Ask question

Ask question

All categories

3 years ago

11

A rectangle flower garden has a length that is 7 feet less than twice it's width. A 5-ft brick border is added around the garden

, and the area of the garden and the brick border is a total of 195 square ft. Find the dimensions of the garden without the brick border. L=? W=?

1 answer:

Delvig [45]3 years ago

7 0

Ok so if we call the width x then the length is 2x-7
Now by adding a 5 foot brick border around the edge the new dimensions are:
x+10 and 2x+3
Now we can form an equation to solve:
(x+10)(2x+3)=195
2x²+23x+30=195
2x²+23x-165=0
Now we can solve this for x
(2x+33)(x-5)=0
So x=-33/2 or x=5
As x cannot be less than 0 x must be equal to 5
So the dimensions of the garden are 5 feet by 3 feet

You might be interested in

16x - 5y = -33<br> 16x + y = -51

timofeeve [1]

Use the elimination process

6 0

2 years ago

Read 2 more answers

Find x?<br> In 3x - In(x - 4) = ln(2x - 1) +ln3

earnstyle [38]

Answer:

$x = \displaystyle \frac{5 + \sqrt{17}}{2}$ .

Step-by-step explanation:

Because $3\, x$ is found in the input to a logarithm function in the original equation, it must be true that $3\, x > 0$ . Therefore, $x > 0$ .

Similarly, because $(x - 4)$ and $(2\, x - 1)$ are two other inputs to the logarithm function in the original equation, they should also be positive. Therefore, $x > 4$ .

Let $a$ and $b$ represent two positive numbers (that is: $a > 0$ and $b > 0$ .) The following are two properties of logarithm:

$\displaystyle \ln (a) + \ln(b) = \ln\left(a \cdot b\right)$ .

$\displaystyle \ln (a) - \ln(b) = \ln\left(\frac{a}{b}\right)$ .

Apply these two properties to rewrite the original equation.

Left-hand side of this equation:

$\begin{aligned}&\ln(3\, x) - \ln(x - 4)= \ln\left(\frac{3\, x}{x -4}\right)\end{aligned}$

Right-hand side of this equation:

$\ln(2\, x- 1) + \ln(3) = \ln\left(3 \left(2\, x - 1\right)\right)$ .

Equate these two expressions:

$\begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned}$ .

The natural logarithm function $\ln$ is one-to-one for all positive inputs. Therefore, for the equality $\begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned}$ to hold, the two inputs to the logarithm function have to be equal and positive. That is:

$\displaystyle \frac{3\ x}{x - 4} = 3\, (2\, x - 1)$ .

Simplify and solve this equation for $x$ :

$x^2 - 5\, x + 2 = 0$ .

There are two real (but not rational) solutions to this quadratic equation: $\displaystyle \frac{5 + \sqrt{17}}{2}$ and $\displaystyle \frac{5 - \sqrt{17}}{2}$ .

However, the second solution, $\displaystyle \frac{5 - \sqrt{17}}{2}$ , is not suitable. The reason is that if $x = \displaystyle \frac{5 - \sqrt{17}}{2}$ , then $(x - 4)$ , one of the inputs to the logarithm function in the original equation, would be smaller than zero. That is not acceptable because the inputs to logarithm functions should be greater than zero.

The only solution that satisfies the requirements would be $\displaystyle \frac{5 + \sqrt{17}}{2}$ .

Therefore, $x = \displaystyle \frac{5 + \sqrt{17}}{2}$ .

7 0

2 years ago

What is the value of T?

galina1969 [7]

H
You had it right...................

3 0

2 years ago

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

KiRa [710]

Answer:

1863 $meters^{2}$

Step-by-step explanation:

( 23 x 12 ) x 2 = 552

69 x 19 = 1311

1311

<u>+552</u>

= 1863 $meters^{2}$

8 0

2 years ago

Can someone help me .

insens350 [35]

Y-y1=m(x-x1)
m= slope =-3
y-y1=-3(x-x1),
y1=-7, x1=5
y--7=-3(x-5)
y+7=-3(x-5) this is C

7 0

3 years ago