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2 years ago

13

For each 3 mm of coloured fabric Alex uses to make his curtains, he also uses 2 cm of white fabric. Express the amount of white

fabric to coloured fabric as a ratio in its simplest form.

1 answer:

Leokris [45]2 years ago

5 0

Answer: 2cm/.2cm

Step-by-step explanation:

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Stacey has a square piece of cloth. She cuts 3 inches off of the length of the square and 3 inches off of the width. The area of

ratelena [41]

Answer:

The side length of the original square was 6 inches

Step-by-step explanation:

we know that

The area of a square is

$A=b^2$

where

b is the length side of the square

Let

x ---> the length of the original square

The area of the original square is

$A=x^{2}\ in^2$

The length of the smaller square is

$b=(x-3)\ in$

The area of the smaller square is

$A=(x-3)^2\ in^2$

The area of the smaller square is 1/4 the area of the original square

so

$(x-3)^2=\frac{1}{4} x^{2}$

solve for x

$x^2-6x+9=\frac{1}{4} x^{2}$

Multiply by 4 both sides

$4x^2-24x+36=x^{2}$

$4x^2-x^2-24x+36=0\\3x^2-24x+36=0$

Solve the quadratic equation by graphing

using a graphing tool

x=2, x=6

see the attached figure

The solution is x=6 in

Remember that the solution must be greater than 3 inches (because Stacey cuts 3 inches off of the length of the square and 3 inches off of the width)

therefore

The side length of the original square was 6 inches

3 0

2 years ago

HELP PLEASE!! The cost to fill a car's tank with gas and get a car wash is a linear function of the capacity of the tank. The co

qwelly [4]

The equation would be y=2.10x+3.25!

Also know as A lol

If you plug in 9 as x and add 3.25 it is an easy way to check the answers for further questions!

Have a good day! :-)

If it is not correct or doesn't look quite right or needs to show proof please comment!

6 0

2 years ago

Read 2 more answers

The steps below show the work of a student used to calculate the number of yards in 6,436 meters.

Novay_Z [31]

The conversion factor should be multiplied in Step 2 instead of being divided.

7 0

2 years ago

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Archimedes (ca. 287-212 B.C.) was able to use clever geometric means to determine the relative volumes of a cylinder and the con

VLD [36.1K]

Answer:

The ration of the volume of cone to that of cylinder is $\frac{V_{cone}}{V_{cy}} = \frac{1}{3}$

Step-by-step explanation:

From the question we are told that

The volume of a cone is mathematically represented as

$V_{cone} = \frac{1}{3} \pi r^2 h$

The volume of a cylinder is mathematically represented as

$V_{cy} = \pi r^2 h$

Now the ratio we are to obtain is

$\frac{V_{cone}}{V_{cy}} = \frac{\frac{1}{3} \pi r^2 h}{\pi r^2 h}$

$\frac{V_{cone}}{V_{cy}} = \frac{\frac{1}{3} }{1}$ Note: this is possible because the height and base

$\frac{V_{cone}}{V_{cy}} = \frac{1}{3}$ radius are the same

6 0

2 years ago

The cost of producing x bags of dog food is given by C(x) = 800 + 400 + 10x - x where 0 SX 55000. Find the marginal-cost functio

nikdorinn [45]

Answer:

The marginal-cost function is;

c'(x)= (20x-1)/(2√(400 + 10x² - x))

Completed question;

The cost of producing x bags of dog food is given by C(x) = 800 + √(400 + 10x² - x) where 0≤x≤55000. Find the marginal-cost function.

The marginal-cost function is c'(x)=

(Use integers or fractions for any numbers in the expression.)

Step-by-step explanation:

The marginal-cost function is c'(x)= = dC(x)/dx

Where;

C(x) = 800 + √(400 + 10x² - x)

c'(x) = d(800 + √(400 + 10x² - x) )/dx

Using function of function rule of differentiation or chain rule;

c'(x) = (20x-1)×(1/2√(400 + 10x² - x))

c'(x) = (20x-1)/(2√(400 + 10x² - x))

The marginal-cost function is;

c'(x)= (20x-1)/(2√(400 + 10x² - x))

3 0

2 years ago