Write an equation for (-5,3) and (0,-7)

Answers

Answer 1

The equation of line is y + 2x +7 =0 for the points (-5,3) and (0,-7).

What is equation of line?

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.

The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

The given points are (-5, 3) and (0, -7).

To find the equation of line, use formula,

y - y₁ = m(x - x₁) where m = (y₂-y₁)/(x₂-x₁),

y - 3 = (-7 - 3)/(0-(-5)) (x - (-5))

y - 3 = -10 / 5 (x + 5)

y - 3 = -2 (x + 5)

y + 2x +7 =0

The required equation of line is y + 2x +7 =0 .

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Related Questions

what is the missing lengths for the problems?

Answers

Answer:

≈5.6

Step-by-step explanation:

Use ratios: 4/3 = 7.5/x

3 times 7.5 then divide by 4 to get 5.6

Let me know if this helped you out!

A vending machine has a total of 41 chocolate bars and bags of pretzels The number of chocolate bars is one less than twice the number of bags of pretzels. How many chocolate bars are in the vending machine?​

Answers

The number of chocolate bars that are in the vending machine are; 27 bars

How to solve algebra word problems?

We are told that the total number of chocolate bars and bags of pretzels in the vending machine is 41.

Let the number of bags of pretzels be x.

Now, we are told that number of chocolate bars is one less than twice the number of bags of pretzels. Thus;

Number of chocolate bars = 2x - 1

Thus, we can develop the algebraic expression as;

x + 2x - 1 = 41

3x - 1 = 41

3x = 42

x = 42/3

x = 14

Number of chocolate bars = 2(14) - 1 = 27 bars

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How does
modifying the input or the output of a linear e
function rule transform its graph?

Answers

Answer:

Step-by-step explanation:

Adding a constant k to the output of a linear function translates the graph vertically by k units. If k < 0 k<0 k<0, then the translation is downwards and if k > 0 k>0 k>0. Adding a constant k to the input of the function translates the graph horizontally by k k k units.

i need helpp please tell me what is the perimeter of the​ rectangle, in​ units, if b= 2 1/2??

Answers

1.The perimeter of a rectangle is found by adding up the length of all four sides. Since the two long sides are 12 cm, and the two shorter sides are 7 cm the perimeter can be found by:

The perimeter is 38 cm.

2.To find the perimeter of a rectangle, add the lengths of the rectangle's four sides. If you have only the width and the height, then you can easily find all four sides (two sides are each equal to the height and the other two sides are equal to the width). Multiply both the height and width by two and add the results.

hope this helps

Find the value of x.

Answers

Answer:

x = 10

Step-by-step explanation:

we see that the two triangle are equivalent and therefore the two angles degrees are the same

set them equal to each other

5x - 11 = 8x - 41

then solve

add 41 to both sides

5x + 30 = 8x

subtract 5x to both sides

30 = 3x

swap them

3x = 30

divide all by 3

x = 10

thats your answer

Define a variable and write an equation for each real-world problem. (Examples 1-4) 1. The Marriott Rivercenter in San Antonio, Texas has a main roof height of 441 feet. With the additional height of antennas, the structure is 546 feet tall. What is the height of the antennas?​

Answers

The height of antennas added to the main roof of the Marriott Rivercenter in San Antonio is 105 feet.

Explain the term variable of the equation?A symbol (often a letter) used in mathematics to represent an unknowable numerical value in an expression or algebraic statement. A variable can be defined as a quantity that is changeable and not fixed. Variables are crucial since they make up a significant portion of algebra.

For the stated question-

Height of the main roof of Texas = 441 feet.

Height along with additional height of antennas = 546 feet.

Then,

Height of antennas = Total height - height of main roof.

Height of antennas = 546 feet - 441 feet

Height of antennas = 105 feet.

Thus, the height of the antennas added to the main roof of the Marriott Rivercenter in San Antonio is 105 feet.

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An object was launched from the top of a hill with an upward vertical velocity of 170 feet per second. The height of the object can be
modeled by the function h(t) = -16t2 + 170t + 100, where t represents the number of seconds after the launch. Assume the object landed on the ground at sea level. Use technology to find the answer.
The object was __ feet in the air 9 seconds after it was launched.

Answers

The object was 334 feet in the air 9 seconds after it was launched.

The height of an object launched from the top of a hill can be modeled by the function h(t) = -16t² + 170t + 100, where t represents the number of seconds after the launch.

This function gives the height of the object in feet at any time t after the launch.

To find the height of the object 9 seconds after it was launched,

Substitute 9 for t in the function h(t) to calculate the height of the object at that time. This gives us the equation :

⇒ h(9)  = -16(9)² + 170(9) + 100

⇒ h(9)  = -16(81) + 1530 + 100

⇒ h(9)  = -1296 + 1530 + 100

⇒ h(9)  = 334 feet.

Therefore, 9 seconds after being launched, the object had reached a height of 334 feet.

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"The question is on a test I have to do today! pls help me!
10. Which situation can be modeled by the equation y=m x+b ?
A. The number of butterflies (y) in a population doubles every month (x).
B. The time (y) it takes a car to travel 100 miles depends on the speed (x) of the car.
C. The volume (y) of a cylindrical tank with a height of 2 feet depends on the radius (x) of the tank.
D. The total income (y) of a worker who earns 8 dollars per hour depends on the number of hours (x) worked."

Answers

The situation that can be modeled by the linear function y = mx + b is given as follows:

D. The total income (y) of a worker who earns 8 dollars per hour depends on the number of hours (x) worked.

Which situations can be modeled by linear functions?

Situations that can be modeled by linear functions are situations in which there is a constant change per unit interval.

The example in this problem is given by option D, as for each hour worked, the rate of change is given as follows:

8 dollars.

That is, for each hour worked, the total income of the worker increases by $8, hence the slope is of:

m = 8.

Then the intercept b represents the flat pay of the worker, which is how much the worker earns no matter the amount sold.

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Will give brainliest. urgent, 100 points

Answers

a) Yes , the variable y varies directly with x

b) The constant of variation is k = 1/3

c) The function rule is given by the equation y = x/3

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be A

Now , the values of x are in set P = { 57 , 63 , 66 }

The values of y are in the set Q = { 19 , 21 , 22 }

a)

From the data set of P and Q , we can see that when the value of y increase the value of x also increases

Therefore , the value of variable y varies directly with x

And , y ∝ x

b)

The value of variable y varies directly with x

And , y ∝ x

So , y = kx

Substituting the value for x and y from the data set , we get

The equation will be

y = kx

19 = 57k

Divide by 57 on both sides of the equation , we get

k = 19 / 57

k = 1/3

Therefore , the constant of variation k is 1/3

c)

The function rule is given by the equation

y = kx

Substituting the value for k in the equation , we get

y = ( 1/3 ) x

y = x/3

Hence ,

a) Yes , the variable y varies directly with x

b) The constant of variation is k = 1/3

c) The function rule is given by the equation y = x/3

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Answer:

its six hundred men

Step-by-step explanation:

its Six hundred men, six hundred men under my command

With only one goal in mind

Make it back alive to our homeland

Six hundred men, six hundred miles of open sea

But the problem's not the distance

It's what lies in between

And Ithaca's waiting Ithaca's waiting

My kingdom is waiting The kingdom is waiting

Penelope's waiting for me

So full speed ahead, full speed ahead

This article says short sleepers (fewer than 6 hours) are four times more likely to catch a cold than longer sleepers (over 7 hours). The article says "The researchers then sequestered 164 volunteers in a hotel, administered the cold virus via nasal drops and monitored them for a week." Without further info, what is potentially misleading?

Answers

The use of volunteer sampling means that the result of the survey is potentially misleading.

What is volunteer sampling?

Volunteer sampling is a sampling technique in which each participant in the sample opts to join the research, as is the case for this problem, as each participant opted to join in the project to compare their cold lengths.

The drawback of this type of sampling is that it should contain lots of participants that share similar characteristics, such as desiring to weight/diet, and this may influence their recovery to cold. The participants also may lie, which can cause misleading results to the study.

Options to remove misleading conclusions is to use a different type of sampling, such as stratified sampling, as groups of people that are either short or long sleepers are compared to reach a conclusion.

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What is the prime factorization of 16807 1680716807? Enter your answer as a product of prime numbers, like 2 × 3 2×32, times, 3, or as a single prime number, like 17 1717.

Answers

The Prime Factorization of 16807 are:7, 7, 7, 7, 7. This implies 7 raise to power 5.

What is prime factorization?

The term "Prime Factorization" refers to determining which prime numbers multiply together to produce the original number.

The process of writing all numbers as a product of primes is known as prime factorization. As an example, suppose we have the number 20. We can divide this into two categories. "Well, that's 2 time 2 times 5," we can say. Also, 5 is a prime number.

In this case 16807 will be:

16807 ÷ 7 = 2401

2401 ÷ 7 = 343

343 ÷ 7 = 49

49 ÷ 7 = 7

7 ÷ 7 = 1

Again, all the prime numbers you used to divide above are the Prime Factors of 16807. Thus, the Prime Factors of 16807 are:7, 7, 7, 7, 7.

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How do you solve #18?
Find the value of X.

Answers

Answer:

x = 3

Step-by-step explanation:

Notice the markings in the lower two angles of the triangle. We are dealing with Angle Bisectors.

Angle Bisectors of a triangle intersect at the Incenter, which is Equidistant from the sides of the triangle (given by the perpendicular symbols).

Therefore, 2x = x+3  =>  x = 3

I need help with this please help me

Answers

Answer:

67.38

Step-by-step explanation:

134.76/2 = 67.38

May I please have brainliest for this? Thank you!

Im having trouble with my homework and im not sure how to do this question could someone please explain?

line u has an equation of y+6=3/2(x–6). Line v is perpendicular to line u and passes through (2,–1). What is the equation of line v?

Answers

First write out the equation. Use distributive property for 3/2(x-6) by multiplying 3/2 by x and by -6. Then, subtract 6 from both sides and add -6 and the -18/2 from the previous distributive property step.
y= 3/2x -15
To find the perpendicular line, you need to change the slope (which is 3/2) to its negative reciprocal.
In order to do that, flip the order to 2/3 and multiply it by negative 1 to get -2/3.
y = -2/3x + b
You still can’t fully write out the equation because you don’t know b, which is the y intercept. To find it, plug in the x and y of (2,-1) to y = -2/3x + b.
-1 = -4/3 + b

Next move 4/3 to the left by adding it to both sides.
1/3 = b (aka y intercept)
Then you can write the final equation of line v.
y = -2/3x + 1/3

Not super sure if it’s correct, but I hope it helped!

Ann is 10 years older than Bob. Ten years ago, Ann was twice as the old as Bob. How old is Ann now? How old is Bob now?

Answers

It doesn't seem like there is enough information to solve the scenario.

The biggest part we are missing to properly solve this would be:

We are missing the current age of Ann.

Solve the system of linear equations by graphing. y = 3/4x-4 y= -1/2x+11​

Answers

Taking into account the definition of a system of linear equations, the solution of the linear equation is (12,5).

System of linear equations

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.

This case

In this case, the system of equations to be solved is

y = 3/4x-4

y= -1/2x+11​

There are several methods to solve a system of equations, it is decided to solve it using the graphical method. This method consists of representing the graphs associated with the equations of the system to deduce its solution. The solution of the system is the point of intersection between the graphs since the coordinates of said point satisfy both equations.

In this case, graphing both equations, it is obtained that the point of intersection, and therefore the solution, is (12,5).

The graph of the system of equations is attached.

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A car advertisement states that a certain car can accelerate from rest to 72 km/h in 12.5 seconds.
Initially the car is at rest, so the initial velocity is ______
m/s.

The car speeds up to 72 km/h which is equivalent to _______
m/s. Find the car’s average acceleration.

The acceleration of the car is _______
m/s2

Answers

The initial velocity is  0 m/sec

The car speed up to 72km/h which is equivalent to  36m/sec

The acceleration of the car is 2.88 m/sec².

What is acceleration?

Acceleration is the rate of change of the velocity of an object with respect to time. Vector quantities are accelerations. Acceleration = (Final Velocity - Initial Velocity)/ Time taken

Given that car can accelerate from rest to 72km/h in 12.5 seconds. Therefore, we can write:

Initial Velocity = 0 m/sec

Final Velocity = 72 km/hr = 72×(0.50) m/sec = 36m/sec

Time taken = 12.5 second

Now, the car’s acceleration in m/s can be written as,

Acceleration = (Final Velocity - Initial Velocity)/ Time taken

(36 m/sec - 0 m/sec)/12.5 seconds

= 2.88 m/sec²

Hence, the car’s acceleration in m/s is 2.88 m/sec².

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PLEASE TELL ME WHERE TO PUT IT AND IF IT SHOULD BE FILLED IN OR NOT

Answers

Answer:

Step-by-step explanation:

5x≥15

/5. /5

x≥3


On the number line we put a filled dot since it is both equal to and greater then at 3 and make it point to the right since it is greater it has to go up

Hopes this helps please mark brainliest

Answer:

Choose the bottom right ray and put it at 3.

Step-by-step explanation:

Brainliest, please!

When Hudson runs the 400 meter dash, his finishing times are normally distributed with a mean on 70 seconds and a standard deviation of 2 seconds. If Hudson were to run 22 practice trials of the 400 meter dash, how many of those trials would be between 71 and 73 seconds, to the nearest whole number?

Answers

The required number of trials is between 71 and 73 second is 5 trials.

Given that,
Hudson runs the 400-meter dash, his finishing times are normally distributed with a mean of 70 seconds and a standard deviation of 2 seconds. If Hudson were to run 22 practice trials of the 400-meter dash,

What is probability?

Probability can be defined as the ratio of favorable outcomes to the total number of events.

here,
let x be the time,
According to the question,
z = x - 70 / 2 then Z ≈ N(0, 1)
71 < x < 73
71 - 70 / 2 < z < 73 - 70 / 2
1 / 2 < Z < 3/2
P[1/2 < Z < 3/2] = 0.9332- 0.691
                      = 0.2417
Now,
Required trials = 22 [0.2417] = 5.3174

Thus, the required number of trials is between 71 and 73 second is 5 trials.

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Convert 8 ounces into grams. Round your
answer to the nearest whole number.
*Note: you must use these exact conversion factors to
get this question right.

Answers

Answer:

227

Step-by-step explanation:

I think

a line that passes thru (-3,4) and is parallel to y=2

Answers

Parallel lines have the same slope.

y=2 is a horizontal line and has a slope of 0, so the line parallel to it must also be horizontal and have a slope of 0.

Horizontal lines always have the form " y = k " for some number k and every point on that line has a y-value of k.

In this case, if you want the line to go through the point (-3,4), then the equation will be  " y = 4 ", since that's the y-value of the point on the line.

Answer:

y = 4

Step-by-step explanation:

A line with the equation y = a is a horizontal line that intercepts the y-axis at (0, a).

A line parallel to a horizontal line is another horizontal line.

If a horizontal line passes through point (p, q), then its equation is y = q, where q is the y-value of the point.

Therefore, the equation of a line that passes through (-3, 4) and is parallel to y = 2 is:

y = 4

In exercises 11-14, solve the system of nonlinear equations using the graph.

Answers

Answer:

No solution

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

We see two graphs on the opposite sides of the x-axis.

There is no intersection, so no common points. It means there is no solution.

32x = 3(5x−8) is equivalent to the equation 3(2x) = 3(5x − 8).

True

False

Answers

Answer: False

Step-by-step explanation:

This is because when u simplify 32x = 3(5x−8), it is 32x = 15x - 24

When u simplify 3(2x) = 3(5x − 8), you will get 6x = 15x - 24

The product of a number and 3 is twice the sum of that number and 5

Answers

The number that the product and 3 is twice the sum of that number and 5 is 10.

How to find the number?

The product of a number and 3 is twice the sum of that number and 5.

Therefore,

let

x = the number

Hence,

3 × x = 2(x + 5)

3x = 2(x + 5)

3x = 2x + 10

subtract 2x from both sides of the equation

3x = 2x + 10

3x  - 2x = 2x - 2x + 10

x = 10

Therefore, the number is 10.

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If f(x)=2x-3 and g(x)= [tex]\sqrt{x} +7[/tex]
then find f(g(x))

Answers

The value of the function, f(g(x)), is f(g(x)) = 2√x + 11

Evaluating a function

From the question, we are to determine the value of the given function f(g(x))

From the given information,

The given functions are

f(x) = 2x - 3

and

g(x) = √x + 7

To determine f(g(x)), we will substitute the value of g(x) for x in f(x)

That is,

f(x) = 2x - 3

f(g(x)) = 2(√x + 7) - 3

Apply the distributive property

f(g(x)) = 2√x + 14 - 3

Simplify

f(g(x)) = 2√x + 11

Hence, the value of f(g(x)) is 2√x + 11

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Two cars start moving from the same point. One travels south at 56 km/h and the other travels west at 42 km/h. At what rate (in km/h) is the distance between the cars increasing three hours later?

Answers

The distance between the cars increasing three hours later rate (in km/h) is 70km/h.

What do you mean by distance?

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

According to the given question,

We have given information:

Two cars start moving from the same point. One travels south at 56 km/h and the other travels west at 42 km/h.

Now, we will calculate the distance between the cars increasing three hours later,

S² + W² = D²

where S is the southbound car,

W is the westbound car,

D is the distance,

2 * S  dS/dt  + 2 W dW/dt = 2 D dD/dt

S  dS/dt  +  W dW/dt =  D dD/dt

In 3 hours,

S=3*56 = 168 and W = 3*42 = 126

and D = [tex]\sqrt{(168)^{2}+ (126)^{2}}[/tex] = 210

168 * 56 + 126 * 42 = 210 * dD/dt

(168 * 56 + 126 * 42) / 210 = dD/dt

dD/dt = (9408+5292)/210

dD/dt = 14700/210 = 70

Therefore, the distance between the cars increasing three hours later rate (in km/h) is 70km/h.

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Write an equation of the line that passes through (8,9) and is parallel to the line y = -x-2.
An equation of the parallel line is

Answers

Answer:

y - 9 = -1 (x-8)

Step-by-step explanation:

y - y₁ = m (x - x₁) would be your formula, since it's parallel you already have your slope, -x (which also equals 1 so technically -1). You have a point (8,9) and a slope -1, all you need to do is plug it in the formula.

Hope this helped!!

Please help my cousin needs help i appreciate your help!

Answers

The area of the softball field is 4732 yd²

What is area?

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given is a field with side measurements,

To find the area will we divide the field into a trapezium and a triangle,

Area of trapezium = (sum of parallel sides)x height/2

Area of triangle = 1/2xbasexheight

Area of trapezium = (104+52)x26/2 = 2028 yd²

Area of triangle = 2704 yd²

Area of the field = 2704 + 2028 = 4732 yd²

Hence, The area of the softball field is 4732 yd²

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The Extreme Rock Climbing Club planned a climbing expedition. The total cost was $4400, which was to be divided equally among the members going. Prior to the trip, 15 members decided not to go. If the cost per person increased by $66, how many people went on the expedition?

Answers

25 persons went on the expedition as the total cost was $4400.

What is a quadratic equation?

A quadratic equation in algebra is any equation that can be written in standard form as where x stands for an unknown value and a, b, and c are known quantities. The assumption is that a > 0; equations with a = 0 are thought to be degenerate because they become linear or even simpler.

x denotes number of people

y denotes cost per person

Total cost =$4400

y = 4400 / x

15 members made the decision not to travel before the trip. The price per person went up by $66.

y +66 =4400 / (x -15)

(y +66) (x -15) = 4400

(4400/x +66)(x -15) = 4400

4400 -66000/x +66x -990 =4400

- 66000/x +66x=990

(- 66000 + 66x²) =990x

66x² - 990x - 66000 =0

x²-15x-1000=0

x =40 and x =-25 are the results of applying the quadratic formula to this quadratic equation. There is only sense in the positive x.

x- 15 =40-15=25 persons participated in the mission.

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Anything helps! Thanks you :)

Answers

No.3
X=120

No.4
X=105

No.5
X=95

No.6
X=30

No.7
X=28

No.8
X=11

No.9
X=5.6

No.10
X=3

Hope this helps
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Use at least three different fonts. what were the most important changes ecnomic ideolgical social politcal between 1800 and 1860, that occured in. the south's defense of slavery, and elite planter lifestyle What are tasks that might be different for an elementary schoolteacher versus a high school teachers premenstrual dysphoric disorder (pmdd) is included in the dsm-5 but the name of the diagnosis has been changed from how it was listed in the dsm-iv-tr. product owner wants advice from the scrum master about estimating work in scrum. what guidance should a scrum master give calculate the moment of inertia of a thin, uniform rod of length l and mass m that rotates about a pivot at distance l/3 from one end. a virus mutates, and therefore it has which of the following traits of living things?(1 point) responses it uses energy. it uses energy. it is made of cells. it is made of cells. it evolves. it evolves. it grows and develops. consider three 1-l flasks at stp. flask a contains nh3 gas, flask b contains no2 gas, and flask c contains n2 gas. in which flask are the molecules most ideal in behavior? (1)College classrooms are often drab and dreary places. (2)Walls are painted a variation of institutional gray; furniture is easy to clean, but uncomfortable and unattractive. (3)Chairs are lined up in straight rows facing the teachers desk or lectern. (4)In one study, over 80 percent of university students rated their classrooms negatively, describing them as ugly, cramped, stuffy, and uncomfortable. (5)Research by environmental psychologists is beginning to show that unattractive classrooms are not only unappealing; they may also adversely affect academic performance.(6)A carefully controlled study of classroom environments was conducted by Wolling and Montage (1981). (7)They selected two identical classrooms located side by side in the psychology building. (8)The control classroom, which they called the sterile classroom, had white walls, a gray carpet, and rows of plastic desks. (9)The experimental classroom, which they called the friendly classroom, was redecorated with the help of a design consultant. (10)Several walls were painted bright colors, art posters were hung on the walls, large plants were added to the room, and colorful Chinese kites were hung from the ceiling. (11)In addition to traditional desks, a part of the room was outfitted with area rugs, color-coordinated cushions, and wooden cubes to provide nontraditional seating.(12)The researchers investigated how these two different environments affected performance in actual college classes. (13)Two professors teaching introductory psychology agreed to participate in the study, although they were not informed of the purpose of the research. (14)When school began, each class was randomly assigned to one of the two rooms. (15)Halfway through the term, the classes switched rooms. (16)Thus students in both classes spent half the term in the control room and half in the friendly room. (17)Students were not told they were being studied; the switch in rooms was explained as occurring because the original room was needed for videotaping.(18)The most striking finding from this study was that students performed significantly better on regular course exams when they were in the friendly rather than the sterile classroom.Question4. The students in the studya. helped design the friendly classroom.b. took two different courses.c. stayed in one room throughout the course.d. were not told they were involved in a study. Complete the car class by creating an attribute purchase_price (type int) and the method print_info() that outputs the car's information. Ex: if the input is: 2011 18000 2018 where 2011 is the car's model year, 18000 is the purchase price, and 2018 is the current year, then print_info() outputs:. Solve the equation cos 2 = -5 cos - 3 on the interval 0 < 2 Answers must be exact. a client who had a roux-en-y bypass procedure for morbid obesity ate a chocolate chip cookie after a meal. after ingestion of the cookie, the client reported cramping pains, dizziness, and palpitation. after having a bowel movement, the symptoms resolved. what should the nurse educate the client about regarding this event? bile reflux 2 + 4(2x-1) = 6.25x-26with solution please a femur 18 inches long is placed in traction with an elevation of 6.2 inches. what is the angle of elevation of the femur? A container with volume 1.61 L is initially evacuated. Then it is filled with 0.246 g of N2. Assume that the pressure of the gas is low enough for the gas to obey the ideal-gas law to a high degree of accuracy. of the root-mean-square speed of the gas molecules is 192 m/s, what is the pressure of the gas? Express your answer in pascals. a constant magnetic field of 7 7 t passes through a square with side 3 3 m at an angle of 55 55 from the surface. calculate the magnetic flux that passes through the square. round your answer to two decimal places