Answers
Since the two ends of graph are in opposite direction, the exponent of variable has to be odd. For an even exponent of leading term, the two ends are in same direction.
Since the graph is falling on left and rising on right, this indicates that the coefficient of leading term is positive.
So, the leading term must have:
1) Odd exponent
2) Positive Coefficient
Thus, option Fourth is the correct answer
Related Questions
Classify each polynomial by its degree and number of terms
Answers
1) 7x/4+3 (Name using degree: First degree polynomial),(Name using number of terms:binomial)
2) 5.2x^2-4x+2.5 (Name using degree: Quadratic polynomial),(Name using number of terms:trinomial)
3) 3/5 (Name using degree: zero degree polynomial),(Name using number of terms:monomial)
4) 0.75x^2 (Name using degree: Quadratic degree polynomial),(Name using number of terms:monomial).
Answer with explanation:
We know that a polynomial is classified based on the degree as follows:
Constant-
If it has a degree zero.
and the equation of such a polynomial is:
p(x)=a
Linear--
It has degree 1.
and the equation of such a polynomial is: p(x)=ax+b
Quadratic--
If it has degree two and the equation of the polynomial is given by:
[tex]p(x)=ax^2+bx+c[/tex]
Based on number of Terms--
Monomial--
If it has just one term.
Binomial--
If it has two terms.
Trinomial--
If it has three terms.
There are 25 counters is a bag 6 red, 4 white, 7 blue, and 8 yellow. you choose one counter at random. which color you least likely to choose
Answers
By calculating the probability of choosing a counter at random, we find that we are least likely to choose a white counter as it has the least probability.
What is probability?Probability is simply how likely something is to happen.
Probability of choosing a red counter = 6/25 = 0.24
Probability of choosing a white counter = 4/25 = 0.16
Probability of choosing a blue counter = 7/25 = 0.28
Probability of choosing a yellow counter = 8/25 = 0.32
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A soccer league has 170 players. Of those players 60% are boys. How many boys are in the soccer league
Answers
170•0.6 = 102
There are 102 boys in the soccer league.
Pleaseee helpppp!!!!!!!!!!!!!!!!
Answers
(change in y)/(change in x) = (-18 -(-20))/(1 - 0) = 2
so can be written in slope-intercept form as
g(x) = 2x -20
The x-intercept of this line is at x=10.
0 = 2x -20 . . . . the x-intercept is where g(x) = 0
20 = 2x
10 = x
The circle also intersects the x-axis at x=10, so that will be one point that is shared by the circle and g(x). A graph shows there is also another point of intersection, (6, -8).
Yes, the linear function g(x) will intersect the circle at 2 points with positive x-coordinates.
Manuel bought a balloon (that is a perfect sphere) with a radius of 2 \text{ cm}2 cm2, space, c, m. He wanted his balloon to be bigger, so he blew 222 big breaths of air into the balloon. Each big breath increased the balloon's radius by 1 \text{ cm}1 cm1, space, c, m. What is the ratio of the current volume of the balloon to the original volume of the balloon?
Answers
Answer:
8 times
Step-by-step explanation:
I found the volume of the sphere. Then increased it how many times he blew. That was the ratio.
Also, Khan :)
The ratio of the current volume of the balloon to the original volume of the balloon is 8.
What is the volume of a sphere?The volume of a sphere is given by (4\3)πr³ where r is the radius of the sphere.
The initial volume of the balloon = [tex]\frac{4}{3} \pi 2^{3}[/tex]
The initial volume of the balloon =[tex]\frac{32}{3} \pi[/tex]
Radius of the balloon after first breath = 2+1 =3cm
The Radius of the balloon after the second breath = 2+2=4cm
So, the new volume of the balloon = [tex]\frac{4}{3} \pi 4^{3}[/tex]
The new volume of the balloon = [tex]\frac{256}{3} \pi[/tex]
The ratio of new volume to the initial volume = [tex]\frac{\frac{256}{3 } \pi }{\frac{32}{3}\pi }[/tex]
The ratio of new volume to the initial volume =8
Hence, the ratio of the current volume of the balloon to the original volume of the balloon is 8.
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Solve the system of equations y = 40x2 and y = 19x + 3 algebraically.
Answers
We have been given a system of nonlinear equations.
[tex]\\y=40x^{2},y=19x+3[/tex]
In order to solve this system we can first equate the two equations in order to get a quadratic in x.
[tex]\\40x^{2}=19x+3[/tex]
Our next step is to bring all the terms on one side.
[tex]\\40x^{2}-19x-3=0[/tex]
Now we have to solve this equation. We can solve it by factoring using the splitting middle term method.
[tex]\\40x^{2}-24x+5x-3=0[/tex]
[tex]\\8x(5x-3)+(5x-3)=0[/tex]
[tex]\\(8x+1)(5x-3)=0[/tex]
Upon setting each of these factors equal to zero using zero product property we get
[tex]\\8x+1=0 \text{ or } 5x-3 = 0[/tex]
Upon solving both these equations we get
[tex]\\x=-\frac{1}{8} \text{ or } x=\frac{3}{5}[/tex]
Now we can substitute these values of x in the equation
[tex]y=19x+3[/tex]
We get
[tex]\text{For }x=- \frac{1}{8} \Rightarrow y=19(- \frac{1}{8})+3= \frac{5}{8}\\[/tex]
[tex]\text{For }x= \frac{3}{5}\Rightarrow y=19( \frac{3}{5})+3= \frac{72}{5}\\[/tex]
Therefore, our final set of solutions are
[tex](x,y)=(- \frac{1}{8},\frac{5}{8}) \text{ and } ( \frac{3}{5}, \frac{72}{5})[/tex]
A tank holds 1,000 gallons of syrup. Danielle filled 65 5-gallon cans with syrup. How much syrup was left in the tank when she finished? 3. Draw a picture or a chart that shows the information and the question.
675 gallons
935 gallons
325 gallons
350 gallons
Answers
Draw a picture of someone taking away 325 gallons of syrup from a 1000 gallon bin.
Hope that helped;)
Answer:
the answer is 675
Step-by-step explanation:
1. there is a tank with 1000 gallons, and we have 65 cans with a capacity of 5 gallons, so if we multiply the 65 cans with the capacity we would have as result
65 x 5 = 325
2- already having the value of gallons used (325) we can subtract this difference to the 1000 gallons that were in the tank at first.
1000 - 325 = 675
A sphere has a radius of 12 meters. What is the approximate volume of the sphere? Use 3.14 for π . Round your answer to the nearest whole number.
Answers
What are the x intercepts of this function f(x) =2x^2-7x-4?
Answers
2x² - 8x + x - 4 = 0
2x(x - 4) + 1(x - 4) = 0
(2x + 1)(x - 4) = 0
Set each binomial equal to zero.
2x + 1 = 0
2x = - 1
x = - 1/2
x - 4 = 0
x = 4
Your x-intercepts are x = - 1/2, 4 or (- 1/2, 0) and (4, 0)
A bag contains a variety of different-colored marbles. If P(red) = , P(green) = , and P(red and green) = , which statement is true?
Answers
Answer:
The answer is A. The events are independent because P(red) • P(green) = P(red and green).
Answer:
A. The events are independent because P(red) • P(green) = P(red and green).
Step-by-step explanation:
EDGE 2021 AQR
If BC is tangent to circle O and OB is a radius, what kind of triangle is OBC?
Answers
Triangle OBC is a right triangle. This is because where the radius and the tangent meet creates a right angle. A right angle is created due to the theorem that states that a radius is perpendicular to its tangent.
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
This is Josh’s solution for the equation
x2-6x-7=0:
x2-6x-7=0
x2-6x=7
x2-6x+9=7+9
(x-3)2=16
x=19
x-3=-16
x=-13
Is Josh’s solution correct? Explain
Answers
x - 3 = 4 OR x - 3 = -4
And the result answer would have been x = 7 or x = -1
Given that the values in the table represent the graph of a continuous function, y has at least how many zeros? HELLLLP!!!!!!!!!
Answers
We have the following sign changes:
x y
-2.4 0.69
-1.8 -0.39
-1.2 0.24
0 0
0.6 -0.46
1.2 -0.24
1.8 0.39
2.4 -0.69
Therefore, the number of zeros is:
5
Answer:
5
Solution:
x y
-2.4 0.69
-1.8 -0.39
-1.2 0.24
0 0
0.6 -0.46
1.2 -0.24
1.8 0.39
2.4 -0.69
So there will be 5zeros.
NEED HELPPPPPPP!!!!!!! PLEASE!!!!!!!!
Which statement best describes the graph of -x3 - x2 + 4x + 4?
A. It starts down on the left and goes up on the right and intersects the axis at x = -2, 2, and 4.
B.It starts down on the left and goes up on the right and intersects the axis at x = -2, -1, and 2.
C.It starts up on the left and goes down on the right and intersects the x-axis at x = -2, -1, and 2.
D.It starts up on the left and goes down on the right and intersects the axis at x = -2, 2, and 4.
Answers
Firstly, simplife the function [tex] -x^3-x^2+4x+4 [/tex] in the following way:
[tex] -x^3-x^2+4x+4=-(x^3+x^2)+4(x+1)=-x^2(x+1)+4(x+1)=(x+1)(4-x^2)=(x+1)(2-x)(2+x)=-(x+2)(x+1)(x-2) [/tex].
There are three x-intercepts: x=-1; x=2 and x=-2 (therefore, options A and D are incorrect).
Since before brackets is sign "-", you should state that graph starts down on the left (you can check this substituting smaller negative number than -2 into function expression. For example, if x=-10, then f(-10)=-(-10+2)(-10+1)(-10-2)=-(-8)(-9)(-12)>0) and goes up on the right (you can check this substituting greater positive number than 2 into function expression. For example, if x=10, then f(-10)=-(10+2)(10+1)(10-2)=-(12)(11)(8)<0).
Answer: correct choice is B.
please help will give brainiest!!!
Answers
How: Re-arrange formulae knowing tan(theta) = sin(theta)/cos(theta)
such that it become: cos(theta) -sin(theta)/cos(theta) x cos(theta) = 0.
From there; cos (theta) = sin(theta) (by re-arranging). Now, substitute figures of b), pie/4 = 45 degrees. At 45 degrees, sin(45) = cos(45) = 1/square root of 2. Also, 5pie/4 = 235 degrees. At 235 degrees, sin(235) = cos(235) = -1/square root of 2
b. [tex] \frac{ \pi }{4} or \frac{5 \pi }{4} [/tex]
Explanation:
Before we begin, remember that:
tan α = [tex] \frac{sin \alpha }{cos \alpha } [/tex]
Now for the given, we have:
cos θ - tan θ * cos θ = 0
cos θ - [tex] \frac{sin theta }{cos theta } [/tex] * cos θ = 0
cos θ - sin θ = 0
cos θ = sin θ
Now, divide both sides by cos θ, we get:
1 = tan θ
Following the ASTC rule, we know that the tan function is positive in the first and third quadrants.
This means that:
either θ = [tex] \frac{ \pi }{4} [/tex]
or θ = π + [tex] \frac{ \pi }{4} [/tex] = [tex] \frac{ 5 \pi }{4} [/tex]
Hope this helps :)
Rafael has ridden 14 miles of a bike course. The course is 40 miles long. What percentage of the course has Rafael ridden so far
Answers
Answer: 35%
Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = 3 - 4 sin θ
Answers
Explanation:
The equation r = 3 - 4 sin θ may be graphed using cartesian coordinates (i.e. x and y) or polar coordinates.
The logical way is to graph in polar coordinates. I did it using a graphing software and obtained the attached graph.
Also, I attached the graph in cartesian coordinates.
Here you have a table that you can build by your self and use the pairs to draw the graph (either cartesian or polar coordinates).
θ (rad) r = 3 - 4 sin θ
0 3
π/8 2.61731657
π/4 2.29289322
3π/8 2.07612047
π/2 2
5π/8 2.07612047
3π/4 2.29289322
7π/8 2.61731657
π 3
9π/8 3.38268343
5π/4 3.70710678
11π/8 3.92387953
3π/2 4
13π/8 3.92387953
7π/4 3.70710678
15π/8 3.38268343
2π 3
In both of the attached graphs you can see that the left side is equal to the right side, but the upper side is not equal to the bottom side.
Therefore, the graph is symmetric about the y-axis.
Answer:
y-axis... just look at the graph on desmos.com
How do do a 3/4 as a fraction, decimal, and percent?
Answers
Answer:
3/40.7575%Step-by-step explanation:
How do do a 3/4 as a fraction, decimal, and percent?
1) 3/4 is just a fraction
2) 3:4 = 0.75 (0.75 = 75%)
3) 75%
What is the volume of the coffee in a can if the can has a radius of 4 inches and a height of 9 inches? (use 3.14 for π.) 113.04 in.3 226.08 in.3 339.12 in.3 452.16 in.3?
Answers
your answer is here...
we know that almost all cans are cylindrical.
given the radius of the coffee can is 4 in and height is 9 in.
volume of the coffee can = πr²h
= 3.14 × 4 × 4 × 9
= 452.16 in³
cheers!!
The volume of the coffee in the can if the can has a radius of 4 inches and height of 9 inches is 452.16 inches³.
The can must be in the shape of a cylinder.
The formula to find the volume of the cylinder is,
Volume of cylinder = π r² h
Here r is the radius of the base of the cylinder and h is the height of the cylinder.
Given, Radius, r = 4 inches and Height, h = 9 inches
Volume of the coffee = π (4)² (9)
= 144 π
= 144 × 3.14
= 452.16 inches³
Thus, the volume of the coffee in the can is 452.16 inches³.
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What is the degree of the polynomial function f(x) = 2x3 + 7x5 − 4x − 12?
Answers
A plane intersects one cone of a double-napped cone such that the plane is neither parallel to the generating line nor perpendicular to the axis. What conic section is formed?
circle
hyperbola
ellipse
parabola
Answers
ellipse
Hope this Helped!
;D
The three undefined terms in geometry are point , line, and plane. True or false
Answers
Hope this helps :)
A grocer stacks oranges in a four-sided pyramid that is 7 layers high. How many oranges are in the pile?
A.504 B.840 C.140 D.120
Answers
Answer:
Option C. 140
Step-by-step explanation:
Base of a pyramid which has four triangular sides is four sided.
If pyramid contains seven layers of oranges then the layer at the bottom will have 7 oranges.
Since base is a square then other side of the square base will have the same number of oranges = 7.
Therefore number of oranges at the first layer will be = 7×7
Similarly other layers above this layer will have the same sequence
6×6, 5×5, 4×4, 3×3, 2×2, 1×1
Therefore total number of oranges = 7×7 + 6×6 + 5×5 + 4×4 + 3×3 + 2×2 + 1×1 = 49 + 36 + 25 + 16 + 9 + 4 + 1 = 140
Option C. 140 is the answer.
A grocer stacks oranges in a four-sided pyramid that is 7 layers high. Many oranges are in the pile are C.140
Further explanationThe orange is the fruit of the citrus species Citrus and sinensis in the family Rutaceae, native to China. Orange is also called sweet orange, to distinguish it from the related Citrus and aurantium, referred to as bitter orange.
The proper name of four-sided pyramid is a "tetrahedron". The tetrahedron has the extra interesting property of having all four triangular sides congruent
1st Layer: The 1st layer contains only 1 orange so it has only 1 orange
2nd layer: The 2nd layer has total 4 oranges. Calculation: [tex]2*2=4[/tex]
3rd layer: The 3rd layer has total 9 oranges. Calculation: [tex]3 * 3 = 9[/tex]
4th Layer: The 4th layer has total 16 oranges. Calculation: [tex]4 * 4 = 16[/tex].
5th layer: The 5th layer has total 25 oranges. Calculation: [tex]5 * 5 = 25[/tex]
6th layer: The 6th layer has total 36 oranges. Calculation: [tex]6 * 6 = 36[/tex]
7th layer: The 7th layer has total 49 oranges. Calculation: [tex]7 * 7 = 49[/tex].
Sum of all layers:
[tex]1+4+9+16+25+36+49 = 140[/tex]
Learn moreLearn more about oranges https://brainly.com/question/10744522Learn more about pyramid https://brainly.com/question/10262815Learn more about pile https://brainly.com/question/9094265Answer detailsGrade: 9
Subject: mathematics
Chapter: pyramid
Keywords: oranges, pyramid, four-sided, layers, pile
Use a calculator to find the mean and standard deviation of the data. Round to the nearest tenth.
20, 16, 18, 9, 20, 16,14
A. mean=15.9 standard deviation= 3.6
B. mean= 16 standard deviation= 12.7
C. mean= 16.1 standard deviation= 3.6
D. mean= 16.1 standard deviation= 12.7
Answers
Please, see the attached file.
Thanks.
A jar contains 133 pennies.A bigger jar contains 1 2/7 times as many.What is the value of the pennies in the bigger jar?
Answers
133 divided by seven is 19, (that's one-seventh right there) so multiply 19 by two to get 38, then add that to 133 (your "one")
A sample of 16 from a population produced a mean of 85.4 and a standard deviation of 14.8. a sample of 18 from another population produced a mean of 74.9 and a standard deviation of 16.0. assume that the two populations are normally distributed and the standard deviations of the two populations are equal. the null hypothesis is that the two population means are equal, while the alternative hypothesis is that the mean of the first population is different than the mean of the second population. the significance level is 1%.
Answers
Solution: The test statistic under the null hypothesis is:
[tex]t=\frac{\bar{x_{1}}-\bar{x_{2}}}{s_{p}\sqrt{(\frac{1}{n_{1}})+(\frac{1}{n_{2}})}}[/tex]
Where:
[tex]s_{p} = \sqrt{\frac{(n_{1}-1)s^{2}_{1}+(n_{2}-1)s^{2}_{2}}{n_{1}+n_{2}-2} }[/tex]
[tex]s_{p} = \sqrt{\frac{(16-1)14.8^{2}+(18-1)16^{2}}{16+18-2} }[/tex]
[tex]=15.45[/tex]
[tex]\therefore t=\frac{85.4-74.9}{15.45\sqrt{(\frac{1}{16})+(\frac{1}{18})}}[/tex]
[tex]=\frac{10.5}{5.31}[/tex]
[tex]=1.98[/tex]
Now, to find the critical values, we need to use the t distribution table at 0.01 significance level for [tex]df=n_{1} + n_{2} -2 = 16+18-2=32[/tex] and is given below:
[tex]t_{critical}=-2.738,2.738[/tex]
Since the t statistic is less than the t critical value, we therefore fail to reject the null hypothesis and conclude that the two population means are equal.
Area of figure? Geometry help???
Answers
[tex] A = \dfrac{172^\circ}{360^\circ} \times 3.14159 \times (4~in.)^2 [/tex]
[tex] A = \dfrac{172^\circ}{360^\circ} \times 3.14159 \times 16~in.^2 [/tex]
[tex] A = 24.0~in.^2 [/tex]
Write the partial fraction decomposition of the given rational expression. startfraction 5 x plus 2 over x superscript 4 baseline minus 4 x squared endfraction
Answers
Answer:
Step-by-step explanation:
Given is a rational algebraic expression in x as
[tex]\frac{5x+2}{x^4-4x^2}[/tex]
First let us factorize the denominator.
[tex]x^2(x^2-4)\\=x^2(x+2)(x-2)[/tex]
Let the given term be
[tex]\frac{A}{x} +\frac{B}{x^2} +\frac{C}{x-2} +\frac{c}{x+2} \\\\=\frac{Ax(x^2-4)+B(x^2-4)+cx^2(x+2)+Dx^2(x-2)}{x^4-4x^2}[/tex]
Equate the numerator to get
[tex]Ax(x^2-4)+B(x^2-4)+cx^2(x+2)+Dx^2(x-2)[/tex]=[tex]5x+2[/tex]
Substitute x =-2
[tex]4D (-4) = -8\\D=\frac{1}{2}[/tex]
Now substitute x =2
We get
[tex]16C=12\\C=\frac{3}{4}[/tex]
Put x=0
[tex]-4B=2\\B=\frac{-1}{2}[/tex]
Next equate X cube terms to 0 on right side
[tex]A+C+D=0\\A=\frac{-5}{4}[/tex]
Hence partial fraction is
[tex]\frac{-1}{2x^2} -\frac{5}{4x} +\frac{1}{2(x+2)} +\frac{3}{4(x-2)}[/tex]
To decompose the rational expression startfraction 5x + 2 over x4 - 4x2 endfraction into partial fractions, we need to factor the denominator. The partial fraction decomposition of the given rational expression is startfraction A over x + B over x2 + C over (x - 2)2, where A, B, and C are the determined coefficients.
Explanation:To decompose the rational expression startfraction 5x + 2 over x4 - 4x2 endfraction into partial fractions, we need to factor the denominator. The denominator can be factored as x2(x2 - 4) which gives us two distinct linear factors x and x + 2, and a repeated linear factor x - 2. Therefore, we can express the rational expression as follows: startfraction A over x + B over x2 + C over (x - 2)2.
To find the values of A, B, and C, we can use the method of equating coefficients. By multiplying both sides of the equation by the common denominator, we can eliminate the fractions and solve for the unknowns. Finally, we substitute the values of A, B, and C back into the partial fraction decomposition expression.
Therefore, the partial fraction decomposition of the given rational expression is startfraction A over x + B over x2 + C over (x - 2)2, where A, B, and C are the determined coefficients.
Which accurately shows how to use inverse operations to find the value of a in a + 5 = 14?
Answers
a+5=14
using the additive inverse property we shall have:
a+5+(-5)=14+(-5)
simplifying the above we get:
a+5-5=14-5
a+0=9
thus
a=9
∠ABD is formed by a tangent and a secant intersecting outside of a circle. If minor arc AC = 72° and minor arc CD = 132°, what is the measure of ∠ABD?
A) 30°
B) 36°
C) 42°
D) 48°
Answers
m∠ABD=1/2(mCD-mAC)
m∠ABD=1/2(132-72)
m∠ABD=1/2(60)=30
Answer:
c 42 degrees
Step-by-step explanation: