Answer:
Perimeter of a rectangle = 2(L + W)
Step-by-step explanation:
L = length
W = width
In a rectangle, of the four sides, there are two equal length and 2 equal width
Length = 2 sides
Width = 2 sides
perimeter of a rectangle is the sum of the lenths of its four sides.
Perimeter of a rectangle = L + L + W + W
= 2L + 2W
Factorize
= 2(L + W)
Perimeter of a rectangle = 2(L + W)
This expression shows the relationship
Okay, So you have 24x+25=6y+7
Step 1: Pull out like factors : 24x + 18 + 6y = 6 • (4x + y + 3)
Step 2: 4x+y+3 = 0
y-intercept = -3/1 = -3.00000
x-intercept = -3/4 = -0.75000
Slope = -8.000/2.000 = -4.000
And bam, you have a straight line
<span>The border width is x
The sides are now (80 - 2x) + 2x, and (60 - 2x) + 2x
The area along one side is
2x^2 + x(80 - 2x)
adding the other side doubles the area
so far,
4x^2 +2x(80 - 2x)
now add in the areas left along the other two sides
2x(60-2x)
(This is hard to follow without a picture. Try drawing it)
The interior area is 800.
The whole area is 4800, so the difference is the border.
4800 - 800 = 4000
4x^2 + 2x(80 - 2x) + 2x(60 - 2x) = 4000
4x^2 + 160x - 4x^2 + 120x - 4x^2 = 4000
-4x^2 + 280x = 4000
-x^2 + 70x - 1000 = 0
multiply both sides by -1
x^2 - 70x + 1000 = 0
(x - 50)(x - 20) = 0
x = 50, 20 are the solutions
The answer can't be 50 because the width on both sides would be
50 + 50 = 100, and that's greater than 80, the longest side.
That leaves x = 20 for the width of the strip.
check
4x^2 + 2x(80 - 2x) + 2x(60 - 2x) = 4000
4(20)^2 + 2*20(80 - 2*20) + 2*20(60 - 2*20) = 4000
4*400 + 40*40 + 40*20 = 4000
1600 +1600 + 800 = 4000
3200 + 800 = 4000
4000 = 4000</span>
<h3>
Answer:</h3>
1/17 or 0.0588 (without replacement)
<h3>
Step-by-step explanation:</h3>
To answer this question we need to know the following about a deck of cards
- A deck of cards contains 4 of each card (4 Aces, 4 Kings, 4 Queens, etc.)
- Also there are 4 suits (Clubs, Hearts, Diamonds, and Spades).
- Additionally, there are 13 cards in each suit (Clubs/Spades are black, Hearts/Diamonds are red)
.
In this case, we are required to determine the probability of choosing two diamonds.
- There are 13 diamonds in the deck.
- Assuming, the cards were chosen without replacement;
P(Both cards are diamonds) = P(first card is diamond) × P(second card is diamond)
P(First card is diamond) = 13/52
If there was no replacement, then after picking the first diamond card, there are 12 diamond cards remaining and a total of 51 cards remaining in the deck.
Therefore;
P(Second card is diamond) = 12/51
Thus;
P(Both cards are diamonds) = 13/52 × 12/51
= 156/2652
= 1/17 or 0.0588
Hence, the probability of choosing two diamonds at random (without replacement) is 1/17 or 0.0588.