sign.
Here, the three different absolute value expressions will change their behavior at three different values of x. That is, this equation will be described by a piecewise linear function in four (4) pieces.
For x < 2:
y = (3 -x) +(2 -x) -(5 -x) = -x
For 2 ≤ x < 3:
y = (3 -x) +(x -2) -(5 -x) = x -4
For 3 ≤ x < 5:
y = (x -3) +(x -2) -(5 -x) = 3x -10
For 5 ≤ x:
y = (x -3) +(x -2) -(x -5) = x
In summary, the equation can be written ...
[tex]y=\begin{cases}-x,&\text{for }x < 2\\x-4,&\text{for }2\le x < 3\\3x-10,&\text{for }3\le x < 5\\x,&\text{for }5\le x\end{cases}[/tex]
_____
Additional comment
The absolute value function itself can be described by ...
[tex]y=|x-a|=\begin{cases}a-x,&\text{for }x < a\\x-a,&\text{for }a\le x\end{cases}[/tex]
State the period, midline, amplitude, and range of the given graph. (I got them wrong, I will mark brainliest!)
Answer:
Period: [tex]\pi[/tex]
Midline: y = -3
Amplitude: 4
Range: [-7, 1]
Step-by-step explanation:
Period - from one peak to the next (or from one trough to the next)
⇒ Period: [tex]\pi[/tex]
Midline - center line
Range = -7 ≤ f(x) ≤ 1
[tex]\implies \sf midline =\dfrac{1-(-7)}{2}+(-7)=-3[/tex]
⇒ Midline: y = -3
Amplitude - height from the center line to the peak (or to the trough)
Maximum height: y = 1
center line: y = -3
Therefore, amplitude = 1 - (-3) = 4
Range - the set of all values that the function takes
-7 ≤ f(x) ≤ 1 → [-7, 1]
#Period
Find the distance between two peaks
It's π#Midline
Range of the pitch (Peak to trough distance)
(-7,1)Midline:-
[tex]\\ \tt\Rrightarrow \dfrac{1+7}{2}-7=4-7=-3[/tex]
Midline is y=-3#Amplitude
Midline is y=-3Trough=y=-7Distance:-
A=-3+7=4#Range
The pitch
[-7,-1]If h(x) = −2x − 10, find h(−4).
Group of answer choices
−16
−2
−18
−3
Answer:
-2
Step-by-step explanation:
h(x) = −2x − 10, find h(−4).
h(−4) = -2 × (-4) - 10
= 8 - 10
= -2
Answer:
-2
Step-by-step explanation:
did the test
A line with a slope of
–
6 passes through the points (
–
6,
–
5) and (
–
7,c). What is the value of c?
Answer:
c=11
Step-by-step explanation:
We have two points ( 6,5) and (7,c) and a slope of 6
The slope formula is
m = ( y2-y1)/(x2-x1)
6 = (c-5)/(7-6)
6 = (c-5)/1
6 = c-5
Add 5 to each side
6+5 = c-5+5
11 =c
PLEASE HELP! I WILL MAKE YOU BRAINLIST!
Answer: I think it is C
Step-by-step explanation: 32/4=8 so 1 cm = 8km
A simple random sample of size n is drawn from a normally distributed population, and the mean of the sample is x overbar, while the standard deviation is s. what is the 99% confidence interval for the population mean? use the table below to help you answer the question. confidence level 90% 95% 99% z*-score 1.645 1.96 2.58 x overbar plus-or-minus startfraction 0.90 times s over startroot n endroot endfraction x overbar plus-or-minus startfraction 0.99 times s over startroot n endroot endfraction x overbar plus-or-minus startfraction 1.645 times s over startroot n endroot endfraction x overbar plus-or-minus startfraction 2.58 times s over startroot n endroot endfraction
The 99% confidence interval for the population mean will be x± [tex]\frac{2.58 s}{\sqrt{n} }[/tex].
What is a confidence interval?
A confidence interval is a set of calculations for an unrecognized parameter that is specified as a range with a lower and upper bound.
If we take an n-sample from a normal population and wish to estimate the population mean, the confidence interval for the mean is:
[tex]\bar x[/tex]±[tex]Z_\frac{\alpha }{2} \times \frac{s}{\sqrt{n} }[/tex]
The level of significance is found by;
[tex]\rm \alpha =1- \ condifidence\ level \\\\\ \rm \alpha =1- 0.99 \\\\\ \rm \alpha = 0.001[/tex]
The value of z is
[tex]\rm Z_{\frac{\alpha}{2}} = \rm Z_{\frac{0.01}{2}} = Z_{0.005}=2.58[/tex]
Hence the 99% confidence interval for the population mean will be x± [tex]\frac{2.58 s}{\sqrt{n} }[/tex].
To learn more about the confidence interval refer to the link;
https://brainly.com/question/2396419
Answer:
x Overbar plus-or-minus StartFraction 2.58 times s Over StartRoot n EndRoot EndFraction
Step-by-step explanation:
The answer above is correct.
A ladder is resting against a wall. The foot of the ladder is `5`feet from the wall, and the top of the ladder is `16`feet from the ground. What is the slope of the ladder?
Step-by-step explanation:
that's wrong .....wait ...........
Please Help its A Math Problem!!! Please & thank you
Answer:
The last one is correct answer.
Given the sequence: 4.5, 5.75, 7, 8.25, Find the common difference
Answer:
1.25 is the common difference
Step-by-step explanation:
Which of these is a reason an engineer may choose to use a prefabricated building component?
Answer: She wants to reduce costs
Step-by-step explanation:
Answer:
She wants the construction to move more quickly
Step-by-step explanation:
this was the correct answer as shown on the quiz. the choices were changed
Manny invested $1,200 at a simple interest rate of 5% (0.05). How much money would he have after 7 years?
Determine the missing interior and exterior angles of the triangle shown below.
Answer:
∠c=50°, ∠1=95°, ∠2=135°, ∠3=130°
Step-by-step explanation:
Let's start with [tex]c[/tex]. We know that, universally, every angle in a triangle will add up to be 180°. Therefore, we do [tex]45+85=130[/tex]. Then, [tex]180-130=50.[/tex] This means ∠[tex]c[/tex] = 50°.
Then, for the other angles, we can use the rule that a straight line is equal to 180°. So for example, ∠1 + 85° = 180.
As a result:
∠1 = [tex]180-85=95[/tex]°
∠2 = [tex]180-45=135[/tex]°
∠3 = [tex]180-50=130[/tex]°
Which professional’s advice is Peter seeking?
Peter wants to buy office space for his new business. However, he is not sure if the current market is suitable for buying property. Hence, he consults his agent for advice.
Answer:Real estate agent
Step-by-step explanation:
got it right
Answer:
Real Estate Agent
Step-by-step explanation:
Which of the following differences could not give a distance between two points on a number
line? Explain why.
(1) 19-7
(3) -12 -(-7)
(2) -3-(-18)
(4) 14-(-6)
Answer:
Choice: (3) -12 -(-7)
Step-by-step explanation:
The distance between two points is by definition a positive number. If we wanted to know the distance between points 5 and 8, we should use the absolute value of the difference:
d=|5-8|=8-5=3
The same applies to negative points like -2 and -7:
d=|-2+7|=|2-7|=7-2=5
The only choice that does not result in a positive distance is (3) because
-12-(-7)=-12+7=-5
Thus this is not a distance between two points on a number line.
Choice: (3) -12 -(-7)
Food cost for the last 5 months has been 600. What is the average amount spend?
Helppppppppp
Answer:
The average amount spent is $120
Step-by-step explanation:
To find the average, divide 600 by 5 to get 120.
Answer:
120
Step-by-step explanation:
Solve for n.
11(n – 1) + 35 = 3nSolve for n.
11(n – 1) + 35 = 3n
Answer:
n is equal to -3
Step-by-step explanation:
11n - 11 + 35 = 3n
11n + 24 = 3n
11n - 3n = -24
8n = -24
n =-3
Answer:
n is equal to -3
Step-by-step explanation:
.
solve for x (x+2)(x-1)
Answer:
See below.
Step-by-step explanation:
Given :-
x + 2x - 1To Find :-
Values of xSolving :-
x + 2 = 0x = -2x - 1 = 0x = 1Solution :-
x = -2x = 1AB←→is reflected to form A'B'←→−.
The coordinates of point A are (0, 2) and the coordinates of point B are (2, 5).
Which reflection results in the transformation of AB←→ to A'B'←→−?
reflection across the x-axis.
reflection across the y-axis
reflection across y = x.
reflection across y=−x.
Answer: reflection across y = x
Step-by-step explanation:
Answer:
Rotation of 180°
Step-by-step explanation:
Write the following quotient in scientific notation:
Step-by-step explanation:
Let's start by simplifying our light terms.
[tex]q = \frac{33 \times 10 {}^{9} }{11 \times 10 {}^{7} } [/tex]
33 is divisible by 11 so i can simplify up and down by 11.
[tex]q = \frac{3 \times 10 {}^{9} }{1 \times 10 {}^{7} } [/tex]
Now i have 10^9 in the numerator and 10^7 in the denominator. I can remove 10^7 from up and down to get;
[tex]q = \frac{3 \times 10 {}^{9 - 7} }{1 \times 10 {}^{7 - 7} } = \frac{3 \times 10 {}^{2} }{1 \times 10 {}^{0} } = \frac{3 \times 10 {}^{2} }{1 \times 1} [/tex]
[tex]q = 3 \times 10 {}^{2} [/tex]
And that is your scientific notation.
Bob made 25 free throws out of 40 free throws he attempted every 5 minutes. How many free throw did bob make in 12 minutes
Answer: 300
Step-by-step explanation: 25 times 12 = 300. 20 times 12 = 240. 5 times 12 = 60. 60 + 240 = 300
Answer:
300
Step-by-step explanation:
25 times 12 = 300. 20 times 12 = 240. 5 times 12 = 60. 60 + 240 = 300
The slope of a line is 2/3 . What is the slope of a line that is perpendicular to this line?
- 3/2
Step-by-step explanation:
for perpendicular:
m1×m2= -1
50 POINTS!
Determine which function has the greater rate of change, if either.
A. Function B has a greater rate of change because it's rate of change is 4/3
B. Function A has a greater rate of change because it's rate of change is 4/3
C. Neither function has a greater rate of change because their slopes are both 4/3
EXPLAIN
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
so let's get two points from each table to get their slope or rate
for function A hmmm (2 , -5) and (6 , -2), and for function B hmmm (-5, -46) and (7 , -30)
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}}\implies \cfrac{-2+5}{4}\implies \stackrel{\textit{\Large A}}{\cfrac{3}{4}} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-46})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{-30})[/tex]
[tex]\stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-30}-\stackrel{y1}{(-46)}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{(-5)}}}\implies \cfrac{-30+46}{7+5}\implies \cfrac{16}{12}\implies \stackrel{\textit{\Large B}}{\cfrac{4}{3}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{\Large B}}{\cfrac{4}{3}}~~ > ~~\stackrel{\textit{\Large A}}{\cfrac{3}{4}}~\hfill[/tex]
A tent has the shape of a pyramid on a rectangular base of length 6 meters and width 4 meters.How much space is inside the tent if its 5 meters high
Answer:
Space inside tent is 60m³
Step-by-step explanation:
Given length 6m, width 4m is rectangular base and height of tent 5m
Space = Volume of Pyramid = ⅓ × area of base × height
⅓ × 6 × 4 × 5 = 60m³
PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY :)