Which function has the most x-intercepts?

Which Function Has The Most X-intercepts?

Answers

Answer 1

The function with the most x-intercepts in the image is g(x), which has four x-intercepts. The function f(x) has three x-intercepts, and the function h(x) has two x-intercepts.

The number of x-intercepts a function has is equal to the number of times the function crosses the x-axis. The x-axis is also known as the line y = 0, so any point where the function's graph touches the x-axis is a solution to the equation f(x) = 0.

g(x) crosses the x-axis four times, at approximately -10, 3/2, 2, and 15.

f(x) crosses the x-axis three times, at approximately -2, 1, and 12.

h(x) crosses the x-axis twice, at approximately -1 and 3.

Therefore, g(x) has the most x-intercepts because its graph intersects the x-axis the most times.


Related Questions

Solve log2(6-2x)-log2x=3

Answers

Assuming you have log in base 2.

Join logarithms (always):

log2(6-2x)-log2(x) = log2( (6-2x/x) )

Then get rid of it! :)

(6-2x)/x = 2^3=8,

Solve the equation:

6-2x=8x ---> 10x=6 ---> x = 3/5.

Please show work on how you got the answer

Answers

(See attached diagram.)  The positions of the vaulter's left and right hands are marked. The length of the entire pole is 15 feet. The segment below her left hand is twice as long as the segment above, so label those two parts with x and 2x. Those two segments add up to 15 feet:

[tex]x+2x=15[/tex]
[tex]3x=15 \newline x=5[/tex]

The lower segment is 10 feet long. The vaulter's right hand is 1.5 feet above her left, so it is 10 + 1.5 = 11.5 from the bottom of the pole.

What is the probability that when a fair coin is flipped 25 times, there will be exactly five heads

Answers

The probabability of this is 5/25
Your answer is 0.00158

PLEASE HELP!!!!!!!

f(x)=x^2−3x+9
g(x)=3x^3+2x^2−4x−9

Find (f−g)(x)

Select one:
a. −3x^3−x^2+x+18

b. 3x^3+3x^2−7x

c. 3x^3+x^2−x−18

d. 3x^3−x^2−x

Answers

Answer: Choice A) -3x^3-x^2+x+18

-----------------------------

Work Shown:

(f-g)(x) = f(x) - g(x)
(f-g)(x) = [ f(x) ] - [ g(x) ]
(f-g)(x) = [ x^2-3x+9 ] - [ 3x^3+2x^2-4x-9 ]
(f-g)(x) = x^2-3x+9 -3x^3-2x^2+4x+9
(f-g)(x) = -3x^3+(x^2-2x^2)+(-3x+4x)+(9+9)
(f-g)(x) = -3x^3-x^2+x+18

If n is a positive integer and the product all the integeres from 1 to n inclusive is a multiple of 990 what is the least possible value of n

Answers

Hello,

Since 990=2*3²*5*11 ==>n=11

The sum of four consecutive even integer numbers is 84. find the four numbers.

Answers

84/4=21

 now take the 2 even numbers below 21 and the 2 even numbers above 21

18 +20 + 22 +24 = 84

 the numbers are 18, 20, 22 & 24

Planes Q and R are parallel. Explain how you know lines a and b are skew.



Sample Response: Skew lines are noncoplanar and do not intersect. Line a lies in plane Q and line b lies in plane R, so the lines are not coplanar. No other plane can be drawn through the lines, so they are not parallel. So, a and b are skew

Answers

By definition, skew lines are a pair of lines that are not parallel but do not intersect each other either. Hence, the conclusion would be, the lines are non-coplanar. An example would two random lines drawn in the x and y axes in a cartesian plane, respectively.

Sample Response:

Skew lines are noncoplanar and do not intersect. Line a lies in plane Q and line b lies in plane R, so the lines are not coplanar. No other plane can be drawn through the lines, so they are not parallel. So, a and b are skew.

Is #7 correct? Please explain.

Answers

#7 is correct coplaner because I had that same work in class and the teacher gave us the answers to all of them

How many different selections of 4 books can be made from a bookcase displaying 12 books?

Answers

(12 x 11 x10 x9) / (4 x3 x 2 x 1) = 495

there are 495 different ways to select 4 books

A sum of money amounting to $4.25 consists of dimes and quarters if there are 26 coins in all how many are quarters

Answers

d= dimes

q = quarters

d+q=26 coins

 rewrite as d=26-q

0.25q +0.10d=4.25

0.25q+0.10(26-q)=4.25

0.25q+2.6-0.10q=4.25

0.15q=1.65

q=11

d=26-11=15

11*0.25 = 2.75, 15*0.10=1.50, 2.75+1.50=4.25

 there are 11 quarters

The law of cosines is a^2+b^2-2abcos(C). Find the value of 2abcos(C).
A. 37
B. -40
C. 40
D. 20

Answers

[tex]\bf \textit{Law of Cosines}\\ \quad \\ c^2 = {{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)\\\\ -------------------------------\\\\ \begin{cases} c=2\\ a=4\\ b=5 \end{cases}\implies 2^2=4^2+5^2-(2ab)cos(C) \\\\\\ (2ab)cos(C)=4^2+5^2-2^2[/tex]

and surely you know how much that is.

Solve x3 = 64 over 27.

±8 over 3
8 over 3
±4 over 3

Answers

x³=64/27
Cube root the answer
³√x³=³√64/27
x=4/3.
Check:
x=4/3
x³=(4/3)³
x³=64/27. As a result, the correct answer is 4/3 or 4 over 3. If you wonder why don't I choose the answer as ±4 over 3 because of this
±4/3
Choose positive first
(4/3)²=64/27 Correct. However, then choose negative signs
(-4/3)³=-64/27 Incorrect. Hope it help!

The solution of the given equation is ±8/3.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

The given equation is x³= 64/27

x=±∛(64/27)

x=±∛(8³/3³)

x=±8/3

Therefore, the solution of the given equation is ±8/3.

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3. Elizabeth opened a library with 19,000 books in the year 1998. The number of books increases at a rate of 6.49% each year. Use a graph to predict the number of books in 2020.
A) ≈ 71,160
B) ≈ 75,779
C) ≈ 80,697
D) ≈ 66,824

Answers

The number of books increases at a rate of 6.49% each year so it's a growth function which is
V (t)=V0 (1+r)^t
V (t) number of books in 2020 ?
V0 books in the year 1998 19000
R rate of growth 0.0649
T time 2,020−1,998=22 years

V (22)=19,000×(1+0.0649)^(22)
V (22)=75,778.81 Round your answer to get 75779

Answer:            ≈ 75,779

Step-by-step explanation:

The length of a rectangular lawn is measured to twice its width. the perimeter of the lawn is given as 30 m. find the length and width of the lawn.

Answers

The length is 15m and the width is 5.25m

The function P(t) = 5,000 (0.93)t is the value of a motor scooter t years after it is purchased. Which of the following values show the annual depreciation of the value of the motor scooter?
93
-7
50
7

Answers

P(t) = 5,000 (1-r)t
P(t) = 5,000 (1-7%)t
P(t) = 5,000 (0.93)t

The annual depreciation rate is 7%

Answer:

Option 4 - 7%

Step-by-step explanation:

Given : The function [tex]P(t) = 5000 (0.93)^t[/tex] is the value of a motor scooter t years after it is purchased.

To find : Which of the following values show the annual depreciation of the value of the motor scooter?

Solution :

We are given a function p(t) which is represented as:

[tex]P(t) = 5000 (0.93)^t[/tex]

Where, p(t) is the value of a motor scooter t years after it is purchased.

Depreciation is the amount that has been deducted from the cost of an item.

The rate of change is 1-0.93=0.07 i.e. 7%.

So, The function P(t) has 7% of the amount has been deducted each year and the value of the motor scooter is 93% of the amount of the previous year.

Therefore, The annual rate of depreciation is 7%.

So, option 4 is correct.

How do I simplify this problem?

Answers

Expanding (x+h)^3, we get (5x^3+15x^2h+15xh^2+5h^3-5x^3)/h=
(15x^2h+15xh^2+5h^3)/h= 15x^2+15xh+h^2

Last year, there were n pies baked for the bake sale. This year, there were 156 pies baked. Using n, write an expression for the total number of pies baked in the two years

Answers

Number of pies last year: n
Number of pies this year: 156

n + 156 = total number of pies baked in 2 years.
n + 156 = total number of pies baked in 2 years.

18 divided by 5593 equals 31-5400 = 193 what number should be placed in the box to help complete the division calculation?

Answers

The number that should be placed in the box to complete the division calculation is -7.

To find the number that should be placed in the box to complete the division calculation, let's analyze the given information:

- Dividend: 5593

- Divisor: 18

- Quotient: 31 (hundreds place is 3 and tens place is 1)

- When 5400 is subtracted from 5593, the result is 193.

- The box represents an unknown number in the ones place of the quotient.

To find the value in the box, we need to consider the units place. Since 5400 is subtracted from 5593 to give 193, the difference between the units places should be the value in the box.

193 - 5400 = -5207

So, the number that should be placed in the box to complete the division calculation is -7.

Correct question is:  

What number should be placed in the box to help complete the division calculation?

Long division setup showing an incomplete calculation. 18 is in the divisor, 5593 is in the dividend, and 3 hundreds and 1 tens is written in the quotient.

5400 is subtracted from 5593 to give 193.

An unknown value represented by a box is being subtracted from 193.

What are the phase shift and period for the function y = 3cos[4(θ + 60°)] − 2?

 Phase shift = right 60°, period = 90°

 Phase shift = right 60°, period = −90°

 Phase shift = left 60°, period = 90°

 Phase shift = left 60°, period = −90°

Answers

The plus sign inside the parenthesis indicates that the shift is to the left, And the formula for the period is 2pi/B and our B is 4, so 2pi/4 = pi/2 which is 90. So your answer is the third one down, left 60 period 90

Find the value of n in the equation 6.2n – 3.7n = 85 + 45. A. 16 B. 52 C. 13.13 D. 325

Answers

6.2n-3.7n=85+45
2.5n=130
N=130/2.5
N=52

The answer is B. Hope this helps!

cot^2x-csc^2x=-1 for all values of x true or falsse

Answers

Our basis for this equality is the pythagorean theorems of trigonometry. There are three equations for the pythagorean theorems. These are:

sin²x + cos²x =1
1 + tan²x = sec² x
1 + cot² x = csc² x

These are all derived from circle geometry on the cartesian plane. Now, the useful trigonometric property to be used is the third one. Rearranging this, we come up with

cot²x - csc²x = -1

This coincided with the given equation. Therefore, this is true. This is because it is already established from the pythagorean theorems.

The original equation cot^2x - csc^2x = -1 is true for all values of x.

How to determine if cot^2x-csc^2x=-1 for all values of x

The equation cot^2x - csc^2x = -1 is true for certain values of x, but not for all values of x.

To see why, let's break down the equation using trigonometric identities:

cot^2x - csc^2x = -1

Using the reciprocal identities, we can rewrite cot^2x and csc^2x in terms of sine and cosine:

(cos^2x / sin^2x) - (1 / sin^2x) = -1

Now, let's simplify:

(cos^2x - 1) / sin^2x = -1

Using the Pythagorean identity cos^2x + sin^2x = 1, we can substitute cos^2x with (1 - sin^2x):

(1 - sin^2x - 1) / sin^2x = -1

-sin^2x / sin^2x = -1

Now, we can cancel out the sin^2x terms:

-1 = -1

This equation holds true for all values of x. Therefore, the original equation cot^2x - csc^2x = -1 is true for all values of x.

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Bicycle city makes custom bicycles. They charge $160 plus $80 for each day that it takes to build the bicycle. If you have $480 to spend on your new bicycle, how many days can it take Bicycle City to build the bike?

Answers

It would take Bicycle City 4 days to build the bike 
160+80d≤480 subtract 160 from both sides

80d≤320  divide both sides by 80

d≤4

So the maximum number of days it can take them to build the bicycle so that $480 will cover the cost.

Adam has $450. he spends $210 on food. later he divides all the money into four parts out of which three parts were distributed and one part he keeps for himself. then he found $50 on the road. write the final expression and find the money he has left?

Answers

To answer this item, we let x be the amount of money he has left that was initially part of the total $450.

First, subtract $210 from it (spent by Adam on food)
         $450 - $210 = $240

Then, divide the remaining amount of money by 4
           $240 / 4 = $60

Since, it was only one part that he kept to himself, the amount of money left with him, x, is
                       x = $60

Then, the total amount of money he has including that which he only picked from the road is,
             T = $60 + $50 = $110

In the end, Adam had $110. 

Which sample fairly represents the population? CHECK ALL THAT APPLY.

--measuring the heights of every fiftieth person on the school roster to determine the average heights of the boys in the school

--calling every third person on the soccer team’s roster to determine how many of the team members have completed their fundraising assignment

--observing every person walking down Main Street at 5 p.m. one evening to determine the percentage of people who wear glasses

--sending a confidential e-mail survey to every one-hundredth parent in the school district to determine the overall satisfaction of the residents of the town

--taking a poll in the lunch room (where all students currently have to eat lunch) to determine the number of students who want to be able to leave campus during lunch

Answers

taking a poll in the lunch room (where all students currently have to eat lunch) to determine the number of students who want to be able to leave campus during lunch

Answer:

The population is defined by: The set of all possible individuals who are likely to be selected for a study and who also share some observable characteristic. In this way, the correct answer is:

Taking a poll in the lunch room (where all students currently have to eat lunch) to determine the number of students who want to be able to leave campus during lunch

Step-by-step explanation:

Find two positive numbers such that their product is 192 and their sum is a minimum pre-calc

Answers

This problem is a combination of algebra and calculus. First, we formulate an equation for the product. Let x be the first positive number and y be the other positive number. So, the equation would be

xy = 192

Let's rearrange this to make the equation explicit: y = 192/x
Then, the other equation is for the sum. Let S be the sum of the two positive numbers.

S = x + y

Now, substitute the other equation into this one:

S = x + 192/x

Here's where we apply calculus. We can determine the minimum S by getting the first derivative of S with respect to y and equating to zero. Thus,

dS/dx = 1 - 192x⁻² = 0
1 = 192x⁻²
x² = 192
x = +/- √192

But since we are finding the positive number,  x = + √192
Then, we use this to the first equation:

y = 192/√192 = √192

Therefore, the two positive numbers are equal which is √192 or 13.86. 

The two numbers with a product equal to 192 such that their sum is minimized are:

A = √192 and B = √192

How to find the two numbers?

Let's define A and B as our two numbers, we know that their product must be equal to 192, then we have:

A*B = 192.

Now, the sum of these two numbers is:

A + B.

And we want to minimize this, to do it, we need to use the first equation to rewrite one variable in terms of the other. For example, if we isolate A, we get:

A = 192/B

Replacing this in the sum, we get:

192/B + B

To minimize this, we need to find the values of B that make 0 the differentiation of the above expression.

The differentiation is:

-192/B^2 + 1

Then we need to solve:

-192/B^2 + 1 = 0

192/B^2 = 1

192 = B^2

√192 = B

To get the value of A, we use:

A = 192/B = 192/√192  = √192

Then we can conclude that the two positive numbers such that their product is 192, and their sum is minimized, is:

A = √192 and B = √192.

If you want to learn more about minimization, you can read:

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PLEASE HELP ON THESE ILL GIVE 20 POINTS AND A BRAINLIEST IF YOUR CORRECT!!

Variation is a term that is used to describe __________.

A.
how repetitive a data set is
B.
how large or small a data set is
C.
how spread out or scattered a data set is
D.
how different a data set is from other data sets

Answers

C. how spread out or scattered a data set is
C. How spread out or scattered a data set is

Prove that if one solution for a quadratic equation of the form x 2 + bx + c = 0 is rational (where b and c are rational), then the other solution is also rational. (use the fact that if the solutions of the equation are r and s, then x 2 + bx + c = (x − r)(x − s).)

Answers

[tex]x^2+bx+c = (x-r)(x-s)\\ x^2+bx+c = x^2-(r+s)x+rs\\\\ b = -(r+s)\\ c = rs[/tex]

Say r is rational. Suppose for a second, that s is not. Then, r+s is irrational. But this contradicts the fact that b is rational.

So, if one root is rational, then the other root is also rational

Final answer:

If one root of a quadratic equation with rational coefficients is rational, the other root must be rational too because the sum and product of the roots are related to the coefficients, which are also rational.

Explanation:

To prove that if one solution for a quadratic equation of the form x^2 + bx + c = 0 is rational, then the other solution is also rational, we can use the quadratic formula and properties of rational numbers. If the quadratic equation has rational coefficients and one rational solution, then the sum and product of the roots must also be rational. This is because a quadratic equation with roots r and s can be factored as (x - r)(x - s) = 0, which expands to x^2 - (r + s)x + rs = 0. Matching coefficients, we see that - (r + s) = b and rs = c. Since b and c are rational, r + s and rs must be rational as well.

Given that we have one rational root, let's say r, the sum of the roots r + s is rational, so s must also be rational because the difference of two rational numbers is rational. Hence, if one root of a quadratic equation with rational coefficients is rational, the other root must be rational as well.

The following two-way table shows the number of students of a school who have a video game and/or have a laptop:


Have Video Game Do Not Have Video Game Total
Have Laptop
15
50
65
Do Not Have Laptop
50
15
65
Total
65
65
130


Based on the table, how many students have both a laptop and a video game?
15
50
65
130

Answers

                                have game               dont have it               total
have laptop                   15                              50                         65
dont have                       50                             15                         65
total                                65                              65                       130

have both a laptop and a game : 15

Based on the table given, the number of students who have both a laptop and a video game is 15 students.

Which students have both laptops and video games?

In order to solve this question, look at the part of the table where the row on students who have laptops intersects with the column on those who have video games.

That part of the table has 15 in the cell. This means that 15 students have both video games and laptops.

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The tip of an 11-inch wiper blade wipes a path that is 31 inches long. What is the angle of rotation of the blade in radians to the nearest tenth?

Answers

length of arc = Cr    where C = angle of rotation and r = radius

31 = C*11

C =  31/11 =  2.8 radians to nearest tenth

2.8 radians is the answer.

A trapezoid has two right angles and bases that measure 16m and 8m. The right triangle formed by an altitude has a hypotenuse of 4 square root 5m. Sketch the trapezoid. What are its perimeter and area?

Answers

The trapezoid would that would be formed from the description would have a rectangle and a triangle. The shorter base of the trapezoid would be the length of the rectangle while the longer base would be the sum of the length of the rectangle and the base of the triangle. So, the dimensions would be:

length of the rectangle = 8 m
base of triangle = 16 - 8  = 8 m 
hypotenuse = 4√5 m

width of the rectangle = √(4√5 - 8) = 4 m 

Perimeter = 8 + 16 + 4√5 + 4 = 28 + 4√5 m 
Area = area of triangle + area of rectangle
Area = 8(4) / 2 + 8(4) = 48 m^2

Final answer:

The trapezoid forms a right-angled triangle with one additional rectangle. Its area is found to be 48m^2, and its approximate perimeter is 36.944m, by adding the lengths of all its sides together.

Explanation:

To find the perimeter and area of a trapezoid with two right angles and bases of 16m and 8m, we must first visualize the trapezoid. This trapezoid appears like a right-angled triangle with an additional rectangle attached to its hypotenuse.

We are given the hypotenuse of the altitude's right triangle is 4√5m, thanks to Pythagoras' theorem, we can find the two legs (which are the altitude h and the difference in bases). Let's call the altitude h and the difference in bases 'd'. Now, we know that the length of the longer leg of the right triangle is 16m - 8m = 8m.

Using the Pythagorean theorem where hypotenuse2 = altitude2 + difference in bases2, we have (4√5)2 = h2 + 82. Solving for 'h', we have h = √(80 - 64) = √16 = 4m. The area of a trapezoid is given by the formula A = (1/2) × (sum of the bases) × (height), which in this case is A = (1/2) × (16m + 8m) × 4m = 48m2.

For the perimeter, it can be calculated by adding the lengths of all sides. So, perimeter = 16m + 8m + 4m + 4√5m = 28m + 4√5m. To find the approximate value of 4√5m, we can calculate 4 × 2.236 (since √5 = 2.236), which gives us approximately 8.944m. Adding this to 28m gives us a perimeter of approximately 36.944m.

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