According to the Rational Root Theorem, the following are potential roots of f(x) = 2x2 2x â€" 24. â€"4, â€"3, 2, 3, 4 Which are actual roots of f(x)?.
Rational root theorems are used to determine the potential roots of a polynomial function
The actual roots are 3 and -4The potential roots are [tex]\pm0.5, \pm1, \pm 1.5, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24[/tex]The function is given as:
[tex]f(x) = 2x^2 + 2x - 24[/tex]
Expand
[tex]f(x) = 2x^2 + 8x - 6x - 24[/tex]
Expand
[tex]f(x) = 2x(x + 4) - 6(x + 4)[/tex]
Factor out x + 4
[tex]f(x) = (2x -6)(x + 4)[/tex]
Set to 0
[tex](2x -6)(x + 4) = 0[/tex]
Split
[tex](2x -6) = 0\ or\ (x + 4) = 0[/tex]
Make x the subject in both cases
[tex]2x = 6\ or\ x= -4[/tex]
Solve for x
[tex]x = 3\ or\ x= -4[/tex]
So, the actual roots are 3 and -4
Recall that, the function is:
[tex]f(x) = 2x^2 + 2x - 24[/tex]
For a function,
[tex]f(x) = px^n + ax^{n-1} +.......+q[/tex]
According to rational root theorem, the roots of f(x) are:
[tex]Roots = \pm \frac{Factors\ of\ q}{Factors\ of\ p}[/tex]
The roots of 24 are:
[tex]24 = \pm1, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24[/tex]
The roots of 2 are:
[tex]2 = \pm1, \pm2[/tex]
So, the possible roots are:
[tex]Roots = \frac{\pm1, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24}{\pm 1, \pm 2}[/tex]
This gives:
[tex]Roots = \pm1, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24,\pm0.5, \pm1, \pm 1.5, \pm 2, \pm 3, \pm 4, \pm6\pm 12[/tex]
Remove repetitions
[tex]Roots = \pm0.5, \pm1, \pm 1.5, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24[/tex]
Read more about rational root theorem at:
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3 and -4 dudes and dudettes
edg2022
solve each equation by factoring 12p^2+78p-151= -7
Answer:
Ok so im not to sure but I think its 40.62 but i could be wrong since it was worded odd
Step-by-step explanation
What is 1/3 of 9/5 please help.
A rectangular sticker has an area of 50 square centimeters. Its perimeter is 30 centimeters. What are the dimensions of the sticker?
___centimeters by ____ centimeters
Length + width = 1/2 the perimeter:30/2 = 15
Area = length x width
List the factors of 50: 1, 2, 5, 10, 25, 50.
Find the two factors that when added together equal 15:
Dimensions are 5 cm by 10 cm.
See attachments for answer and math work.
Solve the equation 6(2x+4)^2=(2x+4)+2 a x=-5/3 or -9/4
Answer:
x=5/3
Step-by-step explanation:
Answer:
-5/3 or -9/4 is the answer
Step-by-step explanation:
Just completed it
Help on these two please
Answer:
21
Step-by-step explanation:
CANT SEE THEM
How to slove this equation in simple form -9(8v-2v)+10b - (100v+6)
Answer:
- 154v + 10b - 6
Step-by-step explanation:
-54v + 10b - 100v - 6
-154v + 10b - 6
Carl placed $2,600 in a savings account that compounds interest annually at a rate of 0.5%. How much will he have in the account after 7 years
Answer:
$2,691
Step-by-step explanation:
Interest (I) = Principal x Rate x Time
Total Amount (A) = Interest + Principal
I = 2600(.005)(7)
I = 91
A = 2600 + 91
A = 2691
Plz help I really need help, I’m gonna give brainlist
Answer:
angle 4 is 47 degrees....
The mass of Earth is 5.97x10^24 kg and the mass of Moon in 7.35x10^22 kg. What is the total mass? Thank you in advance
Answer:
Total mass = 5.97 × 1024 kg + 7.35 × 1022 kg. = 604.35 × 1022 kg.
Step-by-step explanation:
Please help me :)
ty ty
Answer:
the slope is stepper and the line is shifted up
I think this is the last thing I need help with, but I REALLY need this done to raise my grade!!! I'll mark brainliest!!
Answer:
Step-by-step explanation: there you go
hehehehehehhhehehe help
Answer:
Y=2
Step-by-step explanation:
If x=3 we can see that every two lines is 1 number up then the last
same for y access. Y=-2
Answer:
-2
Step-by-step explanation:
Can someone pls help me
Answer:
6π Km
Step-by-step explanation:
The arc length is calculated as
arc = circumference of circle × fraction of circle
= 2πr × [tex]\frac{120}{360}[/tex]
= 2π × 9 × [tex]\frac{1}{3}[/tex]
= 18π × [tex]\frac{1}{3}[/tex]
= 6π Km ← exact value
Which equation could have been used to create this table?
y = 3x
y = x + 3
y = x + 2
y = 4x
Answer:
y = 3x
Step-by-step explanation:
Calculate the measure of angle ADB if angle ACB is 50 degrees.
Answer:
ADB=50°
Step-by-step explanation:
Angles subtended by the same segment are equal
Therefore,the angle ∠[tex]ADB=40[/tex] degree.
What are the angles?
An angle is a form of geometrical shape, that is constructed by joining two rays to each other at their end-points.
Here given that ∠[tex]ACB=50[/tex] degree and we know alternates angles are equal so ∠[tex]CAD=50[/tex] degree.
And [tex]AD[/tex] is parallel to [tex]BC[/tex].
Therefore, the diagonals of a rhombus are at right angled.
So, ∠[tex]AOD=90[/tex] degree
Now, In Δ[tex]AOD[/tex],
∠[tex]ADO+[/tex]∠[tex]DAO+[/tex]∠[tex]AOD=180[/tex] degree
∠[tex]ADO+50+90=180[/tex]
∠[tex]ADO=+140=180[/tex]
∠[tex]ADO=180-140[/tex]
∠[tex]ADO=40[/tex] degree
or
∠[tex]ADB=40[/tex] degree.
Hence, the angle ∠[tex]ADB=40[/tex] degree.
To know more about the angles
https://brainly.com/question/15277238
#SPJ2
What is the measure of 2C?
30
30
А
30
O A. 60°
O B. 90°
O C. Cannot be determined
D. 30°
Answer:
60
Step-by-step explanation:
All sides are equal, so all angles are equal.
All angles equal 60 because 180 ÷ 3 = 60
I hope this helps!!
The difference between three times a number and seven is twenty. What is the number?
20
7
13
3
O9
O 27
Answer:
the number is 9
Step-by-step explanation:
hope this helps
Term insurance has no value as an investment and is the most expensive type of life insurance.
True
Or false
Answer:
False
Step-by-step explanation:
It is true that term insurance has no value as an investment. However, it is the least expensive type of life insurance. The compound statement is false, because one of the elements of the statement is false.
Answer:
false
Step-by-step explanation:
29. ERROR ANALYSIS Describe and correct the error in
rewriting the expression in rational exponent form.
Answer:
eeeeeeeeeeeeeeeeeeeeeeeeeee nose perdon xd
1. Find the surface area of the pyramid to the nearest whole number.
12 m
6 m
Your yard is a mess, and you decide to hire a landscaper. The garden pros charges 50$ consultation fee plus 30$ per hour for the actual work. What is the total cost if your yard takes 5 hour’s to fix up
Answer:
$200
Step-by-step explanation:
$50 consutation + $150 5 hour fee.
=$200
The height, h, in feet of a piece of cloth tied to a waterwheel in relation to sea level as a function of time, t, in seconds can be modeled by the equation h = 15 cosine (StartFraction pi Over 20 EndFraction t). How long does it take for the waterwheel to complete one turn? 5 seconds 10 seconds 20 seconds 40 seconds.
Solving the trigonometric equation, it is found that it takes 40 seconds to complete one turn.
The height is modeled by:
[tex]h(t) = 15\cos{\left(\frac{\pi}{20}t\right)}[/tex]
The initial height is [tex]h(0) = 15[/tex], hence, one turn is completed when h(t) = 15.
[tex]h(t) = 15\cos{\left(\frac{\pi}{20}t\right)}[/tex]
[tex]15 = 15\cos{\left(\frac{\pi}{20}t\right)}[/tex]
[tex]\cos{\left(\frac{\pi}{20}t\right)} = \frac{15}{15}[/tex]
[tex]\cos{\left(\frac{\pi}{20}t\right)} = 1[/tex]
The length of one turn is of [tex]2\pi[/tex], and [tex]\cos{(2\pi)} = 1[/tex], hence, the solution is found according to:
[tex]\frac{\pi}{20}t = 2\pi[/tex]
[tex]t = \frac{40\pi}{\pi}[/tex]
[tex]t = 40[/tex]
It takes 40 seconds to complete one turn.
You can learn more about trigonometric equations at https://brainly.com/question/24680641
Answer:
D. 40 seconds!! Props to guy above.
solve similar triangles (advanced)
Step-by-step explanation:
since m<CBA = m<EDA = 90
, < A is a common angle
then : triangle EDA is similar to triangle CBA
then : 11/3+X = 2/3
33=6+2X
27=2X
X=13.5
What’s the difference between an event and in event handler
Answer:
There’s a subtle, but important difference between these 2 methods of handling events. If you’ll use the first method, event handlers, the difference is that if you add two event handlers for the same button click, the second event handler will overwrite the first and only that event will trigger
Step-by-step explanation:
i hope this answer your questions
A polygon with area 10 square units is dilated by a scale factor of k. Find the area of the image for each value of k.
a k=4
square units
b. k=1.5
square units
ck=1
square units
Answer:
a = 160 square units
Step-by-step explanation:
The areas of the image are 160, 22.5 and 10 square units
The area of the polygon is given as:
A =10 square unit
The area of the image of the polygon is calculated as:
[tex]A_k = A * k^2[/tex]
When k = 4, we have:
[tex]A_4 = 10 * 4^2[/tex]
[tex]A_4 = 160[/tex]
When k = 1.5, we have:
[tex]A_{1.5} = 10 * 1.5^2[/tex]
[tex]A_{1.5} = 22.5[/tex]
When k = 1, we have:
[tex]A_{1} = 10 * 1^2[/tex]
[tex]A_{1} =10[/tex]
Hence, the areas of the image are 160, 22.5 and 10 square units
Read more about dilation at:
https://brainly.com/question/3457976
Can someone please help me with this and tell me the points?
Answer:
Graph: Refer to attached image
Solution: (-5,-3)
Step-by-step explanation:
First graph to two equations.
Refer to the image attached to see what the equations would look like when graphed.
Wherever they intersect is the solution.
They intersect at (-5,-3) therefore (-5,-3) is the solution to the system of equations
help pls the image below represents ____
Answer:
I think it's a Box Plot, hope this helps
Harry and Matthew, have 56 toys to build. harry builds three fourths of the toys, while matthew builds one seventh of the toys. How many toys are there left to build?
Answer:
i don't know
Step-by-step explanation:
if a necklace was on discount 10% and the original price was $20 what was the amount of discount?
Answer:
10$
Step-by-step explanation:
dollars hope it helps
Answer:
its 10$
Step-by-step explanation: