Rationalize the denominator and simplify 6/√2-√3

Answer: The boat 1 moves with a speed of 40mi/h, and boat 2 moves with a speed of 20mi/h.

Step-by-step explanation:

First, we know the relation:

Distance = Speed*Time.

We can define the average rate of the boats as the average speed of the boats.

Now, we know that two boats travel in the same direction, let's define:

S₁ = speed of boat 1.

S₂ = speed of boat 2.

We know that one travels twice as fast as the other, then we can write:

S₁ = 2*S₂

We also know that after 3 hours of travel, they are 60mi apart, then if the slower one travelled a distance D in 3 hours, then:

S₂*3h = D

And the faster one will travel D + 60mi

S₁*3h = (D + 60mi)

Then we have the equations:

S₂*3h = D

S₁*3h = (D + 60mi)

We can replace S₁ by 2*S₂ to get:

S₂*3h = D

(2*S₂)*3h = (D + 60mi)

Now we have isolated D in the above equation, we can just replace it in the second equation to get:

(2*S₂)*3h = (S₂*3h + 60mi)

Now we can solve this for S₂

S₂*6h = S₂*3h + 60mi

S₂*6h - S₂*3h = 60mi

S₂*3h = 60mi

S₂ = 60mi/3h = 20mi/h

The speed of boat 2 is 20mi/h

And we knew that:

S₁ = 2*S₂

then:

S₁ = 2*(20mi/h) = 40mi/h

Answer:

11x+21

Step-by-step explanation:

blue square= x squared

green square=3x

pink square=7x

orange square=21

=

11x+21

Answer:

The solution is -1,-1

Step-by-step explanation:

The solution of a graph is where the two lines intersects and the this graph intersects at -1,-1

Answer:

The total number of employees is 377.

Step-by-step explanation:

1. You divide total number of women (232) by the ratio of women. (8)

232/8 =29

2. You take 29 and multiply it by the amount of men in the ratio. (5)

29*5=145

3. Finally you just add the total amount of men (145) and the total amount of women. (232)

232+145=377

I hope this helps!

I tried to explain to the best of my ability.

Answer: 377 employees

Step-by-step explanation:

The ratio of men to women can be represented as [tex]\frac{5}{8}[/tex] where the numerator represents how many men are in the company, and the denominator represents how many women are in the company. Given that there are 232 women in the company, we can replace denominator with 232, and then cross multiply.

[tex]\frac{5}{8}= \frac{x}{232}[/tex]    After cross multiplying, the expression left would be 8x = 1160. To get the final answer, we would only need to simplify this. It would give us a total of 145, which is how many men work in the company.

Lastly, add the the number or men and women working in the company, and that would be the total people that work in the company

Answer is: 50%

pretty easy/simple solution, you could have just looked it up.

Answer: continuous random variable.

Step-by-step explanation:

A discrete random variable is defined as a random variable which consists of countable number. Examples include numbers of shoes, number of sales etc.

A continuous random variable is a random variable whereby the data can take several values. It is a random variable that takes time into consideration.

Therefore, the amount of time six randomly selected volleyball players play during a game will be a continuous random variable since time so involved.

Answer:

39 pounds of type A coffee were used.

Step-by-step explanation:

Given: Cost of type A coffee is $4.15 per pound and cost of type B coffee is $5.25 per pound. Also, blend used four times as many pounds of type B coffee as type A.

To find: How many pounds of type A coffee were used.

Let [tex]x[/tex] be the number of pounds of type A coffee and [tex]y[/tex] be the number of pounds of type B coffee.

Then, according to question,

[tex]4.15x+5.25y=980.85[/tex] and [tex]y=4x[/tex]

Substituting [tex]y=4x[/tex] in [tex]4.15x+5.25y=980.85[/tex], we get

[tex]4.15x+5.25(4x)=980.85[/tex]

⇒[tex]4.15x+21x=980.85[/tex]

⇒[tex]25.15x=980.85[/tex]

⇒[tex]x=\frac{980.85}{25.15}[/tex]

⇒[tex]x=39[/tex]

Therefore, 39 pounds of type A coffee were used.

Answer:

Solving the expression: [tex]2\frac{3}{5}\div \frac{2}{3}[/tex] we get [tex]\mathbf{3\frac{9}{10}}[/tex]

Option A is correct.

Step-by-step explanation:

We need to solve the expression: [tex]2\frac{3}{5}\div \frac{2}{3}[/tex]

We need to divide both the terms.

Solving:

[tex]2\frac{3}{5}\div \frac{2}{3}[/tex]

First we will convert the mixed fraction into improper one

[tex]\frac{13}{5}\div \frac{2}{3}[/tex]

Now, we will convert division sign into multiplication, the term 2/3 is reciprocated

[tex]\frac{13}{5}\times \frac{3}{2}[/tex]

Now, multiply numerator with numerator and denominator with denominator

[tex]\frac{39}{10}[/tex]

Now, we will convert into mixed fraction

[tex]3\frac{9}{10}[/tex]

So, Solving the expression: [tex]2\frac{3}{5}\div \frac{2}{3}[/tex] we get [tex]\mathbf{3\frac{9}{10}}[/tex]

Option A is correct.

Answer:

14

Step-by-step explanation:

Answer:

Graph ii and iii

Step-by-step explanation:

In graph ii and iii, every input has one and only output. Another way to check is by doing the vertical line test.

Answer:

Each notebook costs $3.96 each.

3168 divided by 8 = 396

move the decimal two places left.

Step-by-step explanation:

           May I have brainiest I'm trying to level up!

                            </3 PureBeauty

Answer:

Each notebook costs $3.96

Step-by-step explanation:

We assume each notebook costs the same amount, the total cost is $31.68, and that is for 8 notebooks. So, we divide 31.68 by 8 and get our answer of $3.96 per notebook.

I hope this helps:)

Answer:

$6.75

Step-by-step explanation:

Interest = [tex]\frac{1.5}{100}[/tex] × 2 × $225

             = $6.75

Answer:

x= 7.41 (3 s.f.)

y= 9.53 (3 s.f.)

∠B= 51°

Step-by-step explanation:

Please see the attached picture for the full solution.

Answer:

x = 8.4

Step-by-step explanation:

In a right triangle, an angle, the length of its adjacent side and the length of the hypotenuse can be related by the cosine.

In this question:

Angle of 40º.

Adjacent side of x, hypotenuse of 11. So

[tex]\cos{40} = \frac{x}{11}[/tex]

Using a calculator, we have that [tex]\cos{40} = 0.766[/tex]. So

[tex]x = 11*0.766 = 8.4[/tex]

The answer is x = 8.4

Answer:

y = 4x -3

Step-by-step explanation:

The slope intercept form of an equation is

y = mx+b where m is the slope and b is the y ntercept

y = 4x -3

Answer:

RZ = 71

SW = 142

x = 22

Step-by-step explanation:

[tex]3x + 5 + 3x + 5 = 7x - 12 \\ \: \: \: \: \: \: \: \: \: \: \: 6x + 10 = 7x - 12 \\ \frac{ - 7x \: \: \: \: \: \: \: = - 7x}{ - 1x + 10 = - 12} \\ \frac{ \: \: \: \: \: \: \: \: \: - 10 = - 10}{ \frac{ - 1x}{ - 1} = \frac{ - 22}{ - 1} } \\ \\ x = 22[/tex]

Answer:

She has 2,660 combinations

Step-by-step explanation:

Here, we want to calculate the number of different combinations of 3 movies that can be rented

The condition is at least two horror movies

What this means is that she can select 2 or 3 horror movies

if two horror movies, then 1 foreign film

The combination is as follows;

20 C 2 * 8 C 1

= 190 * 8 = 1,520

If she is selecting 3 horror movies, then no foreign film will be selected

Number of ways this can be done is;

20 C 3 = 1,140

So the

number of different combinations would be;

1,140 + 1,520 = 2.660

Answer:

Step-by-step explanation:

If you divide 33 by 11 it’ll be 3 so we can cross B off, and A too because it’s not a double digit

So that leaves us with C & D.

If we divided 222 and 11 it would leave us with 10 which doesn’t match 11, so that leaves us with D

(Sorry if I didn’t’t explain right )

Answer:

d

Step-by-step explanation:

Answer:

y=291

Step-by-step explanation:

I did the math got 291.

Answer:

-9x + 5y =-1

x-intercept:   ( 1 9 , 0 )

y-intercept:  ( 0 , − 1 5 )

-3x + y = 4

x-intercept:  ( − 4 3 , 0 )

y-intercept:  ( 0 , 4 )

Answer:

There is not enough information to say they are congruent

Step-by-step explanation:

To prove two triangles are congruent, you need 3 things, which you can see through the list of options you were given. But since we only have two, there isn't enough information to prove the are congruent.

Step-by-step explanation:

The given numbers are : 32 , 48 , 140 , 120

First number is 32

Second number is 48

Third number is 140

Fourth number is 120

First number/second number :

[tex]\dfrac{N_1}{N_2}=\dfrac{32}{48}\\\\=\dfrac{2}{3}\ ....(1)[/tex]

Third number/Fouth number :

[tex]\dfrac{N_3}{N_4}=\dfrac{140}{120}\\\\=\dfrac{7}{6}\ ....(2)[/tex]

From equation (1) and (2) we can see that the ratio is not same. Hence, they are not in proportion.

Answer:

4(x - 3)(x^2 + 3x + 9)

Step-by-step explanation:

4x^3 - 108 = 4(x^3 - 27), or

                    4(x^3 - 3^3), or

                     4(x - 3)(x^2 + 3x + 9)    

We could choose to let 4 represent the height of the prism, x - 3 the width and x^2 + 3x + 9 the length.

Answer:

The solution to the system of equations given is:

Step-by-step explanation:

First, we must see our two equations given:

We can use the reduction method, with this, we must eliminate a variable, in this case, de x variable, this can do multiply the equation 2 by (-2) and add the two equations:

     3. -4x+12y = -12

Now, we operate the equations 1 and 3:

     4. 13y = 39

We solve the equation 4 and obtain the value for "y":

With the value of "y," we can replace this value in equation 1 or 2 to obtain the value of "x," in this case, we're gonna use the equation 1:

In this form, we know the solution to the system of two equations is: x = 12 and y = 3.

Answer:

Equation of line u in slope-intercept form is: [tex]\mathbf{y=\frac{1}{2}x+9 }[/tex]

Step-by-step explanation:

Equation of line t : y = -2x + 9.

We need to find equation of line u, which is perpendicular to line t and passes through point (-10,4)

The equation must be in slope-intercept form.

The general equation of slope-intercept form is: [tex]y=mx+b[/tex] where m is slope and b is y-intercept

Finding Slope:

If two lines are perpendicular, their slopes are opposite i.e [tex]m=-\frac{1}{m}[/tex]

Slope of line t: y=-2x+9 we get m =-2 (Comparing with general form y=mx+b, we get m =-2)

Slope of line u: [tex]\frac{1}{2}[/tex]

So, we get Slope of line u: m= [tex]\frac{1}{2}[/tex]

Finding y-intercept:

Using slope m= [tex]\frac{1}{2}[/tex] and point(-10,4) we can find y-intercept

[tex]y=mx+b\\4=\frac{1}{2}(-10)+b\\4=-5+b\\b=4+5\\b=9[/tex]

Equation of line u:

So, equation of line u, having slope m= [tex]\frac{1}{2}[/tex] and y-intercept b=9, we get:

[tex]y=mx+b\\y=\frac{1}{2}x+9[/tex]

So, Equation of line u in slope-intercept form is: [tex]\mathbf{y=\frac{1}{2}x+9 }[/tex]

Answer:

1,254 sqaure ft

Step-by-step explanation:

Use the radius of the circle, 202=10, to find the area of the circle: A=πr2=π(10)2=π⋅100≈3.14⋅100=314square meters. The area of the triangle is: A=12b⋅h=12⋅56⋅56=12⋅3,136=1,568 The area of the shaded region equals the area of the triangle minus the area of the circle. This is approximately 1,568-314=1,254 square meters.

The area of the shaded region is 1,254 square ft, consisting of a right triangle with a circle cut out of it.

The area of the circle is equal to the product of the square of the radius of the circle and pi.

A = πr²

where 'r' is the radius of the circle

Use the radius of the circle, 20/2 =10, to find the area of the circle:

A = πr²= π(10)² = π⋅100 ≈ 3.14⋅100 = 314 square meters.

The area of the triangle is:

A=12b⋅h = 12⋅56⋅56 = 12⋅3,136 = 1,568

The area of the shaded region equals the area of the triangle and subtracts the area of the circle.

This is approximately 1,568 - 314 = 1,254 square meters.

Hence, the correct answer would be an option (B).

Learn more about the area of the circle here:

brainly.com/question/19794723

#SPJ2

Answer:

3

+

3

−

6

Step-by-step explanation: