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:
https://brainly.com/question/11015301
3 and -4 dudes and dudettes
edg2022
A baseball traveled 330 feet in 5 seconds. Which rate is equivalent to the rate at which the baseball traveled?
Answer:
the baseball traveled 66 feet per second if that helps
Step-by-step explanation:
I don’t understand someone please give me answer
YES OR NOOO PLEASEE ANSWER
Answer:
Not a Function.... hope you pass!
What is the slope of a line perpendicular to the line y = 8x -5?
Answer:
-1/8
Step-by-step explanation:
the slope would be the opposite reciprocal of 8, which would be -1/8
Answer:
Y=-1/8x-5
Step-by-step explanation:
Perpendicular lines are negative reciprocals to each other
3x+4y=12 find x-intercept and y- intercept
Answer:
x-intercept(s): ( 4 , 0 )
y-intercept(s): ( 0 , 3 )
x = 4
y = 3
Step-by-step explanation:
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept(s): ( 4 , 0 )
y-intercept(s): ( 0 , 3 )
slope = -0.750
(4,-5), (4, -1)
what is the slope
Answer:
there is no slope
Step-by-step explanation:
you cannot divide by zero
Answer:
slope is undefined
Step-by-step explanation:
The slope is the difference in y divided by the difference in x.
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
That is the 2nd point's value minus the first, where the points are (x1, y1) and (x2, y2)
Given these 2 points, calculate the slope:
[tex]m=\frac{-1--5}{4-4}\\\\m=\frac{4}{0}[/tex]
In this case, the slope is undefined. A function cannot have multiple outputs for the same input, and an undefined slope has infinite outputs for 1 input. You can see that in the attached image, it's a vertical line.
please solve this problem using the foil method
[tex] {x}^{2} - 9[/tex]
Answer:
This is already in its simplest form, but if you set the equation equal to zero, it's (x-3)(x+3).
Step-by-step explanation:
x^2-9=0
a= 1
b=0
c=-9
Factors of c (-9) that add up to make b (0): -3, 3
(x-3)(x+3)
we know: [tex]a^2-b^2=(a+b)(a-b)[/tex]
So: [tex]x^{2} -9=x^{2} -3^2=(x+3)(x-3)[/tex]
Ok done. Thank to me :>
write f(2)=3 in coordinate
form (x,y)
Answer:
Coordinate form is [tex](x,y)=(2,3)[/tex]
Step-by-step explanation:
Usually the form is
[tex]f(x)=y[/tex]
Here
We have [tex]f(2)=3[/tex]
Hence [tex](x,y)=(2,3)[/tex]
How do I solve this?
Answer: A: 3x^2y^(3/2)
Step-by-step explanation:
This can be written as
(81*x^8*y^6)^(1/4)
Then multiply each exponent by (1/4):
81^(1/4)*x^(8(1/4))y^6(1/4))
81^(1/4) = 3
x^(8(1/4)) = x^2
y^6(1/4)) = y^(3/2)
The result: 3x^2y^(3/2)
Are the figures below similar?
NO LINKS!! NEED ANSWER ASAP
Answer:
no
Step-by-step explanation:
If f(x)= x^2 - x+ 1 and f (-1), then the result is
Answer:
3
Step-by-step explanation:
To solve f(-1), entails to replace x by -1 in the function
f(-1)= (-1)^2 - (-1)+ 1
= 1 + 1 + 1
= 3
Help please!! Ill give 100 points!
Answer:
B)
Step-by-step explanation:
10/5 + 4(72 - 6)
10/5 + 288 - 24 Distribute the 4 to 72 and 6
2 + 288 - 24 Divide
2 + 264 Combine the like terms
262
What is the vertex of y = 2(x - 3)^2 - + 67
a) (-3. -6)
b) (3, -6)
C) (-3. 6)
d) (3, 6)
A rectangular lawn 80 m x 60 m has two roads each 10m wide running in the middle of it, one parallel to the length and the other parallel to the breadth. Find the cost of gravelling them at ₹ 1.20 per sq meter.
Answer:
₹1680
Step-by-step explanation:
Road Length (m) Width (m) Area ([tex]m^{2}[/tex])
1 80 10 800
2 60 10 600
(800+600) = 1400 ([tex]m^{2}[/tex])
1400 ([tex]m^{2}[/tex])*(₹ 1.20/m) = ₹1680
Alyssa has fifty-quarters and dimes
She has a total of $9.80
How many dimes does she have?
a.)32
b.)30
c.)20
d.)18
Given that 35.8 x 4.23= 151.434
write down a division sum with an answer of 423.
Answer:
151434/358 = 423
Step-by-step explanation:
Every product with non-zero factors can be written as an equivalent division relation.
a·b = c ⇒ a = c/b
Here, we have 35.8 × 4.23 = 151.434. This can be written as the equivalent ...
4.23 = 151.434/35.8
We can multiply this by 100 to get a division relation with a quotient of 423:
423 = 15143.4/35.8
If we want, we can move the decimal points another place to the right to get ...
151434/358 = 423
HELP. RIGHT NOW PLEASE :>
Simplify
Answer:
√
4
x
5
√
(
x
−
1
)
2
−
3
2
+
3
y
−
3
Step-by-step explanation:
√
4
x
5
√
(
x
−
1
)
2
−
3
2
+
3
y
−
3
Problem #3
Imagine you are building a triangular garden. Two sides of the garden measure 230 ft and
360 ft and the included angle between these two sides of the garden measures 38°. What is
the measure of the third side?
С
230ft
38
360ft
Answer:
b = 115.4 feet
Step-by-step explanation:
b^2 = a^2 + c^2 - 2 (a)(b) x cos B
b^2 = 230^2 + 360^2 - 2(230)(360) x cos(38 degrees)
b^2 = 52,900 + 129,600 - 2(230)(360) x cos(38 degrees)
b^2 = 182,500 - 165,600 x cos(38 degrees)
b = [tex]\sqrt{(16,900)(cos(38)) }[/tex]
b = 115.4 feet
i hope this helps!! :)
Answer:
115.4 ft
Step-by-step explanation:
Please help me!
ty ty :)
Answer:
The answer is steeper.
I'm not sure about the slope thingy. But the line looks Steeper instead of flatter
What is the answer step by step explanation please.
w (3w + 2) + 5w
Answer:8w^2+2
w(3w+2)+5w
First distribute the w to the parentheses:
3w^2+w
Add on the 5w to the new equation:
3w^2+2w+5w
Combine like terms:
8w^2+2
The first term of an arithmetic sequence is 4 and the tenth term is 67.
What is the common difference? Show your work or explain your answer.
Answer:
Step-by-step explanation:
Formula
tn = a1 + (n-1)* d
Givens
tn = 67 (it is the last term or the nth term
n = 10
a1 = 4
find d
Solution
67 = 4 + (10 - 1)*d
67 = 4 + 9*d Subtract 4 from both sides
67 - 4 = 9d
63 = 9d Divide by 9
63/9 = 9d/9
7 = d
Remark: This is a fundamental application of the arithmetic sequence. You pretty much have to know how to juggle it's parts.
what is the answer please help!!!
(asap)
So I could only figure out question 8, 9, 10, and maybe 12.
Answer:
8.) x=29
9.) <b=32
10.) <z=106
?? 12.) 128 i think
Step-by-step explanation:
8.) 1st step is to take the angle on the outside and subtract it from 180 to get the inside missing angle. You then get 49. Then you add up all of the inner angles and equal it to 180.
2x+1+3x-15+49=180
After this you add up all of the similar terms.
5x+35=180
Now subtract 35 from both side to get
5x=145
Now divide each side by 5 and you should get 29
so x=29.
9.) First step is to add all of the angles together and equal to 180.
x+28+x-28+x=180
Next add all of the like terms together.
3x=180
Now divide each side by 3 to get x=60.
Don't stop there. Now fill in the x at <b.
(60)-28 which equals 32. so <b=32
10.) First step is to add all of the angles together and equal them to 180.
x-9+x-1+3x-20=180
Next add all of the like terms together.
5x-30=180
Now add 30 to both sides.
5x=210
now divide both sides by 5 to get x=42
Don't stop there.
Now fill in the answer for x in the <z spot.
3(42)-20
<z=106
12.) Okay so I am not 100% sure this is right but I tried it on desmos and it worked out.
Okay so first i did 3x-28+x=180
By using desmos, I got the answer x=52
Basically all it did was
4x-28=180
add 28 to both sides to get 4x=208
then we divide by 4 on both sides to get x=52
after that you fill in the x for the outer angle because that is what it is asking for.
you then get <QST=128
I know its not all of them but i hope this helps!!
Find y
Find m
Find m
Answer:
y= -21; m∠MNO=40°.
Step-by-step explanation:
1) m∠MON+m∠MNO=90°;
2) -3y-13°-2y-2°=90°;
5y=-105°; ⇒ y= -21;
3) m∠MNO=-2y-2°=42°-2°=40°.
It takes 1 3/4 cups of cherries to make a cherry pie. Emma wants to make 3 cherry pies. How many cups of cherries will Emma need
Answer:
5 1/4 please give brainliest
Step-by-step explanation:
1 x 3 = 3 3/4 x 3 = 2 1/4
Answer:
5 1/4 please give brainliest
Step-by-step explanation:
1 x 3 = 3 3/4 x 3 = 2 1/4
Say that Thailand has a workforce of 35,709,487 people, each of whom earns an average salary of (equivalent USD) $8,630 annually. If the Thai government wants to raise $70 billion in tax revenue, approximately where should it set the income tax rate? a. 5% b. 15% c. 23% d. 29%.
The income tax rate must be 29%.
Given that,
Thailand has a workforce of 35,709,487 people, each of whom earns an average salary of (equivalent USD) $8,630 annually.
If the Thai government wants to raise $70 billion in tax revenue,
We have to find,
The approximately where should it set the income tax rate?
According to the question,
Thailand has a workforce of 35,709,487 people, each of whom earns an average salary of (equivalent USD) $8,630 annually.
[tex]\rm Total \ income = Number \ of \ people \times Income \ per \ person\\\\Total \ income = 35,709,487 \times 8,630\\\\Total \ income = 308,172,872,810[/tex]
If the Thai government wants to raise $70 billion in tax revenue,
Then,
The income tax rate is,
[tex]\rm Tax\ rate = \dfrac{70,000,000,000,}{308,172,872,810}\\\\Tax \ rate = 0.29\\\\Tax \ rate = 29 \ percent[/tex]
Hence, The income tax rate must be 29%.
For more details refer to the link given below.
https://brainly.com/question/16016455
Answer:
c
Step-by-step explanation:
Trust me, I got 100%
Subtract
-
Iw +
W + 4 from įw + 3
1w -
- 1
- 1w + 1
1w7
w + 7
- 1w + 7
aro
Answer:
what grade are u in so I know
what is the area of the rectangle.
Answer:
54 units^2
Step-by-step explanation:
Find the area of trapezium where area=5cm base=6cm height=8cm
Answer:
44cm2
Step-by-step explanation:
[8×(5+6)]/2
=(8×11)/2
=88/2
=44cm2
how to tell if an equation is linear without graphing
Answer:
A linear equation has the greatest x power at 1.
If you see an equation with only x (no x^2 or x^3 or stuff like that), you will know that it is linear.
What is the slope of the following line?
The slope of the line is 1/-2
You only have to rise one time, then go over to the left two times in order to get to another point.
