According to the rational root theorem, which of the following are possible
roots of the polynomial function below?
F(x) = 4x2 - 6x2 + 9x + 10
A.5/4
B.1/3
C.-1/2
D.5
E.6
F.-2
Answers
Given:
The polynomial function is
[tex]F(x)=4x^3-6x^2+9x+10[/tex]
To find:
The possible roots of the given polynomial using rational root theorem.
Solution:
According to the rational root theorem, all the rational roots and in the form of [tex]\dfrac{p}{q}[/tex], where, p is a factor of constant and q is the factor of leading coefficient.
We have,
[tex]F(x)=4x^3-6x^2+9x+10[/tex]
Here, the constant term is 10 and the leading coefficient is 4.
Factors of constant term 10 are ±1, ±2, ±5, ±10.
Factors of leading term 4 are ±1, ±2, ±4.
Using rational root theorem, the possible rational roots are
[tex]x=\pm 1+,\pm 2, \pm 5, \pm 10,\pm \dfrac{1}{2}, \pm \dfrac{5}{2}, \dfrac{1}{4}, \pm \dfrac{5}{4}[/tex]
Therefore, the correct options are A, C, D, F.
Related Questions
An example of an irrational number is
O A. V16
B. V25
C V36
O D. V47
Answers
Answer:
i think b is the answer
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
from what I gathered, the V is supposed to be a square root. if this is the case, then D is the only answer that does not produce a rational number. V16 is equal to 4, V25 is equal to 5, and V36 is equal to 6.
y= 14 - 0.5x what does y=
Answers
you can’t do anything else to the eq
How many sides are there on a standard pencil.
Answers
i put jericho but it’s wrong so i’m not sure
Answers
=================================================================
Explanation:
This is because the value -16 is closest to 0, which represents sea level.
I recommend drawing out a vertical number line. Positive numbers are above 0, to indicate elevations above sea level. Negative numbers represent elevations below sea level.
The diagram is shown below. The diagram is not to scale because the red tickmarks shouldn't be equally spaced out; however, the order is correct, and that's all we need to worry about.
Note how -16 is the highest of the four choices, which makes it the closest to sea level. Also note how as you move further down, the negative values get larger in absolute value. It might be helpful to think of a thermometer.
A garden box has a perimeter of 18½ feet. If the length is 5 feet, what is the area of the garden box?
Answers
Answer:
[tex]area=\frac{85}{4}feet^{2}[/tex]
Step-by-step explanation:
1. Approach
Since it is given that the garden box is a rectangle, then the opposite sides are congruent. One can use this to their advantage, by setting up an equation that enables them to solve for the width of the rectangle. After doing so, one will multiply the width by the given length and solve for the area.
2. Solve for the width
It is given that the garden box is a rectangle. As per its definition, opposite sides in a rectangle are congruent. The problem gives the length and the perimeter of the rectangle, therefore, one can set up an equation and solve for the width.
[tex]perimeter=18\frac{1}{2}\\\\length=5[/tex]
[tex]2(length+width)=perimeter[/tex]
Substitute,
[tex]2(5+width)=18\frac{1}{2}[/tex]
Conver the mixed number to an improper fraction. This can be done by multiplying the "number" part of the mixed number by the denominator of the fraction. Then add the result to the numerator.
[tex]2(5+width)=\frac{37}{2}[/tex]
Inverse operations,
[tex]2(5+width)=\frac{37}{2}\\/2\\\\5+width=\frac{37}{4}\\-5\\\\width=\frac{17}{4}[/tex]
3. Solve for the area
Now that one has solved for the width of the box, one must solve for the area. This can be done by multiplying the length by the width. Since the width is a fraction, one must remember, that when multiplying an integer by a fraction, one will multiply the integer by the numerator (the top of the fraction), and then simplify by reducing the fraction, if possible. Reducing the fraction is when one divides both the numerator and the denominator by the GCF (Greatest Common Factor).
[tex]length=5\\\\width = \frac{17}{4}[/tex]
[tex]length*width=area[/tex]
Substitute,
[tex]5*\frac{17}{4}\\\\=\frac{85}{4}[/tex]
[tex]area=\frac{85}{4}feet^{2}[/tex]
2^14=16,384 use this information to work out 2^15
Answers
Answer:
32768
Brainiest plz :)
Heeellllppppp!!!!
(9,-4); slope=-2/3
Answers
Answer:
(y - y') = m ( x - x') [m = slope]
y - (-4) = 2/3 (x - 9)
(y +4) = 2/3 (x - 9)
3(y +4) = 2(x - 9)
3y +12 = 2x - 18
2x - 3y - 18 - 12 =0
2x - 3y - 30 =0
hope it helps ☺️☺️
The equation of the line passing through (9, -4) having slope = -2/3 will be y = (-2/3)x + 2
What is the general equation of a Straight line?
The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
y = mx also represents direct proportionality. We can write [m] as -
m = y/x
OR
y₁/x₁ = y₂/x₂
Given is a line passing through (9, -4) having slope=-2/3.
The general equation of a straight line is -
[y] = [m]x + [c]
Now -
m = - 2/3
and
- 4 = -2/3 x 9 + c
- 4 = - 6 + c
c = - 4 + 6
c = 2
The equation will be -
y = (-2/3)x + 2
Therefore, the equation of the line passing through (9, -4) having slope = -2/3 will be y = (-2/3)x + 2
To solve more questions on straight line, visit the link below-
https://brainly.com/question/29030795
#SPJ2
Solve for x.
3(2)x−24=0
Answers
Answer:
I love algebra anyways
the steps are in the picture with the ans
(hope this helps can i plz have brainlist :D hehe)
Step-by-step explanation:
Find the equation of a line that passes through the points (-2, -1) and (0, -5)
Answers
Answer:
Step-by-step explanation:
slope = (-5-(-1))/(0-(-2)) = (-4)/2 = -2
y+5 = -2(x-0)
y = -2x - 5
Answer:
-2x - 5
Step-by-step explanation:
For which equation is x=5 a solution?
2+x=3
2 plus x is equal to 3
3x=15
3 x is equal to 15
x2=10
, x over 2, is equal to 10
x−7=12
x minus 7 is equal to 12
Answers
Caitlyn reduced the size of a rectangle to a width of 3 in.
What is the new height if it was originally 10 in tall and 15
in wide
Answers
Answer:
h = 2
Step-by-step explanation:
you know the original rectangle [h = 10, w = 15]
1. The height of 15 inches turned to 3 inches by diving by 5
2. You have to do the same with the height too!
3. 10/5 = 2
The new height is 2 inches.
7. Which of the following expressions contains like terms?
5xy - 13y
5x - 13xy
5xy - 13x
5xy - 13xy
Answers
Answer:
The last one
Step-by-step explanation:
Due to there being xy's in both terms
During a cross-country road trip, Nathan predicts that he will average 22.6 miles per gallon.
During the trip, he drives 2,882 miles and uses 131 gallons of gas. Calculate his percent error,
rounded to the nearest whole percent.
3%
6%
13%
22%
Answers
Answer:
22
Step-by-step explanation:
i need help with finding slopes from graphs
Answers
Y=2+-4x
Step-by-step explanation:
Hope ot helps
3
:) A plane has 14 First Class seats, 70 Premium seats and 168 Economy seats
Find the ratio First Class seats : Premium seats : Economy seats.
Give your answer in its simplest form.
2
Answers
Answer:
70-14=56 168-56=112
Step-by-step explanation:
238% of what number is 47,600?
Answers
Answer:
I think 200
Step-by-step explanation:
47600/238=200
200*238=47600
Answer:
the answer is actually 20000
Step-by-step explanation:
238% x =47,600
2.38x=47,600
47,600/2.38= 20000
Kevin plants a total 72 flowers in a equal row. He plants 6 rows of yellow flowers and 2 rows of red flowers. How many flowers are in each row?
Answers
Answer:
9
Step-by-step explanation:
9 is the answer bc
6+2=8
72/8=9
(lol I hope I helped)
Help plz I don’t know the answer!!
Answers
Answer:201 11/21
Step-by-step explanation:
The number 4232 is called the numerator or dividend, and the number 21 is called the denominator or divisor.
The quotient of 4232 and 21, the ratio of 4232 and 21, as well as the fraction of 4232 and 21 all mean (almost) the same:
4232 divided by 21, often written as 4232/21.
Read on to find the result of 4232 divided by 21 in decimal notation, along with its properties.We provide you with the result of the division 4232 by 21 straightaway:
4232 divided by 21 = 201.523809
The result of 4232/21 is a non-terminating, repeating decimal. The repeating pattern above, 523809, is called repetend, and denoted overlined with a vinculum.
This notation in parentheses is also common: 4232/21 = 201.(523809): However, in daily use it’s likely you come across the reptend indicated as ellipsis: 4232 / 21 = 201.523809… .
4232 divided by 21 in decimal = 201.523809
4232 divided by 21 in fraction = 4232/21
4232 divided by 21 in percentage = 20152.38095238%
Note that you may use our state-of-the-art calculator above to obtain the quotient of any two integers or decimals, including 4232 and 21, of course. Repetends, if any, are denoted in ().
The conversion is done automatically once the nominator, e.g. 4232, and the denominator, e.g. 21, have been inserted. No need to press the button, unless you want to start over.
The midpoint of AB is M (4,-2) . If the coordinates of A are (3,-6) , what are the coordinates of B
Answers
Answer:
The coordinates of B are (5,2).
Step-by-step explanation:
Given that,
The midpoint of AB is M (4,-2).
The coordinates of A are (3,-6)
We need to find the coordinates of B. Let the coordinates of B are (x,y).
The mid point is given by :
[tex]M=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})\\\\(4,-2)=(\dfrac{3+x}{2},\dfrac{y-6}{2})\\\\\dfrac{3+x}{2}=4\ \text{and}\ \dfrac{y-6}{2}=-2\\\\3+x=8\ \text{and}\ y-6=-4\\\\x=5,y=2[/tex]
So, the coordinates of B are (5,2).
The area (A) of a rectangle varies jointly as the length (l) and the width (w), and whose A = 60 sq. cm when l = 4 cm and w = 3 cm. What is the area of rectangle if the length is 6 cm and whose width is 3 cm?
Answers
Answer:
The area is 90 sq. cm
Step-by-step explanation:
Given
The variation can be represented as:
[tex]A\ \alpha\ l * w[/tex]
Area = 60, when l = 4 and w = 3
Required
Find Area, when l = 6 and w = 3
Represent the variation as an equation
[tex]A = k(l * w)[/tex]
Where k is the constant of variation.
Substitute 60 for A, 4 for l and 3 for w
[tex]60 = k * (4 * 3)[/tex]
[tex]60 = k * 12[/tex]
Make k the subject
[tex]\frac{60}{12} = k[/tex]
[tex]5=k[/tex]
[tex]k=5[/tex]
To get the value of Area when l = 6 and w = 3.
Substitute 5 for k, 6 for l and 3 for w in [tex]A = k(l * w)[/tex]
[tex]A = 5 * 6 * 3[/tex]
[tex]A = 90[/tex]
The area is 90 sq. cm
A plane leaves an airport traveling at 400 mph in the direction N 45° E. A wind is blowing at 40 mph in the direction N 45° W. What is the ground speed of the plane?
400 mph
402 mph
429 mph
440 mph
Answers
Answer:
402 mph
Step-by-step explanation:
Draw a right triangle with 400 and 40 as the two legs.
You know this is a right angle because 45 degrees NE is perpendicular to 45 degrees NW. (imagine a compass)
So, the two side lengths are 400 and 40
Using the Pythagorean theorem, (a^2 + b^2 = c^2) you can see that the answer is 401.995, or 402
The ground speed of the plane is 402 mph , Option B is the correct answer.
What is a Right Angled Triangle ?A right angle triangle is a triangle with one of its sides 90 degree.
It is given that
airplane is travelling at speed of 400mph in the direction N 45° E
wind is blowing at 40 mph in the direction N 45° W
The resultant of these two vectors will be the ground speed of the plane.
As they both are travelling in perpendicular directions ( NE is perpendicular to NW)
A right angled Triangle as attached in the image will be formed
Hypotenuse by Pythagoras theorem will give the ground speed of the plane
Hypotenuse = [tex]\sqrt { 40 ^2 + 400^2}[/tex]
Hypotenuse = 401.99 mph
Therefore the ground speed of the plane is 402 mph.
To know more about Right Angled Triangle
https://brainly.com/question/3770177
#SPJ2
Which of the following rational functions are graphed below?
A. F(X)=1/x+4
B. F(X)=4/x
C. F(X)=1/4x
D. F(X)=1/x-4
Answers
According to the vertical asymptote of the graph, the rational function is:
A. [tex]F(X) = \frac{1}{x + 4}[/tex]
A vertical asymptote of a function is a point that is outside of it's domain.
In a fraction, they are the roots of the denominator.In the graph, the vertical asymptote is at x = -4, hence [tex]x = -4 \rightarrow x + 4 = 0[/tex] is a root of the denominator, and the correct option is:
A. [tex]F(X) = \frac{1}{x + 4}[/tex]
To learn more about vertical asymptotes, you can take a look at https://brainly.com/question/11598999
Answer to your question is A. F(X)=1/x+4
What is the standard form equation 9(g-5h)
Answers
Answer:
9g - 45h
Step-by-step explanation:
9 (g - 5h)
= 9g - 45h
A retired woman has $80,000 to invest but needs to make $9,000 a year from the interest to meet certain living expenses. One bond investment pays 15% annual interest. The rest of it
she wants to put in a CD that pays 7%.
Set up and solve the equation for how much the woman should invest in each option to sustain exactly a $9,000 annual return.
bond $ ?
CD $?
Answers
Answer:
bond $42,500
CD $37,500
Step-by-step explanation:
While x is investment in bond in k$
y is investment in CD in k$
[tex]x+y=80\\.15x+.07y=9[/tex]
Solving gives
x=42,5
y=37,5
which digit is in the hundredths place in the number 85,607.293×
Answers
Answer:
9
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
A cone has a volume of 414.48 cubic yards and a height of 11 yards. What is its radius?
Answers
Answer:
r ≈ 6
Step-by-step explanation:
r= 414.78
π x 11
≈ 5.99848
Because of this, the answer is rounded up to 6, but the exact answer is about 5.99848
Answer:
this isnt related to the question but i hope ur having a good day
Step-by-step explanation:
puzzle times what kind of cheese comes with a house
Answers
Answer:
WHAT DOES TGAT EVEN MEAN
Step-by-step explanation:
Answer:
Step-by-step explanation:
solve the formula for x
Gx +Hy=J
Answers
Answer:
x = [tex]\frac{J-Hy}{G}[/tex]
Step-by-step explanation:
This question is from the topic subject of formula. It implies expressing x in terms of G, H y and J.
Given that: Gx + Hy = J
Subtract Hy from both sides to have;
Gx + Hy - Hy = J - Hy
⇒ Gx = J - Hy
Then divide both sides by G, so that we have;
x = [tex]\frac{J-Hy}{G}[/tex]
Therefore,
x = [tex]\frac{J-Hy}{G}[/tex]
how many solutions does the equation 7x-4=7x+15
Answers
Answer:
No solution
Step-by-step explanation:
7x-4=7x+15
-4 = 15 = not true
Answer:
0 because is you -7x from both sides you get -4=15 which doesn't work.
Step-by-step explanation:
choose the point slope form of the equation
Answers
Answer:
Step-by-step explanation:
y+3=1/2(x-6)