All categories

2 years ago

A rectangle has a perimeter of 23 cm. Its area is 33 cm2. Determine the

Mathematics

1 answer:

SCORPION-xisa [38]2 years ago

5 0

Answer:

length = 6 cm; width = 5.5 cm

Step-by-step explanation:

Let the length = x. Let the width = y.

We use the formulas for area and perimeter using x and y, and the given values.

area = length * width

perimeter = 2(length + width)

xy = 33

2(x + y) = 23

Solve the first equation for x:

x = 33/y

Substitute 33/y for x in the second equation.

2(33/y + y) = 23

66/y + 2y = 23

Mulrtiply both sides by y.

66 + 2y^2 = 23y

2y^2 - 23y + 66 = 0

(2y - 11)(y - 6) = 0

2y - 11 = 0 or y - 6 = 0

y = 11/2 = 5.5 or y = 6

xy = 33

x * 11/2 = 33

x = 33 * 2/11

x = 6

Answer: length = 6 cm; width = 5.5 cm

You might be interested in

Find the values of x and y.<br> X= __<br> Y= __

azamat

Answer:

x = 20

y = 100

Step-by-step explanation:

To figure out x do this.

3x + 2x = 7x - 40 (collect like terms)

5x = 7x -40 (subtract 7x on both sides)

-2x = -40 (divide by -2 on both sides)

x = 20

Plug in to get y

Since 7x - 40 and y are vertical they equal the same amount

7(20) - 40 = y (multiply 7 by 20)

140 - 40 = y (collect like terms)

100 = y

Hope this helps ya! Keep smiling!

6 0

2 years ago

If f(x) =3x and g(x) =2x, what is (g*f)(x)

alekssr [168]

We are given f(x) =3x and g(x) =2x

Now we have to find (g*f)(x).

so (g*f)(x) means we multiply f(x) and g(x).

So multiplying 3x and 2x,

3x * 2x = 6x²

So (g*f)(x) =6x²

4 0

2 years ago

Read 2 more answers

One number is 3 less than a second number. Twice the second number is 12 more than 3 times the first. Find the two numbers.

Verdich [7]

6 and 3, 3 and 6, or 2 and 6

7 0

3 years ago

What is the percent of decrease from 8 to 4?

poizon [28]

Answer:

50%

Step-by-step explanation:

50% of anything is half that being said half of 8 would be 4. SHEEEEEESH

8 0

2 years ago

Read 2 more answers

Write the rule for the nth term of each sequence.

stira [4]

Rule for sequence a is: a_n = 10-3n

Rule for sequence b is: a_n = -19+8n

Step-by-step explanation:

a.)7, 4, 1, -2, ...

First of all we have to find the common difference. Common difference is the difference between consecutive terms of an arithmetic sequence

Here,

$a_1 = 7\\a_2 = 4\\a_3 = 1\\d = a_2 - a_1 = 4-7 = -3\\d = a_3 - a_2 = 1-4 = -3$

The explicit rule for an arithmetic sequence is:

$a_n = a_1 + (n-1)d$

Putting the value of a1 and d

$a_n = 7 + (n-1)(-3)\\a_n = 7 -3n+3\\a_n = 10-3n$

b.)-11, -3, 5, 13, ...

First of all we have to find the common difference. Common difference is the difference between consecutive terms of an arithmetic sequence

Here,

$a_1 = -11\\a_2 = -3\\a_3 = 5\\d = a_2 - a_1 = -3+11 = 8\\d = a_3 - a_2 = 5+3 = 8$

The explicit rule for an arithmetic sequence is:

$a_n = a_1 + (n-1)d$

Putting the value of a1 and d

$a_n =-11 + (n-1)(8)\\a_n = -11 +8n-8\\a_n = -19+8n$

Hence,

Rule for sequence a is: a_n = 10-3n

Rule for sequence b is: a_n = -19+8n

Keywords: Arithmetic sequence, common difference

Learn more about arithmetic sequence at:

#LearnwithBrainly

8 0

2 years ago