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Likurg_2 [28]
2 years ago
5

The sum of six times a number and nine is equal to the difference of the number and eleven. Find the number. Round your answer t

o the nearest integer, if necessary.
Mathematics
2 answers:
Sladkaya [172]2 years ago
7 0

Suppose the number in this case to be n.

According to the statement given, six times of number would be 6n

and

the sum of 6 times the number (6n) and nine would be ---> 6n + 9

is equal to the difference of the number (6n) and eleven ---> n - 11.

So, the final equation becomes:

6n + 9 = n - 11

Solving this, place both the values of n on one side and the numbers on the other side but do not forget to change the sign of the value that you change the side of.

6n - n = -11 -9 (here we changed the signs of positive n to -n and positive 9 to -9 because we changed their sides)

5n = -20

n = -20/5

n = -4

storchak [24]2 years ago
3 0

the equation would be 6*n+9=n-11

the answer is -4

i think

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A school wishes to enclose its rectangular playground using 480 meters of fencing.
Harlamova29_29 [7]

Answer:

Part a) A(x)=(-x^2+240x)\ m^2

Part b) The side length x that give the maximum area is 120 meters

Part c) The maximum area is 14,400 square meters

Step-by-step explanation:

The picture of the question in the attached figure

Part a) Find a function that gives the area A(x) of the playground (in square meters) in terms of x

we know that

The perimeter of the rectangular playground is given by

P=2(L+W)

we have

P=480\ m\\L=x\ m

substitute

480=2(x+W)

solve for W

240=x+W\\W=(240-x)\ m

<u><em>Find the area of the rectangular playground</em></u>

The area is given by

A=LW

we have

L=x\ m\\W=(240-x)\ m

substitute

A=x(240-x)\\A=-x^2+240x

Convert to function notation

A(x)=(-x^2+240x)\ m^2

Part b) What side length x gives the maximum area that the playground can have?

we have

A(x)=-x^2+240x

This function represent a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

The x-coordinate of the vertex represent the length that give the maximum area that the playground can have

Convert the quadratic equation into vertex form

A(x)=-x^2+240x

Factor -1

A(x)=-(x^2-240x)

Complete the square

A(x)=-(x^2-240x+120^2)+120^2

A(x)=-(x^2-240x+14,400)+14,400

A(x)=-(x-120)^2+14,400

The vertex is the point (120,14,400)

therefore

The side length x that give the maximum area is 120 meters

Part c) What is the maximum area that the playground can have?

we know that

The y-coordinate of the vertex represent the maximum area

The vertex is the point (120,14,400) -----> see part b)

therefore

The maximum area is 14,400 square meters

Verify

x=120\ m

W=(240-120)=120\ m

The playground is a square

A=120^2=14,400\ m^2

8 0
3 years ago
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n200080 [17]

Answer:

5 (grandson's age now)

35 (son's age now)

60 (father's age now)

Step-by-step explanation:

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