Answers
2. End behavior = the direction of the graph for very large positive and negative values of x
3. Irreducible = can’t not be factored
4. Leading coefficient = coefficient of the term with the highest power
5. Leading term = the term in a polynomial with the highest power
6. Quarter polynomial = fourth degree
7. Zeros of polynomials = x-values for which the value of the polynomials zero
1.
Cubic Polynomial--
A cubic polynomial is a polynomial of degree three.
2.
End behavior--
The end behavior of a function is it's behavior when x tends to infinity in both the directions i.e. when x tends to minus infinity and when x tends to plus infinity.
3.
Irreducible--
A polynomial is said to be irreducible if it can't be reduced i.e. it cannot be factored.
4.
Leading coefficient--
It is the coefficient of the highest degree term existing in the expression.
5.
Leading term--
It is the term with the highest degree.
6.
quartic polynomial-
A quadratic polynomial is a polynomial of degree 4.
7.
Zeros of polynomial--
The zeros of a polynomial are all the possible values of x at which the polynomial expression is equal to zero.
Related Questions
if a school has w women and M men and you know that there are 100 more men than women write an algebraic equation relating W and M
Answers
Answer:
W+100=M
Explanation:
So the problem says there will always be 100 more men than woman. So that would mean you just have to add the amount of women and 100 to find the number of men. For example, if there are 3 women, there will be 103 men.
Hope this helps ;)
Certainly! To create an algebraic equation representing the given situation, we can use the information that there are 100 more men than women at the school.
Let's use the variables:
- \( W \) to represent the number of women
- \( M \) to represent the number of men
The key piece of information that we have is that the number of men is 100 more than the number of women. We can write this relationship with an equation:
\[ M = W + 100 \]
This equation states that if you take the number of women (\( W \)) and add 100 to it, you will get the number of men (\( M \)). It directly translates the information given into an algebraic equation, showing the relationship between the number of women and the number of men in the school.
15 points
Line AB←→ passes through the points A(3,−1) and B(1,7).
Which lines are parallel to AB←→?
THIS IS MULTIPLE CHOICES
y=−4x
y=−4x+8
y=4x
y−1=2(x+2)
y+1=−4(x+1)
y=4x+7
y=2x−3
y−6=−4(x−3)
Answers
Lines that are parrellell presume to have the same slope.
So if we just calculate the slope of a function or a line we should be good.
[tex]s=\dfrac{\Delta{y}}{\Delta{x}}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Now put in the data from the coordinates of the points [tex]A(3,-1)\wedge B(1,7)[/tex]
[tex]s=\dfrac{7-(-1)}{1-3}=\dfrac{8}{-2}=\underline{-4}[/tex]
The form of a function now looks like: [tex]
f(x)\vee y=-4x+n[/tex]
From here we are no longer required to calculate anything more. Leave n alone.
The solutions are the equations of the form above.
That would mean:
[tex]
y=-4x \\
y=-4x+8 \\
y+1=-4(x+1) \\
y-6=-4(x-3)
[/tex]
Hope this helps.
Solve the inequality: x+7 < 4 or 7-x < 1 Please show all work!
Answers
Answer:
[tex]\large\boxed{x<-3\ or\ x>6}[/tex]
Step-by-step explanation:
[tex]x+7<4\qquad\text{subtract 7 from both sides}\\\\x+7-7<4-7\\\\x<-3\\\\7-x<1\qquad\text{subtract 7 from both sides}\\\\7-7-x<1-7\\\\-x<-6\qquad\text{change the signs}\\\\x>6[/tex]
Step-by-step explanation:
all work is pictured and shown
A large rectangular movie screen in an IMAX theater has an area of 6,699 square feet. Find the dimensions of the screen if it is 10 feet longer than it is wide
Length =
Width =
Answers
Answer:
Length=87 ft
Width=77 ft
Step-by-step explanation:
Let
L ----> the length of rectangular movie screen
W ----> the width of rectangular movie screen
we know that
The area is equal to
[tex]A=LW[/tex]
[tex]A=6,699\ ft^{2}[/tex]
so
[tex]6,699=LW[/tex] ----> equation A
[tex]L=W+10[/tex] ----> equation B
substitute equation B in equation A
[tex]6,699=(W+10)W\\ \\W^{2} +10W-6,699=0[/tex]
Solve the quadratic equation by graphing
The solution is [tex]W=77\ ft[/tex]
see the attached figure
Find the value of L
[tex]L=77+10=87\ ft[/tex]
On a DVD, information is stored on bumps that spiral around the disk. There are 73,000 ridges (with bumps) and 73,000 valleys (without bumps) across the diameter of the DVD. What is the diameter of the DVD in centimeters? Round your answer to the nearest whole number.
Answers
Answer:18542
Step-by-step explanation:simplemath
The diameter of the circular DVD is d = 12 cm
What is a Circle?A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Given data ,
Let the diameter of the circular DVD be d
The total number of ridges = 73,000
The total number of valleys = 73,000
The width of each ridge = 0.000032 cm
The width of each valley = 0.000074 cm
The length of center portion c = 4.26 cm
And , the diameter of circular DVD = total width of ridges + total width of valleys + center portion
The total width of ridges = ( 0.000032 cm ) x 73,000
The total width of valleys = ( 0.000074 cm ) x 73,000
So , the total width of ridges and valleys = 73,000 ( 0.000106 ) = 7.738 cm
On simplifying , we get
The diameter of circular DVD d = 7.738 cm + 4.26 cm
The diameter of circular DVD d = 11.998 cm
The diameter of circular DVD d ≈ 12 cm
Hence , the diameter of the circular DVD is 12 cm
To learn more about circle click :
https://brainly.com/question/28391204
#SPJ3
write and simplify a multiplication expression to represent 5^4
Answers
Answer:
Step-by-step explanation:
5 * 5 * 5 * 5
= 625
ANSWER
[tex] {5}^{4} = 625[/tex]
EXPLANATION
We want to simplify the exponential expression 5⁴ by writing and simplifying a multiplication expression that represents it.
This implies that
[tex] {5}^{4} = 5 \times 5 \times 5 \times 5[/tex]
This simplifies to
[tex]{5}^{4} = 25 \times 2 5[/tex]
We finally obtain:
[tex] {5}^{4} = 625[/tex]
Johnny has 19 bottles of dish soap and he gives Jeina 5. How much dish soaps will he have now?
Answers
Answer:
14 dish soaps
Step-by-step explanation:
Johnny has 19 bottles of dish soap and he gives 5 to Jeina
19 - 5 = 14
Answer:
14
Step-by-step explanation:
Johnny has 19 bottles of dish soap and he gives 5 to Jeina
19 - 5 = 14
Write two fractions with different denominators whose LCD is 45
Answers
Answer:
2/5 and 8/9 (answers can vary)
Step-by-step explanation:
The lcm of 5 and 9 is 45 so that works for our denominators.
So 2/5 and 8/9 (the answers are many)
Answer:
1/45 and 8/90
Step-by-step explanation:
Between these two fractions, the lowest shared denominator is 45.
What is the area of a circle with a radius of 8 inches? Use = 3.14
Answers
Answer:
200.96 inch²
Step-by-step explanation:
formula for a circle: (pi) x r²
pi= 3.14
3.14 x 8²
=200.96 inch²
For this case we have by definition, that the area of a circle is given by:
[tex]A = \pi * r ^ 2[/tex]
Where:
A: It is the radius of the circle
They tell us as data that the radius is 8 inches.
Substituting we have:
[tex]A = \pi * (8) ^ 2\\A = \pi * 64\\A = (3.14) (64)\\A = 200.96[/tex]
Thus, the area of the circle is [tex]200.96 \ in ^ 2[/tex]
Answer:
[tex]200.96 \ in ^ 2[/tex]
Can (3,5 and square root 34) be sides on a right triangle?
Answers
Answer:
Yes, they are.
Step-by-step explanation:
Remember that a triangle is only a right triangle if its sides meet this mathematical requirement:
(leg)² + (leg)² = (hypotenuse)²
The hypotenuse of a right triangle is the longest side, while the legs are the two shorter sides. We can't say exactly where √34 is, but since √25 = 5 and √36 = 6, we know it must be at least bigger than 5, making it the triangle's longest side.
Using √34 as the "hypotenuse" and 3 and 5 as the "legs" of our triangle makes the equation 3² + 5² = (√34)², and simplifying gets us
9 + 25 = 34
34 = 34
The requirement's been met, so yes, this is a right triangle.
What system of equations is shown on the graph below?
x - 2y = -4 and 2x + y =4
x - 2y = 4 and 2x + y = 4
x - 2y = -2 and 2x + y = -4
x - 2y = 2 and 2x + y =4
Answers
Answer:
x - 2y = 4 and 2x + y = -4Step-by-step explanation:
Look at the picture.
Read the coordinates of intercepts of each line.
Put them to slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b)
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The blue line:
(4, 0), (0, -2) → b= -2
[tex]m=\dfrac{-2-0}{0-4}=\dfrac{-2}{-4}=\dfrac{2}{4}=\dfrac{2:2}{4:2}=\dfrac{1}{2}[/tex]
Substitute the values of a slope and an y-intercept to the equation of a line:
[tex]y=\dfrac{1}{2}x-2[/tex]
Convert to the standard form [tex]Ax+By=C[/tex]:
[tex]y=\dfrac{1}{2}x-2[/tex] multiply both sides by 2
[tex]2y=x-4[/tex] subtract x from both sides
[tex]-x+2y=-4[/tex] change the signs
[tex]x-2y=4[/tex]
The red line:
(-2, 0), (0, -4) → b= -4
[tex]m=\dfrac{-4-0}{0-(-2)}=\dfrac{-4}{2}=-2[/tex]
[tex]y=-2x-4[/tex] add 2x to both sides
[tex]2x+y=-4[/tex]
The answer is B.
Hope it helps
If f(x)=2x+2and g(x)=x^3, what is (g•f)(2)
Answers
Answer: 2x^3+4x+4 would be the answer.
Step-by-step explanation: x^2 can only be combines with another variable with the same exponent. Then you just multiply the whole equation by 2. Hope this helps!
there was a total of 750 and 2015 crickets in a pond, the population increased by 17% the next year. The year after that the population decreased by 10%. what is the percent of change of population from the 2015 to 2017?
Answers
Answer:
5.2% increase
Step-by-step explanation:
In 2015 the total population was 750.
In 2016 the total population was 17% more than in 2015, so 750 x 1.17 = 877.
In 2017 the total population was 10% less than in 2016, so 877 x 0.9 = 789.
Compared to 2015, the population in 2017 was 789/750 = 1.052 or 5.2% greater.
In one step:
((750 x 1.17) x 0.9) / 750 = 5.2%
In this question, we're going to need to find the population in 2017, while using the given information.
Answer: 5.3% increaseLets gather the information we should know from the question.
Key information:
2015 -- Population of 750
Increased by 17% in the next year
Decreased by 10% the next year
With the information above, we can solve the problem.
We know that our starting population for crickets is 750, and it increases by 17% for the next year (2016), so we would multiply 750 by 1.17
[tex]750*1.17=877.5[/tex]
Our population in 2016 is 877.5.
Now, we know that he population in 2016 decreased by 10% going into 2017. We would need to find how much of 877.5 is 10%, and then subtract.
[tex]877.5*.10=87.75\\\\877.5-87.75=789.75[/tex]
When you're done solving, you should get 789.75
This means that the population of crickets in 2017 is 789.75.
Now, we know that we started with 750 crickets, now we have 789.5 crickets.
We would divide 789.5 by 750.
[tex]789.5\div750=1.053[/tex]
We would move the decimal place two times to the right, giving us 5.3.
This means that the population increased by 5.3% from 2015 to 2017.
I hope this helps!Best regards, MasterInvestor.the length and width of a rectangle are consecutive even integers. the area of the rectangle is 8 square units. what are the length and width of the rectangle?
Answers
Answer: 4 feet and 2 feet
Step-by-step explanation: The only factor of 8 that is an even integer is 4 and 2. So the answer is 4 feet and 2 feet.
Johan found that the equation –2|8 – x| – 6 = –12 had two possible solutions: x = 5 and x = –11. Which explains whether his solutions are correct?
He is correct because both solutions satisfy the equation.
He is not correct because he made a sign error.
He is not correct because there are no solutions.
He is not correct because there is only one solution: x = 5.
Answers
Answer:
He is not correct because he made a sign error.
Step-by-step explanation:
-2 |8-x| - 6 = -12
-2 |8-x| = -12 + 6
-2 |8-x| = - 6
2 |8-x| = 6
|8-x| = 3
2 possible solutions:
8-x = 3 ----> x = 5
or
8-x = -3 ----> x = 11
Comparing the answer choices, we can see that Johan got the sign of x = 11 wrong.
Hence the correct answer is:
He is not correct because he made a sign error.
Answer: Just did it on ed, answer is "He is not correct because he made a sign error."
Step-by-step explanation:
5. Triangle MNO is an isosceles
triangle in which only one angle
measures 122.6°. What is the
angle measure of one of the two
congruent angles?
Answers
The measure of the congruent angle of the triangle MNO will be 28.7°.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
Triangle MNO is an isosceles triangle in which only one angle measures 122.6°.
Let the measure of the congruent angle be 'x'. Then the equation is given as,
x + x + 122.6° = 180°
2x = 180° - 122.6°
2x = 57.4°
x = 28.7°
The measure of the congruent angle of the triangle MNO will be 28.7°.
More about the triangle link is given below.
https://brainly.com/question/25813512
#SPJ5
Using the diagram on the right, find the length of GT and TA.
Answers
Answer:
[tex]GT=10\ units[/tex] and [tex]TA=6\ units[/tex]
Step-by-step explanation:
we know that
In the diagram
Triangles GRT and GEA are similar by AA Similarity Postulate
Remember that
If two figures are similar, then the ratio of its corresponding sides is proportional
so
[tex]\frac{GR}{GE}=\frac{GT}{GA}[/tex]
we have
[tex]GR=5\ units[/tex]
[tex]GE=5+3=8\ units[/tex]
[tex]GT=16-x\ units[/tex]
[tex]GA=16\ units[/tex]
substitute
[tex]\frac{5}{8}=\frac{16-x}{16}\\ \\5*16=8*(16-x)\\ \\80=128-8x\\ \\8x=128-80\\ \\x=48/8\\ \\x=6\ units[/tex]
therefore
[tex]GT=16-x=16-6=10\ units[/tex]
[tex]TA=x=6\ units[/tex]
Which of the following is not a real number?
Answers
Answer:
D
Step-by-step explanation:
by definition, the square root of an negative number is known as an imaginary number. i.e Not a real number
[tex]\sqrt{-2}[/tex] = [tex]\sqrt{2}[/tex][tex]\sqrt{-1}[/tex] = [tex]\sqrt{2}[/tex]i (imaginary number)
The [tex]\sqrt{-2}[/tex] is not a real number.
The following information should be considered with respect to the real number:
The numbers should be found in the number line. It should be in fractions, whole, naturals, rational, irrational. But it can't be in imaginary numbers.Therefore, the first three options are considered to be the real number.
Thus we can conclude that the [tex]\sqrt{-2}[/tex] is not a real number.
Learn more: brainly.com/question/17429689
A season pass to the local water park costs 84. If you go to the park ten times during the season, what is the unit rate of cost per visit?
Answers
Answer:
$8.40
Step-by-step explanation:
To find the unit rate, take the total cost and divide by the number of times that you went
84/10
8.4
The unit rate (or cost per visit) is $8.40
PLEASE HELP K12
WILL MARK BRAINLYIST
What is the Length of the line segment with endpoints (12, 6 ) and (12, -9 )
Answers
Answer:
15Step-by-step explanation:
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have the points (12, 6) and (12, -9). Substitute:
[tex]d=\sqrt{(12-12)^2+(-9-6)^2}=\sqrt{0^2+(-15)^2}=\sqrt{225}=15[/tex]
[tex]\text{Hey there!}[/tex]
[tex]\text{The formula is:}\bf{\frac{y_2-y_1}{x_2-x_1}}[/tex] [tex]\text{ or you can say}\rightarrow[/tex] [tex]\frac{Rise}{Run}[/tex]
[tex]\text{y}_2=-9\\\\\text{y}_1=6\\\\\text{x}_2=12\\\\\text{x}_1=12[/tex]
[tex]\text{Now, that we know what our points are we could solve this equation}[/tex]
[tex]\frac{-9-6}{12-12}[/tex]
[tex]\text{-9 - 6 = -15}[/tex]
[tex]\text{12 - 12 = 0}[/tex]
[tex]\bf{= \ \frac{-15}{0}}[/tex]
[tex]\boxed{\boxed{\bf{Answer: \ \frac{-15}{0}}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
If 20% of a number is 12, what is 30% of the same number?
Answers
Answer:
The answer would be 18.
Step-by-step explanation
If 20% of a number is 12, then 30% of that same number would be 18. This means that the number would be 60 (6×2=12, 6×3=18). Hope this helps you to understand your math problem better!
samuel had some carnival tickets to sell. he sold 5/9 of them on monday and 1/8 of the remainder on tuesday. he sold the remaining 98 tickets on wednesday. each ticket was sold at $5 each. how many tickets were sold on tuesday?
Answers
Answer:
poooooooooooooooooop
Step-by-step explanation:
Perform the indicated operation. x+5/3 -x-3/2=
Answers
Step-by-step explanation:
to add or subtract in this case you have to the same common denominator. but what ever you do to the denominator you have to do to the numerator. top = numerator and bottom = denominator.
Answer:
[tex]-x+19/6[/tex]
Step-by-step explanation:
Which graph shows the solution to the system of linear inequalities below? Y>-2x+2 Y<2x-1
Answers
Answer:
That would be B. Graph A.
Step-by-step explanation:
The graph y < 2x - 1 is a dotted line which rises to the right with a slope of 2 and passes through y = -1 and is shaded below the line. The graph y > -2 x + 2 rises to the left and passes through y = 2 and is shaded above the line.
Answer quick please Points N, P, and R all lie on circle O. Arc PR measures 120° How does the measure of angle RNQ relate to the measure of arc PR?
A.Angle RNQ is equal in measure to arc PR.
B.Angle RNQ is half the measure of arc PR.
C.Angle RNQ is twice the measure of arc PR.
D.Angle RNQ is four times the measure of arc PR.
Answers
Answer:
Option A. Angle RNQ is equal in measure to arc PR.
Step-by-step explanation:
we know that
The triangle NOR is an equilateral triangle, because has three equal sides
NO=OR=RN ----> radius of the circle O
therefore
The interior angles of the triangle NOR measures 60 degrees each
so
∠RNO=60°
Find the measure of angle RNQ
we have that
∠RNO+∠RNQ=180° ------> by supplementary angles (linear pair)
substitute
60°+∠RNQ=180°
∠RNQ=180°-60°=120°
we know that
arc PR= 120° ----> see the graph
therefore
∠RNQ=arc PR
Angle RNQ is equal in measure to arc PR.
Answer:
it’s a
Step-by-step explanation:
Find the value of x.
A. 4 root 2/ 2
B. 4
C. 4 root 2
D. 4 root 3
Answers
Answer:
C. 4 root 2
Step-by-step explanation:
Total amount of angles = 45° + 45° = 90°
sin90 * 4 root 2 = 5.656854
Answer:
4
Step-by-step explanation:
You will either use cos or sin solve this problem
1. set up the problem like this
x/sin 45 x 4 root 2/sin 90
2. cross multiply (it will be useful to use calculator or if you know unit circle then you're good)
sin 90 = 1 and sin 45 = .7071067812 (don't really need to know this)
1x = (sin 45 x 4 root 2)
3. Solve for x like normal
1x = 4
1x/1 = 4/1
x = 4
What number line represents the solution set for the inequality -1/2 greater
than or equal to 4
Answers
Answer:
[8, inifinity sign)
Step-by-step explanation:
(2)/1 x -1/2 (greater than or equal to sign) 4(2), You need to get rid of the fraction so times 2 on both sides.
So the fraction cancels out and your answer is x (greater than or equal to) 8
The open side of the sign always is facing the bigger number so like this > so x is positive.
Since i can't show the number line i'll try to explain it if it's a greater than sign its a closed dot on the 8 going right. The 8 is in a bracket and the infinity is with a parenthesis. like this [8, infinity sign)
My teacher may have taught me different but it should be about the same.
Hope my answer has helped you and if not i'm sorry.
A cylinder with a base diameter of x units has a volume of πx3 cubic units. Which statements about the cylinder are true? Check all that apply.
The radius of the cylinder is x units.
The radius of the cylinder is 2x units.
The area of the cylinder’s base is πx2 square units.
The area of the cylinder’s base is πx2 square units.
The height of the cylinder is 2x units.
The height of the cylinder is 4x units.
Answers
Answer:
The height of the cylinder is 4x units
Step-by-step explanation:
see the attached document
Answer:
The answer is 1,3, and 6 Hope this helps
Step-by-step explanation:
Use the properties of exponents to rewrite the expression.
5e•5e•5e•5e
Answers
Answer:
(5e)^4
Step-by-step explanation:
What is the simplest form of this expression?
2x(x2 – 3) – 6x2
Answers
Answer:
-6x - 6x² + 2x³
Step-by-step explanation:
Match each like-term to end up with the above answer.
I hope this helps.