What is the third term in the binomial expansion of (3x+y^3)^4

Answer:

7 minutes

Step-by-step explanation:

g(x) = x^4 - 3x^2 + 4x - 5

g(2) = 2^4 - 3(2^2) + 4(2) - 5

g(2) = 16 - 3(4) + 4(2) - 5

g(2) = 16 - 12 + 8 - 5

16 - 12 = 4

4 + 8 = 12

12 - 5 = 7

input: 2

output: 7

ordered pair: (2,7)

By modeled function, the time taken to reach the school is 7 minutes.

A function which depicts the variation of a given dependent parameter represented by the variable in the function is known as a modeled function. For modeled function, we input the value of the dependent parameter in place of the given variable and the solution of function gives us the result of dependency.

Given that the time it takes to get to school, measured in minutes, is modeled using the function g(x) = [tex]x^{4} - 3x^{2} + 4x - 5[/tex] , where x is the number of stops the bus makes.

Also said that the bus makes 2 stops after we board.

Thus the dependent parameter is stop which is represented by the variable x in the modeled function g(x) and the solution of g(x) gives us the time period. We will get the time period by putting x = 2 in the modeled function.

Putting x = 2 in g(x), we get -

⇒ g(x) = [tex]2^{4} - 3*2^{2} + 4*2 - 5[/tex]

⇒ g(x) = 16 - 12 + 8 - 5

∴  g(x) = 7

Thus the time period is 7 units.

Therefore, by modeled function, the time taken to reach the school is 7 minutes.

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Answer:

The approximate number of years is 10

The graph in the attached figure

Step-by-step explanation:

Let

f(x) the value of an antique plate

x is the number of yeras

we know that

The system of equations that represented the problem is equal to

[tex]f(x)=18(1.05)^{x}[/tex] ----> equation A

[tex]f(x)=30[/tex] ----> equation B

Solve the system by graphing

The solution of the system of equations is the intersection point both graphs

using a graphing tool

The solution is the point (10.47,30)

see the attached figure

therefore

The approximate number of years is 10

Answer:

1st graph

Step-by-step explanation:

just did it in edge

Answer:

The correct option is 2.

Step-by-step explanation:

Given information: Height of both prism are same.

Right rectangular prism has base dimensions of 3 inches by 12 inches.

Volume of a right rectangular prism:

[tex]V=Bh[/tex]

where, B is base area and h is height of the prism.

The volume of right rectangular prism is

[tex]V=(3\times 12)\times h=36h[/tex]

Therefore the volume of right rectangular prism is 36h cubic inches.

An oblique rectangular prism has base dimensions of 4 inches by 9 inches.

Volume of a oblique rectangular prism:

[tex]V=Bh[/tex]

where, B is base area and h is height of the prism.

The volume of right rectangular prism is

[tex]V=(4\times 9)\times h=36h[/tex]

Therefore the volume of oblique rectangular prism is 36h cubic inches.

The volumes are equal, because the heights are equal and the horizontal cross-sectional areas at every level are also equal.

Option 2 is correct .

The volumes are equal, because the heights are equal and the horizontal cross-sectional areas at every level are also equal.

The formula for the Volume of a right rectangular prism is:

V = B * h

where,

B is base area.

h is height of the prism.

Thus:

V = 3 * 12 * h

V = 36h

Similarly, the volume of the oblique rectangle is:

V = Bh

V = 4 * 9 * h

V = 36h

Thus, we can see that the volumes are equal, because the heights are equal and the horizontal cross-sectional areas at every level are also equal.

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Answer:

A composition of transformations is a combination of two or more transformations.A composition of reflections over parallel lines has the same effect as a translation (twice the distance between the parallel lines.

Step-by-step explanation:

Answer:

The correct option is  Y = 1,000(1.15)6 2,313 bacteria

Step-by-step explanation:

According to the given statement a growth medium is  inoculated with 1,000 bacteria.

Bacteria grow at a rate of = 15% = 0.15

Add 1 to make it easier = 0.15+1 = 1.15

We have to find the population of the culture 6 days after inoculation.

= 1000(1.15)^6

=1000(2.313)

= 2313 bacteria

The population of the culture 6 days after inoculation = 2313 bacteria

Therefore the correct option is  Y = 1,000(1.15)6 2,313 bacteria....

Answer:AAAAAAAAAAAAAAAAAAAA

Answer:

C)

Step-by-step explanation:

We are given with a pair of linear equations,

y=x+12

y=3x+2

Let us solve them for x and y

In order to solve them we subtract first equation from the second ,

0=2x-10

Adding 2x on both sides we get

2x=10

Dividing both sides by 2 we get

x=5

Now replacing this value of x  in first equation

y=5+12=17

Hence the solution of the two equations is (5,12)

And by solution of a linear pair of equations, we mean that both the lines passes through that point.

Answer: 0.0228

Step-by-step explanation:

Given : The  mean and the standard deviation of finish times (in minutes) for this event are respectively as :-

[tex]\mu=30\\\\\sigma=5.5[/tex]

If the distribution of finish times is approximately bell-shaped and symmetric, then it must be normally distributed.

Let X be the random variable that represents the finish times for this event.

z score : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]

[tex]z=\dfrac{19-30}{5.5}=-2[/tex]

Now, the probability of runners who finish in under 19 minutes by using standard normal distribution table :-

[tex]P(X<19)=P(z<-2)=0.0227501\approx0.0228[/tex]

Hence, the approximate proportion of runners who finish in under 19 minutes = 0.0228

Final answer:

To find the proportion of runners finishing a 2-mile fun-run in under 19 minutes, we calculate the z-score for a finish time of 19 minutes given the mean of 30 and standard deviation of 5.5. The calculated z-score of -2 corresponds to about 2.28% of runners according to the standard normal distribution.

Explanation:

To find the approximate proportion of runners who finish in under 19 minutes, we will use the properties of the normal distribution because the distribution of finish times is approximately bell-shaped and symmetric. Given that the mean finish time (μ) is 30 minutes and the standard deviation (σ) is 5.5 minutes, we can calculate the z-score for a finish time of 19 minutes.

The z-score is calculated by the formula:
z = (X - μ) / σ
Where X is the finish time of interest (19 minutes), μ is the mean (30 minutes), and σ is the standard deviation (5.5 minutes).

Plugging in our values we get:
z = (19 - 30) / 5.5 = -11 / 5.5 = -2

Using a standard normal distribution table or calculator, we can find the area to the left of z = -2, which corresponds to the proportion of runners finishing in under 19 minutes. This value is approximately 0.0228 or 2.28% of the runners.

For this case we have the following expression:

[tex]\frac {11x-2-3 (1-7x) ^ 2} {(x + 1)}[/tex]

We must indicate the first step that allows to start the simplification of the expression.

It is observed that the first step to follow is to solve the square of the binomial that is in the numerator of the expression.

[tex](1-7x) ^ 2[/tex]

Answer:

Option A

Answer:

0

Step-by-step explanation:

11x-2-3(1-7x)^2/(1x+1)

11x-2-3-21x/1+1

-32x-2-3-1

-32x-1+1

-32=0

/-32 /-32

x=0

Answer:

  see below

Step-by-step explanation:

Option 1: the two solution sets overlap at x=1.

Option 2: the two solution sets do not overlap; no solution.

Option 3: together, the two set describe all real numbers.

Answer:

The ratio of the volume of one sphere to the volume of the right cylinder is 1 : 3 ⇒ answer B

Step-by-step explanation:

* Lets explain how to solve the problem

- The spheres touch the two bases of the cylinder

∴ The height of the cylinder = the diameters of the two spheres

∵ The diameter of the sphere = twice its radius

∴ The diameter of the sphere = 2r, where r is the radius of the sphere

∵ The height of the cylinder = 2 × diameter of the sphere

∴ The height of the cylinder = 2 × 2r = 4r

- The spheres touch the curved surface of the cylinder, that means

  the diameter of the sphere equal the diameter of the cylinder

∴ The maximum possible radius of the sphere is the radius of the

   cylinder

∵ The radius of the sphere is r

∴ The radius of the cylinder is r

- The volume of the cylinder is πr²h and the volume of the sphere is

  4/3 πr³

∵ The height of the cylinder = 4r ⇒ proved up

∵ The radius of the cylinder = r

∵ The volume of the cylinder = πr²h

∴ The volume of the cylinder = πr²(4r) = 4πr³

∵ The radius of the sphere = r

∵ The volume of the sphere = 4/3 πr³

∴ The ratio of the volume of one sphere to the volume of the right

   cylinder = 4/3 πr³ : 4 πr³

- Divide both terms of the ratio by 4 πr³

∴ The ratio = 1/3 : 1

- Multiply both terms of the ratio by 3

∴ The ratio = 1 : 3

∴ The ratio of the volume of one sphere to the volume of the right

  cylinder is 1 : 3

Answer:

Initial velocity is zero.

Step-by-step explanation:

According to second equation of motion

    [tex]s=ut+\frac{1}{2} at^2[/tex]

where s = distance traveled  

           t = time taken

          a = acceleration

          u = initial velocity

here in the question we have

      s = 10 m

     t = 1 second

    a = 20[tex]ms^{-2}[/tex]

plugging the known value in order to find the unknown which is u (initial velocity)

[tex]10=u(1)+\frac{1}{2} (20)(1)^2[/tex

10 = u +10

gives u =0

therefore initial velocity is zero.

Answer:

  4 killer whales

Step-by-step explanation:

The dimensional analysis is ...

  (whales/ft³)(ft³/tank) = whales/tank

Putting the numbers with the units, we get ...

  (1.1142·10^-5 whales/ft³)(3.5900667·10^5 ft³/tank) = 4.00005... whales/tank

The maximum number of killer whales allowed in the main show tank is 4.

Answer:

cos(z) = .3846153846 and angle z = 67.38°

Step-by-step explanation:

Side UV is corresponding to side YX.  Side VW is corresponding to side YZ.  Side UW is corresponding to side XZ.

Starting with the first corresponding pair, we are told that side UV is 36, and that side YX is 3/5 of that.  So side YX is

[tex]\frac{3}{5}*36=21.6[/tex]

We are next told that side VW is 39, so side YZ is

[tex]\frac{3}{5}*39=23.4[/tex]

In order to find the cos of angle z, we need the adjacent side, which is side XZ.  Side XZ is 3/5 of side UW.  Right now we don't know the length of side UW, so we find it using Pythagorean's Theorem:

[tex]39^2-36^2=UW^2[/tex] and

[tex]UW^2=225[/tex] so

UW = 15

Now we can say that side XZ is

[tex]\frac{3}{5}*15=9[/tex]

The cos of an angle is the side adjacent to the angle (9) over the hypotenuse of the triangle (23.4) so our ratio is:

[tex]cos(z)=\frac{9}{23.4}[/tex]

which divides to

cos(z) = .3846153846

If you need the value of the angle, use the inverse cosine function on your calculator in degree mode to find that

angle z = 67.38°

3/6 and 7/14 can both be reduced to 1/2

Lets start with 3/6

3   divided by 3               1

--                                     ----

6  divided by 3                2

now, 7/14

7  divided by 7           1

--                                ----

14 divided by 7           2

Whatever you do to the numerator (top number) you have to do to the denominator (bottom number)

Answer:

x=20

Step-by-step explanation:

we know that

Triangles YNF and YUN are congruent by SSS

Because

YN=YF=YU=r -----> the radius of the circle

FN=NU ----> given problem

therefore

∠FYN=∠NYU

and

arc FN=∠FYN -----> by central angle

arc NU=∠NYU -----> by central angle

so

arc FN=arc NU

substitute the given values

5x-10=3x+30

solve for x

5x-3x=30+10

2x=40

x=20

If two lines l and m are parallel, then a reflection along line l followed by a reflection along line m is the same as a translation. Therefore, the correct answer is: A. translation.

If two lines l and m are parallel, a reflection along l followed by a reflection along m is equivalent to a translation. This can be understood geometrically: when a figure is reflected across parallel lines, it undergoes a displacement without changing its orientation.

The sequence of two reflections results in the figure being shifted along a path parallel to the original lines, akin to a translation. While reflections change orientation and translations shift position, the combination of two reflections across parallel lines maintains the figure's orientation while relocating it.

Answer: Second Option

[tex]b > 49[/tex]

Step-by-step explanation:

We have the following expression:

[tex]log_7(b) > 2[/tex]

We have the following expression:

To solve the expression, apply the inverse of [tex]log_7[/tex] on both sides of the equality.

Remember that:[tex]b ^ {log_b (x)} = x[/tex]

So we have to:

[tex]7^{log_7(b)} > 7^2[/tex]

[tex]b > 7^2[/tex]

[tex]b > 49[/tex]

The answer is the second option

Check the picture below.

where is the -16t² coming from?  that's Earth's gravity pull in feet.

[tex]\bf ~~~~~~\textit{initial velocity} \\\\ \begin{array}{llll} ~~~~~~\textit{in feet} \\\\ h(t) = -16t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\stackrel{30}{\textit{initial velocity of the object}}\\\\ h_o=\stackrel{6}{\textit{initial height of the object}}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases} \\\\\\ h(t)=-16t^2+30t+6 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+30}t\stackrel{\stackrel{c}{\downarrow }}{+6} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]

[tex]\bf \left(-\cfrac{30}{2(-16)}~~,~~6-\cfrac{30^2}{4(-16)} \right)\implies \left( \cfrac{30}{32}~,~6+\cfrac{225}{16} \right)\implies \left(\cfrac{15}{16}~,~\cfrac{321}{16} \right) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (\stackrel{\stackrel{\textit{how many}}{\textit{seconds it took}}}{0.9375}~~,~~\stackrel{\stackrel{\textit{how many feet}}{\textit{up it went}}}{20.0625})~\hfill[/tex]

Answer:

Step-by-step explanation:

I'm not sure if this question is coming from a physics class or an algebra 2 or higher math class, but either way, the behavior of a parabola is the same in both subjects.  If a parabola crosses the x axis, those 2 x values are called zeros of the polynomial.  Those zeros translate to the time an object was initially launched and when it landed.  The midpoint is dead center of where those x values are located.  For example, if an object is launched at 0 seconds and lands on the ground 3 seconds later, it reached its max height at 2 seconds.  So what we need to do is find the zeros of this particular quadratic, and the midpoint of those 2 values is where the object was at a max height of 20.06.

I used the physics equation representing parabolic motion for this, since it has an easier explanation. This equation is

[tex]x-x_{0}=v_{0}+\frac{1}{2}at^2[/tex]

where x is the max height, x₀ is the initial height, v₀ is the initial upwards velocity, t is time (our unknown as of right now), and a is the acceleration due to gravity (here, -32 ft/sec^2).  Filling in our values gives us this quadratic equation:

[tex]20.06-6=30(t)+\frac{1}{2}(-32)t^2[/tex]

Simplifying that a bit gives us

[tex]14.06=30t-16t^2[/tex]

Rearranging into standard form looks like this:

[tex]0=-16t^2+30t-14.06[/tex]

If we factor that using the quadratic formula we find that the 2 times where the ball was launched and then where it came back down are

t = .925 and .95 (the ball wasn't in the air for very long!)

The midpoint occurs between those 2 t values, so we find the midpoint of those 2 values by adding them and dividing the sum in half:

[tex]\frac{.925+.95}{2}=.9375[/tex]

Therefore, the coordinates of the vertex (the max height) of this parabola are (.94, 20.06).  That translates to: at a time of .94 seconds, the ball was at its max height of 20.06 feet

Answer:

Acute

Step-by-step explanation:

The Converse of the Pythagorean Theorem states that:

The side lengths 8, 14, and 15 are given. We can assume the hypotenuse (or c) is the longest side length, so it is 15.

It doesn't matter which order of the numbers are plugged in for a and b, so a and b will be 8 and 14.

Now we have to add [tex]a^2[/tex] and [tex]b^2[/tex] to see if the sum is greater than, less than, or equal to 15 (c).

Calculate the rest of the problem.

We have to find what [tex]15^2[/tex] is before we can make a decision using the Converse of the Pythagorean Theorem.

260 ([tex]a^2+b^2[/tex]) is greater than 225 ([tex]c^2[/tex]). This means that the triangle is acute because [tex]a^2+b^2>c^2[/tex].

Answer:

D. [tex] x = 3 \pm \sqrt{10} [/tex]

Step-by-step explanation:

[tex] x^2 - 6x - 1 = 0 [/tex]

[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]

a = 1; b = -6; c = -1

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

[tex] x = \dfrac{6 \pm \sqrt{36 + 4}}{2} [/tex]

[tex] x = \dfrac{6 \pm \sqrt{40}}{2} [/tex]

[tex] x = \dfrac{6 \pm \sqrt{4 \times 10}}{2} [/tex]

[tex] x = \dfrac{6 \pm 2 \sqrt{10}}{2} [/tex]

[tex] x = 3 \pm \sqrt{10} [/tex]

3x + y = -10. The standard form of the equation that is parallel to y = -3x + 3 and goes through point (-5, 5) is 3x + y = -10.

The equation is written in the slope-intercept form y = mx +b. So:

y = -3x + 3

The slope m = -3

Since the slopes of parallel lines are the same, we are looking for a slope line m = -3 and goes through point (-5, 5).

With the slope-intercept form:

y = mx + b

Introducing the slope m = -3:

y = -3x + b

Introducing the point (-5, 5):

5 = -3(-5) + b

5 = 15 + b

b= 5 - 15

b = -10

then

y = -3x -10

write the equation in standard form ax + by = c:

y = -3x -10

3x + y = -10

To find the standard form of the equation of a line that is parallel to y = -3x + 3 and passes through the point (-5, 5), let's follow these steps:
1. **Identify the slope**: Since parallel lines have the same slope, we can take the slope of the given line y = -3x + 3, which is -3.
2. **Use the point-slope form**: With the slope known and a point provided, we can use the point-slope form of the equation, which is:
  \[ y - y_1 = m(x - x_1) \]
  where \(m\) is the slope and \((x_1, y_1)\) is the point the line passes through.
3. **Apply the point and slope**: Insert the slope (-3) and the point (-5, 5):
  \[ y - 5 = -3(x - (-5)) \]
  \[ y - 5 = -3(x + 5) \]
4. **Distribute the slope**: Multiply -3 by both terms inside the parentheses:
  \[ y - 5 = -3x - 15 \]
5. **Isolate y:** Add 5 to both sides of the equation to isolate y:
  \[ y = -3x - 15 + 5 \]
  \[ y = -3x - 10 \]
6. **Convert to standard form**: The standard form of a linear equation is \(Ax + By = C\), where \(A\), \(B\), and \(C\) are integers, and \(A\) should be non-negative. Arrange the terms:
  \[ 3x + y = -10 \]
So the standard form of the equation that is parallel to y = -3x + 3 and passes through the point (-5, 5) is \(3x + y = -10\).

Answer:

The answer is 1.94

You need to have 1.94 hours a week to loose a monthly weight of 3 pounds

Answer:

10

Step-by-step explanation:

First you do 8 × 4, this gives the total of the four numbers.

[tex]8 \times 4 = 32[/tex]

Then, subtract the total of 3 of the numbers from the total of 4 of the numbers.

[tex]32 - 22 = 10[/tex]

Answer:

16 inches

Step-by-step explanation:

w = width of the rectangle

l = length of the rectangle

The perimeter of a rectangle is the length around it:

P = 2w + 2l

Given:

P = 92

l = w + 14

Substituting:

92 = 2w + 2(w + 14)

92 = 2w + 2w + 28

64 = 4w

w = 16

The width of the rectangle is 16 inches.

Final answer:

The width of the rectangle is 16 inches, deduced by using the perimeter formula for a rectangle and solving for width with given conditions.

Explanation:

To find the width of the rectangle given its perimeter and the fact that its length is 14 inches longer than its width, we start by listing what we know:

The perimeter of the rectangle is 92 inches.

The length (L) is 14 inches longer than the width (W).

Remember, the perimeter (P) of a rectangle is given by P = 2L + 2W. We can substitute L with W + 14, since the length is 14 inches more than the width. This gives us:

P = 2(W + 14) + 2W

Now we can plug in the value for P:

92 = 2(W + 14) + 2W

Then, distribute:

92 = 2W + 28 + 2W

Combine like terms:

92 = 4W + 28

Now, subtract 28 from both sides:

64 = 4W

Lastly, divide by 4 to solve for W:

16 = W

So, the width of the rectangle is 16 inches.

Answer:

x+(-2), y+(-3)

Step-by-step explanation:

Trapezoid ABCD has vertices A(-5,2), B(-3,4), C(-2,4) and D(-1,2).

The reflection across the y-axis has the rule

(x,y)→(-x,y),

so

The translation that maps points A', B', C' and D' to E, H, G, F is

and has a rule

(x,y)→(x-2,y-3)

Answer:y = 18(1.15)^x

Step-by-step explanation:

g o o g ; e

Answer:

The required equation is [tex]y = 18(1.15)^x[/tex].

Step-by-step explanation:

Consider the provided information.

The Initial value of poster = $ 18

After 1 year amount of increase = $ 20.70

With the rate of 15% = 0.15

Let future value is y and the number of years be x.

[tex]y = 18(1.15)^x[/tex]

Now verify this by substituting x=1 in above equation.

[tex]y = 18(1.15)^1=20.7[/tex]

Which is true.

Hence, the required equation is [tex]y = 18(1.15)^x[/tex].

Answer:

The probability is [tex]\frac{5}{9}[/tex]

Step-by-step explanation:

Let A be the event of one red, zero white, and three blue chips,

And, B is the event of at least three blue chips,

Since, A ∩ B = A (because If A happens that it is obvious that B will happen )

Thus, the  conditional probability of A if B is given,

[tex]P(\frac{A}{B})=\frac{P(A\cap B)}{P(B)}=\frac{P(A)}{P(B)}[/tex]

Now, red chips = 5,

White chips = 3,

Blue chips = 7,

Total chips = 5 + 3 + 7 = 15

Since, the probability of one red, zero white, and three blue chips, when four chips are chosen,

[tex]P(A)=\frac{^5C_1\times ^3C_0\times ^7C_3}{^{15}C_4}[/tex]

[tex]=\frac{5\times 35}{1365}[/tex]

[tex]=\frac{175}{1365}[/tex]

[tex]=\frac{5}{39}[/tex]

While, the probability that of at least three blue chips,

[tex]P(B)=\frac{^8C_1\times ^7C_3+^8C_0\times ^7C_4}{^{15}C_4}[/tex]

[tex]=\frac{8\times 35+35}{1365}[/tex]

[tex]=\frac{315}{1365}[/tex]

[tex]=\frac{3}{13}[/tex]

Hence, the required conditional probability would be,

[tex]P(\frac{A}{B})=\frac{5/39}{3/13}[/tex]

[tex]=\frac{65}{117}[/tex]

[tex]=\frac{5}{9}[/tex]

Answer:

$3.45

Step-by-step explanation:

$20.30 / 10  = $2.30 = 10%

$2.30 / 2  = $1.15 = 5%

$2.30 + $1.15 = $3.45 = 15%

Answer:

81

Step-by-step explanation:

(g∘f)(-4) is another way of writing g(f(-4)).

First, find f(-4):

f(-4) = -2(-4) − 5

f(-4) = 3

Now plug into g(x):

g(f(-4)) = g(3)

g(f(-4)) = 3^4

g(f(-4)) = 81

Answer:

45 minutes each

Step-by-step explanation:

Set Plan A clients as x and Plan B clients as y to make a system of equations, the constant is the number of hours worked.

3x+5y=6

9x+7y=12

Now solve using substitution or elimination.  I will use elimination.

-9x-15y=-18 I multiplied the whole first equation by -3 to eliminate x.

9x+7y=12, add the equations

-8y=-6 solve for y

y= 3/4 of an hour or 45 minutes

Next plug y into either equation

3x+5(3/4)=6 Solve for x.

3x+15/4=6

3x=2.25

x=0.75, also 45 minutes

To check plug in each variable value to each equation to see if they work if you need to.