Answer:
Dimensions of the rug = 13 ft × 26 ft
Step-by-step explanation:
Dimensions of the room = 21 ft × 34 ft
Area of the room = 21 × 34 = 714 ft²
Cynthia wants to leave a uniform strip of floor around the rug.
Let the width of the rug = x ft
Then the dimensions of the rug will be = (21- 2x)ft × (34 - 2x)ft
Area of the rug = (21 - 2x)×(34 - 2x) square feet
338 = (21 - 2x)×(34 - 2x)
338 = 714 - 68x - 42x + 4x²
4x² - 110x + 714 - 338 = 0
4x² - 110x + 376 = 0
2x² - 55x + 188 = 0
2x² - 47x - 8x + 188 = 0
x(2x - 47) - 8(x - 47) = 0
(x - 4)(2x - 47) = 0
x = 4, 
For x = 23.5 area of the rug will be negative.
Therefore, x = 4 ft will be the width of the rug.
Dimensions of the rug will be 13 ft × 26 ft.
Answer:
we conclude that:
If 4x - 6≠4, then 2x–5≠5 is the contrapositive of a conditional statement if 2x -5=5, then 4x-6=14.
Step-by-step explanation:
We know that the contrapositive of a conditional statement of the form "If p then q" is termed as "If ~q then ~p".
In other words, it is symbolically represented as:
' ~q ~p is the contrapositive of p q '
For example, the contrapositive of "If it is a rainy day, then they suspend the match" is "If they do not suspend the match, then it won't be a rainy day."
Given
p: 2x -5=5
q: 4x-6=14
As the contrapositive of a conditional statement of the form "If p then q" is termed as "If ~q then ~p
Thus, we conclude that:
If 4x - 6≠4, then 2x–5≠5 is the contrapositive of a conditional statement if 2x -5=5, then 4x-6=14.
Answer:
Step-by-step explanation:
Let j represent the cost of a juice box.
Let w represent the cost of a bottle of water.
One teacher purchased 18 juice boxes and 32 bottles of water, and spent $19.92.. This means that
18j + 32w = 19.92 - - - - - - - - - - - - 1
The other teacher purchased 14 juice boxes and 26 bottles of water, and spent $15.76. This means that
14j + 26w = 15.76- - - - - - - - - - - - 2
Multiplying equation 1 by 14 and equation 2 by 18, it becomes
252j + 448w = 278.88
252j + 468w = 283.68
Subtracting, it becomes
- 20j = - 4.8
j = - 4.8/- 20 = 0.24
Substituting j = 0.24 into equation 1, it becomes
18 × 0.24 + 32w = 19.92
4.32 + 32w = 19.92
32w = 19.92 - 4.32 = 15.6
w = 15.6/32 = 0.4875
Kara's prices are incorrect.
the cost of a juice box is $0.24
the cost of a bottle of water is $0.4875