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SOVA2 [1]
3 years ago
7

Find the inverse of each function. f(n)=n+4/2

Mathematics
1 answer:
Ipatiy [6.2K]3 years ago
3 0

Step-by-step explanation:

f(n) =  \frac{ n +4}{2}  \\ let \: f(n)  = y  \implies \: n =  {f}^{ - 1}(y) \\  \therefore \: y = \frac{ n +4}{2}   \\  \\ \therefore \:2 y = n +4 \\  \\ \therefore \:2 y  - 4= n  \\ \therefore \:n  = 2y - 4 \\  \\ \therefore \:  {f}^{ - 1}(y)   = 2y - 4 \\  \\  \red{ \boxed{\bold{\therefore \:  {f}^{ - 1}(n)   = 2n- 4} }}

(Replacing y by n)

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3) An open top box is to be constructed out of a 90 inch by 70 inch piece of cardboard by cutting squares out of the corners and
Elena L [17]

Answer:

a) The volume in cubic inches is 36000

b) The volume in cubic feet is 125/6

c) The volume in cubic yard is 125/162

Step-by-step explanation:

* Lets study the information of the problem to solve it

- The dimensions of the piece of cardboard are 90 inches by 70 inches

- The side of the cutting square is 15 inches

- The squares are cutting from each corner

∴ Each dimension of the cardboard will decrease by 2 × 15 inches

∴ The new dimensions of the piece of cardboard are;

90 - (15 × 2) = 90 - 30 = 60 inches

70 - (2 × 15) = 70 - 30 = 40 inches

- The dimensions of the box will be:

# Length = 60 inches

# width = 40 inches

# height = 15 inches

- The volume of any box with three different dimensions is

V = Length × width × height

∵ The length = 60 inches

∵ The width = 40 inches

∵ The height = 15 inches

∴ V = 60 × 40 × 15 = 36000 inches³

a) The volume in cubic inches is 36000

* Now lets revise how to change from inch to feet

- 1 foot = 12 inches

∵ 1 foot = 12 inches

∴ 1 foot³ = (12)³ inches³

∴ 1 foot³ = 1728 inches³

∵ The volume of the box is 36000 inches³

∴ The volume of the box in cubic feet = 36000 ÷ 1728 = 125/6  

b) The volume in cubic feet is 125/6

* Now lets revise how to change from feet to yard

- 1 yard = 3 feet

∵ 1 yard = 3 feet

∴ 1 yard³ = (3)³ feet³

∴ 1 yard³ = 27 feet³

∵ The volume of the box is 125/6 feet³

∴ The volume of the box in cubic yard = 125/6 ÷ 27 = 125/162  

c) The volume in cubic yard is 125/162

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steposvetlana [31]

Answer:

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Step-by-step explanation:

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3 years ago
What's 1+1? <br><br>Brainliest With The Correct Answer​
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2 is the answer.........

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2 years ago
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1 question answer please? :)
VashaNatasha [74]
The answer is C. 2. Hope this helped. now go pass that assignment.
8 0
3 years ago
Please help this is important for me.
Anit [1.1K]
<h3>Answer: point Q is located at (-1, 1)</h3>

=================================================

Explanation:

Check out the diagram below.

Plot R(-3,7) and T(3,-11) on the same xy grid.

Draw a vertical line through R and a horizontal line through T. A right triangle forms. At the intersection point is point S(-3,-11)

----------------------

Now measure the distance from point S to point T. You can count out the spaces or subtract the x coordinates and use absolute value.

|x1-x2| = |-3-3| = |-6| = 6

From point S to point T is 6 units.

We want to subdivide this horizontal length in the ratio 1:2

What this means is that we want to plot a point U somewhere such that SU:UT = 1:2

In other words,

SU = x

UT = 2x

SU+UT = ST

x+2x = 6

3x = 6

x = 6/3

x = 2

So we must move 2 spaces to the right from point S to get to U(-1,-11)

Going from point U(-1,-11) to T(3,-11) is 4 spaces

We have SU:UT = 2:4 = 1:2 to help confirm we have the correct location for point U

From point U, we then move straight up to the line segment RT

We'll land on Q(-1,1)

----------------------

Another way to find the y coordinate of point Q is to subdivide the segment RS into the ratio 1:2 similar to how we divided ST up

Segment RS is 18 units long since we go from y = 7 to y = -11 when going from R to S.

If V was on segment RS such that

RV:VS = 1:2

and RV = y

then

RV+VS = RS

y+2y = 18

3y = 18

y = 6

RV = y = 6

VS = 2y = 2*6 = 12

So you'll move 6 units down from y = 7 to land on y = 1 (when going from the y coordinate of R to the y coordinate of Q)

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3 years ago
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