use the quadratic formula to find the solutions to the equation x^2-3x+1=0

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15.9

Answer: 15.9 centimeters.

Step-by-step explanation:

The formula for calculate the circumference of a circle is this one:

[tex]C=2\pi r[/tex]

Where "C" is the circumference of the circle and "r" is the radius.

We know that:

[tex[C=50cm\\\pi=3.14[/tex]

Then, substituting these values into the formula and solving for "r", we get:

[tex]50cm=2(3.14)r\\\\r=\frac{50cm}{6.28}\\\\r=7.96cm[/tex]

Since the diameter of a circle is twice the radius, we can multiply the radius by 2 to get the diameter of this circle. Then, rounded to the nearest tenth of a centimeters, this is:

[tex]D=2r\\\\D=2(7.96cm)\\\\D=15.9cm[/tex]

Answer:

Step-by-step explanation:

Setting the denominator = to 0, we get x = -4.  This is the location of the discontinuity.

Setting the numerator = to 0 and solving for x yields the zeros:  They are {-2, -4}.

Answer:

-a^2 +2ab + b^2

Step-by-step explanation:

b (a+b) - a (a-b)

Distribute

ab +b^2 -a^2 +ab

Combine like terms

b^2 -a^2 +2ab

-a^2 +2ab + b^2

Answer:

The first step would to be use quotient rule.

3

Step-by-step explanation:

ln(x-1)=ln(6)-ln(x)

The first step would to be use quotient rule there on the right hand side:

ln(x-1)=ln(6/x)

*Quotient rule says ln(a/b)=ln(a)-ln(b).

Now that since we have ln(c)=ln(d) then c must equal d, that is c=d.

ln(x-1)=ln(6/x)

implies

x-1=6/x

So you want to shove a 1 underneath the (x-1) and just cross multiply that might be easier.

[tex]\frac{x-1}{1}=\frac{6}{x}[/tex]

Cross multiplying:

[tex]x(x-1)=1(6)[/tex]

Multiplying/distribute[/tex]

[tex]x^2-x=6[/tex]

Subtract 6 on both sides:

[tex]x^2-x-6=0[/tex]

Now this is not too bad to factor since the coefficient of x^2 is 1.  All you have to do is find two numbers that multiply to be -6  and add up to be -1.

These numbers are -3 and 2 since -3(2)=-6 and -3+2=-1.

So the factored form of our equation is

[tex](x-3)(x+2)=0[/tex]

This implies that x-3=0 or x+2=0.

So solving x-3=0 gives us x=3 (just added 3 on both sides).

So solve x+2=0 gives us x=-2 (just subtracted 2 on both sides).

We need to see if these are actually the solutions by plugging them in.

Just a heads up: You can't do log(negative number).

Checking x=3:

ln(3-1)=ln(6)-ln(3)

ln(2)=ln(6/3)

ln(2)=ln(2)

This is true.

Checking x=-2:

ln(-2-1)=ln(6)-ln(-2)

ln(-3)=ln(6)-ln(-2)

We don't need to go further -2 makes the inside of our logarithms negative above.

The only solution is 3.

Step-by-step explanation:

[tex]\ln(x-1)=\ln6-\ln x\\\\D:\ x-1>0\ \wedge\ x>0\\\\x>1\ \wedge\ x>0\Rightarrow x>1[/tex]

[tex]\ln(x-1)=\ln6-\ln x\qquad\text{use}\ \log_ab-\log_ac=\log_a\dfrac{b}{c}\\\\\ln(x-1)=\ln\dfrac{6}{x}\iff x-1=\dfrac{6}{x}\\\\\dfrac{x-1}{1}=\dfrac{6}{x}\qquad\text{cross multiply}\\\\x(x-1)=(1)(6)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\(x)(x)+(x)(-1)=6\\\\x^2-x=6\qquad\text{subtract 6 from both sides}\\\\x^2-x-6=0\\\\x^2+2x-3x-6=0\\\\x(x+2)-3(x+2)=0\\\\(x+2)(x-3)=0\iff x+2=0\ \vee\ x-3=0\\\\x+2=0\qquad\text{subtract 2 from both sides}\\x=-2 \notin D\\\\x-3=0\qquad\text{add 3 to both sides}\\x=3\in D[/tex]

Solution:

Answer:

Step-by-step explanation:

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

Actually 1 and x both are polynomials. Therefore 1/x is already a quotient of polynomials.

Two polynomial expressions whose quotient, when simplified, is 1/x

x+1/x^2+x

Take the common of the denominator

x+1/x(x+1)

x+1 will be cancelled out by x+1

1/x

1/x is not a polynomial, so polynomials are not closed under division.

Polynomials are closed under addition, subtraction and multiplication. Addition and multiplication are associative and commutative.

There is an additive identity which is 0.

There is a multiplicative identity which is 1....

Polynomial expressions involve variables, coefficients, and exponents, combined by addition, subtraction, and multiplication. They are not closed under division, as shown by the quotient 1/x, which is not a polynomial. However, polynomials are closed under addition, subtraction, and multiplication.

A polynomial expression is a mathematical expression that can involve variables, coefficients, and exponents, that are combined using addition, subtraction, and multiplication operations. For your question, we can consider two polynomial expressions: x and 1. The quotient of these two expressions is 1/x.

However, 1/x is not a polynomial expression, because it involves division by a variable. This shows that polynomial expressions are not closed under division.

In contrast, polynomials are closed under the operations of addition, subtraction, and multiplication. For example, if we add, subtract or multiply any two polynomials we will always get another polynomial.

These operations do not generate any new type of expressions outside the realm of polynomials, unlike division, which can produce non-polynomial results, such as rational expressions.

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Answer:

$311.20

Step-by-step explanation:

Here we are required to use the Compound interest formula for finding the Amount at the end of 9th year

The formula is given as

[tex]A=P(1+\frac{r}{n})^{tn}[/tex]

Where ,

A is the final amount

P is the initial amount = $200

r is the rate of interest = 5% annual = 0.05

n is the frequency of compounding in a year ( Here it is compounding monthly) = 12

t is the time period = 9

Now we substitute all these values in the formula and solve for A

[tex]A=200(1+\frac{0.05}{12})^{9\times 12}[/tex]

[tex]A=200(1+0.00416)^{108}[/tex]

[tex]A=200(1.00416)^{108}[/tex]

[tex]A=200 \times 1.556[/tex]

[tex]A=311.20[/tex]

Hence the amount after 9 years will be $311.20

Answer:

30

Step-by-step explanation:

350/12=29.6

(29.6, six is neverending)

Round the decimal

Answer is 30

Mrs. Yamato must bake 30 pans of muffins to have enough for 350 people, as each pan makes 12 muffins and she cannot bake a fraction of a pan.

Mrs. Yamato needs to calculate how many pans of muffins to bake to serve 350 people, given each pan holds 12 muffins. To find the number of pans, we divide the total number of muffins needed by the number of muffins each pan can hold.

The calculation would be 350 muffins  7 12 muffins/pan = 29.17 pans.

Since she cannot bake a fraction of a pan, Mrs. Yamato will need to round up to the nearest whole number, which means she must bake 30 pans of muffins to ensure there are enough muffins to serve 350 people.

Answer:

r=5.15

d=10.31

Step-by-step explanation:

Given:

circumference of circle=32.4 mm

radius=?

diameter=?

formula of circumference of circle is given as:

C=2πr

Putting value we get

32.4=2πr

r=32.4/2π

r=5.15

d=2r

d=2(5.15)

d=10.31 !

For this case we have that by definition, the circumference of a circle is given by:

[tex]C = \pi * d[/tex]

Where:

d: It is the diameter of the circle

We have as data that:

[tex]C = 32.4 \ mm[/tex]

Taking[tex]\pi = 3.14[/tex]

We have:

[tex]32.4 = 3.14 * d\\d = \frac {32.4} {3.14}\\d = 10.32 \ mm[/tex]

The radius is given by:

[tex]\frac {10.32} {2} = 5.16 \ mm[/tex]

Answer:

[tex]Diameter: 10.32 \ mm\\Radius: 5.16 \ mm[/tex]

Answer:

b) −8x+6

Step-by-step explanation:

-3x+4 - (5x-2)

Distribute the minus sign

-3x+4 -5x+2

Combine like terms

-3x-5x +4+2

-8x+6

Answer:

the answer is b -8x+6

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

Given

6x² - 2x + 36 = 5x² + 10x ( subtract 5x² + 10x from both sides )

x² - 12x + 36 = 0 ← in standard form

This is a perfect square of the form

(x - a)² = x² - 2ax + a²

36 = 6² ⇒ a = 6 and 2ax = (2 × 6)x = 12x, hence

(x - 6)² = 0

x - 6 = 0 ⇒ x = 6

Answer:

1,779.33 ft³

Step-by-step explanation:

volume of cone = 1/3(pi)r²h (r=radius, h=height)

= 1/3 x 3.14 x (10)² x 17,

= 1/3 x 314 x 17

= 1/3 x 5338

= 1779.33 ft³

Answer:

just answering so this guy can get brainiest

Answer:

1176

Step-by-step explanation:

A room with dimensions 10 ft by 5 ft has an area of 50 ft².

A room with dimension 7 ft by 21 ft has an area of 147 ft².

Writing a proportion:

400 tiles / 50 ft² = x / 147 ft²

x = 1176 tiles

Answer:

1176

Step-by-step explanation:

A room with dimensions 10 ft by 5 ft require 400 tiles. There would be 1176 tiles needed for a room that measures 7 ft by 21 ft.

Answer:

Probability = 5/6

Step-by-step explanation:

Step 1: Write the formula of probability

Probability = number of possible outcomes/total number of outcomes

There is only one 28 so the chance of getting a 28 is 1/6.

Not getting a 28 would mean getting any one number from 23, 24, 25, 26 and 27.

Step 2: Apply the probability formula

Probability = number of possible outcomes/total number of outcomes

Probability of not getting 28 = 5/6

!!

Answer:

7/8

Step-by-step explanation:

Answer:

-12 <p <12

Step-by-step explanation:

|p|<12

We can write this without the absolute values

Take the equation with the positive value on the right hand side  and take the equation with a negative value on the right side remembering to flip the inequality.  Since this is less than we use and in between

p < 12 and p >-12

-12 <p <12

Step-by-step explanation:

[tex]For\ a>0\\\\|x|<a\Rightarrow x<a\ \wedge\ x>-a\\\\|x|>a\Rightarrow x>a\ \wedge\ x<-a\\\\===============================\\\\|p|<12\Rightarrow p<-12\ \wedge\ p>-12\Rightarrow-12<p<12[/tex]

Answer:

a)[tex]40\pi ft^3[/tex]

b)125.68ft³

Step-by-step explanation:

The formula for volume of a cylinder is

[tex]V=\pi *r^2*h[/tex]

Given in the question

Diameter=4ft and height =10ft

You know radius is half the diameter,

radius, r=4/2= 2ft

Finding the volume in terms of pi

[tex]V=\pi *r^2*h\\\\V=\pi *2*2*10\\\\\\V=40\pi ft^3[/tex]

Substitute pi with its value,

pi=3.142

Find volume

[tex]V=\pi *r^2*h\\\\\\V=3.142*2*2*10\\\\V=125.68ft^3[/tex]

Answer:

The surface area of the triangular prism is 468 square centimeters. Therefore the correct option is 4.

Step-by-step explanation:

It is given that the bases are right triangles with perpendicular legs measuring 9 centimeters and 12 centimeters. Using Pythagoras theorem, the third side of the base is

[tex]hypotenuse^2=leg_1^2+leg_2^2[/tex]

[tex]hypotenuse^2=(9)^2+(12)^2[/tex]

[tex]hypotenuse^2=225[/tex]

[tex]hypotenuse=\sqrt{225}[/tex]

[tex]hypotenuse=15[/tex]

The area of a triangle is

[tex]A=\frac{1}{2}\times base \times height[/tex]

Area of the base is

[tex]A_1=\frac{1}{2}\times 9\times 12=54[/tex]

The curved surface area of triangular prism is

[tex]A_2=\text{perimeter of base}\times height[/tex]

[tex]A_2=(9+12+15)\times 10[/tex]

[tex]A_2=9\times 10+12\times 10+15\times 10[/tex]

[tex]A_2=360[/tex]

The surface area of the triangular prism is

[tex]A=2A_1+A_2[/tex]

[tex]A=2(54)+360[/tex]

[tex]A=108+360[/tex]

[tex]A=468[/tex]

The surface area of the triangular prism is 468 square centimeters. Therefore the correct option is 4.

Answer:

468 square centimeters

Step-by-step explanation:

The value of z in the table is 40.

To find the value of z in the table, we can set up an equation using the concentrations and amounts of the solutions. Let's denote the amount of the 4% peroxide solution as x and the amount of the 10% peroxide solution as y. We can then set up the equation:

0.04x + 0.1y = 0.08(100)

Simplifying this equation, we have:

0.04x + 0.1y = 8

Now, let's refer to the table to find the values of x and y. Since the sum of the amounts is 100 L, we have:

x + y = 100

From the information in the table, we can see that the value of x is 60. This means that y must be 40, as the sum of the amounts is 100. Now we can substitute the values of x and y into the equation:

0.04x + 0.1y = 8

0.04(60) + 0.1(40) = 8

2.4 + 4 = 8

The equation holds true, so the value of z in the table is 40.

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Answer:

m=-2/3  (slope)

b=3        (y-intercept)

Step-by-step explanation:

Slope-intercept form is y=mx+b where the slope is m and the y-intercept is b.

You have 3y+2x=9.

We need to solve this for y to get it into y=mx+b form.

3y+2x=9

Subtract 2x on both sides:

3y     =-2x+9

Divide both sides by 3:

[tex]y=\frac{-2}{3}x+\frac{9}{3}[/tex]

[tex]y=\frac{-2}{3}x+3[/tex]

Now compare this to:

y=mx+b

m=-2/3  

b=3

Answer:

The correct answer is second option

78°

Step-by-step explanation:

Points to remember

The measure of arc BC = 2 * measure of angle BDC

To find the measure of arc BC

From the figure we can see the BD is the diameter of the given circle.

Therefore the ΔBDC is right angled triangle. m<C = 90°

m<CBD = 51°   (given)

m<CBD + m<BDC = 90

m<BDC = 90 - m<CBD

 = 90 - 51 = 39

Therefore measure of arc BC = 2 *m<BDC

  = 2 * 39

 = 78°

The correct answer is second option

78°

Answer:

Segment, line and Ray

Step-by-step explanation:

Lets discuss all the options one by one.

Point:

A point has no length, no width and no depth. It is 0 dimensional.

Line:

A line extends in both directions. It is straight and has no thickness. It is 1 dimensional

Segment:

It is a part of a line bounded by two distinct end points. As it is a part of a line than it is also 1 dimensional.

Triangle:

A triangle has three sides and three corners. It is two dimensional figure. Its interior or oval is also two dimensional.

Plane:

A plane is a two dimensional flat surface with no thickness.

Ray:

A ray is a part of a line with single end point. It goes off in a particular direction infinitely. As it is a part of a line hence it is also 1 dimensional:

Thus according to the above description Segment, Line and Ray are one dimensional

Answer:

C. Line.  F.  Ray   B. Segment ( but see below.)

Step-by-step explanation:

A line is one dimensional, so is a Ray.

As for a segment it depends on what you mean . A line segment is one dimensional, but a segment of a circle has 2 dimensions.

Answer:

B. is correct

Answer:  B. HA

Step-by-step explanation:

In the given picture we have two right triangles ΔABC and ΔSPR.

In ΔABC and ΔSPR, we have

AB≅SP     [Hypotenuse]

∠B≅∠P    [Angle]

Thus by HA theorem we have

ΔABC ≅ ΔSPR

Answer:

y=(x-3)^2 -2

Step-by-step explanation:

when the number to the power of two is positive the graph will aslo go up, (both ends go up as shown in the graph. the parabula of the graph is -2.

Answer:

Hi there!

The answer to this question is: The lines are perpendicular.

Step-by-step explanation:

If you take the slope of the first equation its 3. To find its perpendicular slope you take the negative reciprocal of it. You flip the number into a fraction and make it negative, this case you get -1/3 which is the slope of the second equation therefore they are perpendicular

Answer:

The lines are perpendicular.

Step-by-step explanation:

If two lines are graphed on the coordinate plane showing y equals 3 x plus 1 and y equals negative one third x minus 2, we can conclude that the lines are perpendicular.

Slope = 3

Slope of second equation: -1/3

Therefore, thee slopes are perpendicular.

Answer:

6 terms

Step-by-step explanation:

To find the number of terms we will use the formula:

Sn = a(1-r^n)/1-r

where a is the first term= 1

r is the common ratio = 2

Sn is the sum of series = 63

n is the number of terms = ?

Now substitute the values in the formula:

Sn = a(1-r^n)/1-r

63= 1(1-2^n)/1-2

63=1(1-2^n)/-1

63*-1 = 1(1-2^n)

-63 = 1-2^n

Now combine the constants:

-63-1= -2^n

-64= -2^n

64= 2^n

2^6 = 2^n

When the base are same powers are equal to each other.

6=n

Thus there are 6 terms....

Answer:

Please mark as Brainliest :)

Step-by-step explanation:

Answer:

See below in bold.

Step-by-step explanation:

The x intercepts occur when f(x) = 0.

1.  logx  - 1 = 0

logx = 1

By the definition of a log ( to the base 10):

x  = 10^1 = 10

So the x-intercept is  c (10,0).

2. - (logx - 2) = 0

logx - 2 = 0

log x = 2

so x = 100.

So it is d (100,0).

3 .   log(-x - 2)  = 0

-x - 2 = 10^0 = 1

-x = 3

x = -3

So it is  b (-3, 0).

4.  f(x) = -log -(x - 1)

log - (x - 1) = 0

log 1 = 0

so -(x - 1) = 1

- x + 1 = 1

x = 1-1 = 0

So  it is a. (0,0).

     Function                               x-intercept

[tex]f(x)=\log x-1[/tex]                              [tex](10,0)[/tex]

[tex]f(x)=-(\log x-2)[/tex]                        [tex](100,0)[/tex]

[tex]f(x)=\log (-x-2)[/tex]                         [tex](-3,0)[/tex]

[tex]f(x)=-\log -(x-1)[/tex]                     [tex](0,0)[/tex]

We know that the x-intercept of a function is the point where the function value is zero.

i.e. the x where f(x)=0

1)

[tex]f(x)=\log x-1[/tex]

when [tex]f(x)=0[/tex] we have:

[tex]\log x-1=0\\\\i.e.\\\\\log x=1\\\\i.e.\\\\\log x=\log 10[/tex]

Hence, taking the exponential function on both the sides of the equation we have:

[tex]x=10[/tex]

The x-intercept is: (10,0)

2)

[tex]f(x)=-(\log x-2)[/tex]

when, [tex]f(x)=0[/tex]

we have:

[tex]-(\log x-2)=0\\\\i.e.\\\\\log x-2=0\\\\i.e.\\\\\log x=2\\\\i.e.\\\\\log x=2\cdot 1\\\\i.e.\\\\\log x=2\cdot \log 10\\\\i.e.\\\\\log x=\log (10)^2[/tex]

Since,

[tex]m\log n=\log n^m[/tex]

Hence, we have:

[tex]\log x=\log 100[/tex]

Taking anti logarithm on both side we get:

[tex]x=100[/tex]

Hence, the x-intercept is:

(100,0)

3)

[tex]f(x)=\log (-x-2)[/tex]

when

[tex]f(x)=0[/tex]

we have:

[tex]\log (-x-2)=0\\\\i.e.\\\\\log (-x-2)=\log 1[/tex]

On taking anti logarithm on both the side of the equation we get:

[tex]-x-2=1\\\\i.e.\\\\x=-2-1\\\\i.e.\\\\x=-3[/tex]

Hence, the x-intercept is: (-3,0)

4)

[tex]f(x)=-\log -(x-1)[/tex]

when,

[tex]f(x)=0\ we\ have:[/tex]

[tex]-\log -(x-1)=0\\\\i.e.\\\\\log -(x-1)=0\\\\i.e.\\\\\log -(x-1)=\log 1\\\\i.e.\\\\-(x-1)=1\\\\i.e.\\\\x-1=-1\\\\i.e.\\\\x=-1+1\\\\i.e.\\\\x=0[/tex]

Hence, the x-intercept is:  (0,0)

Answer:

Step-by-step explanation:

We know:

The root with an odd degree is exist for any real number.

The root with an even degree is exist for any non-negative real number.

The domain:

[tex]\sqrt[n]{a}[/tex]

is all real number if n is odd number.

is alle non-negative real number if n is even number.

Answer:

Step-by-step explanation:

sin=y/r

cos=x/r

sin=21/29

cos=x/29

x^2+y^2=r^2

x^2+21^2=29^2

x^2+441=841

x=sqrt(841-441)

x=20

cos=20/29

  Only              |

   sin +             |     All Positive

---------------------|-------------------

           only      |    Only cos +

            tan +    |

Answer:

C

Step-by-step explanation:

Using the trigonometric identity

sin²x + cos²x = 1 ⇒ cosx = ± [tex]\sqrt{1-sin^2x}[/tex]

Given

sinx = [tex]\frac{21}{29}[/tex], then

cosx = [tex]\sqrt{1-(\frac{21}{29})^2 }[/tex] ( positive since 0 < x < 90 )

       = [tex]\sqrt{1-\frac{441}{841} }[/tex]

       = [tex]\sqrt{\frac{400}{841} }[/tex] = [tex]\frac{20}{29}[/tex]

Answer: [tex]201.06\ in^3[/tex]

Step-by-step explanation:

The volume of a cone can be calculated with this formula:

[tex]V=\frac{1}{3}\pi r^2h[/tex]

Where "r" is the radius and "h" is the height.

In this case you know that this cone  has a base with a radius of 4 inches and a height of 12 inches. Then:

[tex]r=4\ in\\h=12\ in[/tex]

So, in order to calculate its volume, you must substitute these values into the formula. Then:

[tex]V=\frac{1}{3}\pi (4\ in)^2(12\ in)\\\\V=201.06\ in^3[/tex]

Answer:

The volume of given cone =  200.96 inches³

Step-by-step explanation:

Points to remember

Volume of cone =(1/3) πr²h

Where 'r' is the radius and 'h' is the height of the cone

To find the volume of cone

Here r = 4 inches and h = 12 inches

Volume =  (1/3)πr²h

 =  (1/3) * 3.14 * 4² *12

 = 200.96 inches²

Therefore the volume of given cone =  200.96 inches³

Median: The middle number when all the numbers are listed in order.

First, we would put our numbers in order from least to greatest.

0 - 0 - 1 - 1 - 1 - 2 - 2 - 2 - 4 - 4

Next, we need to find the middle number. When we cross of one number from the left and one number from the right and keep doing this, we come across two numbers that are in the middle. The two numbers that are in the middle are 1 and 2. We find the median by adding 2 and 1 together to get a sum of 3 and then divide it by 2 to get an answer of 1.5

The median of this set of numbers is 1.5

Answer:

1.5

Step-by-step explanation:

the median if even if the two middle added then divided like.

0,0,1,1,(1,2,)2,2,4,4

1+2=3 ÷2 = 1.5

Step-by-step explanation:

Length of arc = (Central Angle/360) × 2

[tex]\pi[/tex]

r

= 21/360 × 2 × 3.14 × 3

Length = 1.099 feet

Please mark Brainliest if this helps!

Answer:

Your answer is [tex]\frac{7\pi}{20}[/tex].

If you prefer an answer rounded to nearest hundredths you would have 1.10 or just 1.1.

Step-by-step explanation:

The formula for finding the arc length s is given by:

[tex]s=r \cdot \frac{\theta \pi}{180^\circ}[/tex]

where [tex]\theta[/tex] is in degrees.

Plug in 3 for r and 21 for [tex]theta[/tex]:

[tex]s=3 \cdot \frac{21 \pi}{180}[/tex]

I'm going to reduce 21/180 by dividing top and bottom by 3:

[tex]s=3 \cdot \frac{7 \pi}{60}{/tex]

I'm going to multiply 3 and 7:

[tex]s=\frac{21 \pi}{60}[/tex]

I'm going to reduce 21/60 by dividing top and bottom by 3:

[tex]s=\frac{7\pi}{20}[/tex]

Your answer is [tex]\frac{7\pi}{20}[/tex].

If you prefer an answer rounded to nearest hundredths you would have 1.10 or just 1.1.