Answer:
-7
Step-by-step explanation:
A constant number is a number that contains no variables like x and y. The only constant in that problem is -7.
The answer is 80 square meters.
The square area is expressed as:
A = a²,
where A is the area of the square, and a is the side of the square.
The rectangle area is expressed as:
A₁ = a₁ · b₁,
where A₁ is the area of the rectangle, and a₁ and b₁ are the sides of the rectangle.
After renovations, square garden becomes rectangular.
One side is doubled in length:
a₁ = 2a
The other side is decreased by three meters.
b₁ = a - 3
The new area is 25% than the original square garden:
A₁ = A + 25%A =
= A + 25/100·A
= A + 1/25·A
= a² + 1/25·a²
= <span>a² + 0.25·a²
</span> = 1.25·a²
If the starting equation is:
A₁ = a₁ · b₁
Thus, the equation is:
1.25a² = 2a·(<span>a - 3)
</span>1.25a² = 2a · a - 2a · 3
1.25a² = 2a² - 6a
<span>Therefore, the equation that could be used to determine the length of a side of the original square garden is:
</span><u>2a² - 6a = </u><span><u>1.25a²</u></span>
Now, we will solve the equation:
2a² - 6a = 1.25a²
2a² - 1.25a² - 6a = 0
0.75a² - 6a = 0
⇒ a(0.75a - 6) = 0
From here, one of the multiplier must be zero - either a or (0.75a - 6). Since a could not be zero, (0.75a - 6) is:
0.75a - 6 = 0
0.75a = 6
a = 6 ÷ 0.75
a = 8
If the side of the square is 8, then the area of the rectangle is
A₁ = 1.25 · a²
A₁ = 1.25 ·8²
A₁ = 1.25 · 64
A₁ = 80
Therefore, the area of the new rectangle garden is 80 square meters.
Your question asks for an expression, so you would expect an answer in the form of an equation containing variables. This is because you have only 2 independent equations with 3 unknowns. That makes the system unsolvable.
Suppose v₁ is the mountaineer's velocity during the 1,000-foot trail. Then, v₂ is his speed for the 5,000-foot trail. The equation relating these two variables is:
v₂ = 2v₁ - 10 ---> equation 1
Then, you find the equation for the total number of hours he climbed. That would be the distance divided by their respective speed.
t = 1000/v₁ + 5000/v₂ ----> equation 2
Substituting equation 1 to equation 2,
t = 1000/v₁ + 5000/(2v₁ - 10)
t = 1000/v₁ + 5000/2(v₁-5)
t = 1,000/v₁ + 2,500/(v₁-5)
Answer:
58464
Step-by-step explanation:
Multiply the two numbers