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3 years ago

5(n+1) = 2n + 20 can someone tell me the answer and explain

Mathematics

2 answers:

finlep [7]3 years ago

8 0

Answer:

n=15

Step-by-step explanation:

5(n+1)=2n+20

U start by expanding the first term which will give you 5n+5

Then after that u collect like terms giving u

5n-2n=20-5

Finally u evaluate it giving u

n=15

Tomtit [17]3 years ago

4 0

First we have to expand 5(n + 1)
Meaning we have to multiply everything in the bracket by 5. That would mean 5n + 5.

Now we have 5n + 5 = 2n +20

Subtract 2n from both sides to get rid of the 2n on the right

So you will have 3n + 5 = 20

Now subtract 5 from both sides to get rid of the 5 on the left.

So you will have 3n = 15

Divide both sides by 3 to get n = 5

Answer is n = 5

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A cone-shaped paper drinking cup is to be made to hold 27 cm of water. Find the height h and radius r of the cup that will use t

andreyandreev [35.5K]

Answer:

r = 2.632 cm
h = 3.722 cm

Step-by-step explanation:

The formula for the volume of a cone of radius r and height h is ...

V = (1/3)πr²h

Then r² can be found in terms of h and V as ...

r² = 3V/(πh)

The lateral surface area of the cone is ...

A = (1/2)(2πr)√(r² +h²) = πr√(r² +h²)

The square of the area is ...

T = A² = π²r²(r² +h²)

Substituting for r² using the expression above, we have ...

T = π²(3V/(πh))((3V/(πh) +h²) = 9V²/h² +3πVh

We want to find the minimum, which we can do by setting the derivative to zero.

dT/dh = -18V²/h³ +3πV

This will be zero when ...

3πV = 18V²/h³

h³ = 6V/π . . . . . multiply by h³/(3πV)

For V = 27 cm³, the value of h that minimizes paper area is ...

h = 3∛(6/π) ≈ 3.7221029

The corresponding value of r is ...

r = √(3V/(πh)) = 9/√(π·h) ≈ 2.6319242

The optimal radius is 2.632 cm; the optimal height is 3.722 cm.

_____

The second derivative test applied to T finds that T is always concave upward, so the value we found is a minimum.

Interestingly, the ratio of h to r is √2.

8 0

3 years ago

1. Solve for x: x/12 + 15 = 648

Vesnalui [34]

Answer:

1. x = 7596

2. x = -6.25

3. x = 8.5

hope this helps:)

6 0

3 years ago

Will give Brainlest Answer please answer i need help

Rashid [163]

Answer:

C. {-1, 5, 8}

Step-by-step explanation:

Use each of the domain values in the function to see what the corresponding range value is.

f(-1) = 5 -3(-1) = 8

f(0) = 5 -3(0) = 5

f(2) = 5 -3(2) = -1

The range is the set of numbers {-1, 5, 8}.

_____

<em>Additional comment</em>

The values in a set are generally listed lowest to highest. The coefficient of x in the equation for f(x) is negative, meaning the lowest range value will correspond to the highest domain value. If you start by finding f(2) = -1, you immediately eliminate all answer choices except B and C.

Those choices differ only in the middle value, so you can tell which is correct by evaluating f(x) for the middle domain value: f(0) = 5. Only one answer choice has both -1 and 5 in the set.

(There are two answers here: how you work the problem, and how you game a multiple choice question.)

4 0

2 years ago

How do you Convert feet to metres<br>

poizon [28]

The conversion of feet to meters is obtained by multiplying 1 foot = 0.3048 meters.

<h3>What are the basic measurements for length?</h3>

Foot, inches, centimeters, and meters are the basic measuring units for length.

<h3>What are the basic conversions?</h3>

The basic conversions are:

1 kilometer = 1000 meters

1 meter = 100 cm

1 cm = 10 mm

1 mm = 0.03937 inch

1 inch = 0.0833 feet.

<h3>How to convert feet to meters?</h3>

According to the international system of units,

1 foot = 12 inches ...(1)

But we know,

1 inch = 25.4 mm, 1 mm = 0.1 cm, and 1 cm = 0.01 m

By substituting all of these in equation (1), we get

1 foot = 12(25.4 mm)

= 304.8 mm

= 304.8 (0.1 cm)

= 30.48 cm

= 30.48(0.01 m)

= 0.3048 meters

Therefore, 1 foot = 0.3048 meters.

Learn more about converting measuring units here:

brainly.com/question/174910

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4 0

2 years ago

If we inscribe a circle such that it is touching all six corners of a regular hexagon of side 10 inches, what is the area of the

Brrunno [24]

Answer:

$\left(100\pi - 150\sqrt{3}\right)$ square inches.

Step-by-step explanation:

<h3>Area of the Inscribed Hexagon</h3>

Refer to the first diagram attached. This inscribed regular hexagon can be split into six equilateral triangles. The length of each side of these triangle will be $10$ inches (same as the length of each side of the regular hexagon.)

Refer to the second attachment for one of these equilateral triangles.

Let segment $\sf CH$ be a height on side $\sf AB$ . Since this triangle is equilateral, the size of each internal angle will be $\sf 60^\circ$ . The length of segment

$\displaystyle 10\, \sin\left(60^\circ\right) = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt{3}$ .

The area (in square inches) of this equilateral triangle will be:

$\begin{aligned}&\frac{1}{2} \times \text{Base} \times\text{Height} \\ &= \frac{1}{2} \times 10 \times 5\sqrt{3}= 25\sqrt{3} \end{aligned}$ .

Note that the inscribed hexagon in this question is made up of six equilateral triangles like this one. Therefore, the area (in square inches) of this hexagon will be:

$\displaystyle 6 \times 25\sqrt{3} = 150\sqrt{3}$ .

<h3>Area of of the circle that is not covered</h3>

Refer to the first diagram. The length of each side of these equilateral triangles is the same as the radius of the circle. Since the length of one such side is $10$ inches, the radius of this circle will also be $10$ inches.

The area (in square inches) of a circle of radius $10$ inches is:

$\pi \times (\text{radius})^2 = \pi \times 10^2 = 100\pi$ .

The area (in square inches) of the circle that the hexagon did not cover would be:

$\begin{aligned}&\text{Area of circle} - \text{Area of hexagon} \\ &= 100\pi - 150\sqrt{3}\end{aligned}$ .

3 0

3 years ago