What are the roots of the polynomial equation x^4 + x^2 = 4x^3 -12x +12 ? Use a graphing calculator and a system of equations. Round noninteger roots to the nearest hundredth.
A)–12
B) –2.73, 2.73
C) –1.73, 1.73
D) 12
Answers
Answer : option C
Explanation:
there will be 4 roots for the given polynomial but in graph you will see 3 points because (2,0) is repeating two times
we can see the root graphically
the points that intersect x-axis are the roots
Here, x-axis is cut at 3 points so, these points will be the root of given polynomial.
please see the attached graph
Related Questions
A box of 24 chocolate truffles cost $28.50 and individual truffle cost $1.50 how much do you save by purchasing a box of 24
Answers
[tex]1.50 \times 24 = 36 \\ 36 - 28.50 = 7.5[/tex]
you save $7.50
You are selling items from a catalog for a school fundraiser. Select two inequalities that you can use to find the range of sales that will earn you at least $40 and at most $50. Then find the range of sales. Let x represent the amount of sales (in dollars).
Answers
5(x/50)≤50
Selling between $400 and $500 will earn you between $40 and $50.
The range of sales that will earn at least $40 and at most $50 is represented by the inequalities x >= 40 and x <= 50. Hence, the range of possible sales is x such that 40 <= x <= 50.
Explanation:The subject of this question is inequalities and the concept of a range of numbers in mathematics. Here, we're looking at a range of sales values that will result in the organizer earning between $40 and $50.
The two inequalities that represent this scenario are: x >= 40 and x <= 50.
To find the range of sales, we look at the values that satisfy both conditions. Therefore, the range of sales is all the sales amounts (x) such that: 40 <= x <= 50. This means that any amount of sales that is greater than or equal to $40 and less than or equal to $50 will meet the criteria.
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A bag contains 15 red candies, 20 blue candies, and 10yellow candies. What is the probability of drawing a red candy? A blue candy? Something besides a yellow candy?
Answers
The probability of drawing a red, blue, and a candy that is not yellow from the bag is 1/3, 4/9, and 7/9 respectively.
Explanation:The question involves the concept of probability in mathematics, with a scenario of drawing candies from a bag. The total number of candies in the bag is 45 (15 red + 20 blue + 10 yellow).
The probability of drawing a red candy is the number of red candies divided by the total number of candies, which is 15/45 or 1/3.
The probability of drawing a blue candy is the number of blue candies divided by the total number of candies, which is 20/45 or 4/9.
If we want to find the probability of drawing something other than a yellow candy, this is essentially the sum of the probabilities of drawing a red or blue candy. This is 35 out of 45 (15 red candies + 20 blue candies), which reduces to 7/9.
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Solve for W!
W - 2.76 = 6.7
Answers
isolate the W by adding 2.76 to both sides of the equal sign
W - 2.76 (+2.76) = 6.7 (+2.76)
W = 6.7 + 2.76
W = 9.46
9.46 is your answer
hope this helps
W= 9.46
WILL GIVE BRAINLIEST TO PERSON WHO ANSWERS CORRECTLY!!!!!!!!!
Tony is baking cakes and loaves of bread for a family reunion. His cake recipe uses 5 cups of flour for each cake, and his bread recipe uses 6 cups of flour for each loaf. He has 90 cups of flour on hand.
Let c represent the number of cakes and b represent the number of loaves of bread that Tony bakes.
Create an inequality that symbolizes this situation, and then answer the question below.
Can Tony bake 8 cakes and 9 loaves of bread without buying more flour?
Answers
5*6=30*3=90 YES
Peyton has 2 pizzas. Each pizza is cut into 10 equal slices. She and her friends eat 14 slices. What part of the pizzas did they eat?
Answers
70% part of the pizzas they ate.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given, Peyton has 2 pizzas. Each pizza is cut into 10 equal slices.
Thus, total slices of pizza = 10 *2
total slices of pizza = 20
Since, She and her friends eat 14 slices.
Thus,
Percentage of pizza they eat = 14/20*100
Percentage of pizza they eat = 14*5
Percentage of pizza they eat = 70%
Therefore, Alex and her friends Eat 70% of the pizza.
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Randall is going to the grocery store. It is 3 3/5 miles from his house. He walks 2 2/5 miles before it starts to rain. How far will he have to walk in the rain?
Answers
3.1 Q19
Mona has 440 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?
Answers
x + x + y + y = 440
2x + 2y = 440
Divide by 2 through ...
x + y = 220
y = 220 - x
Area = xy
Area = x(220 -x) = 220x - [tex] x^{2} [/tex]
Given that that max length of x will be -b/2a
a = -1 b = 220
x = [tex] \frac{-220}{-2} [/tex] = 110
x = 110
y = 220 - 110 = 110
Therefore max area = 110 x 110 = 12100 square yards
Kevin rented a truck for obe day. There was a base fee of $15.99, and there was an additional charge of 83 cents for each mile driven. Kevin had to pay $177.01 when he returned the trunk. For how many miles did ge drive the trunk?
Answers
This should give you 161.02
Then divide 161.02 by .83
He drove 194 miles :)
A used bookstore will trade 2 of its books foe of yours, If Val brings in 18 books to trade,how many books can she get from the store
Answers
Hope this helps!
♤MidnightQueen
What is the median of this set of data? 1, 2, 5, 6, 9 1 5 8 9
Answers
evaluate r s + 14s when r= 6 and s= 1/4
Answers
(6)(1/4) + 14(1/4)
1.5 + 14(1/4)
1.5 + 3.5
5
What is the surface area of the right cone below?
Answers
[tex]A= \pi r(r+ \sqrt{h^2+r^2} )[/tex]
Here Radius, r= 6 units
To find the height of cone, we use Pythagorean theorem.
c²=a²+b²
Put values
15²=6²+h²
225=36+h²
h²=189
Put values in formula.
A=6π(6+√189+36)
A=6π+(6+√225)
A=6π(6+15)
A=126π units²
Answer:
Te correct option B.
Step-by-step explanation:
The surface area of a cone is
[tex]A=\pi r(r+l)[/tex]
Where, r is the radius and l is slant height.
From the given figure it is noticed that the radius of the cone is 6 and slant height is 15.
The surface area of cone is
[tex]A=\pi \times 6\times (6+15)[/tex]
[tex]A=\pi \times 6\times 21[/tex]
[tex]A=126\pi[/tex]
The area of the cone is 126π units². Therefore option B is correct.
what is the explicit rule for the following sequence -10 - 12 -14 -16
Answers
Please help me with questions 14 and 15
Answers
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Problem 15: The answer is choice A
cos(angle) = adjacent/hypotenuse
cos(B) = BC/AB
cos(B) = 12/13
Describe the relationship that must exist between a, b, and c in the equation ax^2+bx+c=0 in order for the equation to have exactly one solution
Answers
The [tex]b^2-4ac[/tex] bit is called the discriminant and it tells you what kind of solutions occur,
-if [tex]b^2-4ac \ \textgreater \ 0[/tex] then the equation has two different solutions
-if [tex]b^2-4ac=0[/tex] then the equation has exactly one solution
-if [tex]b^2-4ac\ \textless \ 0[/tex] then the equation has no (real) solutions.
So you are interested in exactly one solution which happens if [tex]b^2-4ac=0[/tex] or equivalently [tex]b^2=4ac[/tex].
The equation of a circle whose center is at (4, 0) and radius is length 2√(3) is (x - 4)² + y² = 2√3 (x - 4)² + y² = 12 (x + 4)² + y² = 12
Answers
(x-4)²+(y-0)²=(2√3)²
(x-4)²+y²=12
Answer:
Equation of the circle is
[tex](x-4)^2+y^2=12[/tex]
Step-by-step explanation:
We have been given that
center of the circle = (4,0)
Radius of the circle = [tex]2\sqrt3[/tex]
The standard form of a circle is given by
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Here, (h,k) is the center and r is the radius. Thus, we have
h = 4, k = 0, r = 2√(3)
Substituting these values in the above equation, we get
[tex](x-4)^2+(y-0)^2=(2\sqrt3)^2[/tex]
Simplifying, we get
[tex](x-4)^2+y^2=12[/tex]
Therefore, equation of the circle is
[tex](x-4)^2+y^2=12[/tex]
Assume Triangle EFG equals triangle JKL
Answers
Since ΔEFG is congruent to ΔJKL, their corresponding angles are congruent (CPCTC). The congruence statement tells you which angles of the triangle correspond; ∠E corresponds to ∠J, ∠F corresponds to ∠K, and ∠G corresponds to ∠L. The measures of all the angles of ΔJKL are given, so you just have to name the angle of ΔJKL that corresponds to ∠E of ΔEFG.
Looking at the congruence statement, ∠J corresponds to ∠E, and the m∠J is 90°. Thus the answer is 90°.
Answer:
m∠E = 90°
Marge cut 16 pieces of tape for mounting pictures on poster board. Each piece of tape was 3/8 inch long. How much tape did Marge use?
Answers
Let's convert 3/8 to a decimal and then multiply the length of each piece of tape by how many pieces Marge used.
To convert a fraction to a decimal, simply divide its numerator by its denominator:
3 ÷ 8 = 0.375
Next, multiply this by the amount of pieces Marge cut.
0.375 × 16 = 6
Therefore, Marge used 6 inches of tape.
The common denominator of 3/4 and 9/10
Answers
So 3/4 would be 15/20, and 9/10 would become 18/20.
Describe two different sequences of transformations that will map ABCD to EFGH.
Answers
Translation before rotation:
.. translate down 5 units
.. rotate counterclockwise 90° about the origin
Translation after rotation:
.. rotate counterclockwise 90° about the origin
.. translate right 5 units
This can also be accomplished by a double reflection.
.. reflect across the line y=x
.. reflect across the line x=2.5
Or,
.. reflect across the line y=2.5
.. reflect across the line y=x
Answer:
The orientation of the figure has been changed by 90°, but the points are not all rotated around the same center. Translation is involved.
Translation before rotation:
.. translate down 5 units
.. rotate counterclockwise 90° about the origin
Translation after rotation:
.. rotate counterclockwise 90° about the origin
.. translate right 5 units
This can also be accomplished by a double reflection.
.. reflect across the line y=x
.. reflect across the line x=2.5
Or,
.. reflect across the line y=2.5
.. reflect across the line y=x
Step-by-step explanation:
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A hacker is trying to guess someone's password. the hacker knows (somehow) that the password is 6 digits long, and that each digit cound be a number between 0 and 8. assume that the hacker makes random guesses. what is the probability that the hacker guesses the password on his first try? round to four decimal places.
Answers
The probability that the hacker guesses the password on his first try is 0
How to determine the probability?The password is given as:
Password = 6 digit long
The usable numbers are:
Digits = 0 to 8 i.e. 9 digits
If the digits can be repeated, then the number of passwords is:
Password = 9^6
Evaluate the exponent
Password = 531441
The probability that the hacker guesses the password on his first try is
P = 1/531441
Evaluate
P = 0.00000188167
Approximate
P = 0.0000
Hence, the probability that the hacker guesses the password on his first try is 0
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The probability of guessing the password on the first try is 0.000001881.
Explanation:To calculate the probability of guessing the password on the first try, we need to determine the number of possible passwords and divide it by the total number of possible guesses. In this case, the password is 6 digits long and each digit can be a number between 0 and 8.
So, there are 9 possible digits for each of the 6 positions, giving us a total of 9^6 = 531441 possible passwords.
The hacker makes random guesses, so there are 9^6 = 531441 possible guesses they can make.
The probability of guessing the password on the first try is therefore 1/531441 = 0.000001881, rounded to four decimal places.
Which of the following is a polynomial function in standard form with zeros at 0, 2, and 4?
Answers
x(x² - 6x + 8)
x³ - 6x² + 8x
Answer:
polynomial x³ -6x² +8x .
Step-by-step explanation:
Given : polynomial function in standard form with zeros at 0, 2, and 4.
To find : Which of the following is a polynomial function.
Solution : we have given that
zeros at 0, 2, and 4.
x = 0 .
x = 2
x = 4
(x -0)(x -2) (x -4).
x (x-2)(x-4).
x( x² -4x -2x +8).
x (x² -6x +8).
x³ -6x² +8x .
Therefore, polynomial x³ -6x² +8x .
The sum of two numbers is 46 and the difference is 14. What are the numbers?
Answers
.. x -(46 -x) = 14 . .the difference is 14
.. 2x = 60 . . . . . . simplify
.. x = 30 . . . . . . . divide by 2
The larger number is 30; the smaller is 16.
x + y = 46
x - y = 14 Add these two equations.
2x = 60 Divide by 2.
x = 60/2
x = 30
x + y = 46 Put 30 in for x
30 + y = 46 Subtract 30
y = 36 - 30
y = 16
the larger number is 30. The smaller is 16
What is the ninth term in the binomial expansion of (x – 2y)13? 329,472x5y8 –329,472x5y8 –41,184x8y5 41,184x8y5
Answers
Please, see the detailed solution in the attached file.
Thanks.
Find all real numbers X such that 4x+2>14 AND -21x+1>22
Answers
To solve the system of inequalities, we find the values of x that satisfy both conditions: x > 3 and x < -1.
Explanation:To solve this problem, we need to find the values of x that satisfy the given inequalities:
4x+2 > 14
-21x+1 > 22
For the first inequality, subtracting 2 from both sides gives us:
4x > 12
Dividing both sides by 4, we get:
x > 3
For the second inequality, subtracting 1 from both sides gives us:
-21x > 21
Dividing both sides by -21 (and flipping the inequality sign), we get:
x < -1
Therefore, the values of x that satisfy both inequalities are:
x > 3 and x < -1
Subtract 1.05 from a certain number. Multiply the difference by 0.8, add 2.84 to the product then divide the sum by 0.01 and get 700. What is the number?
Answers
We will set up an equation for this. Let x be the unknown number. Subtracting 1.05 from it gives us
(x-1.05)
Multiplying the difference by 0.8 would give us
0.8(x-1.05)
Adding 2.84 to the product would give us
0.8(x-1.05)+2.84
Dividing the sum by 0.01 would give us
[0.8(x-1.05)+2.84]/0.01 = 700
We will start working backward, cancelling the division by 0.01 first by multiplying:
([0.8(x-1.05)+2.84]/0.01)*0.01 = 700*0.01
0.8(x-1.05)+2.84 =7
Subtract 2.84 from both sides:
0.8(x-1.05)+2.84-2.84 = 7-2.84
0.8(x-1.05) = 4.16
Use the distributive property on the left side:
0.8*x - 0.8*1.05 = 4.16
0.8x - 0.84 = 4.16
Add 0.84 to both sides:
0.8x - 0.84+0.84 = 4.16+0.84
0.8x = 5
Divide both sides by 0.8:
0.8x/0.8 = 5/0.8
x = 6.25
Answer:
6.25
Step-by-step explanation:
I go to rsm and this answer worked
A graduated cylinder is filled with 36π of liquid. The liquid is poured into a different cylinder that has a radius of 3 cm. What will the height of the liquid be in the new cylinder?
Answers
Answer:
The height of the liquid in the new cylinder = 4 cm
Step-by-step explanation:
∵ The volume of the liquid = 36π cm³
∵ It poured into a cylinder that has radius 3 cm
∵ The volume of any cylinder = πr²h
∴ The volume of the liquid in the cylinder = π(3)²h = 9πh
- Where h is the height of the liquid inside the cylinder
∴ 9πh = 36π ⇒ divide both sides by π
∴ 9h = 36 ⇒ h = 36/9
∴ h = 4 cm
∴ The height of the liquid in the new cylinder = 4 cm
The height of the liquid in the new cylinder will be 4 cm. The term height is frequently used to describe someone's or something's height.
What is the height?Height is defined as the vertical distance between an object's top and bottom. It is measured in centimeters, millimeters, meters, and other units.
From the given conditions;
The volume of the liquid is, [tex]\rm V_L=36 \pi \ cm^3[/tex]
The radius of the cylinder is,[tex]\rm r=3 cm[/tex]
The volume of the cylinder is found as;
[tex]\rm V= \pi r^2 h \\\\ \rm V= \pi (3)^2 h \\\\ \rm V=9\pi h[/tex]
The height of the liquid is in the new cylinder is found as;
The volume of cylinder = Volume of liquid
[tex]\rm 9 \pi h= 36 \pi \\\\ \rm h=\frac{36}{9} \\\\ h= 4 \ cm[/tex]
Hence the height of the liquid in the new cylinder will be 4 cm.
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A smaller number is 3 less than half a larger number. The larger number is 10 times 1 less than the smaller number. Let x represent the smaller number, and let y represent the larger number. Which equations can be used to model the situation? Check all that apply.
Answers
Answer:
A,B,E
Step-by-step explanation:
HAVE A GOOD DAY
The required expressions that represent the given conditions are x = 1/2y - 3 or 2x - y = -6 and y = 10[x - 1]. Options A, B, and E are correct.
Given that,
A smaller number is 3 less than half a larger number. The larger number is 10 times 1 less than the smaller number. Let x represent the smaller number, and let y represent the larger number.
The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
According to the question,
A smaller number is 3 less than half a larger number.
x = 1/2y - 3
or
2x -y = -6
The larger number is 10 times 1 less than the smaller number.
y = 10[x - 1]
Thus, the required expressions that represent the given conditions are x = 1/2y - 3 or 2x - y = -6 and y = 10[x - 1]. Options A, B, and E are correct.
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which answer is a reasonable estimate to the following problem? 94.689