by definition, a rectangle has 90° angles so you can use the Pythagorean Theorem
width (w) = w
Length (L) = 4w - 5
Diagonal (D) = L + 10 = (4w - 5) + 10 = 4w + 5
w² + L² = D²
w² + (4w - 5)² = (4w + 5)²
w² + (16w² - 40w + 25) = (16w² + 40w + 25) <em>expanded the squares</em>
w² - 40w = 40w <em>subtracted 16w² and 25 from both sides</em>
w² - 80w = 0 <em>subtracted 40w from both sides</em>
w(w - 80) = 0 <em>factored the equation</em>
w = 0, w - 80 = 0 <em> Zero Product Property staes to set each equal to 0</em>
w = 0, w = 80 <em> solved each equation</em>
w = 80 <em>eliminated w = 0 ... width must have a dimension!</em>
Length (L) = 4w - 5 = 4(80) - 5 = 320 - 5 = 315
Diagonal (D) = L + 10 = (315) + 10 = 325
Answer: width=80, Length=315, Diagonal=325
Answer:
s can take any real value.
Step-by-step explanation:
Given that
-2(6+s)_>-15-2s
Distribute -2 over 6+s
-12-2s >= -15-2s
Simplify both the sides
Add 2s to both the sides.
We get 2s cancel out and -12>=-15 which is true.
Hence the given inequality is valid for all values of s.
This is a special case of inequality which has infinite number of solutions.
s can take any real number and this inequality is valid.
First you would do subtract because you work left to right giving you 1=2+. Then you would add giving you 1 = 9. giving you 9 over 1 so the answer is 9. I think
Using prime factorization, the LCM and GCF of numbers are
1) For 46 and 4
GCF = 2
LCM = 92
2) For 2 and 34
GCF = 2
LCM = 34
3) For 32 and 4
GCF = 4
LCM = 32
<h3>What is meant by prime factorization?</h3>
A natural number other than 1 with just the number 1 and itself as factors is known as a prime factor. Actually, 2, 3, 5, 7, 11, and so on are the first few prime numbers. For numbers, we may now also employ what is known as prime factorization, which really involves utilizing factor trees.
When a number is expressed as the product of its prime factors, this is known as prime factorization.
1) The factors of the numbers are
46 = 2 × 23
4 = 2 × 2
GCF = 2
LCM = 2 × 2 × 23
= 92
2) The factors of 34 are
34 = 2 × 17
GCF = 2
LCM = 2 × 17
=34
3) The factors of the numbers are
32 = 2 × 2 × 2 × 2 × 2
4 = 2 × 2
GCF = 2 × 2
= 4
LCM = 2 × 2 × 2 × 2 × 2
= 32
To know more about prime factorization, visit:
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Answer:
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Step-by-step explanation: