The length of a rectangle is 2 inches more than the width. The perimeter is 24 inches. Find the length and width

Misha Larkins [42]

Answer:

18

Step-by-step explanation:

The formula for this is a x b = c x d where a is SR, b is FR, c is QR and d is PR. This will give us the equation 9(16) = 8(5x + 8); 144 = 40x + 64; 80 = 40x; x = 2. Now, plug this into PR which will be 5(2)+8 = 18. This is your answer.

3 0

3 years ago

From a thin piece of cardboard 30 in. by 30 in., square corners are cut out so that the sides can be folded up to make a box. Wh

Brilliant_brown [7]

Answer:

Dimensions 5in x 10in x 10in will yeild a box with a max. volume of 500 cubic inches

Step-by-step explanation:

Volume = height x length x width

considering 'x' as the length of the square corners that has been cut out from the cardboard and also, that is height of the cardboard box.

square corners are cut out so that the sides can be folded up to make a box, cardboard sides would reduce by 2x

therefore,

V = x (30-2x) (30-2x) ---> eq(1)

V=( 30x - 2x²) (30-2x)

V= 900x- 60x² - 60x² + 4x³

V= 4x³ - 120 x²+ 900x

Taking derivative w.r.t 'x'

dV/dx = 12x² - 240 x +900

dV/dx = 4 (3x² - 60x +225)

For maximum dV/dx, make it equal zero

dV/dx = 0

so, 4 (3x² - 60x +225)=0

3x² - 60x+225=0 (taking 3 common)

x² - 20x + 75 =0

Solving this quadratic equation

x² - 15x -5x + 75 =0

x(x-15) - 5(x-15) =0

Either (x-15)=0

x=15

Or x-5=0

x = 5

if we substitute x=15 in eq(1), volume becomes zero.

therefore, x cannot be 15

When x= 5

eq(1)=>V = 5 (30-2(5)) (30-2(5))

V= 5 (10) (10)

V= 500 cubic inches,

Therefore, Dimensions 5in x 10in x 10in will yeild a box with a max. volume of 500 cubic inches

7 0

3 years ago

Equation -1-7v+3= how do i slove this i dont know

TEA [102]

Negative one minus negative seven times volume plus three equals BLANK. If v is a variable, the question is wrong.

7 0

3 years ago

Suppose that receiving stations X, Y, and Z are located on a coordinate plane at the points (6,2), (negative 2,negative 4

marin [14]

Answer:

(2,-1)

Step-by-step explanation:

A graph is useful here. Points X and Y have coordinate differences of ...

X -Y = (6, 2) -(-2, -4) = (6+2, 2+4) = (8, 6)

Then the distance between X and Y is ...

d = √(8² +6²) = √100 = 10

The point 5 units from X and from Y is the midpoint of XY:

E = (X +Y)/2 = ((6, 2) +(-2, -4))/2 = (4, -2)/2 = (2, -1)

The epicenter is (2, -1).

_____

The graph shows circles of radius 5 around X and Y, and a circle of radius 13 around Z. The circles intersect at the point (2, -1), the epicenter.

5 0

2 years ago

I need help on this math problem !

xeze [42]

Answer:

181 units²

Step-by-step explanation:

Let's break up the polygon into 3 shapes

Step 1: Area of the left rectangle

4(7) = 28 units²

Step 2: Area of middle rectangle

9(13) = 117 units²

Step 3: Area of top square

6² = 36 units²

Step 4: Add them all up

28 + 117 + 36 = 181 units²

8 0

3 years ago