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Select the output of this algorithm

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storchak [24]2 years ago

8 0

Answer:

bvjh

Step-by-step explanation:

bn

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A rectangle has an area of 24 sq. inches and a perimeter of 50 in. what are the dimensions of the rectangle

gulaghasi [49]

Answer:

Length of rectangle = 24 inches

Width of rectangle = 1 inches

Step-by-step explanation:

Area of rectangle = 24 square inches

Perimeter of rectangle = 50 inches

Formulas:

Area of rectangle = $l\times w$

Perimeter of rectangle = $2(l+w)$

where $l$ represents length of rectangle and $w$ represents width of rectangle.

So, we can get two equations for $l$ and $w$

A) $l\times w=24$ [Area]

B) $2(l+w)=50$ [ Perimeter ]

Simplifying equation B.

Dividing both sides by 2.

$\frac{2(l+w)}{2}=\frac{50}{2}$

$l+w=25$

Solving for $l$ in terms of width.

Subtracting $w$ both sides.

$l+w-w=25-w$

∴ $l=25-w$

Substituting value of $l$ in terms of $w$ in equation A.

$(25-w)w=24$

Using distribution.

$25w-w^2=24$

Adding $w^2$ both sides.

$25w-w^2+w^2=24+w^2$

$25w=24+w^2$

subtracting $25 w$ both sides

$25w-25w=24+w^2-25w$

$0=w^2-25w+24$

We have a quadratic equation. $w^2-25w+24=0$

We solve for $w$ by factor method.

Splitting middle term into two terms such that the sum of the two = $-25w$ and product of two = $24w^2$

$w^2-24w-w+24=0$

Factoring in pairs.

$w(w-24)-1(w-24)=0$

Factoring as a whole

$(w-24)(w-1)=0$

So, we have

$w-24=0$ and $w-1=0$

By adding 24 to one equation and adding 1 to other we get

$w-24+24=0+24$ and $w-1+1=0+1$

$w=24$ and $w=1$

So length can be found out by plugging value of $w$ in the length equation.

$l=25-24=1$ and $l=25-1=24$

Since length is always the longer side of rectangle so, the dimensions of rectangle can be given by.

length = 24 inches (answer)

width = 1 inches (answer)

6 0

3 years ago

A carpenter wants to put four shelves on a 8-foot wall(=b) so that the five spaces created decrease by 7 inches(=a) as we move u

nadezda [96]

Height of wall = 8 feet

1 feet = 12 inches

⇒ Height of wall = 8 × 12 inches

⇒ Height of wall = 96 inches

We know that the 4 shelves are to be placed such that that the 5 spaces created decrease by 7 inches as we move up the wall

Let height of 1st space = h inches

⇒ Height of 2nd space = h - 7 inches

⇒ Height of 3rd space = h - 14 inches

⇒ Height of 4th space = h - 21 inches

⇒ Height of 5th space = h - 28 inches

Thickness of each shelf = 3/4 inch

⇒ Thickness of 4 shelves = $\frac{3}{4}$ × 4 inches = 3 inches

So, Height of Wall = Height of 1st space + Height of 2nd space + Height of 3rd space + Height of 4th space + Height of 5th space + Thickness of 4 shelves

⇒ 96 = h + h - 7 + h - 14 + h -21 + h - 28 + 3

⇒ 95 = 5h - 70 + 3

⇒ 95 = 5h - 67

⇒ 5h = 162

⇒ h = 32.4 inches

So the first shelf is placed 32.4 inches from the floor

3 0

4 years ago

Which equation is rewritten in vertex form

ser-zykov [4K]

Answer:

Option (2)

Step-by-step explanation:

Given expression is, y = (x + 3)² + (x + 4)²

By solving this expression,

y = x² + 6x + 9 + x² + 8x + 16

y = 2x² + 14x + 25

y = (2x² + 14x) + 25

y = 2(x² + 7x) + 25

y = 2[x² + 2(3.5x) + (3.5)² - (3.5)²] + 25

y = 2[x² + 2(3.5x) + (3.5)²] - 2(3.5)² + 25

y = 2(x + 3.5)² - 24.5 + 25

y = 2(x + 3.5)² + 0.5

$y=(x+\frac{7}{2})^2+\frac{1}{2}$

Therefore, Option (2) will be the vertex form.

6 0

3 years ago

Is y = 4x4 + 11 a linear or nonlinear equation

Elza [17]

It will be a linear not a nonlinear

4 0

3 years ago

How do you turn a mix number into a fraction?

Tomtit [17]

You must add or subtract, depending on which fraction your going for at that time.

5 0

3 years ago

Read 2 more answers