which expression is equivalent to (125^2/ 124^4/3)

Answer:

PQ = 10 units

Step-by-step explanation:

to find where the lines cross the x- axis let y = 0 and solve for x , that is

2x + 8 = 0 ( subtract 8 from both sides )

2x = - 8 ( divide both sides by 2 )

x = - 4 ← point P

and

2x - 12 = 0 ( add 12 to both sides )

2x = 12 ( divide both sides by 2 )

x = 6 ← point Q

the lines cross the x- axis at x = - 4 and x = 6

using the absolute value of the difference , then

PQ = | - 4 - 6 | = | - 10 | = 10 units

or

PQ = | 6 - (- 4) | = | 6 + 4 | = | 10 | = 10 units

Answer: [tex]\Huge\boxed{Distance=10~units}[/tex]

Step-by-step explanation:

Given expression

y = 2x + 8

Substitute 0 for the y value to find the x value

This is the definition of x-intercepts

(0) = 2x + 8

Subtract 8 on both sides

0 - 8 = 2x + 8 - 8

-8 = 2x

Divide 2 on both sides

-8 / 2 = 2x / 2

x = -4

[tex]\large\boxed{P~(-4,0)}[/tex]

Given expression

y = 2x - 12

Substitute 0 for the y value to find the x value

(0) = 2x - 12

Add 12 on both sides

0 + 12 = 2x - 12 + 12

12 = 2x

Divide 2 on both sides

12 / 2 = 2x / 2

x = 6

[tex]\large\boxed{Q~(6,0)}[/tex]

Given information

[tex](x_1,~y_1)=(-4,~0)[/tex]

[tex](x_2,~y_2)=(6,~0)[/tex]

Substitute values into the distance formula

[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]Distance=\sqrt{(6-(-4))^2+(0-0)^2}[/tex]

Simplify values in the parenthesis

[tex]Distance=\sqrt{(10)^2+(0)^2}[/tex]

Simplify values in the radical sign

[tex]Distance=\sqrt{100}[/tex]

[tex]\Huge\boxed{Distance=10~units}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

By evaluating the function, we conclude that f(10) = -7

Here we know that:

g(x) = 2x - 8

And f(x) = 5 - g(x).

Then we can write:

f(x) = 5 - (2x - 8) = 5 - 2x + 8 = -2x + 13

Now we want ot evaluate it in x = 10, this means replace the variable by the number 10.

f(10) = -2*10 + 13 = -20 + 13 = -7

Then, we conclude that f(10) = 7

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Answer:

Step-by-step explanation:

let we suppose the ratios as x , 2x and 3x

we know that,

x + 2x + 3x = -----

6x= -------

x= -----/6

therefore x = ......

2x = 2 * x (value of x)

3x = 3 * x (value of x)

and the question is solved

Answer:

let the ratio be 1x,2x,3x

Now,

1x+2x+3x=180°(sum of angles of triangle are 180)

or,6x=180°

or,x=180/6

or,x=30°

Then,

1x=1*30

=30°

2x=2*30

=60°

3x=3*30

=90°

The solution of the differential equation is [tex]y = (C_{1} + C_{2} x)e^{-2x} +\frac{1}{2} [x^{3} -\frac{3}{2} x-6][/tex] .

According to the given question.

We have a differential equation

[tex]y^{"} + 4y^{'} + 4y = 2x^{3}[/tex]

The above differerntial equation acn be written as

[tex](D^{2} +4D+ 4)= 2x^{3}[/tex]

Now, the auxillary equation for the above differential equation is given by

[tex]m^{2} + 4m + 4 = 0[/tex]

[tex]\implies m^{2} + 2m + 2m + 4 = 0[/tex]

⇒ m (m + 2) + 2(m + 2) = 0

⇒ m(m + 2)(m + 2) = 0

Therefore,

[tex]C.F = (C_{1} + C_{2}x)e^{-2x}[/tex]

Now,

[tex]PI = \frac{1}{D^{2} +4D+4} 2x^{3}[/tex]

[tex]\implies PI = \frac{1}{4(1+\frac{D^{2}+4D }{4} )} 2x^{3}[/tex]

[tex]\implies PI = \frac{1}{4} [1+(\frac{D^{2}+4D }{4} )]^{-1} 2x^{3}[/tex]

[tex]\implies PI = \frac{1}{4} [ 1 - (\frac{D^{2} +4D}{4} )+(\frac{D^{2} +4D}{4} )^{2} -(\frac{D^{2}+4D }{4}) ^{3} ...]2x^{3}[/tex]

[tex]\implies PI =\frac{1}{2} [ x^{3} -\frac{1}{4} (6x)-3x^{2} +3x^{2} -6][/tex]

[tex]\implies PI = \frac{1}{2} [x^{3} -\frac{3}{2} x-6][/tex]

Therefore, the solution of the differential equation will be

y = CI + PI

[tex]y = (C_{1} + C_{2} x)e^{-2x} +\frac{1}{2} [x^{3} -\frac{3}{2} x-6][/tex]

Hence, the solution of the differential equation is [tex]y = (C_{1} + C_{2} x)e^{-2x} +\frac{1}{2} [x^{3} -\frac{3}{2} x-6][/tex] .

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The cost of one yard of black fabric is $4.

The cost of one yard of red fabric is $5.

2r + b = 14 equation 1

2r + 4b = 26 equation 2

Where:

r = cost of one yard of red fabric

b = cost of one yard of black fabric

Subtract equation 1 from equation 2

3b = 12

b = 12 / 3

b = 4

Substitute for b in equation 1

2r + 4 = 14

2r = 14 - 4

2r = 10

r = 10 / 2

r = $5

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The given condition on the basis of truth table is true.

According to the statement

we have given that the some condition p and q. and we have to find that  the given condition is true or false on the basis of the truth table.

So, The given conditions are:

If 3 + 2 = 5, Then 5 + 5 = 10

Now,

The Truth table is a tabular representation of all the combinations of values for inputs and their corresponding outputs. It is a mathematical table that shows all possible outcomes that would occur from all possible scenarios that are considered.

So, the given conditions are properly verified with the truth table. So, it is true.

So, The given condition on the basis of truth table is true.

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Answer:

x =  -1,  7,  3 + i,  3 - i.

Step-by-step explanation:

(x^2-6x+9)^2-15(x^2-6x+10)=1

(x^2 - 6x + 9)^2  - 15(x^2 - 6x + 9) - 15*1 = 1

(x^2 - 6x + 9)^2  - 15(x^2 - 6x + 9) - 16 = 0

Let Z = x^2 - 6x + 9, then we have:

Z^2 - 15Z - 16 = 0

(Z - 16)(Z + 1) = 0

Z = 16 or Z = -1

so  x^2 - 6x + 9 = -1 or x^2 - 6x + 9 = 16

x^2 - 6x + 9 = -1

---> x^2 - 6x + 10 = 0

Using the Quadratic Formula:

---> x = [6 +/- √((-6)^2 - 4* 1* 10) / 2

---> x = 6/2 +/- √-4/2

---> x = 3 + i , 3 - i.

x^2 - 6x + 9 = 16

---> x^2 - 6x - 7 = 0

---> (x - 7)(x + 1) = 0

---> x = 7, -1.

45 square feet is the area of the base of the pedestal.

what is rectangular prism?

we know that

The volume of the pedestal (rectangular prism) is given by the formula

   V =   B × h

where

B is the area of the rectangular base of pedestal

V = 405 ft³

h = 9 ft

put the given values in the formula and solve for B

405 = B × 9

B = 405/9

B = 45 ft²

Therefore, 45 square feet is the area of the base of the pedestal.

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Answer:

Answer:

  48 minutes

Step-by-step explanation:

The rate of filling from both pipes is the sum of the rates in units of tanks per hour. We want the time for 2/3 of a tank.

The sum of the filling rates is ...

  rate A + rate B = (1/3) tank/hour + (1/2) tank/hour = 5/6 tank/hour

The time to fill a tank or part thereof will be the number of tanks divided by the rate in tanks per hour:

  time = (2/3 tank)/(5/6 tank/hour) = ((4/6)/(5/6)) hour = 4/5 hour

There are 60 minutes in an hour, so the fill time is ...

  (4/5 hour)×(60 min/hour) = 48 min

It will take 48 minutes for both pipes to fill 2/3 of the tank.

See below for the values of the probabilities

The complete question is added as an attachment

Write down the probability he gets 'Miss a turn'.

From the spinner, we have

Sections = 6

Miss a turn = 1

So, the probability that he gets 'Miss a turn is

P = 1/6

Write down the probability that he gets 'Go back 1 square'.

Here, we have:

Number of rows = 4

'Go back 1 square' = 4

The probability that he gets 'Go back 1 square' is

P = 'Go back 1 square'/Number of rows

This gives

P = 4/4

Evaluate

P = 1

How many of these spins are expected to be 'Go forward 3 squares'?

Here, we have

Spins = 96

From the spinner, the probability of 'Go forward 3 squares' is

P =1/6

So, the expected number is

E(x) = np

This gives

E(x) = 96 * 1/6

Evaluate

E(x) = 16

Hence, 16 spins are expected to be 'Go forward 3 squares'

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The answer is tenths

Step-by-step explanation:

According to the place value chart of decimals,the first number after the decimal point starts from tenths and continues.so the answer is tenths

Hi :)

Remember Place value in decimal numbers

[tex]\large\boldsymbol{\hfill\stackrel{hundreds}{9}~\hfill\stackrel{tenths}0~\hfill\stackrel{ones}6.\hfill\stackrel{tenths}{7}}[/tex]

Then

The place-value of [tex]\boldsymbol{7}[/tex] is [tex]\boldsymbol{tenths}[/tex].

[tex]\tt{Learn~More;Work~Harder}[/tex]

:)

Answer:

Hey! I'm gonna go ahead and give ya the "meaning" of the fundamental theorem of algebra but not the answer to the A. B. and C.

Step-by-step explanation:

fundamental theorem of algebra, theorem of equations proved by Carl Friedrich Gauss in 1799. It states that every polynomial equation of degree n with complex number coefficients has n roots, or solutions, in the complex numbers. The roots can have a multiplicity greater than zero.

18 liters of 14% bleach contains 0.14×18 = 2.52 liters of bleach.

Adding [tex]x[/tex] liters of pure water to the solution increases the total volume to [tex]18+x[/tex] liters without changing the total amount of bleach.

To end up with a 10% bleach solution, we must add

[tex]\dfrac{2.52}{18+x} = 0.10 \implies 2.52 = 1.8 + 0.10x \implies 0.10x = 0.72 \implies x=\boxed{7.2}[/tex]

liters of water.

Answer:

b

Step-by-step explanation:

1) [tex]\triangle ABC[/tex] with [tex]\overline{AC} \cong \overline{BC}[/tex], [tex]\overline{AB} \parallel \vec{CE}[/tex] (given)

2) [tex]\angle A \cong \angle B[/tex] (base angles theorem)

3) [tex]\angle A \cong \angle 1[/tex] (corresponding angles theorem)

4) [tex]\angle B \cong \angle 2[/tex] (alternate interior angles theorem)

5) [tex]\angle 1 \cong \angle 2[/tex] (transitive property of congruence)

6) [tex]\vec{CE}[/tex] bisects [tex]\angle BCD[/tex] (if a ray splits an angle into two congruent parts, it is a bisector)

Answer:

baiBsiasbisvdxhsbhssj

Answer:

-1/7

is the answer of your question

Using the binomial distribution, we have that you would expected to draw a face card 8 times.

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected value of the binomial distribution is:

E(X) = np

For this problem, the parameters are given as follows:

Then the expected value is found as follows:

E(X) = np = 35 x 0.2308 = 8

You would expected to draw a face card 8 times.

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Using it's concept, it is found that there is a 0.3 = 30% probability to select a pupil that uses the swimming pool but not the gym.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, we have that 50 - 7 = 43 pupils use at least one of the pool or the gym.

We use the following relation, considering the numbers of each:

Both = Pool + Gym - At least one

Hence:

Both = 31 + 28 - 43 = 16.

From this, we have that out of 50 pupils, there are 31 - 16 = 15 pupils who use the pool but not the gym, hence the probability is:

p = 15/50 = 0.3 = 30%.

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Answer:

  67 square units

Step-by-step explanation:

The area using the left-hand sum is the sum of products of the function value at the left side of the interval and the width of the interval.

The attachment shows a table of the x-value at the left side of each interval, and the corresponding function value there. The interval width is 1 unit in every case, so the desired area is simply the sum of the function values.

The approximate area is 67 square units.

Split up the interval [0, 6] into 6 equally spaced subintervals of length [tex]\Delta x = \frac{6-0}6 = 1[/tex]. So we have the partition

[0, 1] U [1, 2] U [2, 3] U [3, 4] U [4, 5] U [5, 6]

where the left endpoint of the [tex]i[/tex]-th interval is

[tex]\ell_i = i - 1[/tex]

with [tex]i\in\{1,2,3,4,5,6\}[/tex].

The area under [tex]f(x)=x^2+2[/tex] on the interval [0, 6] is then given by the definite integral and approximated by the Riemann sum,

[tex]\displaystyle \int_0^6 f(x) \, dx \approx \sum_{i=1}^6 f(\ell_i) \Delta x \\\\ ~~~~~~~~ = \sum_{i=1}^6 \bigg((i-1)^2 + 2\bigg) \\\\ ~~~~~~~~ = \sum_{i=1}^6 \bigg(i^2 - 2i + 3\bigg) \\\\ ~~~~~~~~ = \frac{6\cdot7\cdot13}6 - 6\cdot7 + 3\cdot6 = \boxed{67}[/tex]

where we use the well-known sums,

[tex]\displaystyle \sum_{i=1}^n 1 = \underbrace{1 + 1 + \cdots + 1}_{n\,\rm times} = n[/tex]

[tex]\displaystyle \sum_{i=1}^n i = 1 + 2 + \cdots + n = \frac{n(n+1)}2[/tex]

[tex]\displaystyle \sum_{i=1}^n i^2 = 1 + 4 + \cdots + n^2 = \frac{n(n+1)(2n+1)}6[/tex]

The correct choices based on the integers are: 1a, 2b, 3d, and 4c.

In the question, we are asked to match the scenarios to their corresponding boundaries.

Thus, the correct choices based on the integers are: 1a, 2b, 3d, and 4c.

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The $315 cost of the couch after tax, gives the cost before tax, C, as the following equation;

[tex]Cost \: before \: tax, \: \: \mathbf {C} = \frac{315}{1 + t} [/tex]

The cost of the couch with tax = $315

Let, t, represent the tax rate, and let C, represent the cost before tax, we have;

315 = C + C × t

Which gives;

Mathematically, we have the following equation;

[tex]Cost \: before \: tax, \: \: \mathbf {C} = \frac{315}{1 + t} [/tex]

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Answer:

a

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (4, - 1 ) and (x₂, y₂ ) = (- 2, 3 )

m = [tex]\frac{3-(-1)}{-2-4}[/tex] = [tex]\frac{3+1}{-6}[/tex] = [tex]\frac{4}{-6}[/tex] = - [tex]\frac{2}{3}[/tex] , then

y = - [tex]\frac{2}{3}[/tex] x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (- 2, 3 ) , then

3 = [tex]\frac{4}{3}[/tex] + c ⇒ c = 3 - [tex]\frac{4}{3}[/tex] = [tex]\frac{5}{3}[/tex]

y = - [tex]\frac{2}{3}[/tex] x + [tex]\frac{5}{3}[/tex] ← in slope- intercept form

multiply through by 3 to clear the fractions

3y = - 2x + 5 ( subtract - 2x + 5 from both sides )

2x + 3y - 5 = 0 ← in general form

Answer:

Step-by-step explanation:

The graph of the straight line [tex]y = -\frac{1}{3}x -2[/tex] is plotted. The graph is shown below.

A straight line is of the form y = mx + c, where m is the slope and c is the y-intercept.

To plot the given straight line [tex]y = -\frac{1}{3}x -2[/tex], follow the following steps:

Step 1: Substitute x = 0 in the given equation to obtain the point where the line intersects the y-axis.

y = 0 - 2

y = -2

The point at the y-axis is (0, -2).

Step 2: Substitute y = 0 in the given equation to obtain the point where the line intersects the x-axis.

[tex]0 = -\frac{1}{3}x -2\\x = -6[/tex]

The point at the x-axis is (-6, 0).

Step 3: Draw a straight line passing through both points.

Thus, the straight line [tex]y = -\frac{1}{3}x -2[/tex] is plotted.

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Answer:

Step-by-step explanation:

A. a = $1350 b. b= 89%

B. 1350(.89)^t = 675

    t = 5.9 years

Answer:

D It repeats

Step-by-step explanation:

square root of 15 is 3.87298334621

11/25= 0.44

3/20=.6

D = 0.33333333333

Answer: 144

Step-by-step explanation:

The length of DF is 16.

The horizontal distance from DF to E is 18.

So, the area is [tex]\frac{1}{2}(16)(18)=144[/tex]

The area of the triangle DEF is approximately equal to 144.014 square units.

Triangles can be generated on a Cartesian plane by marking three non-colinear points on there. Heron's formula offers the possibility of calculating the area of a triangle by only using the lengths of its three sides, whose formula is now introduced:

A = √ [s · (s - DE) · (s - EF) · (s - DF)]     (1)

s = (DE + EF + DF) / 2     (2)

Where s is the semiperimeter of the triangle.

First, we determine the lengths of the sides DE, EF and DF by Pythagorean theorem:

Side DE

DE = √ [[10 - (- 8)]² + (- 2 - 8)²]

DE ≈ 20.591

Side EF

EF = √ [(- 8 - 10)² + [- 8 - (- 2)]²]

EF ≈ 18.974

Side DF

DF = √[[- 8 - (- 8)]² + (- 8 - 8)²]

DF = 16

Then, the area of the triangle DEF is by Heron's formula:

s = (16 + 18.974 + 20.591) / 2

s = 27.783

A = √[27.783 · (27.783 - 20.591) · (27.783 - 18.974) · (27.783 - 16)]

A ≈ 144.014

The area of the triangle DEF is approximately equal to 144.014 square units.

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The volume of the cylinder that has same height and radius with the given cone is 5,346 cm³

Pyramids and prisms are examples of three-dimensional shapes, as are shapes with curved surfaces. The three-dimensional prism shape has two bases that are parallel and congruent. Any polygon is acceptable for the bases, which are two of the faces. Rectangles make up the remaining faces.

Given that the cylinder and the cone have the same radius and height, the volume of a cylinder equals 3 times the volume of a cone.

According to the given figure:

Given, a cone that has a volume of 1,782 cubic cm, has the same radius and height with a cylinder,

therefore,

Volume of the cylinder = 3 x (1,782)

Volume of the cylinder = 5,346 cubic centimeters

Hence,  the volume of the cylinder is 5,346 cubic centimeter.

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The number of contemporary titles and classic titles in Jarred DVDs collection is 2,921 and 579 respectively.

Simultaneous equation is an equation which involves the solving for two unknown values at the same time.

x + y = 3,500

x – y = 2,342

Add both be equation

x + x = 3,500 + 2,342

2x = 5,842

x = 5,842 ÷ 2

x = 2,921

Substitute x = 2,921 into

x – y = 2,342

2,921 - y = 2, 342

-y = 2,342 - 2,921

-y = -579

y = 579

Therefore, the number of contemporary titles and classic titles in Jarred DVDs collection is 2,921 and 579 respectively.

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Answer:

36 units

Step-by-step explanation:

to find the distance take the absolute value of the difference, that is

| - 42 - (- 78) | = | - 42 + 78 | = | 36 | = 36

or

| - 78 - (- 42) | = | - 78 + 42 | = | - 36 | = 36

Answer:

-36

Step-by-step explanation:

-78 - (-42)

= -78 + 42

= -36

Answer:

B {3/2, -5/3}

Step-by-step explanation:

6x² + x - 15 = 0

6x² + 10x - 9x - 15 = 0

2x(3x + 5) - 3(3x + 5) = 0

(3x + 5)(2x - 3) = 0

3x + 5 = 0  or  2x - 3 = 0

3x = -5  or  2x = 3

x = -5/3  or  x = 3/2

Answer: B {3/2, -5/3}

Answer:

[tex]\left\{\dfrac{3}{2},\ -\dfrac{5}{3}\right\}[/tex]

Step-by-step explanation:

Given quadratic equation: [tex]6x^2+x-15=0[/tex]

[tex]\implies a=\textsf{6},b=\textsf{1},c=\textsf{-15}[/tex]

..................................................................................................................................................

[tex]{\large \textsf{ Quadratic Formula: }}x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\ \Bigg{\|}\ \textsf{when }ax^2+bx+c=0[/tex]

..................................................................................................................................................

Step 1: Substitute the given values into the formula and simplify.

[tex]\implies x=\dfrac{-{(\textsf1})\pm \sqrt{\textsf{(1)}^2-4(\textsf{6}){(\textsf{-15})}}}{2{(\textsf{6})}}[/tex]

[tex]\implies x=\dfrac{-1\pm \sqrt{1-4(-90)}}{12}[/tex]

[tex]\implies x=\dfrac{-1\pm \sqrt{1+360}}{12}[/tex]

[tex]\implies x=\dfrac{-1\pm \sqrt{361}}{12}[/tex]

[tex]\implies x=\dfrac{-1\pm 19}{12}[/tex]

Step 2: Separate into two cases.

[tex]x_1=\dfrac{-1+19}{2}[/tex]

[tex]x_2=\dfrac{-1-19}{2}[/tex]

Step 3: Solve both cases.

[tex]\implies x_1=\dfrac{-1+19}{12}=\dfrac{18}{12}=\dfrac{6\times3}{6\times2}=\boxed{\dfrac{3}{2}}[/tex]

[tex]\implies x_2=\dfrac{-1-19}{12}=\dfrac{-20}{12}=\dfrac{-4\times5}{4\times3}=\boxed{-\dfrac{5}{3}}[/tex]

The solutions to this quadratic are: [tex]x_1=\dfrac{3}{2},\ x_2=-\dfrac{5}{3}[/tex]

..................................................................................................................................................

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Answer:

d. 9

Step-by-step explanation:

y= 0.22x^2 - 1.76x +4.75

x is the time in months so we should replace x by 10

y = 0.22 (10)^2 - 1.76(10) + 4.75

0.22 (100) - 17.6 + 4.75

22 - 17.6 + 4.75

9.15

So the number of laptops that will be sold during month 10 is 9. (you can't have 0.15 of a computer)

Answer:

d. 9

Step-by-step explanation:

The equation: y = 0.22x^2 - 1.76x + 4.75

x: Time in months

y: Number of laptops sold

Since we need to predict the number of laptops that will be sold during month 10, we can replace the x with 10.

The new equation will be: y = 22 - 17.6 + 4.75

Then y will be 9.15

Since there cannot be 0.15 of a laptop, we round the number 9.15 to a whole number, which is 9.

D) 9 is our final answer to this question.