How do you factor f(x) = x^3 – 3x^2 – 10x + 24 ?
Answer:
f(x) = x³ – 3x² – 10x + 24 = (x + 3)(x – 2)(x – 4)Step-by-step explanation:
I would use the Horner method.
f(x) = x³ – 3x² – 10x + 24
f(2) = 2³ - 3·2² - 10·2 +24 = 0 ⇒ x=2 is the root of function
So:
| 1 | -3 | -10 | 24 |
2 | 1 | -1 | -12 | 0 |
therefore:
f(x) = x³ – 3x² – 10x + 24 = (x – 2)(x² – x – 12)
For x² – x – 12:
[tex]x=\dfrac{1\pm\sqrt{(-1)^2-4\cdot1\cdot(-12)}}{2\cdot1}=\dfrac{1\pm\sqrt{1+48}}{2}=\dfrac{1\pm7}{2}\\\\x_1=\dfrac{1+7}{2}=4\ ,\qquad x_2=\dfrac{1-7}{2}=-3[/tex]
It means:
f(x) = x³ – 3x² – 10x + 24 = (x – 2)(x – 4)(x + 3)
A sequence has the recursive definition f(1)= 2/3, f(n)= f(n-1)•
3/2 for n > 2
Write the first 5 terms of the sequence. Keep the answers as fractions.
Which ordered pair can be removed so that the resulting graph represents a function?
(–2, 2)
(1, 3)
(5, –4)
(–4, –4)
Answer:
(1, 3)
Step-by-step explanation:
Answer: B. 1, 3
Step-by-step explanation: On Edge!!!!
The directrix of a parabola is y = 4. Its focus is (2,6).
What is the standard form of the parabola?
Answer:
Step-by-step explanation:
The standard form of parabola having vertex ( 2 , 5) is given by y = [tex]\frac{1}{4}[/tex] ( x - 2 )² + 5.
What is a parabola ?
A parabola is a plane curve that is produced when a point moves so that its distance from a given point equals its distance from a fixed line.
We know that , the standard form or general equation of a parabola is given by :
y = a ( x - h )² + k
where : vertex is (h, k) and focus ( h , k + p)
We know that here directrix is y = k - p and a is a = [tex]\frac{1}{4p}[/tex]
It is given that focus is (2 , 6).
From focus :
h = 2 and k + p = 6
whereas from directrix :
k - p = 4
Adding both
k + p = 4
k - p = 6
We get :
2k = 10
or
k = 5
So ,
p = 1
And vertex will be :
(h , k) = (2 , 5).
The vertical distance from vertex to directrix p = 1 :
y = a ( x - 2 )² + 5
here , a = [tex]\frac{1}{4p}[/tex] or a = 1/4
So , the standard form of given parabola will be :
y = [tex]\frac{1}{4}[/tex] ( x - 2 )² + 5
Therefore , the standard form of parabola having vertex ( 2 , 5) is given by y = [tex]\frac{1}{4}[/tex] ( x - 2 )² + 5.
Learn more about parabola here :
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What is m? 45º 90º 180º 270º
need help asap
Answer:
90
Step-by-step explanation:
it looks like it's a right angle
Answer:
The answer is 90 degrees
Step-by-step explanation:
What is the first step in solving this equation?
3(2x+6) -4 = 2(5x-2) +6
Answer:
Distrubutative property
Step-by-step explanation:
what is the slope to y=−3x+7
Answer: slope= -3
Step-by-step explanation: use the slope intercept form to find slope
What is the solution 8x-3(2x-4)=3(x-6)
Answer:
x = 30
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASEquality PropertiesStep-by-step explanation:
Step 1: Define equation
8x - 3(2x - 4) = 3(x - 6)
Step 2: Solve for x
Distribute: 8x - 6x + 12 = 3x - 18Combine like terms: 2x + 12 = 3x - 18Subtract 2x on both sides: 12 = x - 18Add 18 to both sides: 30 = xRewrite: x = 30Step 3: Check
Plug in x to verify it's a solution.
Substitute: 8(30) - 3(2(30) - 4) = 3(30 - 6)Multiply: 240 - 3(60 - 4) = 3(30 - 6)Subtract: 240 - 3(56) = 3(24)Multiply: 240 - 168 = 72Subtract: 72 = 72Charlie bought 2 3/4 pounds of pears for $.76 per pound and 2 3/4 pounds of grapes for $1.40 per pound how much money in dollars and cents did Charlie pay for the pears and grapes
Answer:
$5.94
Step-by-step explanation:
Multiply 2.75 by $0.76 to get $2.09
Multiply 2.75 by $1.40 to get $3.85
Add $3.85 and $2.09 to get $5.94
Answer:
$5.94
Step-by-step explanation:
Use the law of exponents to rewrite (4x2)^9
Identify the domain and range of y = 3x - 7.
A volleyball has a mass of 4 kg Calculate the potential energy of a volleyball that is in the air at a height of 15 m. (g = 9.8 m/s
Gravitational Potential Energy = mass x acceleration due to gravity x height
GPE = mgh
ОА
147J
B
588 J
O C60
O
D
360 J
There are 12 pencils and 24 map colors to be boxed. Each box must contain only one type of item, and every item must be boxed. What is the most that can be placed in a box so that each box has the same number of items?
Answer:
the answer is 2
Step-by-step explanation:
The way I no this is because I used division and got two for each box. 24 divided by 12 = 2 for every box
Find the area of a square with side length x when x is equal to the given value.
Are the area of a square and the length of its side directly proportional? Justify your answer.
x=15 ft
Answer:
The area is 225 and they are not directly proportional
Step-by-step explanation:
find the area by doing 15 x 15 which is 225
Answer:
225
Step-by-step explanation:
easy
Y=-2(x-1)^2+8 a) Determine the coordinates of its turning point and state whether it is a Maximum or minimum B) Determine the y-intercept C)Determine the coordinates of the x-intercepts(if any)
Answer:
(a) The coordinates of the inflection point are (1; 8) and, being the value of a less than zero, then these coordinates indicate the maximum of the function.
(b) The y-intercept has a value of 6
(c) The coordinates of the x-intercepts have a value of x=3 and x=-1
Step-by-step explanation:
You know y= -2*(x-1)² + 8
(a) Every quadratic function can be expressed by the canonical form:
f(x)=y= a*( x- h)² + k
where a is the principal coefficient and the ordered pair (h; k) are the coordinates of the vertex of the parabola.
The quadratic function will have a maximum or minimum value at the vertex. If a> 0, the parabola is concave, that is, it will have its branches upwards, therefore the vertex will indicate the minimum of the function. But if a <0 the parabola is convex and the vertex will indicate the maximum of the function.
Comparing the given equation with the canonical form of a quadratic function you can see that:
a=-2h=1k=8Then, the coordinates of the inflection point are (1; 8) and, being the value of a less than zero, then these coordinates indicate the maximum of the function.
(b) The y-intercept arises from evaluating the function at x = 0. So, in this case:
y= -2*(0-1)² + 8
Solving:
y= -2*(-1)² + 8
y= -2*1 + 8
y= -2+8
y= 6
The y-intercept has a value of 6
(c) The roots or coordinates of the x-intercepts arise from evaluating the function at y = 0. So, in this case:
0= -2*(x-1)² + 8
Solving:
-8= -2*(x-1)²
[tex]\frac{-8}{-2} =(x-1)^{2}[/tex]
4= (x-1)²
√4= |x-1|
⇒ 2=x-1 → 2+1=x → 3=x
⇒ -2=x-1 → -2+1=x → -1=x
The coordinates of the x-intercepts have a value of x=3 and x=-1
julissa gave out an equal number of oranges to each of the 6 apartments on her floor. if she gave each apartment 5 oranges how many oranges did julissa give out in all
Micah's Family ate some of the two pies that he baked. which number represents the amount of pies that is left
Answer:
The answer is 6/8
Step-by-step explanation:
6/8 is the only logical answer because you need to have an answer that is less than one, 8/6 evens out to 1 1/3, 6/2 evens out to 3, and 8/4 evens out to 2. 6/8 is the only fraction that is less than one.
Answer:
its 6/8
Step-by-step explanation:
What is the radius of a circle that has a circumference of 3.14 meters?
Answer:
r≈0.5m
Step-by-step explanation:
she was right
Answer:
r≈0.5m
Step-by-step explanation:
how do I work this out, I've tried
[tex] \frac{6}{4} = \frac{k \times - 4}{ - 4} [/tex]
and that gave me
[tex] \frac{1}{ - 1.5} x[/tex]
Answer:
The required answer is [tex]y=-\mathbf{\frac{3}{2}}x\\[/tex]
Step-by-step explanation:
We are given that value of x and y vary directly so , if two values vary directly we can write
y∝x
y=kx
Now, we are given x=-4 and y=6 and we have to fill in the blank. We actually have to find value of k i.e y=____x . Yhe blanks must be filled by value of k because y=kx
Using values of x and y i.e x=-4 and y=6 to find value of k
[tex]y=kx\\6=k(-4)\\Divide \ both \ sides \ with \ -4\\\frac{6}{-4}= \frac{k(-4)}{-4} \\k=\frac{-3}{2}[/tex]
The value of k is [tex]\mathbf{\frac{-3}{2}}[/tex]
So, the required answer is [tex]y=-\mathbf{\frac{3}{2}}x\\[/tex]
3) Where do planes M and NJF intersect?
A. KJH
B. FG
C. JFG
D.GN
Answer:
C) JFG BECAUSE THAT IS WERE IT CROSSES AT
Answer:
the origen is where they all start
$11.13-$5.50-$6.12=$10.51; $30- $10.51
Please help me the picture is above, I’ll mark as brainliest.
Using the slope, state whether the lines are parallel, perpendicular, or neither.
Y= 2x-3
y=-1/2x+2
Answer:
Parralel lines have the exact same slope.
in the equation y=mx+b m is the slope
Both of these equations are in slope intercept form (y=mx+b) meaning that the coefficient in both equations is the slope.
Parralel lines have the same slope and perpendicular lines have the inverse opposite slope. For example if a line had a slope of 2 or 2/1 then the perpendicular line to it would have a slope of -1/2.
With that knowledge we can easily see that the lines are perpendicular since their slopes (represented by the coefficient) are the inverse opposite.
Perpendicular is your answer
Step-by-step explanation:
A number is called flippy if its digits alternate between two distinct digits. For example, 2020 and 37373 are flippy, but 3883 and 123123 are not. How many five-digit flippy numbers are divisible by 15?
A 3
B 4
C 5
D 6
E 8
Answer:
A
Step-by-step explanation:
The number of five-digit flippy numbers are divisible by 15 is;
Option B; 4 Numbers
We want 5 digit flippy numbers that are divisible by 15.For a number to be divisible 15, it has to be divisible by 3 and 5.
Also, for a number to be divisible by 5, it's last digit has to be 0 or 5.
Since it is a flippy digit and 0 cannot start it as it is a five digit number, then the first and last digits must be 5. Also, the center digit must be 0 or 5 to fulfill both conditions.Thus, the format of the number should be;5N5N5
For it to be divisible by 3, since 5 + 5 + 5 = 15 is divisible by 3, the N + N can be equal to 0, 6, 12, or 18 since N is identical.
Thus, possible numbers are; 50505, 53535, 56565, 59595.Read more at; https://brainly.com/question/19238760
x + 2x + 12y + 4 Using the expression shown, add like terms and produce an equivalent expression.
Answer: 3x+12y+4
Step-by-step explanation:
The only like terms are the x+2x so we add them to get the simplfied answer
Answer:
3x + 12y + 4
I dont really know how to explain but since there is an X at the and of the 2, you can add X + 2x to get 3x. Since 3x, 12y, and 4 are not alike, this is the simplest form.
What is 2x(3+x2) when x = −2?
it would be -4 i think
come back and tell me if im wrong
Peter bought 8 lemons for $6. Each lemon was the same price.
What was the cost of 1 lemon?
Answer:
The price for 1 lemon is $0.75
Step-by-step explanation:
8x=$6
8x/8=6/8
x=$0.75
write this equation in word form.
x3 + 1
Answer:
X cubed plus one
Step-by-step explanation:
Determine if each quotient is correct.
Choose true or false for each equation.
A. -4 ÷ 1 = -4 true or false
B. -6 ÷ (-2) = -3 true or false
C. -7 ÷ (-7) = 1 true or false
D. 10 ÷ (-5) = 2 true or false
(1+sinA-cosA)/1+sinA+cosA=(1+sinA+cosA)/1+sinA-cosA=2cosecA
Answer:
Hi,
LHS = sinA-cosA+1/sinA+cosA-1
divide both numerator and denominator by cosA
LHS=(tanA−1+secA)/(tanA+1−secA)LHS=(tanA−1+secA)/(tanA+1−secA)
Now
sec2A=1+tan2Asec2A=1+tan2A
sec2A−tan2A=1sec2A−tan2A=1
Using above relation at denominator of LHS
LHS=(tanA−1+secA)/(tanA−secA+sec2A−tan2A)LHS=(tanA−1+secA)/(tanA−secA+sec2A−tan2A)
LHS=(tanA−1+secA)/((secA−tanA)(−1+secA+tanA))LHS=(tanA−1+secA)/((secA−tanA)(−1+secA+tanA))
LHS=1/(secA−tanA)LHS=1/(secA−tanA)
LHS=RHSLHS=RHS
Hence Proved.
I think above proof will clear your doubt,
All the best.