The rational zero of the function f(x)=2x^3+15x^2−4x+32 is -8.
To find a rational zero of the function f(x) = 2x^3 + 15x^2 - 4x + 32 using the Rational Zero Theorem, follow these steps:
1. Identify the coefficients of the polynomial. In this case, they are 2, 15, -4, and 32.
2. List all the factors of the constant term (32) and the leading coefficient (2).
Factors of 32: ±1, ±2, ±4, ±8, ±16, ±32
Factors of 2: ±1, ±2
3. Create all possible fractions using factors of the constant term as numerators and factors of the leading coefficient as denominators. These fractions represent the possible rational zeros.
Possible rational zeros: ±1/1, ±2/1, ±4/1, ±8/1, ±16/1, ±32/1, ±1/2, ±2/2, ±4/2, ±8/2, ±16/2, ±32/2
Simplified rational zeros: ±1, ±2, ±4, ±8, ±16, ±32, ±1/2, ±4/2, ±8/2, ±16/2, ±32/2
4. Test each possible rational zero using synthetic division or by plugging the value into the function until you find one that results in f(x) = 0.
After testing the possible rational zeros, you'll find that the rational zero is -8.
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9x -7u > 9x -21u
solve please :)
Answer:
(-∞,∞) is your answer sorry if it looks like a face
Step-by-step explanation:
Ten people put 63 boxes on a red truck and 38 boxes on a blue track About how many boxes did they load in all
Answer:
63+38=101
Step-by-step explanation:
determine if JK and LM are parallel, perpendicular,or neither . HELP AND PLS SHOW WORK !!
Answer:
1) not parallel
2)not parallel
Step-by-step explanation:
fist one intersect already
and second one will eventually intersect
Answer:
1 - Perpendicular.
2 - Neither.
Step-by-step explanation:
Use the slop formula to find the slope of the two sides.
[tex]m = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
[tex]JK = \frac{4-9}{7-1} = \frac{-5}{6}[/tex]
[tex]LM = \frac{1-13}{-2-8} = \frac{-12}{-10} = \frac{6}{5}[/tex]
Perpendicular - because a line that is perpendicular to another must have a slope that is the negative reciprocal of the first line.
[tex]JK = \frac{6-(-5)}{2-13} = \frac{11}{-11} = 1[/tex]
[tex]LM = \frac{-2-(-5)}{-4-(-1)} = \frac{3}{-3} = -1[/tex]
Not Parallel. Nor perpendicular.
plsss help if u can 6th grade math
Answer:
The minimum: 3
The lower Q: 7
The median: 7
The upper Q: 6
Maximum: 11
Step-by-step explanation:
HELP I NEED HELP ASAP
Answer:
d.
Step-by-step explanation:
Answer:
option c I guess - "It increases exponentially "
Answer this question and you get brainiest? Also 85 points so answer it correctly and it’s all yours btw i put the picture up so you can answer it . Thanks
Answer:
114
Step-by-step explanation:
those angles are supplementary meaning that they will add up to 180. 180-66=114 so x=114
Write the expression in expanded form (1 + 3b)(6)
Answer:
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Identity:
An identity is an equality which is true for all values of a variable in the equality.
(a + b)³ = a³+ b³+ 3ab(a + b)
In an identity the right hand side expression is called expanded form of the left hand side expression.
---------------------------------------------------------------------------------------------------
Solution:
(i) (2x + 1)³
Using identity
(a + b)³ = a³+ b³+ 3ab(a + b)
(2x + 1)³
= (2x)³ + 1³ + (3×2x×1)(2x + 1)
= 8x³+ 1 + 6x(2x + 1)
= 8x³ + 1 + 12x² + 6x
(ii) (2a – 3b)³
Using identity,
(a – b)³ = a³–b³ – 3ab(a – b)
(2a – 3b)³ = (2a)³– (3b)³ – (3×2a×3b)(2a – 3b)
=8a³–27b³–18ab(2a –3b)
= 8a³–27b³–36a²b + 54ab²
(iii) [3x/2 + 1]³
Using identity,
(a + b)³ = a³+ b³+ 3ab(a + b)
[3x/2 +1]³
=(3x/2)³+1³+ (3×(3x/2)×1)(3x/2+ 1)
=27x³/8+1+9/2x×(3x/2+1)
= 27x³/8 + 1 + 27/4 x² + 9/2x
= (27/8)x³ + (27/4) x² + 9/2 x + 1
(iv) [x–2/3 y]³
Using identity,
(a - b)³=a³-b³-3ab(a-b)
(X+ 2/3y)³
= (x)³–(2/3 y)³– (3×x×2/3 y)(x – 2/3 y)
= x³– 8y³/27–2xy(x – 2/3 y)
= x³– (8/27)y³–2x²y+ 4/3xy²
=========================================================
Hope this will help you....
Step-by-step explanation:
How many solutions does this equation have?
4v = 6v − 2v
no solution
one solution
Infinitely many solutions
Answer:
Infinitely many solutions.
Step-by-step explanation:
4v=6v-2v Combine like terms.
4v=4v These are already equal without diving, so there are infinitely many solutions.
Hope this helps and have a nice day ❤
Answer:
Infinitely many solutions
Step-by-step explanation:
4v=6v-2v
4v=4v
when two expressions on opposite sides of an equals sign are equivalent, that means there are infinitely many solutions
P.S. Please mark me Brainliest if it is correct.
2/3 times 3/4 I need an sender
Answer:
6/12 but to simplify it would be 1/2
Answer:
[tex]\frac{2}{3} *\frac{3}{4}[/tex] = 1/2
Step-by-step explanation:
2/3 * 3/4
6/12=1/2
Canada was once a British colony. Based on the information presented in the movie, what can you infer about Canada?
Answer:
In 1763, Canada formally became part of British Empire. The colony of Canada was enlarged under the province of Quebec.
Step-by-step explanation:
Modern day Canadian province was once British Colony. In 1949, Newfoundland became part of Canada instead of British Colony. The information presented in the movie is about the British Empire that governed the Canadians. After the free from British rule Canada was free to act in his own way in the country. The country also gained financial independence.
find the value of x
Answer:
x=32
Step-by-step explanation:
52=whatever angle x+20 is.
Sorry um but help pleasee
Answer:
For the first one the answer is the 2nd and 3rd one
Step-by-step explanation:
the 2nd one is the 2nd and 3rd one
make brainliest please
I hope i am rigth
need help with this question
Answer:
bc=-4
Step-by-step explanation:
4x -1 is -4. because your adding a negative and a positive
Answer:
-4
Step-by-step explanation:
thats the answer
- (cd2 + 4c + 21)
simplify it?
Answer: = -cd^2 - 4c - 21
Step-by-step explanation:
It‘s suppose to read negative cd the 2 is squared - 4c - 21
please answer correctly and quickly
Answer:
#6:10
Step-by-step explanation:
Answer:
#9 is x=14
#7 is C 138
#6 is x=10
#5 is p=40
In a video game, a bird is flung on a sling shot and follows a parabolic path. The path of the bird can be modeled by the equation h=-16t²+55t+50, where h is the height of the bird t and is the amount of time, in seconds, the bird has been in the air. How long will it take the bird to reach a height of 40 feet in the air for the first time?
9514 1404 393
Answer:
3.61 seconds
Step-by-step explanation:
The bird starts 50 feet in the air, so will come down to a height of 40 feet after 3.61 seconds.
We want to solve h = 40.
40 = -16t^2 +55t +50
16t^2 -55t -10 = 0
t = (55 +√(55^2 -4(16)(-10)))/(2(16)) = (55 + √3665)/32 ≈ 3.61060
The bird will be 40 ft above the ground the first time after about 3.61 seconds.
A piece of machinery was purchased by a factory. It depreciates at 10percent every year. At the end of second year its value is rs 1,29,600.What is the cost price
Answer:
160000
Step-by-step explanation:
Let the cost price = x
At the end of the first price, it loses ten percent = 0.9x
At the end of the second year, it loses an extra ten = 0.9(0.9x)= 0.81x
0.81x=129600
x=160000
What is 25% of 160?
Instructions
100 of 100 words remaining
BUI EEE Tv
b. What is 39 of 2007
Instructions
100 watt
Done and Review
2021
Answer:
I have no idea what ur saying
Step-by-step explanation:
Can someone help me please. I have to show my work.
Answer:
Step-by-step explanation:
1. P = (width + lengh) * 2 = (23 + 10) * 2 = 33 * 2 = 66
A = width * lengh = 23 * 10 = 230
2. width = 7
P = (width + lengh) * 2 = ( 7 + 9) * 2 = 16 * 2 = 32
Answer:
4. area= 230cm^2 perimeter= 66cm
5. width= 7m perimeter= 32m
Step-by-step explanation:
4. a = w*l
23cm*10cm=230cm^2
p= add all sides
23cm+23cm+10cm+10cm=66cm
5. w= a/l
63m^2/9m=7m
p= add all sides
7m+7m+9m+9m=32m
What errors did her coach make in the following example
Answer:
its the last one & the 3rd one.
hope that helps
1/4 to 1/2
Find a percent of change, round to the nearest 10th of a percent if necessary.
__% of increase or decrease (ANSWER ASAP)
Given:
[tex]\dfrac{1}{4}\text{ to }\dfrac{1}{2}[/tex]
To find:
The percent of change, round to the nearest 10th of a percent.
Solution:
We have,
Initial value = [tex]\dfrac{1}{4}[/tex]
New value = [tex]\dfrac{1}{2}[/tex]
We know that, the percentage change is
[tex]\%\text{ change}=\dfrac{\text{New value - Initial value}}{\text{Initial value}}\times 100[/tex]
Putting the given values, we get
[tex]\%\text{ change}=\dfrac{\dfrac{1}{2}-\dfrac{1}{4}}{\dfrac{1}{4}}\times 100[/tex]
[tex]\%\text{ change}=\dfrac{\dfrac{2-1}{4}}{\dfrac{1}{4}}\times 100[/tex]
[tex]\%\text{ change}=\dfrac{\dfrac{1}{4}}{\dfrac{1}{4}}\times 100[/tex]
[tex]\%\text{ change}=1\times 100[/tex]
[tex]\%\text{ change}=100\%[/tex]
Here, the % change is positive, it represents the percent increase.
Therefore, the percent of change is 100% of increase.
HELPP PLSSSS Im failing school :(
Answer:
D.540
if im wrong sorry
Step-by-step explanation:
A farmer has a house that sits at the edge of a field, with all sides meeting at right
angles.
The field has the following measurements.
40 m
100 m
The farmer wants to know how much fencing he will need to surround the field.
Calculate the total length of fencing.
Step-by-step explanation:
total length = l×b therefore 40m×100m=400m
i need help with this anyone pleaseee
Answer:
41 dollars
Step-by-step explanation:
3r+2.5p is the cost of roses and petunias, just number of roses as r and petunias as p:
3(7) + 2.5(8)=
21+20=41 dollars
4 _ (3 _ 2) _ 6 _ 1 = 14 Please help ill give you brainly!
For which equation is 3 a solution(I need help)
Answer:
B
Step-by-step explanation:
I did it on paper
After substituting, what is the first step when evaluating (4y+9)/7 when Y = 8
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A. Add 4 and 9.
B. Multiply 8 by 4.
C. Divide 9 by 7.
D. Divide 4 by 7.
✧･ﾟ: *✧･ﾟ:*✧･ﾟ: *✧･ﾟ:*✧･ﾟ: *✧･ﾟ:*✧･ﾟ: *✧･ﾟ:*
Answer:
B. Multiply 8 by 4 is the answer
Which expressions are equivalent to 56x + 24 divided by 8?
A.7x + 24
B.56x + 24
8
C. 8(24 + 56x)
D.3x + 7
F.3 + 7x
The expression (56x + 24) / 8 is equivalent to the expression will be 7x + 3. Then the correct option is F.
What is an equivalent expression?The equivalent is the expression that is in different forms but is equal to the same value.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ (56x + 24) / 8
Simplify the expression, then we have
⇒ (56x + 24) / 8
⇒ (56/8)x + 24/8
⇒ 7x + 3
The expression (56x + 24) / 8 is equivalent to the expression will be 7x + 3. Then the correct option is F.
More about the equivalent link is given below.
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An expression equivalent to 56x + 24 divided by 8 is 3x+7. So, option F. is correct.
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given the following expression:
56x + 24
It is required to divide the given expression by 8,
Thus, dividing the expression by 8 as follows:
[tex]\dfrac{56x+24}{8}\\\\\dfrac{56x}{8}+\dfrac{24}{8}\\\\7x+3[/tex]
Thus, 3+7x is the expression equivalent to 56x + 24 divided by 8. So, option F is correct.
Learn more about mathematical operation, here:
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What is 3 3/4 - 2 1/3
Answer:
1 5/12
Step-by-step explanation:
decimal form, 1.416
Answer:
3 1/4 + 2 1/3 = 67/
12
= 5 7/
12
≅ 5.5833333
Step-by-step explanation:
b-3/15=1 What does b equal??
Answer:
1 3/15
Step-by-step explanation:
All you have to do is add 3/15 to both sides of the equation:
b - 3/15 = 1
b = 1 3/15