Find all of the rational zeros of the function. f(x)=x 4 −3x 3 −6x 2 +6x+8
Answer:
The "possible" rational zeros are:
±
1
,
±
2
,
±
4
,
±
8
The actual zeros are:
−
1
,
4
,
±
√
2
Explanation:
f
(
x
)
=
x
4
−
3
x
3
−
6
x
2
+
6
x
+
8
By the rational root theorem, any rational zeros of
f
(
x
)
are expressible in the form
p
q
for integers
p
,
q
with
p
a divisor of the constant term
8
and
q
a divisor of the coefficient
1
of the leading term.
That means that the only possible rational zeros are:
±
1
,
±
2
,
±
4
,
±
8
We find:
f
(
−
1
)
=
1
+
3
−
6
−
6
+
8
=
0
So
x
=
−
1
is a zero and
(
x
+
1
)
a factor:
x
4
−
3
x
3
−
6
x
2
+
6
x
+
8
=
(
x
+
1
)
(
x
3
−
4
x
2
−
2
x
+
8
)
Notice that the ratio between the first and second terms of the remaining cubic is the same as that between the third and fourth terms. So this cubic will factor by grouping:
x
3
−
4
x
2
−
2
x
+
8
=
(
x
3
−
4
x
2
)
−
(
2
x
−
8
)
x
3
−
4
x
2
−
2
x
+
8
=
x
2
(
x
−
4
)
−
2
(
x
−
4
)
x
3
−
4
x
2
−
2
x
+
8
=
(
x
2
−
2
)
(
x
−
4
)
Finally we can factor the quadratic as a difference of squares:
x
2
−
2
=
x
2
−
(
√
2
)
2
=
(
x
−
√
2
)
(
x
+
√
2
)
So the zeros are:
−
1
,
4
,
±
√
2
helpppppppppppppppppppppppppppp
What do you need help with? Are you in danger?
write the equation of the line in fully simplified slope-intercept form
Answer:
y = 3/5x+1
Step-by-step explanation:
y intercept - (0,1), so b=1
Slope = rise/run = 3/5, so m = 3/5
Our Answer is y = 3/5x+1
Use the Distributive Property to
simplify the following:
7(y + 3) =
Answer:
7y+21
Step-by-step explanation: i solve it hope this help.
Answer:
[tex]\bold{7y+21}[/tex]
Step-by-step explanation:
Hi there!
Let's solve this math problem by using the Distributive Property.
All we have to do is "distribute" 7 (multiply it by all the terms inside the parentheses):
[tex]\bold{7(y+3)}[/tex][tex]\bold{7y+21}[/tex]Hope it helps! Enjoy your day!
~ Just a teenage girl willing to help
[tex]\bold{Besties4Ever:-):-)}[/tex]
If you get it right ill give brainliest hurry pls
|9+40i| = |√9^2 + -40^2| = √1681 = 41
Answer: 41
Answer:
41
Step-by-step explanation:
We know that complex numbers are a combination of real and imaginary numbers
Real part is x and imaginary part y is multiplied by i, square root of -1
Modulus of x+iy =
Here instead of x and y are given 9 and 40
i.e. 9+40i
Hence to find modulus we square the coefficients add them and then find square root
|9+49i| =
By long division method we find that
|9+40i| =41
Philip currently has $450 in his checking account. Each month Netflix withdraws $15 for dues. Which equation can be used to find y, the current amount in Philip's checking account after x number of months?
solve for x in the triangle!!!
Answer:
13
Step-by-step explanation:
Combine all like terms:
14x-2
Since there are 180 degrees in a triangle, all three angles are going to equal 180.
14x-2=180
Add 2
14x=182
Divide by 14
x=13
(4 x 100,000) + (6 x 10.000) =
Answer:
answer is 400060
have a good day!!
If it's help pls give me Brainliest
tysm
Answer:
4000,060
answer explanation : when you add 4 times 100,000 ypu get 400,000 and now you get 400,000 and now you are going to muptiple 4,000,6 and 10.000 which is equal to 4,000,060
Which choice models this situation? Marcus needs to sell 25 tickets to a fundraiser by Friday. So far, he has sold 9 tickets. How many tickets does he still need to sell?
Answer:
16
Step-by-step explanation:
Because 25 - 9 = 16
pleaseeeeeeeeee helppppppppp meeeeeeeeeee
Answers:
FunctionNot a functionFunctionNot a function========================================
Explanation:
If x repeats itself, then we don't have a function. For instance, relation 2 has the x value -4 show up twice. That input leads to multiple outputs which is why we don't have a function. Relation 4 is a similar story (this time the input 'u' shows up twice).
Relations 1 and 3 don't have this issue, so they are functions.
Shanti wrote the predicted values for a data set using the line of best fit y = 2. 55x â€" 3. 15. She computed two of the residual values. A 4-column table with 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled given with entries negative 0. 7, 2. 3, 4. 1, 7. 2. The third column is labeled predicted with entries negative 0. 6, 1. 95, 4. 5, 7. 2. The fourth column is labeled residual with entries negative 1, 0. 35, a, b. What are the values of a and b?.
The residual column is given by the difference between the given values
and the values from the fitted line.
The values of a and b are; a = -0.4 and b = 0.18Reasons:
The line of best fit equation is; y = 2.55·x - 3.15
The 4-column table is presented s follows;
[tex]\begin{tabular}{|c|c|c|c|}\underline{x}&\underline{Given}&\underline{Predicted}&\underline{Residual}\\1&-0.7&-0.6&-0.1\\2&2.3&1.95&0.35\\3&4.1&4.5&a\\4&7.2&7.02&b\end{array}\right][/tex]
Required:
The values of a and b
Solution;
The residual is given by the difference between actually observed value and the predicted value
RESID = [tex]\mathbf{y_i}[/tex] - [tex]\mathbf{x_i}[/tex]·b
Where;
[tex]y_i[/tex] = The given value at point i
[tex]x_i[/tex]·b = The predicted value at point i
Therefore;
At x = 1, the residual = -0.7 - (-0.6) = -0.1
At x = 2, the residual = 2.3 - 1.95 = 0.35
At x = 3, the residual = a = 4.1 - 4.5 = -0.4
Therefore;
a = -0.4At x = 4, the residual = b = 7.2 - 7.02 = 0.18
Therefore;
b = 0.18Learn more about line of best fit here:
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A jar contains 6 red marbles numbered 1 to 6 and 10 blue marbles numbered 1 to 10. A marble is drawn at random from the jar. Find the probability of the given event.
Answer:
Step-by-step explanation:
a)
p
(
red marbles
)
=
6
6
+
8
p
(
red marble
)
=
3
7
b)
p
(
o
d
d
n
u
m
b
e
r
s
)
=
3
+
4
6
+
8
p
(
o
d
d
n
u
m
b
e
r
s
)
=
1
2
c)
p
(
red marbles or odd numbers
)
=
p
(
red marbles
)
+
p
(
odd numbers
)
−
p
(
red marbles and odd numbers
)
p
(
red marbles or odd numbers
)
=
6
14
+
7
14
−
3
14
p
(
red marbles or odd numbers
)
=
10
14
d)
p
(
Blue marbles or even number
)
=
p
(
Blue marbles
)
+
p
(
even numbers
)
−
p
(
blue marbles and even numbers
)
p
(
Blue marbles
)
=
8
14
p
(
even numbers
)
=
7
14
p
(
Blue marbles or even number
)
=
8
14
+
7
14
−
4
14
p
(
Blue marbles or even number
)
=
11
14
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Learn more about this topic:
What is Probability in Math? - Definition & Overview
from
Chapter 24 / Lesson 7
49K
The formula of probability is possible choices over the total number of options. Discover the definition of probability and get an overview of its calculation and application in math.
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3 shirts for 9.99 2 pairs of shorts for 14.95 a bathing suit for 24.50 the sales tax was 7% how much did she spend in all ?
Answer:
If a shirt is on sale for 50% off, and you have another offer that gives you an "additional 20% off the sale price", does that mean you get a total of 70% off? Not usually. If the shirt was $20, then the SALE price would be $10 and the additional 20% would apply to the SALE price of $10 instead of the original price of $20. This isn't too bad when the sales are nice even percentages, but when it gets more complicated, you can use this calculator to find out the final cost (sales tax not included).Step-by-step explanation:
Without calculating, explain how you can tell if the value of the expression (-2.37) - (.7.91) - (2.45)?
Answer:
33343555
4
3
4
34
2354555444
5224
34
32555555
555
5
32
55233=3=44
Step-by-step explanation:
brian says that 8n+2=82 when n=1 explain why he is incorrect
simplify this addition 20+(-6x)+6x+(-20)
Answer:
0
Step-by-step explanation:
20+(-6x)+6x+(-20)=20-6x+6x-20
=0
Assume that lines which appear to be tangent are tangent.
Find the value of the?
Answer:
12
Step-by-step explanation:
Assume that lines which appear to be tangent are tangent.
Therefor this is a right triangle.
Use the pythagorean theorem
c^2 = a^2 + b^2
15^2 = ?^2 + 9^2
225 = ?^2 + 81
subtract 81 from both sides
144 = ?^2
Take the square root of both sides
12 = ?
9514 1404 393
Answer:
? = 12
Step-by-step explanation:
The tangent makes a right angle with the radius at the point of tangency. That means the Pythagorean theorem can be used to find the missing length.
?² +9² = 12²
?² = 225 -81 = 144
? = √144 = 12
The value of ? is 12.
__
Additional comment
When you see a right triangle with the ratio of hypotenuse to leg of 15:9 = 5:3, you know immediately that it is a multiple of a 3:4:5 right triangle. Here, the scale factor is 3, so the missing side is 3×4 = 12.
Help please! I do not understand
how do you convert decimal to fraction
you convert decimals to fractions by how much more numbers are after the point the more 0Answer:
for example 0.2=2/10 and0.25= 25/100
and if a zero is infront of the number like this 0.02 then it will be the same except it will be 2/100
Step-by-step explanation:
These are already solved but can someone explain how we got them, steps please! I really need it..
Answer:
1A,) 5x 2 and 3x are unlike terms and 9x 3 and 2x 2 are also unlike term
* so you have to put the like terms together to solve the equation
*then you say 9x 3 first because it is the biggest number (I think)
* then you put 5x 2 and 2x 2 together and 3x and x together too
* then you will get : 9x 3+ (5x 2 + 2x 2) + (3x -x)
:9x 3 + 7x 2 +2x
Note:in algebra 3x -x is like saying 3-1 aka x is seen as 1 but the one is invisible
haha
and unlike terms are terms that do not have the same variables or powers while like terms are terms that have the same variables or powers
#1 Twenty five members of a travel club are planning their next club trip. Each member
has ranked their choices according to the following preference schedules. Is the plurality
winner the same as the majority winner?
Answer: France
Step-by-step explanation:
Fill in the blank with the correct math term, and give an example of each.
A. A(n) ________is a mathematical relationship that uses one or more variables, numbers or operation symbols.
Example:
B. A(n)________is a symbol that can be replaced by a number in a mathematical expression or equation.
Example:
C. A(n)_________is a mathematical sentence with an equal sign
Example:
Hellooo! Can someone please help me with this. I’m struggling, and need help. if u can help i would appreciate it. Also on the example parts please give a example, thank u.
A. A(n) equation is a mathematical relationship that uses one or more variables, numbers, or operation symbols.
B. A(n) variable is a symbol that can be replaced by a number in a mathematical expression or equation.
C. A(n) equation is a mathematical sentence with an equal sign.
A. A(n) equation is a mathematical relationship that uses one or more variables, numbers, or operation symbols.
Example: The variable "x" is used in the equation 2x + 3 = 7. It demonstrates the relationship that arises when "x" is multiplied by 2, added to 3, and the result is 7 as the outcome.
B. A(n) variable is a symbol that can be replaced by a number in a mathematical expression or equation.
Example: In the equation 3y + 2 = 11, "Y" is the variable. The equation can be solved by changing the value of "y," which can take on a variety of possibilities.
C. A(n) equation is a mathematical sentence with an equal sign.
Example: 4 + 5 = 9 is an illustration of an equation. It states that combining 4 and 5 yields the number 9. The equal symbol denotes the equality or balance of the two sides of the equation.
Explanation:
A. An equation is a statement that demonstrates the relationship between different quantities, variables, or numbers using mathematical operations. It might have a variable or several that need to be figured out in order to arrive at a particular value or link.
B. A variable is a symbol that is used to signify an ambiguous or fluctuating quantity in mathematical statements or equations. It is made flexible and generic to represent different values or relationships inside the confines of a mathematical issue.
C. An equation is a mathematical statement that establishes the equality of two expressions by using the equal sign. It indicates that the values of the two sides of the equation are equal or the same. In order to show mathematical relationships and properties, equations are frequently utilised.
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8.
Write the equation of the parabola in vertex form.
A. y = –x^2 + 4
B. y = –x^2 + 3
C. y = –(x – 1)^2 + 3
D. y = –x^2 – 4
Answer:
A. y = –x^2 + 4
Step-by-step explanation:
Find the vertex form.
y = − ( x + 0 ) 2 + 4
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Down
Vertex:
( 0 , 4 )
Focus:
( 0 , 15 /4 )
Axis of Symmetry:
x = 0
Directrix:
y
=
17
4
x
y
−
2
0
−
1
3
0
4
1
3
2
0
kelly has 47 model cars. Jamal has 58 model cars. Yesterday , jamal traded 8 model cars to kelly for 14 of her cars. How many cars did kelly have before the trade
Answer:
33 cars please give Brainliest
I need help with question 5
Answer:Hi!
where is the question?
Step-by-step explanation:
4x+3y=2 solve for y pls help omg i cant
Answer: 3 y = 2 − 4 x
Step-by-step explanation: 3 y = 2 − 4 x
1. What is the range of the function y = 2x-3 when the
domain is {-1, 0,5}?
y=2x-3
2x-3
2(-1)-3=-5
What is the slope of the line?
7x + 2y=5
A. 7/2
B. -7/2
C. -2/7
D. 2/7
Answer:
B) -7/2
Step-by-step explanation:
You would have to convert to slope-intercept form.
[tex]y=mx+b\\[/tex]
7x+2y=5
2y= -7x+5
y= -7/2x+5/2,
m= -7/2 = slope
What is the solution to the equation 1/4x−3/4=1/2, given the replacement set {−1, 1, 5} ?
Answer:
x=5
Step-by-step explanation:
I took the test. Hope this helps
The solution of the given equation is when the x = 5.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that the equation 1/4x−3/4=1/2, also the replacement set {−1, 1, 5}
First, substitute the values from the given set;
When x = -1
1/4x−3/4=1/2
1/4(-1) − 3/4 = 1/2
-1/4 - 3/4 = 1/2
-4/4 = 1/2
-1= 1/2
This is not the solution to the given equation.
When x = 1
1/4x−3/4=1/2
1/4(1) − 3/4 = 1/2
1/4 - 3/4 = 1/2
-2/4 = 1/2
-1/2 = 1/2
This is not the solution to the given equation.
When x = 5
1/4x−3/4=1/2
1/4(5) − 3/4 = 1/2
5/4 - 3/4 = 1/2
2/4 = 1/2
1/2 = 1/2
This is the solution to the given equation.
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What is the distance between points A and B?
A
B
-87-6 5 4 3 -2 -1
0
-
3
2
-
5
4
+
7
6
8
- 6 units
-1 units
O 5 units
6 units
Answer:
6 units
Step-by-step explanation:
Just count
The distance between points A and B is 6 units.
What is Subtraction?Subtraction can be done for any numbers or algebraic expressions. It is the process of taking out certain value from a given amount of number.
The process of subtraction can also be termed as finding difference.
In geometry, Distance between two points will be always a positive number.
Distance will be 0, if the points coincide.
Here on a number line, A is marked at -5 and B at 1.
We have to find the distance between A and B.
Distance between A and B = 1 - -5 = 1 + 5 = 6 units
Hence distance between A and B is 6 units.
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