Brianna was cutting ribbons for an art project. She had a ribbon that was 5.760 cm. long, one that was 5.670 cm. long, and one that was 5.876 cm. long, Which one is the longest? which one is the shortest?​

Answers

Answer 1
5.876=longest
5.670=shortest

Related Questions

= 118

1=52

Ms. Boyd has 9 bills in her purse that consist

of five-dollar bills and twenty-dollar bills. The

value of the bills is worth $105. How many

five-dollars bills and twenty-dollar bills does

Ms. Boyd have?

Answers

Answer:

number of $20 bill = 4

Number of $5 bill = 5

Step-by-step explanation:

Given that:

Total number of $5 and $20 bills = 9

Let :

Number of $5 bills = x

Number of $20 bills = y

Combined worth of all bills = $105

x + y = 9 - - - (1)

5x + 20y = 105 - - - (2)

From (1)

x = 9 - y

Substitute x = 9 - y into (2)

5(9 - y) + 20y = 105

45 - 5y + 20y = 105

15y = 105 - 45

15y = 60

y = 60/15

y = 4

x = 9 - y

x = 9 - 4 = 5

Hence,

number of $20 bill = 4

Number of $5 bill = 5

what's the value of
\( \frac{2 {}^{2} }{ {5}^{2} } \)

Answers

Answer:

your answer will be 4/25

Step-by-step explanation:

.....

\( \sf Q) \frac{2 {}^{2} }{ {5}^{2} } = {?} \)

\( \sf \implies \frac{2 {}^{2} }{ {5}^{2} }\)

\( \sf \implies \frac{4}{25}\)is the required answer.

20 points please help me i need this answer

The box plots show the weights, in pounds, of the dogs in two different animal shelters.

Weights of Dogs in Shelter A
2 box plots. The number line goes from 6 to 30. For the weights of dogs in shelter A, the whiskers range from 8 to 30, and the box ranges from 17 to 28. A line divides the box at 21. For shelter B, the whiskers range from 10 to 28, and the box ranges from 16 to 20. A line divides the box at 18.
Weights of Dogs in Shelter B

Which is true of the data in the box plots? Select three choices.
The median weight for shelter A is greater than that for shelter B.
The median weight for shelter B is greater than that for shelter A.
The data for shelter A are a symmetric data set.
The data for shelter B are a symmetric data set.
The interquartile range of shelter A is greater than the interquartile range of shelter B.

Answers

The statements that are TRUE regarding the box plots are:

A, D, and E.

The box plots are given in the image attached below.

The Five-number Summary Displayed by a Box Plot

The values displayed by a box plot for a given data are:

MedianMinimumMaximumFirst QuartileThird Quartile

Interquartile range = Third Quartile - First Quartile.

Thus, shelter's A median is 21, shelter B's 18.

Interquartile range for shelter A = 28 - 8 = 20

Interquartile range for shelter B = 28 - 10 = 18

What is a Symmetric Data Set?If a data set is symmetric, a box plot that represents the data set will have the median in the middle of the box, while both whiskers will be about the same on both sides of the box.For example, the data set for shelter B is symmetric.

Therefore, the statements that are TRUE regarding the box plots are:

A, D, and E.

Learn more about box plots on:

https://brainly.com/question/14277132

20 points please help me i need this answer The box plots show the weights, in pounds, of the dogs in

can someone help plz

can someone help plz

Answers

Answer: 5/4x

Step-by-step explanation:

To solve this you'll need to use the slope formula which is

Y2 - Y1 over

X1 - X2

You already have two points so that's what we'll use.

(4, 7) (12, 17)

17 - 7

12 - 4  = 10/8

10/8 can be simplified further to 5/4

Why is the number that satisfies this equation not a real number?
x^2=--1

Answers

Answer:

I assume that says \(x^2=-1\), but that is the case because when we square a number, we can NEVER get a negative number. The smallest square we can get is 0. 1^2 is 1, and no real number squared gives us a negative number.

Step-by-step explanation:

Which student walked at the fastest rate down the hallway?

6th grader: Walked 120 feet in
15 seconds

7th grader:walked 100 feet in 10 seconds

8th grader: Walked 180 feet in 20 secs

Answers

Answer:

8th grader

Step-by-step explanation:

They walked the the fastest since they walked 50 feet more than the 6th grader in 5 more seconds ( im sorry if you dont understand! i tried my best explaining it! hope this helps :) )

if x=5, y=-3, and z=-7 z=-7, evaluate 3x^2-9y/yz

Answers

here you go, hope this helped
if x=5, y=-3, and z=-7 z=-7, evaluate 3x^2-9y/yz

Prime numbers have ________.

Composite numbers have ________.

The number 1 is ________.

Answers

Answer:

1:eaxctly two factors  2:more than two factors  3:neither prime nor composite

Step-by-step explanation:

I GOT IT RIGHT!

Answer:

Answer time!!

1. exactly 2 factors

2. more than 2 factors

3. niether prime nor compisite

I need help with this math hw its' in the image

I need help with this math hw its' in the image

Answers

Answer:

x = 7y = 37

Step-by-step explanation:

You want to know the values of x and y that make the angle measures consistent with the triangles being congruent in the given figure.

Congruence

The side markings show congruent triangles with corresponding vertices (and angles) ...

  L (3x+24)° ⇔ P (8x -11)°

  M 84° ⇔ Q 84°

  N (2x +y)° ⇔ R (no marking)

Corresponding angles L and P have the same measure, so ...

  3x +24 = 8x -11

  35 = 5x . . . . . . . . add 11-3x

  7 = x . . . . . . . . . divide by 5

The measures of these angles are ...

  (3(7) +24)° = 45°

Angle sum theorem

The sum of the angles in each triangle is 180°, so the measure of angle N is found to be ...

  L +M +N = 180°

  45° +84° +N = 180°

  N = 51°

This lets us find the value of y from ...

  (2x +y)° = 51°

  2(7) +y = 51

  y = 37 . . . . . . . . subtract 14

The value of x is 7. The value of y is 37.

I need help!! im stuck and dont understand and this is due at 12

I need help!! im stuck and dont understand and this is due at 12

Answers

Answer:

K is the midpoint of JL.

I hope this helps:)

A landscaper buried a water line around a rectangular lawn to serve as a supply line for a sprinkler system. The length of the lawn is 6 times its width. If 630 feet of pipe was used to do the job, what is the length and the width of the lawn

Answers

Answers:

Length = 270 feet

Width = 45 feet

========================================================

Work Shown:

x = width

6x = length, since it is 6 times the width

P = perimeter of rectangle

P = 2*(Length + Width)

P = 2*(6x + x)

P = 2*(7x)

P = 14x

Plug in the given perimeter P = 630 and solve for x.

P = 14x

14x = P

14x = 630

x = 630/14

x = 45

The width is 45 feet.

The length must be 6x = 6*45 = 270 feet.

The required length and width of the lawn is given as Length = 270 feet and Width = 45 feet.

Given that,
A landscaper buried a water line around a rectangular lawn to serve as a supply line for a sprinkler system. The length of the lawn is 6 times its width. If 630 feet of pipe was used to do the job, what is the length and the width of the lawn is to be determined.

What is the perimeter?

Perimeter is the measure of the figure on its circumference.

Here,
let the length be l and the width be w,
According to the question,
l = 6w
and
Perimeter of the lawn = 630
2 [l + w] = 630
2 [6w + w] = 630
14w = 630
w = 45
Now,
l = 45[6] = 270

Thus, the required length and width of the lawn is given as Length = 270 feet and Width = 45 feet.

learn more about perimeter here:

brainly.com/question/6465134

#SPJ2

It is estimated that the world's population is growing at a rate of 1.14% per year. On January 1st 2014 the population was 7.23 billion. (a) Find the expected population on January 1st 2020. (b) Find the year when the population is expected to reach 10 billion.​

Answers

Answer:

\(f(t) = 7.23( {1.0114}^{t} )\)

t = 0 represents January 1, 2014

(a)

\(f(6) = 7.23( {1.0114}^{6} ) = 7.739\)

The population of the world is expected to be about 7.739 billion people on January 1, 2020.

(b)

\(7.23( {1.0114}^{t} ) = 10\)

\(t = about \: 28.61 \: years\)

The population of the world is expected to be 10 billion people in about 28.61 years after January 1, 2014 (sometime in August 2042).

Solve the following inequality:
- 4x + 14 = 54

Answers

the answer to this question is -10.

-4x + 14 = 54

you subtract 14 from both sides and get:
-4x= 40

then divide -4 from both sides to get x alone
you get x= -10

answer: x= -10

For this pair of functions, explain how you can tell if the two functions are inverses?

For this pair of functions, explain how you can tell if the two functions are inverses?

Answers

The inputs and outputs match up with each other implying that they are inverses of each other.

How to determine if the functions are inverse?

To determine if the functions are inverses of each other, you need to check two conditions:

Composition of Functions: If two functions, let's call them f(x) and g(x), are inverses, then when you compose them in either order, you should get the identity function. Domain and Range: The domain of one function should match the range of the other function, and vice versa.

According to the previous information we can conclude that the inputs and outputs match up with each other implying that they are inverses of each other.

Learn more about inverse function in: https://brainly.com/question/29141206
#SPJ1

only one of the following graphs could be the graph of a polynomial function. which one? why are the others not graphs of polynomials? (select all that apply.) the graph could be that of a polynomial function. the graph could not be that of a polynomial function because it has a cusp. the graph could not be that of a polynomial function because it has a break. the graph could not be that of a polynomial function because it does not pass the horizontal line test. the graph could not be that of a polynomial function because it is not smooth. the graph could be that of a polynomial function. the graph could not be that of a polynomial function because it has a cusp. the graph could not be that of a polynomial function because it has a break. the graph could not be that of a polynomial function because it does not pass the horizontal line test. the graph could not be that of a polynomial function because it is not smooth. the graph could be that of a polynomial function. the graph could not be that of a polynomial function because it has a cusp. the graph could not be that of a polynomial function because it has a break. the graph could not be that of a polynomial function because it does not pass the horizontal line test. the graph could not be that of a polynomial function because it is not smooth. the graph could be that of a polynomial function. the graph could not be that of a polynomial function because it has a cusp. the graph could not be that of a polynomial function because it has a break. the graph could not be that of a polynomial function because it does not pass the horizontal line test. the graph could not be that of a polynomial function because it is not smooth.

Answers

The graphs that are not graphs of polynomials are the ones that have a cusp, a break, do not pass the horizontal line test, or are not smooth.

The graph could be that of a polynomial function if it meets the following criteria: it is smooth, continuous, and does not have any cusps or breaks.

Reasons why the other graphs are not polynomial functions:

1. The graph has a cusp: Polynomial functions have smooth curves without any sharp points (cusps).

2. The graph has a break: Polynomial functions are continuous, meaning there should not be any breaks or gaps.

3. The graph does not pass the horizontal line test: This is not a criterion for polynomial functions. The horizontal line test checks if a function is one-to-one, which is unrelated to polynomial functions.

4. The graph is not smooth: Polynomial functions have smooth, continuous curves.

Based on these criteria, only the graph that is smooth and continuous without any cusps or breaks could be the graph of a polynomial function.

Learn more about graph here,

https://brainly.com/question/19040584

#SPJ11

A factory makes 160 vans and cars.

the ratio of cars to the ratio of vans is 3:7

1/8 of the cars are electric cars

25% of the cars are diesel cars

the rest are petrol cars.

work out how many petrol cars there are.

Answers

The number of petrol cars, given the ratio of cars to vans and the proportion of types of cars, is 30 cars

How to find the number of cars ?

First, find the number of cars made :

= Number of cars and vans made x Ratio of cars / ( Sum of ratio of cars and vans )

= 160 x 3 / ( 3 + 7 )

= 160 x 3 / 10

= 48 cars

The number of petrol cars would be:

= Number of cars made - Number of electric cars - Diesel cars

= 48 - ( 1 / 8 x 48 ) - ( 25 % x 48 )

= 48 - 6 - 12

= 30 cars

Find out more on ratios at https://brainly.com/question/13892496

#SPJ1

Find the x-coordinate of the vertex of a parabola if the x-intercepts are (3,0) and
(-9,0)

Answers

Answer:

x = -3

Step-by-step explanation:

The vertex lies on the axis of symmetry, whose x-coordinate is halfway between -9 and 3:  x = -3

Decide which shipping box (or combination of boxes) she should use to ship exactly 270 necklaces.

Answers

Ndnsnkskaoaoamdmsksakaopssppskdkxm

28. Given M₁ = 35, M₂ = 45, and SM1-M2= 6.00, what is the value of t? -2.92 -1.67 O-3.81 2.75

Answers

The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers. To calculate the t-value, the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

To learn more about t-distribution value

https://brainly.com/question/30701897

#SPJ4

The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

Given, M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers.

To calculate the t-value,

the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

To learn more about t-distribution value here:

brainly.com/question/30701897

#SPJ4

consider an experiment in which a fair coin is flipped 4 times. define the random variable d to be the number of flips that come up heads minus the number of flips that come up tails. what is the range of d? a. {0, 1, 2, 3, 4} b. {-4, -2, 0, 2 ,4} c. {-4, -3, -2, -1, 0, 1, 2, 3, 4} d. {-4, -3, -2, -1, 0}

Answers

The range of the random variable d is {-4, -2, 0, 2, 4}, so the correct answer is option b.

To find the range of the random variable d, we need to consider all possible outcomes of the experiment and calculate the value of d for each outcome.

In this experiment, a fair coin is flipped 4 times. Each flip can result in either a "heads" or "tails" outcome.

Let's consider the possible outcomes and calculate the corresponding values of d:

1. Four heads (HHHH): d = 4 - 0 = 4

2. Three heads and one tail (HHHT, HHTH, HTHH, THHH): d = 3 - 1 = 2

3. Two heads and two tails (HHTT, HTHH, THHH, TTHH, HTTH, HHTH): d = 2 - 2 = 0

4. Three tails and one head (TTTH, TTHT, THTT, HTTT): d = 1 - 3 = -2

5. Four tails (TTTT): d = 0 - 4 = -4

The range of d is the set of all possible values that d can take on, which is {-4, -2, 0, 2, 4}.

Therefore, the correct answer is option b. {-4, -2, 0, 2, 4}.

Learn more about Range here:

https://brainly.com/question/30339388

#SPJ11

The __________forecasting model uses nonlinear optimization to forecast the adoption of innovative and new technologies in the marketplace.

Answers

The Bass diffusion model is a forecasting model that uses nonlinear optimization to predict the adoption of innovative and new technologies in the marketplace.

It was developed by Frank Bass in 1969 and has since become a widely used method for predicting the spread of new products in the market.

The Bass model assumes that the adoption of a new technology is driven by two factors: the innovative individuals who are the first to adopt, and the imitative individuals who adopt based on the influence of others. The model uses a combination of these two factors to predict the rate of adoption over time.

The Bass model takes into account the potential market size, the rate of innovation, and the rate of imitation. It is based on the assumption that the number of potential adopters is finite and that the rate of adoption will slow down as the market becomes saturated. The model also assumes that the rate of innovation will decrease over time as the technology becomes more established in the market.

for such more question on Bass diffusion model

https://brainly.com/question/4196367

#SPJ11

What is the perimeter of 6(1/2x + 5)

Answers

Answer: The perimeter of a rectangle is the sum of the lengths of all four sides. If one of the sides is 6(1/2x + 5), then we can find the perimeter by multiplying that by 2.

Perimeter = 2*6(1/2x + 5)

Perimeter = 12(1/2x + 5)

To simplify the expression, we can distribute the 12:

Perimeter = 121/2x + 125

Perimeter = 6x + 60

So the perimeter of 6(1/2x + 5) is 6x + 60.

Step-by-step explanation:

The table shows the linear relationship between the total cost of orders of t-shirts and the number of t-shirts ordered.
Based on the table, what is the rate of change of the total cost in dollars with respect to the number of t-shirts ordered

The table shows the linear relationship between the total cost of orders of t-shirts and the number of

Answers

Answer:

$9.95 per shirt.

Step-by-step explanation:

Rate of change = \( \frac{y_2 - y_1}{x_2 - x_1} \)

Using the values of two pairs, (13, 154.50) and (24, 263.95),

rate of change = \( \frac{109.45}{11} \)

rate of change = 9.95 \)

(Note: you'd get the same rate of change if you use the values of any two pairs on the table.)

The rate of change of the total cost of t-shirt with respect to the number of ordered t-shirt is $9.95 per shirt.

A fish swims at a speed of 12 miles per hour a boy swims at a speed of 4.44 feet per second. How much faster does the fish swim than the boy in yards per minute?
3ft = 1yd
5280= 1 mile

Answers

Answer:

I don't know it

Step-by-step explanation:

try with an textbook you have

Julio ​says, "If you subtract 12 from my number and multiply the difference by -5​, the result is -40​." What is ​Julio's ​number?

Answers

Answer:

Julio's number is 212

Step-by-step explanation:

(x - 12) ÷ -5 = -40

x - 12 = -40 times -5

x - 12 = 200

x = 200 + 12

x = 212

Check:

(x - 12) ÷ -5 = -40

((212 - 12)) ÷ -5 = -40

200 ÷ -5 = -40

-40 = -40

ASAP NEED HELP!!!!!!!!!

B=R/H Solve for H

ASAP NEED HELP!!!!!!!!! B=R/H Solve for H

Answers

Answer:

h = r/b

Step-by-step explanation:

Answer:

H = R         B

Step-by-step explanation:

H = R  

      B

Make a the subject of the formula v = u + at.
Hence, find the value of a when t = 4, u = 10 and v=50.

Answers

Step-by-step explanation:

v = u + at

v-u = at

a = (v -u)/t

When t = 4, u=10, v=50

a = (50-10)/4

a= 40/4

a = 10

Plug in what you know into v = 10 + at
You get a = 10
Make a the subject of the formula v = u + at.Hence, find the value of a when t = 4, u = 10 and v=50.

(a) why does the mean accurately summarize a normal distribution? (b) why does the mean inaccurately summarize a skewed distribution?

Answers

The mean accurately summarize a normal distribution because it is the center point. While the mean inaccurately summarize a skewed distribution because the mean is meant to balance the distribution with a tail, it is pulled to a tail and therefore the mean would not be in the center.

The mean is the mathematical average and it is probably the measure of central tendency that is most familiar. One can calculate the mean by adding all the values and dividing it with the total number of observations in a set of data. The normal distribution of mean is observed when the distribution of data near the mean are more frequent in occurrence than data far from the mean, it is also referred as Gaussian distribution. Skewed distribution is not symmetrical nor equal, it is deviated in one or the other side of the graph.

Know more about "mean" visit

brainly.com/question/30727743

#SPJ4

Members of a baseball team raised $1128.75 to go to a tournament. They rented a bus for $856.50 and budgeted $24.75 per player for meals. Write and solve an equation which can be used to determine xx, the number of players the team can bring to the tournament.

Answers

The baseball team can bring 11 players to the tournament based on their budget.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables. An equation is a mathematical statement that represents the equality of two things.

It is made up of two expressions, one on each side of the equal to symbol. An equation, in other words, is a statement that the values of two mathematical expressions are equal.

Let x represent the number of players the team can bring to the tournament. They rented a bus for $856.50 and budgeted $24.75 per player for meals, hence:

24.75x + 856.5 = 1128.75

x = 11

The baseball team can bring 11 players to the tournament based on their budget.

Find out more on equations at:

brainly.com/question/13763238

#SPJ1

If two sides of the triangle are congruent then the triangle is called as _____ triangle

Answers

Answer:

isosceles triangle

Step-by-step explanation:

If two sides of the triangle are congruent then the triangle is called as isosceles triangle.

If no sides of the triangle are congruent then the triangle is called as scalene triangle.

A triangle in which one of the interior angles is 90° is called a right triangle.

Answer:

\(\huge\boxed{\sf Isosceles\ triangle}\)

Step-by-step explanation:

Isosceles triangle:A triangle having two equal sides and angles is called an isosceles triangle.Characteristics:Two equal sidesTwo equal angles

\(\rule[225]{225}{2}\)

Other Questions
a client who has abruptio placentae exhibits cyanosis in the earlobes, capillary filling time >3 seconds, and reports "heartburn." which is the best nursing intervention? 1: What type of acid-base reactions are solely defined by how protons are given up or are taken? (0.5pt)2: What is a Hydroxide ion? (0.5pt)3: What two products do all acid-base neutralization reactions produce (0.5pt)?4: Calculate the pH of a 0.25M solution of H3O+ (0.5pt)5: Calculate the pH of a 6.3x10-8M solution of H3O+ (0.5pt)6: Look at your answer for 4 and 5 which one is a base? (0.25pt)7: Look at 4 and 5 which one is a strong acid (be careful with this one I will know that you didn't watch the recording if you get it wrong) (0.25pt) what kind of fold is on the left if the red is the oldest color?? question 2 options: plunging anticline synclin In his book The prince, ? Please help complete the table to show the coefficents of each term in the expression why do people feel good when it rains A programmer must write a 500 line program. Which is most likely the best approach? Select one: a. Write 1 line, run and debug, write 1 more line, run and debug, repeat b. Write 10-20 lines, run and debug, write 10-20 more lines, run and debug, repeatc. Write 250 lines, run and debug, write 250 lines, run and debug d. Write 500 lines, run and debug zYWhich of these can all be found on the figure? Darla is given the choice between $100 now and some amount of money three years from now. Darla responds that she would require $169 to wait. Darla is then given the choice between $100 in three years and some amount of money in five years. Darla responds that she would wait for $121. She also has a utility function for money of (x) = x, where x is the amount of money.1. Is Darla exponentially discounting?2. Assuming Darla discounts quasi-hyperbolically (the , model), calculate and . your paper airplane is launched from 25ft. it descends at a rate of 5ft per second. write an equation that represents the height y of your airplane after x seconds Pinocchio's nose (-2,-4) grows when he tells a lie. It can grow as much as (25,40) when he tells a whopper! If Pinocchio tells Geppetto a small fib, it only grows of 1/4 the way out. At what coordinate is Pinocchio's nose when he tells a small fib? HELP PLEASE!! MARKING BRAINLIEST.3/4 = 5/6 =1/3 = 20/14 = 1/2 =things to fill the blanks with:6 divided by 810 divided by 73 divided by 950 divided by 60 6 divided by 12 Which of the following accurately describes how switches and hubs work? (Select two) A. A switch uses the logical addresses in a packet to send it through the correct port to all VLANS defined on that port B. A hub repeats frames to all ports, regardless of the destination address C. Switches use the hardware address in the frame to send it only to the port where the device is located D. A hub uses the hardware address in the frame to forward it to the hosts on the VLAN that corresponds to that address an ideal fluid flows from left to right through this horizontal pipe, whose interior is hidden. a higher fluid level in the vertical pipes indicates a higher pressure inside the horizontal pipe. at which point does the pipe have the smallest inner diameter? the values of the sample mean, sample standard deviation, and (estimated) standard error of the mean are 2.481, 1.611, and 0.294, respectively. does this data suggest that the true average percentage of organic matter in such soil is something other than 3%? carry out a test of the appropriate hypotheses at significance level 0.10. [note: a normal probability plot of the data shows an acceptable pattern in light of the reasonably large sample size.] Compare and contrast two charactors from the animal farm What is the cross product of two parallel vectors A and B? For an experiment, you are required to prepare a series of three solutions by diluting a cobalt(II) chloride stock solution. After making each solution, you notice that each is a different shade of pink. Which is the most concentrated? a. the lightest pink solution you prepared b. the darkest pink solution you prepared c. the medium pink solution you prepared d. the stock solution A researcher wants to know the average number of hours college students spend outside of class working on schoolwork a week. They found from a SRS of 1000 students, the associated 95% confidence interval was (10.5 hours, 12.5 hours).a. What is the parameter of interest?b. What is the point estimate for the parameter? a number c is an eigenvalue of a if and only if the equation (a -ci)x = 0 has a nontrivial solution.