Ask question

Ask question

All categories

2 years ago

5

The length of a rectangle is a centimeters, and the width of this rectangle is b centimeters. Write an expression for the area o

f the rectangle. "a" and "b" are variables.

1 answer:

Novay_Z [31]2 years ago

7 0

Answer:

Area = ab

Step-by-step explanation:

Area is length × width, so fill in a for the length and b for the width. Multiply a and b together.

A = a×b

A = ab

You might be interested in

Marsha's house is located on the coordinate plane below. Tasha's house is located 6 units from Marsha's house. Which of the foll

Gekata [30.6K]

B 4,2 because it is 6 units away from the point

3 0

3 years ago

A rectangular swimming pool is bordered by a concrete patio. the width of the patio is the same on every side. the area of the s

andre [41]

Answer:

$x = \frac{1}{4}\left(-(l + w) + \sqrt{l^2 + 6lw + w^2} \right)$

where

l = length of the pool (w/o the patio)
w = width of the pool (w/o the patio)

Explanation:

Let

x = width of the patio
l = length of the pool (w/o the patio)
w = width of the pool (w/o the patio)

Since the pool is bordered by a complete patio,

Length of the pool (with the patio)
= (length of the pool (w/o the patio)) + 2*(width of the patio)
Length of the pool (with the patio) = l + 2x

Width of the pool (with the patio)
= (width of the pool (w/o the patio)) + 2*(width of the patio)
Width of the pool (with the patio) = w + 2x

Note that

Area of the pool (w/o the patio)
= (length of the pool (w/o the patio))(width of the pool (w/o the patio))
Area of the pool (w/o the patio) = lw

Area of the pool (with the patio)
= (length of the pool (w/o the patio))(width of the pool (w/o the patio))
= (l + 2x)(w + 2x)
= w(l + 2x) + 2x(l + 2x)
= lw + 2xw + 2xl + 4x²
Area of the pool (with the patio) = 4x² + 2x(l + w) + lw

Area of the patio
= (Area of the pool (with the patio)) - (Area of the pool (w/o the patio))
= (4x² + 2x(l + w) + lw) - lw
Area of the patio = 4x² + 2x(l + w)

Since the area of the patio is equal to the area of the surface of the pool, the area of the patio is equal to the area of the pool without the patio. In terms of the equation,

Area of the patio = Area of the pool (w/o the patio)
4x² + 2x(l + w) = lw
4x² + 2x(l + w) - lw = 0 (1)

Let

a = numerical coefficient of x² = 4
b = numerical coefficient of x = 2(l + w)
c = constant term = -lw

Then using quadratic formula, the roots of the equation 4x² + 2x(l + w) - lw = 0 is given by

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\\ = \frac{-2(l + w) \pm \sqrt{(2(l + w))^2 - 4(4)(-lw)}}{2(4)} 
\\ = \frac{-2(l + w) \pm \sqrt{(4(l + w)^2) + 16lw}}{8} 
\\ = \frac{-2(l + w) \pm \sqrt{(4(l^2 + 2lw + w^2) + 4(4lw)}}{8}
\\ = \frac{-2(l + w) \pm \sqrt{(4(l^2 + 2lw + w^2 + 4lw)}}{8}
\\ = \frac{-2(l + w) \pm \sqrt{(4(l^2 + 6lw + w^2)}}{8}$
$= \frac{-2(l + w) \pm 2\sqrt{l^2 + 6lw + w^2}}{8} \\= \frac{2}{8}(-(l + w) \pm \sqrt{l^2 + 6lw + w^2}) \\x = \frac{1}{4}(-(l + w) \pm \sqrt{l^2 + 6lw + w^2}) \\\boxed{x = \frac{1}{4}\left(-(l + w) + \sqrt{l^2 + 6lw + w^2} \right) \text{ or }}
\\\boxed{x = -\frac{1}{4}\left((l + w) + \sqrt{l^2 + 6lw + w^2} \right)}$

Since $(l + w) + \sqrt{l^2 + 6lw + w^2} \ \textgreater \ 0$ , $-\frac{1}{4}\left((l + w) + \sqrt{l^2 + 6lw + w^2}\right)$ is negative. Since x represents the patio width, x cannot be negative. Hence, the patio width is given by

$\boxed{x = \frac{1}{4}\left(-(l + w) + \sqrt{l^2 + 6lw + w^2} \right)}$

7 0

3 years ago

Construct a truth table for (p ˄ ⌐q) ↔ (p ˄ q). Explain how this truth table shows whether this statement is a tautology, and co

lara [203]

It's contingency, because for some values of p and q it's true, and for the other values, it's false.

4 0

4 years ago

Cameron is painting one wall of his dining room. It is

Harman [31]

Answer:

me name is cameron

Step-by-step explanation:

6 0

3 years ago

If x varies directly with y and y=12 when x=4,what is the value of y when x=-3

Aneli [31]

Answer:

-9

Step-by-step explanation:

If x varies directly with y, we can write an equation like: x = ky, where k is some constant. We want to solve for k first, so let's use the given numbers of y = 12 and x = 4:

x = ky

4 = 12k

k = 1/3

Now, our equation looks like this: x = (1/3)y. We want to find the value of y when x = -3, so plug -3 in for x:

x = (1/3)y

-3 = (1/3)y

y = -9

Thus, the answer is -9.

Hope this helps!

3 0

3 years ago

Read 2 more answers