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3 years ago

The perimeter of a bedroom is 88 feet. The ratio of the width to the length is 5:6. What are the dimensions of the bedroom?

Mathematics

1 answer:

Elza [17]3 years ago

7 0

Answer:

20 feet wide, 24 feet long

Step-by-step explanation:

Let x - width, y - length.

The perimeter is given by the formula:

P = 2*(width + length) or using x, y

P = 2*(x + y) = 88

x + y = 44

And we know that the ratio between the sides is 5/6:

x/y = 5/6. x is on top because the length is bigger than the width

x = 5y/6

Plug this in the first expression:

y + 5y/6 = 44. Muliply by 6

6y + 5y = 264

11y = 264

y = 264/11 = 24.

So x = 5(24)/6 = 20

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What is 403,000,000,000,000 in scientific

frozen [14]

Answer:

(A) 4.03 x 10^14

Step-by-step explanation:

403,000,000,000,000

Scientific notation is of the form

a * 10 ^b

where a is a number from 1 to a number less than 10

Put the decimal in the number

403,000,000,000,000.

We need to move the decimal 14 places to the left to get the number to be between 1 and 10

4.03000000000000 so the b is 14

Since we moved it to the left b is positive

We can drop the extra zeros at the end (after the last nonzero digit)

4.03 *10^14

6 0

3 years ago

Read 2 more answers

An evergreen nursery usually sells a certain shrub after 7 years of growth and shaping. The growth rate during those 7 years is

Ne4ueva [31]

Answer:

( 0.6 t^2 + 3t + 11 ) cm

Step-by-step explanation:

dh/dt = 1.2t + 3

at t = 0, h = 11 cm

(a)

dh / dt = 1.2 t + 3

dh = (1.2 t + 3) dt

integrate on both sides

h = 0.6 t^2 + 3t + c .... (1)

where c is the integrating constant

put t = 0

11 = c

Put in equation (1) , we get

h = ( 0.6 t^2 + 3t + 11 ) cm

Thus, teh height of tree after t years is given by

( 0.6 t^2 + 3t + 11 ) cm.

3 0

2 years ago

Solve the following quadratics. State the FACTORS AND SOLUTIONS. 1. 2x^2 - 7x + 3 2. 3x^2 + 7x +2

tekilochka [14]

Answer:

1. x = 3, 1/2 (solutions); (x - 3)(2x - 1) (factors)

2. x = -1/3, -2 (solutions); (3x + 1)(x + 2) (factors)

Step-by-step explanation:

1. 2x^2 - 7x + 3

To solve problem 1, you will need to identify your a, b, and c values in this quadratic function.

Since this problem is in standard form, it will be easy to identify these values. The standard form of a quadratic function is ax^2 + bx + c.

The a value is 2, the b value is -7, and the c value is 3 if we use our standard form and see which numbers are plugged into it.

Since we know that

a = 2
b = -7
c = 3

we can use the quadratic formula: $x = \frac{-b~\pm~\sqrt{b^2~-~4ac} }{2a}$

Substitute the a, b, and c values into the quadratic formula: $x=\frac{-(-7)\pm\sqrt{(-7)^2-4(2)(3)} }{2(2)}$

Now simplify using the laws of pemdas: $x=\frac{7\pm\sqrt{(49)-(24)} }{4}$

Simplify even further: $x=\frac{7\pm\sqrt{(25)} }{4} \rightarrow x=\frac{7\pm (5) }{4}$

Now split this equation into two equations to solve for x: $x=\frac{12 }{4} ~~and~~ x=\frac{2 }{4}$

12/4 can be simplified to 3, and 2/4 can be simplified to 1/2.

This means your solutions to problem 1 is 3, 1/2.

$\boxed {x=3,\frac{1}{2} }$

There is also another way to solve for the quadratic functions, and this was by factoring.

If you factor 2x^2 - 7x + 3 using the bottoms-up method, you will get (x - 3)(2x - 1).

After factoring, solving for the solutions is simple because all you have to do is set each factor to 0.

x - 3 = 0
2x - 1 = 0

After solving for x by adding 3 to both sides, or by adding 1 to both sides then dividing by 2, you will end up with the same solutions: x = 3 and x = 1/2.

2. 3x^2 + 7x + 2

To save time I'll be using the bottoms-up factoring method, but remember to refer back to problem 1 (quadratic formula) if you prefer that method.

Factor this quadratic function using the bottoms-up method. After factoring you will have (3x + 1)(x + 2). These are your factors.

Now to solve for x and find the solutions of the quadratic function, you will set both factors equal to 0.

3x + 1 = 0
x + 2 = 0

Solve.

First factor: 3x + 1 = 0

Subtract 1 from both sides.

3x = -1

Divide both sides by 3.

x = -1/3

Second factor: x + 2 = 0

Subtract 2 from both sides.

x = -2

Your solutions are x = -1/3 and x = -2.

$\boxed {x = -\frac{1}{3} , -2}$

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2 years ago

Susan wants to divide 2 hours of computer time equally among 10 students. What fraction of an hour of computer time will each st

Andreas93 [3]

2 hours of computer time divide by 10 students:

2/10 = 1/5

7 0

1 year ago

For the spinner above, the probability of landing on black is 1/2, and the probability of landing on red is 1/3. Suppose it is s

8_murik_8 [283]

Answer:

1/8

Step-by-step explanation:

P = 1/2 × 1/2 × 1/2

P = 1/8

7 0

3 years ago