Find the volume of 12 cm

The expression with rational denominator is [tex]\frac{(\sqrt 5 - \sqrt{3} + 1)(- 5+2\sqrt 3)}{13}[/tex]

From the question, the fraction is given as

[tex]\frac{1}{\sqrt 5 + \sqrt{3} - 1}[/tex]

To rewrite the fraction with a rational denominator, we simply rationalize the fraction

When the fraction is rationalized, we have the following equation

[tex]\frac{1}{\sqrt 5 + \sqrt{3} - 1} = \frac{1}{\sqrt 5 + \sqrt{3} - 1} \times \frac{\sqrt 5 - \sqrt{3} + 1}{\sqrt 5 - \sqrt{3} + 1}[/tex]

Evaluate the products in the above equation

So, we have

[tex]\frac{1}{\sqrt 5 + \sqrt{3} - 1} = \frac{\sqrt 5 - \sqrt{3} + 1}{(\sqrt 5)^2 - (\sqrt{3} + 1)^2}[/tex]

This gives

[tex]\frac{1}{\sqrt 5 + \sqrt{3} - 1} = \frac{\sqrt 5 - \sqrt{3} + 1}{5 - 10 - 2\sqrt 3}[/tex]

So, we have

[tex]\frac{1}{\sqrt 5 + \sqrt{3} - 1} = \frac{\sqrt 5 - \sqrt{3} + 1}{- 5 - 2\sqrt 3}[/tex]

Rationalize again

[tex]\frac{1}{\sqrt 5 + \sqrt{3} - 1} = \frac{\sqrt 5 - \sqrt{3} + 1}{- 5 - 2\sqrt 3} \times \frac{- 5+2\sqrt 3}{- 5 +2\sqrt 3}[/tex]

This gives

[tex]\frac{1}{\sqrt 5 + \sqrt{3} - 1} = \frac{(\sqrt 5 - \sqrt{3} + 1)(- 5+2\sqrt 3)}{(-5)^2 - (2\sqrt 3)^2}[/tex]

So, we have

[tex]\frac{1}{\sqrt 5 + \sqrt{3} - 1} = \frac{(\sqrt 5 - \sqrt{3} + 1)(- 5+2\sqrt 3)}{25 -12}[/tex]

Evaluate

[tex]\frac{1}{\sqrt 5 + \sqrt{3} - 1} = \frac{(\sqrt 5 - \sqrt{3} + 1)(- 5+2\sqrt 3)}{13}[/tex]

Hence, the expression is [tex]\frac{(\sqrt 5 - \sqrt{3} + 1)(- 5+2\sqrt 3)}{13}[/tex]

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We need to find the product of :

So, the result as following:

So, the answer is the option 4. 8y3 + 6y2 − 29y + 15​

So we want to find the equation of a line parallel to

Passing through the point (-6,2).

First, remember that a line is parallel to other if their slopes are the same.

Then, the slope of our parallel line will be also -4/5.

Remember that a line has the following equation:

Where m is the slope and b is the y-intercept.

Now, we know that the parallel line has slope = -4/5 and passes through the point (x,y) = (-6,2), so we could replace in our previous equation as follows:

Therefore, the equation of the parallel line to y=(-4/5)x+12 passing through (-6,2) is:

It could be assembled a rectangular prism

and

Step 1

Given;

Putting these values in, we have;

Therefore,

Answer;

Explanation:

The elimination method consists in substracting one equation from the other, so you eliminate one of the variables and you have only one equation to solve for one variable.

In this case, y has the same coefficient in both equations, so this is the variable we will eliminate.

Substract the first equation from the second:

And solve for x:

Now, we replace x = 3 into one of the equations and solve for y:

Answer:

• x = 3

• y = 2

Since each vase should be 6 millimeters and can only deviate by no more than 1 millimeter, the inequality for the thickness would be:

And the maximum thickness would be 7 millimeters.

For an arithmetric progression, we need to find the common difference in the sequence

common difference = d = 2nd term - 1st term = 3rd term - 2nd term = 4th term - 3rd term

2nd term - 1st term = 27 -15 = 12

3rd term - 2nd term = 39-27 = 12

The result are the same.

Hence, d = 12

The first trm = 15

The formula for arithmetric sequence:

The nth term = 1st term + d(n - 1)

Replacing with the values we got above:

The nth term = 15 + 12(n - 1)

Since none of the options have the above, we would expand the parenthesis.

The nth term = 15 + 12×n - 12×1

The nth term = 15 + 12n - 12

= 15 -12 + 12n

The nth term = 3 + 12n = 12n + 3

From the options:

The nth term = 12n + 3 (option B)

The most appropriate choice for tangent to a curve will be given by-

[tex]3x + 2y = 73[/tex] is the required equation of tangent.

What is tangent to a curve?

Tangent to a curve at a point is the straight line that just touches the curve at that point.

Equation of tangent to a curve at a point [tex](x_1, y_1)[/tex] is given by

[tex]y - y_1 = \frac{dy}{dx}|_{(x_1,y_1)} (x - x_1)[/tex]

Here,

y = B(x), B(25) = -1, B'(25) = -1.5

Equation of tangent =

[tex](y - (-1)) = -1.5(x - 25)[/tex]

[tex]y + 1=-1.5x +37.5\\y + 1 = -\frac{3}{2}x + 37.5\\2y + 2 = -3x + 75\\3x+2y = 75-2\\3x+2y=73[/tex]

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Step 1: Problem

To determine the equation of a circle with centre (5, -3) and radius 7

Step 2: Substitute the centre value and radius to the equation

Step 3: Simplify the above equation

Hence the equation of the circle is

Since

then:

Then:

Answer:

We determine the greatest common factor as follows:

So, we factor:

So, the greatest common factor is 2n^3.

From the information provided we will have that the predictions will be:

*Line of best fit:

So, the extrapolation from the line of best fit is 4.9 sold.

*Curve of best fit:

So, the extrapolation for the curve of best fit is 32.2 sold.

Solution

Question A:

- The number of households in the sample that lost electricity is 5

Question B:

- The standard deviation is 2.121

Final answers

- The number of households in the sample that lost electricity is 5

- The standard deviation is 2.121

Answer

Option A is correct.

Explanation

Sample survey refers to the statistic

Equation of parabola in vertex form is 13x² + 26x + 17

Define Parabola

A symmetrical open plane curve created when a cone and a plane that runs perpendicular to its side collide. Ideally, a projectile traveling under the pull of gravity will travel along a curve similar to this one.

Given,

vertex (h,k) = (-1, 4)

points (x,y) = (-2, 17)

We know, The equation in vertex form is

y = a(x - h)² + k

put the (h,k) values,

y = a(x - (-1))² + 4

y = a(x + 1)² + 4                     --------- eq(i)

Next, find the value of 'a' by plug in the points of (x, y) in eq(i)

y = a(x + 1)² + 4

⇒17 = a(-2 + 1)² + 4

⇒17 = a(-1)² + 4

⇒17 = a + 4

⇒a = 13

Now, substitute 'a' value in eq(i) to find the equation of parabola

y = a(x + 1)² + 4

⇒ y = 13(x + 1)² + 4

⇒ y = 13(x² + 1 +  2x) + 4

⇒ y = 13x² + 13 + 26x + 4

⇒ y = 13x² + 26x + 17

Therefore, equation of parabola in vertex form is 13x² + 26x + 17

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Given:

Two ships left a port at the same time.

One travelled due north at an average speed of 25.5 km/h

And the other ship was due east at average speeds of 20.8 km/h

We will find their distance apart using the Pythagorean theorem.

The distance = Speed * Time

Let the time = t

So, the distance of the first ship = 25.5t

And the distance of the second ship = 20.8t

So, the distance between the ships (d) will be as follows:

So, the answer will be:

The distance in terms of time = 32.907t

We will find the distance when t = hours

So, distance = 164.54 km

We have that the line passes by the points (0, -2) & (1, 2). Using this we determine the slope (m) and then the function. After that we transformate the function. We proceed as follows:

Now, using one of the points [In our case we will use (0, -2), but we can use any point of the line] and the slope, we replace in:

Then:

Now, we solve for y:

And we apply the transformation to our line, that is f(x) -> f(x) + 6:

Therefore our final line (After the transformation) is y = 4x + 4, and graphed that is:

Answer:

Explanation:

Here, we want to write an equation that relates C to M

From the given question, we have to add the insurance to the standard charge to get the total cost

Mathematically:

Now, we substitute the values for both S and I

That would be:

Answer:

Step-by-step explanation:

The y-value of Function A when x = - 2 is less than the y-value of Function B when x = - 2.

Integers are rational numbers because it consists of zero, positive and negative numbers till infinity only.

This is referred to as a number which can be expressed as the quotient p/q of two integers such that q ≠ 0 and they are present till infinity due to the large numbers and examples include 2000, 25 etc.

Integers are rational numbers because they contain zero, positive and negative numbers. Decimals and fractions are not included in this context and an example is 12, 100 etc which is why the aforementioned above was chosen as the correct choice.

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Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

hope you get it thats the last pen that works in my house

Answer:  There are five possible outcomes with a sum of 8:

2 and 6,

3 and 5,

4 and 4,

5 and 3,

6 and 2.

There is only one outcome, 4 and 4, that is doubles. Therefore, the probability is 1/5.

Step-by-step explanation: Got it right on Edmentum

Answer:

A is an included angle between 3 and 5

Answer:

Explanation:

Given the equation:

To solve an equation using the square root property, begin by isolating the term that contains the square.

After isolating the variable that contains the square, take the square root of both sides and solve for the variable.

Therefore, the solutions to the equation are:

Answer:

3x−2y)(4x+3y)

It can be written as =3x(4x+3y)−2y(4x+3y)

By further calculation =12x

2

+9xy−8xy−6y

2

So we get =12x

2

+xy−6y

2

Since all the information in the study, such as the type, the age and the weight are related to the pet, individuals in each data-set are the pets.

The individual of a data-set is the object which is being analyzed in the study, the object that has it's characteristics analyzed.

In the context of this problem, these following information are analyzed, at the register when the doctor attends each pet and registers the information.

All these information belong to the pet that visits the veterinary, hence the individuals in each data-set are the pets.

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a large community college has professors and lectures. total number of facility members is 228. the school reported that they had five professors for every 14 lectures. how many of each type of faculty member does the community college employee? ​

Let

x -----> number of professors

y ----> number of lectures

we have that

x+y=228

x=228-y -------> equation A

x/y=5/14

x=(5/14)y ------> equation B

equate equation A and equation B

228-y=(5/14)y

solve for y

(5/14)y+y=228

(19/14)y=228

y=228*14/19

y=168

Find the value of x

x=228-168=60

therefore

An athlete run in 22 minutes is 19.232 laps

Given,

An athlete runs at a speed of 9 miles per hour.

and,  If one lap is 349 yards.

To find the how many laps does he run in 22 minutes?

Now, According to the question:

Firstly, Convert the mph into yard per minute,

Remember that:

I mile = 1,760 yard

1hour = 60 minute

Convert the speed in miles/hour to yards/minute

9 [tex]\frac{miles}{hour}[/tex] = 9[tex]\frac{1760}{60}[/tex] = 264 yard/ min

We know that

The speed is equal to divide the distance by the time

Let

s → the speed

d → the distance in yards

t → the time in minutes

Using the formula :

Speed = distance/ time

Solve the distance:
d = speed x time

Speed = 264 yard/ minute

Time = 22 minute

Therefore,

Distance = 264 x 22

Distance = 5,808 yards

Divide the distance by 302 yards to find out the number of laps

= 5,808/ 302 = 19.232 laps

Hence, An athlete run in 22 minutes is 19.232 laps

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