This is an algabraic problem, so we would use variables:
Length=x
Width=y
The length is four times the width, so
x=4y
Since the equation for perimeter is P= 2(x+y), you would instead substitute 4y for x, and 7 for the perimeter.
7=2(4y+y)
Simplify.
7=2(5y)
7=10y
y=7/10
Since y is 7/10, you would substitute 7/10 into the equation x=4y.
x=4(7/10)
x=14/5
So, the dimensions are 7/10 x 14/5.
Hope this helps!
Answer:
Step-by-step explanation:
1). x² - 8x
To convert this expression into a perfect square trinomial,
x² - 2(4x) + 4² = (x - 2)²
Therefore , 4² = 16 should be added.
Option (4) is the answer.
2). x² + 2x = 3
x² + 2(1)(x) = 3
x² + 2(1)(x) + 1 = 3 + 1 [By adding 1 on both the sides]
(x + 1)² = 4
x + 1 = ±2
x = -3, -1
Option (1) is the answer.
3). 3x²- 18x = 21
x² - 6x = 7
x² - 2(3x) = 7
x² - 2(3x) + 3² = 7 + 3²
(x - 3)² = 7 + 9
(x - 3)² = 16
x - 3 = ±4
x = -1, 7
Determine whether the stated conclusion is valid based on the given information. If not, write invalid. Explain your reasoning.
3. Given: If a number is divisible by 4, then the number is divisible by 2. 12 is divisible by four.
Conclusion: 12 is divisible by 2.
SOLUTION:
If p → q is a true statement and p is true, then q. Here, a number divisible 4 is divisible by 2 also and 12 is divisible by 4. So, 12 is divisible by 2 is a valid statement by the Law of Detachment.
ANSWER:
valid; Law of Detachment
4. Given: If Elan stays up late, he will be tired the next day. Elan is tired.
Conclusion: Elan stayed up late.
SOLUTION:
If p is true, then q is true, but q being true does not necessarily mean that p is true. Elan could be tired because he worked out. So, the statement is invalid.
ANSWER:
Invalid; Elan could be tired because he worked out.
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