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Crazy boy [7]
3 years ago
11

The length of a rectangle is twice the width. Find the width if the perimeter is 60 centimeters. Define a variable, write an equ

ation, and solve the problem.
Mathematics
2 answers:
inn [45]3 years ago
6 0
Call the length l and the width w. We know that:
1. "<span>The length of a rectangle is twice the width." i.e.: l=2w
</span>2. "<span>the perimeter is 60 centimeters." i.e.: P=60
</span>
Using the perimeter formula P=wl+2w we have:
60=2l+2w
60=2l+l
Thus:
l=20
and:
w=\frac{l}{2}
w=10

The rectangle is 20cm long by 10cm wide. 

To check:
P=2l+2w
60=2(20)+2(10)
60=40+20
60=60  Checks true. 
-Dominant- [34]3 years ago
3 0

width = w

length = 2w

perimeter = 2w + 2 l

perimeter = 2w +2(2w)

60 = 2w + 4w

60= 6w

60=6w

w = 60/6 = 10

length = 10x2 = 20

10+10+20+20 = 60

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Answer:

11.39

Step-by-step explanation:

-3.86+6.82=2.96

abs(2.96)=2.96

----------------------

4.02-12.45=-8.43

abs(-8.43)=8.43

-----------------------

1(2.96)+8.43=2.96+8.43=11.39

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In a competition between players X and Y, the first player to win three games in a row or a total of four games wins. How many w
OLEGan [10]

Answer:

The competition can be played in 7 different ways

Step-by-step explanation:

First game : X

Second game : Y

Third game : Y

After that either X or Y can win

<h3>¹Case - 1: Y wins the fourth game:</h3>

The competition ends with Y winning as he/she won 3 games in a row

<h3>Case - 2: X wins the fourth game:</h3>

more games are required to decide the winner

<h3>Sub-case - a: X wins the fifth game:</h3>

more games are required to decide the winner

<h3>²Sub-sub-case - i: X wins the sixth game:</h3>

The competition ends with X winning as he/she won 3 games in a row

<h3>³⁻⁴Sub-sub-case - ii: Y wins the sixth game:</h3>

The competition ends after the seventh game. Whoever wins seventh game wins the competition as he/she would've won 4 games in total by then.

<h3>Sub-case - b: Y wins the fifth game:</h3>

more games are required to decide the winner

<h3>⁵Sub-sub-case - i: Y wins the sixth game:</h3>

The competition ends with Y winning as he/she won 4 games in total

<h3>⁶⁻⁷Sub-sub-case - ii: X wins the sixth game:</h3>

The competition ends after the seventh game. Whoever wins seventh game wins the competition as he/she would've won 4 games in total by then.

∴<u>The competition can be played in 7 different ways</u>

7 0
3 years ago
What are the coordinates of the point on the directed line segment from (3, 3) to (7,−5) that partitions the segment into a rati
Annette [7]

Answer:

The coordinates of the point is (5.5, -2)

Step-by-step explanation:

Okay, what we want to do here is to get the point that divides the line that joins the points (3,3) to (7,-5) in the ratio 5 to 3

Generally, given the ratio a:b and we want to divide the line joining the points (x1,y1) and (x2,y2) in that ratio, we use the condensed formula below;

Let’s call the point dividing the line in the given ratio z.

The coordinates of Z is;

{(bx1 + ax2)/(a+b), (by1 + ay2)/(a+b)}

In this question (x1,y1) = (3,3)

While (x2,y2) = (7,-5)

while a:b = 5:3

Substituting these values into the coordinate equation for point z, we have ;

{((3(3) + 5(7))/(5+3), ((3)(3) + 5(-5))/(5+3)}

= {44/8 , -16/8} = {5.5, -2}

4 0
3 years ago
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