Answer:
Potential roots: [tex]\frac{9}{4},\frac{9}{2},9,\frac{3}{4},\frac{3}{2},3, \frac{1}{4},\frac{1}{2},1[/tex]
Step-by-step explanation:
Simply put, the rational roots theorem tells us that if there are any rational roots of a polynomial function, they must be in the form
± [tex]\frac{FactorsOfa_{0}}{FactorsOfa_n}[/tex]
Where
a_n is the number before the highest power of the polynomial, and
a_0 is the constant in the polynomial
From the polynomial shown, we have a_n = 9 and a_0 = 4
The factors of 9 are 9, 3, 1
and
The factors of 4 are 4,2,1
So, if there are any rational roots, they would be:
± [tex]\frac{FactorsOfa_{0}}{FactorsOfa_n}[/tex]
± [tex]\frac{9,3,1}{4,2,1}[/tex]
Which is ± 9/4, 9/2, 9/1, 3/4, 3/2, 3/1, 1/4, 1/2, 1/1
or
[tex]\frac{9}{4},\frac{9}{2},9,\frac{3}{4},\frac{3}{2},3, \frac{1}{4},\frac{1}{2},1[/tex]
Using the Rational Root Theorem, the polynomial f(x) = 9x^4 - 2x^2 - 3x + 4 has potential rational roots which are ±4, ±2, ±1, and their counterparts divided by 3. In the complex number system, every nth-order polynomial can be factored into n roots, including imaginary roots for equations that lack real solutions.
Explanation:Rational Root Theorem and Potential Roots
The Rational Root Theorem is a useful tool for identifying all potential rational roots of a polynomial equation. When applying this theorem to the given polynomial f(x) = 9x^4 - 2x^2 - 3x + 4, we note that the potential rational roots are the divisors of the constant term (in this case, 4) divided by the divisors of the leading coefficient (in this case, 9). Therefore, the potential roots are ±4, ±2, ±1, and their counterparts divided by 3, which are ±4/3, ±2/3, and ±1/3. To determine which of these are actual roots, each must be tested in the polynomial equation.
The concept of complex number system further elaborates on polynomials by stating that every nth-order polynomial can have up to n roots, factored into linear factors in accordance with the fundamental theorem of algebra. In the case of second-order polynomials, the real number system may not yield roots for equations like x² + 1, but in the complex number system, such polynomials do have roots and can be factored as (x - i)(x + i), for instance.
What is the measure of PRQ?
Answer:
It makes sense for the answer to be 86 degrees since it's almost a right angle.
Answer:
The correct answer is option C. 86°
Step-by-step explanation:
From the figure we can see a circle.
To find the measure of <PRQ
Consider the triangle PQR,
<PRQ = <PTR + <RPT
From the figure we get,
<PTR = 102/2 = 51
<RPT = 70/2 = 35
<PRQ = <PTR + <RPT
51 + 35 = 86°
Therefore the correct answer is option C. 86°
Need help
Divide
(x^2+5x+4)÷(x+2)
^= to the second
Step-by-step explanation:
[tex](x^2+5x+4)\div(x+2)^2=(x^2+4x+4+x)\div(x+2)^2\\\\=(x^2+2(x)(2)+2^2+x)\div(x+2)^2\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\=\bigg((x+2)^2+x\bigg)\div(x+2)^2=\dfrac{(x+2)^2+x}{(x+2)^2}=\dfrac{(x+2)^2}{(x+2)^2}+\dfrac{x}{(x+2)^2}\\\\=1+\dfrac{x}{(x+2)^2}[/tex]
How to find the diameter?
I'm confused with where to start with this problem
Answer:
From the information, we know that the plate will hold 3 pieces of sushi, each with a diameter of 1 1/2 inches, and there be 1/2 inch space from the edge of the of the suchi to the edge of the plate.
The diamter of the suchi plates we need to puchase should be the sum of the diameter of the sushi and the the space between them and the edge of the plate:
(3 . 1 1/2) + (2 . 1/2)
= (3 . 3/2) + 1
= 9/2 + 1
= 9/2 + 2/2
= 11/2 = 5.5 (inches)
Answer:
From the information, we know that the plate will hold 3 pieces of sushi, each with a diameter of 1 1/2 inches, and there be 1/2 inch space from the edge of the of the suchi to the edge of the plate.
The diamter of the suchi plates we need to puchase should be the sum of the diameter of the sushi and the the space between them and the edge of the plate:
(3 . 1 1/2) + (2 . 1/2)
= (3 . 3/2) + 1
= 9/2 + 1
= 9/2 + 2/2
= 11/2 = 5.5 (inches)
The sum of two numbers is 12. The first number,X, is twice the second number,y, which system of equations could be used to find the two numbers ?
To solve the problem, set up two equations: X + Y = 12 and X = 2Y. Using the substitution method, replace X with 2Y in the first equation to find Y = 4, and subsequently find X = 8.
The problem given to us involves finding two numbers, X and Y, given that the sum of these two numbers is 12 and the first number, X, is twice the second number, Y. To solve for X and Y, we can set up a system of two linear equations.
The first equation comes from the sum of the two numbers:
X + Y = 12
The second equation comes from the statement that X is twice Y:
X = 2Y
Now we have a system of equations:
X + Y = 12X = 2YOne method to find solutions for X and Y is by substitution. We can substitute 2Y in place of X in the first equation:
(2Y) + Y = 123Y = 12Y = 4Now that we know Y is 4, we can find X using the second equation:
X = 2YX = 2(4)X = 8The two numbers are X = 8 and Y = 4.
31)
Note: Figure not drawn to scale.
The circle with center O has a radius of 18 centimeters. If the length of arc AB = 6π centimeters, what is the measure of x?
A) 40°
B) 60°
C) 70°
D) 80°
If circle with center O has a radius of 18 centimeters. If the length of arc AB = 6π centimeters then measure of x is 60°
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Given,
Circle with centre O,
Radius of circle=18 centimeters
length of arc AB = 6π centimeters
We need to find the measure θ of x
We have a formula to find the length of arc.
Length of an Arc = θ × (π/180) × r
Apply the given values in formula
6π=θ × (π/180) × 18
π gets cancelled on both the sides
6=θ/10
θ=60°
Hence if circle with center O has a radius of 18 centimeters. If the length of arc AB = 6π centimeters then measure of x is 60°
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In the figure below, angle y and angle x form vertical angles. Angle x forms a straight line with the 50° angle and the 40° angle. Right and solving equations to determine the measure of angle Y.
Answer:
angle Y = 90 degrees
Step-by-step explanation:
Since it is stated that angle x forms a straight line with the 50 and 50 degree angles, and that angle x is vertical to angle y, we can do 40+50+y=180 to find angle Y.
Helppleaseee!!! It's due tomorrow??!!
Answer:
Part a) The total length of the circular portions is [tex]12\pi\ in[/tex]
Part b) The total length of wire needed is tex]53.7\ in[/tex]
Part c) The total weight of the ornament is [tex]97\ g[/tex]
Step-by-step explanation:
Part a) Find the total length of the circular portions in terms of pi
we know that
The diameter of the circle is equal to the length side of the square
[tex]D=4\ in[/tex]
The total length of the circular portions is equal to the circumference of three complete circle
Because each circular portion is equal to 3/4 of circle
so
[tex](3/4)*4=3[/tex]
The circumference of four three quarter circles is equal to
[tex]C=3(\pi D)[/tex]
substitute the diameter
[tex]C=3(\pi (4))[/tex]
[tex]C=12\pi\ in[/tex]
Part b) Find the total length of wire needed
The total length of the circular portions is [tex]12\pi\ in[/tex]
assume
[tex]\pi =3.14[/tex]
[tex]12(3.14)=37.68\ in[/tex]
The total length of the square portion is equal to
[tex]4b=4(4)=16\ in[/tex] -----> perimeter of a square
Adds the lengths
[tex]37.68+16=53.68\ in[/tex]
Round to the nearest tenth
[tex]53.68=53.7\ in[/tex]
Part c) Find the total weight of the ornament
we know that the ornament weights 1.8 grams per inch
so
Multiply the total length by 1.8 to obtain the total weight
[tex]53.7(1.8)=96.66\ g[/tex]
Round to the nearest gram
[tex]96.66=97\ g[/tex]
write a function rule for the table.
Answer:
the correct answer would be C sorry if I'm wrong but that's how I know how to do it
3x^2-12x+8 in vertex form
Take out the 3 , to make the vertex form easier;)
Write an expression to represent the perimeter of the figure.
Answer:
5x + 2y + z
Step-by-step explanation:
The perimeter of a polygon is the sum of the lengths of all the sides of the polygon. This polygons has 8 sides. Their lengths are:
x, x, x, x, x, y, y, z
The perimeter of the polygon is the sum of the lengths shown above.
perimeter = x + x + x + x + x + y + y + z
The expression above can be simplified by combining like terms.
perimeter = 5x + 2y + z
How many floors does she travel?
Answer:
15 floors
Step-by-step explanation:
She parks on the third floor below ground +3
She goes up to the twelfth floor +12
3+12=15
Find the slope of a line perpendicular to y=3x+7.
Answer:
m=3
Step-by-step explanation:
Formula for m is m=-1/m
m=-1/3
Which logarithmic graph can be used approximate the value of Y in the equation 2^y=5
Absolutely down graph is true!!
because, certainly 2<y<3
and we know 2^y=5 ==> log5 with base 2 =y
so it concludes we must have a node between 2<y<3 in x=5
On a 120:1 scale model floor plan, the kitchen has a length of 3.5 cm and a width of 2.5 cm. What is the area of the actual kitchen in square meters?
Answer: The answer is 12.6 Meters Squared
You get that from multiplying 120 to 3.5 and 2.5 . After doing that you will get 420 cm and 300 cm. Knowing that a meter is 100 cm you will get 4.2 meters and 3 meters. To find the area of the kitchen space you will multiple 4.2 and 3 meters together and get 12.6 Meters, therefore 12.6 meters squared is the area of the kitchen floor.
What is the median of this data set? 100,102,103,106,109
The answer is 103 because it’s in the “middle”
Median means the middle number.
The answer : 103
Is my solution correct?
Answer:
The area of the shaded sector is [tex]51.2\pi \ units^{2}[/tex]
Step-by-step explanation:
I assume that the problem is
Find the area of the shaded sector of the circle with radius equal to 16 units
step 1
Find the value of x
we know that
[tex]8x+2x=360\°[/tex]-----> by complete circle
[tex]10x=360\°[/tex]
[tex]x=36\°[/tex]
The central angle of the shaded sector is 2x
[tex]2(36\°)=72\°[/tex]
step 2
Find the area of the circle
The area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=16\ units[/tex]
substitute
[tex]A=\pi (16)^{2}[/tex]
[tex]A=256\pi\ units^{2}[/tex]
step 3
Find the area of the shaded sector
we know that
A central angle of 360 degrees subtends an area of circle equal to [tex]256\pi\ units^{2}[/tex]
so
by proportion
Find the area of the shaded sector by a central angle of 72 degrees
[tex]\frac{256\pi}{360}=\frac{x}{72} \\ \\ x=256\pi *(72)/360\\ \\x=51.2\pi \ units^{2}[/tex]
Patti's Pet Palace has a 100-gallon fish tank. When it needs to be cleaned, it can be drained at a rate of 5 gallons per minute. Assuming the tank was full, and x represents the number of minutes the tank has been draining, which of the following equations represents the amount of water in the tank after x minutes?
A. y = 5x - 100
B. y = 5x + 100
C. y = 100 - 5x
D. y = 100x - 5
____________________________________________________
Answer:
Your answer would be C). y = 100 - 5x
____________________________________________________
Step-by-step explanation:
Let's break down the question so it would be more easier to figure out the answer.
We would be making a y = mx + b equation
Important information:
100-gallon."Drained" at a rate of 5 gallons PER minute.x represents the number of minutes the tank has been draining.With the information above, we can use that to make our equations.
We know that the place has a 100 gallon fish tank. in the question, it says that for the equation, the tank was full, so that would be our "beginning point" or "starting value. From the equation, it would represent our "B" value.
Our equation should look like this now:
y = mx + 100
Now we need to find the rate of change.
In the question, it says that the tank DRAINS at around 5 gallons per minute, meaning that we would have to subtract 5 (-5). That would represent your "m" value on the equation. Your equations should now look like this:
y = -5x + 100
F.Y.I: y = 100 - 5x is the same that as -5x + 100, it's just flipped, and y = 100 - 5x is the answer choice that looks close to the one we made.
Answer choice C). y = 100 - 5x would be your FINAL answer.
____________________________________________________
The equation that describes the situation where a 100-gallon tank is drained at a rate of 5 gallons per minute is y = 100 - 5x. This because each minute, the volume decreases by 5 gallons from the starting amount of 100 gallons.
Explanation:The question is about how to represent a process which decreases at a constant rate in terms of mathematical expression. In this case, Patti's Pet Palace is draining a 100-gallon fish tank at a rate of 5 gallons per minute. The total amount of water in the tank decreases as time progresses and the tank drains.
This process can be represented using a negative slope linear equation. If y represents the amount of water in the tank after x minutes, the initial amount is 100 gallons and it decreases by 5 gallons each minute.
Therefore, the equation to represent this process is y = 100 - 5x. That means option C is the correct answer. For each minute that passes (represented as 'x'), 5 gallons are subtracted from the initial 100 gallons.
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Which of the following expressions can be? factored to (3x^2+1)(4x-3)
Answer:
I think it's C, sorry if I'm wrong
Answer:
Step-by-step explanation:
(3x²+1)(4x-3) = 12x^3-9x²+4x-3.....answer 1
PLEASSE HELP!! WILL MAKR BRAINLIEST IF CORRECT!!!
Answer:
b. 26cm
oop I didn't realize this was in 2019:-:
The slope of the line passing through the points (-2, 6) and (4, 6) is
A) 0
B) no slope
C) 2
Your answer ish c. 2
A slope is also known as the gradient of a line. The correct option is B.
What is Slope?A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
slope = (y₂-y₁)/(x₂-x₁)
The slope of the line that is passing through (-2, 6) and (4, 6) can be calculated as,
Slope = (6-6)/(-2-4) = 0/(-6)
Hence, there exists no slope between the two of the given points.
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Which category do both shapes belong to?
A.square
B.parallelogram
C.rectangle
D.rhombus
B. Parallelogram
Explanation: both have parallel sides
The two of the given figures are parallelogram. The correct option is B.
What is parallelogram?In parallelogram the opposite sides are equals and it is not formed 90 degree angle between two sides.
In the two of the given figures, it can be observed that the two figures have opposite sides parallel and equal. Therefore, the two of the given figures are a parallelogram.
Hence, the two of the given figures are parallelogram.
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Solve for x: x − 2 > 2x + 12. x > 14 x < 14 x > −14 x < −14
For this case we must solve the following inequality:
[tex]x-2> 2x + 12[/tex]
We follow the steps below:
We subtract 2x on both sides of the inequality:
[tex]x-2-2x> 2x + 12-2x\\-x-2> 12[/tex]
We add 2 to both sides of the inequality:
[tex]-x> 14[/tex]
We multiply by -1 on both sides of the inequality, taking into account that the sense of inequality changes:
[tex]x <14[/tex]
Answer:
[tex]x <14[/tex]
Answer:
The guys above is wrong because it should be x < -14 because you have to balance out both sides of the equation, you can't just do something to one side of the equation and not do it to the other.
Step-by-step explanation:
equation that represents each mixed number as a sum of a whole numbers and unit fractions 3 and 1/4 5 and 1/2 to 1 2/3 and 4 3/8 solve
Answer:
1) [tex]\frac{13}{4}[/tex]
2) [tex]\frac{11}{2}[/tex]
3) [tex]\frac{5}{3}[/tex]
4) [tex]\frac{35}{8}[/tex]
Step-by-step explanation:
we know that
A mixed number is the sum of a whole number and a fraction number
case 1) we have
[tex]3\frac{1}{4}[/tex]
so
[tex]3\frac{1}{4}=3+\frac{1}{4}=\frac{3*4+1}{4}=\frac{13}{4}[/tex]
case 2) we have
[tex]5\frac{1}{2}[/tex]
so
[tex]5\frac{1}{2}=5+\frac{1}{2}=\frac{5*2+1}{2}=\frac{11}{2}[/tex]
case 3) we have
[tex]1\frac{2}{3}[/tex]
so
[tex]1\frac{2}{3}=1+\frac{2}{3}=\frac{1*3+2}{3}=\frac{5}{3}[/tex]
case 4) we have
[tex]4\frac{3}{8}[/tex]
so
[tex]4\frac{3}{8}=4+\frac{3}{8}=\frac{4*8+3}{8}=\frac{35}{8}[/tex]
Larry spends 3/4 hour twice a day walking and playing with his dog. He also spends 1/6 hour twice a day feeding his dog. How much time does Larry spend on his dog each day?
Answer:
1hr 40min.
Step-by-step explanation:
45+45=90+10=100
Which is the solution set of the inequality 15y-9<36?
Answer:
y < 3
Step-by-step explanation:
Given
15y - 9 < 36 ( Isolate 15y by adding 9 to both sides )
15y < 45 ( divide both sides by 15 )
y < 3
Answer:
y < 3
Step-by-step explanation:
on edge 2020
Factor this expression
Answer:
x^2+6x+9
(x+3)^2
Step-by-step explanation:
What values of b satisfy 3(2b + 3)^2 = 36?
Answer:
3(2b+3)^2=36
(2b+3)^2=12
2b+3=+2 radical3
2b+3= 2 radical 3
b=- radical 3 -3 over 2
b= radical 3- 3 over 2
b=- radical 3 - 3 over 2
Answer:
The answer is A
Step-by-step explanation:
Find the experimental probability that the first three students to arrive at school are boys
Answer:
that depends
Step-by-step explanation:
how many students are in the school all together, see you would do the 3 boys over the number of people (or students) in the school
hoped this helped a little
What is the volume of four cubes with a side length of fraction 1 over 4 foot? V = s3, where s is the side length.
A. fraction 1 over 4 ft3
B. fraction 1 over 3 ft3
C. fraction 1 over 12 ft3
D. fraction 1 over 16 ft3
Answer:
D. fraction 1 over 16 ft³Step-by-step explanation:
The formula of a volume of a cube:
V = s³
s - side length
We have s = 1/4 ft. Substitute:
V = (1/4)³ = 1/64 ft³
We have four cubes.
4V = 4 · 1/64 = 1/16 ft³
Number 8 answers? I need help ASAP
Answer: C
Since all the answers have (-6), it means that you multiply the whole equation on both sides by 6, which makes a (2/3)x become a 4x and a (1/2) become 3
Answer:
C
Step-by-step explanation:
Start by multiplying through by 3. That is the first of 2 possible steps.
3[2/3 x - 1 = 1/2]
2x - 3 = 3/2
Now multiply by 2
2 [ 2x - 3 = 3/2]
4x - 6 = 3
That makes C the only possible answer.