Answer:Length: 27m
Step-by-step explanation:
- the formula of area of rectangle is : width*length
- so we just replace the values in the formula
- 162=6*Length
- Length=162/6
- Length=27m
Answer:
20 m by 10 m
Step-by-step explanation:
let w be width and l be length , then
2(l + w) = 60 ( divide both sides by 2 )
l + w = 30 ( subtract w from both sides )
l = 30 - w → (1)
lw = 200 → (2)
Substitute l = 30 - w into (2)
w(30 - w) = 200 ← distribute parenthesis on left side
30w - w² = 200 ( subtract 200 from both sides )
30w - w² - 200 = 0 ( multiply through by - 1 )
w² - 30w + 200 = 0 ← in standard form
(w - 10)(w - 20) = 0 ← in factored form
Equate each factor to zero and solve for w
w - 10 = 0 ⇒ w = 10
w - 20 = 0 ⇒ w = 20
Substitute these values into (1)
l = 30 - 10 = 20
l = 30 - 20 = 10
dimensions of field is 20 m by 10 m
The only way to write 42 as the product of primes (except to change the order of the factors) is 2 × 3 × 7. We call 2 × 3 × 7 the prime factorization of 42. It turns out that every counting number (natural number) has a unique prime factorization, different from any other counting number. This fact is called the Fundamental Theorem of Arithmetic. Fundamental theorem of arithmetic
In order to maintain this property of unique prime factorizations, it is necessary that the number one, 1, be categorized as neither prime nor composite. Otherwise a prime factorization could have any number of factors of 1, and the factorization would no longer be unique.
Prime factorizations can help us with divisibility, simplifying fractions, and finding common denominators for fractions.
make the equation slope-intercept form:
subtract 2x from both sides:
4y = -2x + 12
divide by 4 to get y by itself:
y = -1/2x + 3
to make the new line perpendicular to the existing line, completely flip the slope of the line:
y = 2x + 3
Answer:
a. 96 square units
Step-by-step explanation:
The figure is a rectangle with width AB = (20-12) = 8 units and height BC = (20-8) = 12 units.
The area of the rectangle is (8 units)×(12 units) = 96 square units.