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3 years ago

Could someone help me figure this out?

Mathematics

1 answer:

Zolol [24]3 years ago

3 0

Answer:

The area of a rectangle is the length multiplied by its breadth.

Since the length is $3(n-1)$ and the breadth is $n+2$ and the area is 54, you can form an equation as followed:

$3(n-1)*n+2=54$

$3n(n-1)+2=54$

Expand:

$(3n*n)-(3n*1)+2=54$

$3n^2-3n+2=54$

Subtract both sides by 54:

$3n^2-3n+2-54=54-54$

$3n^2-3n-52=0$

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5. Write two expressions for the area of the big rectangle.

4vir4ik [10]

Answer:

Two expressions for the area are;

i) x/3 + 2·y + 6

ii) (1/3) × (x + 6·y + 18)

Step-by-step explanation:

The given dimension of the rectangle are;

The height of the rectangle, h = 1/3

The width of the smallest rectangle, w₁ = x

The width of the med sized rectangle, w₂ = 6·y

The width the large rectangle, w₃ = 18

The area, 'A', of the entire rectangular figure, the big rectangle, can be expressed as follows;

A = A₁ + A₂ + A₃

Where;

A₁ = The area of the smallest rectangle

A₂ = The area of the mid sized rectangle

A₃ = The area of the large rectangle

∴ A = (1/3) × x + (1/3) × 6·y + (1/3) × 18 = x/3 + 2·y + 6

The area of the big rectangle. 'A', can also be found as follows;

A = (1/3) × (x + 6·y + 18)

Therefore, two expressions for the area of the big rectangle are;

x/3 + 2·y + 6 and (1/3) × (x + 6·y + 18).

3 0

3 years ago

Amy and Mary are playing a board game that uses game money if $5 and $10. At the end of the game, Amy has n bills worth $5 each

loris [4]

Answer:

5n + 10d represented the money spend by the Amy in playing board games of cost $5 and $10 .

Step-by-step explanation:

As given

Amy and Mary are playing a board game that uses game money if $5 and $10.

At the end of the game, Amy has n bills worth $5 each and d bills worth $10 each .

Total amount of n bills = 5n

Total amount of d bills = 10d

Thus

Total money spend by the Amy in playing board games = Total amount of n bills + Total amount of d bills

= 5n + 10d

Therefore 5n + 10d represented the money spend by the Amy in playing board games of cost $5 and $10 .

6 0

3 years ago

Find the product of 17892 and 36

solniwko [45]

The answer to 17892•36 is 644,112

6 0

3 years ago

Read 2 more answers

Solve the following equation on the interval [0, 2π). tan^2x sin x = tan^2x

Alenkasestr [34]

<h3>Given</h3>

tan(x)²·sin(x) = tan(x)²

x on the interval [0, 2π)

<h3>Solution</h3>

Subtract the right side and factor. Then make use of the zero-product rule.

... tan(x)²·sin(x) -tan(x)² = 0

... tan(x)²·(sin(x) -1) = 0

This is an indeterminate form at x = π/2 and undefined at x = 3π/2. We can resolve the indeterminate form by using an identity for tan(x)²:

... tan(x)² = sin(x)²/cos(x)² = sin(x)²/(1 -sin(x)²)

Then our equation becomes

... sin(x)²·(sin(x) -1)/((1 -sin(x))(1 +sin(x))) = 0

... -sin(x)²/(1 +sin(x)) = 0

Now, we know the only solutions are found where sin(x) = 0, at ...

... x ∈ {0, π}

8 0

3 years ago

Please help. Thank you. :)

adelina 88 [10]

Hello!

To find the lateral area you use the equation

$\pi r \sqrt{ h^{2} + r^{2} }$

You put in the values you know and you get 829.4

To find the surface area you use the equation

$\pi r(r+ \sqrt{ h^{2} + r^{2} }$

Put in the values you know and you get 1209.5

The answer is A

Hope this helps!

5 0

3 years ago