All categories

3 years ago

The length of a rectangle is 9 inches longer than the width. If the area is 205 square inches, find the

Mathematics

1 answer:

levacccp [35]3 years ago

8 0

Answer:

L=19.5in w=10.5in

Step-by-step explanation:

Draw a rectangle. If the length is 9 inches longer than its width, we can write the width as "w" and the length as the width + 9

Area is (width)(Length) = (width)(width+9)

----------

| |

| | L = w+9

| |

-----------

A = (w+3)(w)

A = w2 + 9w = 205.

(Problem states that area is 205 sq in)

Need to solve this quadratic equation

w2 + 9y - 205 = 0

Factor:

(w - 10.51) (w + 19.51) = 0

w - 10.51 = 0. or. w + 19.51 = 0

Solve these and get

w = 10.51. or. w = -19.51

Only one that makes sense in real life is the positive one.

So the dimensions are

Width = 10.51 inches

Length = 19.51 inches

You might be interested in

Need help wit #36. Math.

Andrei [34K]

Remark

Write down all the trenches, add them together, divide by 4.

$\dfrac{-(32788 + 31988 + 35840 + 27976) }{4}$

$\dfrac{-128592}{4} = \text{-32148}$

Answer

The average depth is - 32148 to the nearest foot.

4 0

4 years ago

The perimeter of an equilateral triangle is 12\/3 cm. Find the radius, apothem and area of the equilateral triangle.

Irina-Kira [14]

Answer:

Radius - 4

Apothem - 2

Area - $12\sqrt{3}$ or 20.8

Step-by-step explanation:

Try to draw out my explanation so you know what this looks like.

~~~~

This is an equilateral triangle, so all sides are the same length. The perimeter can be divided by 3 to get each side length...

$12\sqrt{3} \div3 = 4\sqrt{3}$

Now that we know the side lengths, we can get this started!

~~~~

Now, an equilateral triangle has angles that all equal 60 degrees. We can bisect this into TWO special case triangles of measures 90-60-30.

4 times the square root of 3 will be the hypotenuse, and the smallest leg is always half of that. The larger leg is represented as the small leg times the square root of 3.

$Small=2\sqrt{3} \\Hypotenuse = 4\sqrt{3} \\Long =6$

By the way, the formula for the area can be either of the two:

$A= \frac{1}{2} bh\\or\\A = \frac{1}{2} NAS$

we can easily find the area using the first formula.

$A= \frac{1}{2} (4\sqrt{3} )(6)\\A=12\sqrt{3}$

The radius is the distance from the center to the corners & the apothem is the distance from the center to a side...

So we can divide the big triangle into a mini triangle at the bottom left/right

The height (small leg) of that triangle would be the apothem

The hypotenuse of that triangle would be the radius.

I did the math really quick because this is getting long. Anyhow, the small leg is 2 so is the apothem, and the hypotenus is 4, so is the radius

Happy April Fool's btw, lol.

4 0

3 years ago

What is the midpoint of Line segment A B ? A number line going from negative 9 to positive 9. A closed circle appears at negativ

Jlenok [28]

Answer:

G is the mid-point of line segment AB ⇒ 2nd answer

Step-by-step explanation:

* Lets explain how to solve the problem

- The mid-point of a line is the point which divides the line into

two equal parts

- There are four points between points A and B

- The four points are F , G , H , L

- one of them is the mid-point of AB

- The location of A is -6

- The location of F is -2

- The location of G is 1

- The location of H is 2

- The location of L is 3

- The location of B is 8

* Lets find the distance between points A and B

∵ Point A is located at -6

∵ Point B is located at 8

∵ The distance between A and B = location of B - location of A

∴ AB = 8 - (-6) = 8 + 6 = 14 units

- The mid-point of AB will divide it into two equal part, the length

of each part is 14/2 = 7 units

∴ The mid-point location will be after point A by 7 units

∵ The location of point A is -6

∴ The location of the mid-point = -6 + 7 = 1

∴ The location of the mid-point of AB is 1

∵ The location of point G is 1

∴ G is the mid-point of line segment AB

7 0

4 years ago

Read 2 more answers

What’s the solution for both 2x+y=4 and y=3x-1

never [62]

Answer:

x=2 -- y/2 y=3x - 1

Step-by-step explanation:

5 0

3 years ago

Solve -8|4b-6|+9=-39

LUCKY_DIMON [66]

Answer:

b=3 b=0

Step-by-step explanation:

-8|4b-6|+9=-39

Subtract 9 from each side

-8|4b-6|+9-9=-39-9

-8 | 4b-6| = -48

Divide by -8

-8/-8 | 4b-6| = -48/-8

| 4b-6| = 6

When solving the absolute value, there is a positive and a negative solutions

4b-6 = 6 and 4b-6 = -6

Add 6 to each side

4b-6+6 =6+6 4b-6+6 = -6+6

4b =12 4b = 0

Divide by 4

4b/4 =12/4 4b/4 = 0/4

b=3 b=0

7 0

3 years ago