If you need to cut 5 pieces of glass from a 14 feet length, how long should each piece be

A farmer plans to fence a rectangular corral. The diagonal distance from one corner of the corral to the opposite corner is five

garik1379 [7]

Answer:

Length of diagonal is 7.3 yards.

Step-by-step explanation:

Given: The diagonal distance from one corner of the corral to the opposite corner is five yards longer than the width of the corral. The length of the corral is three times the width.

To find: The length of the diagonal of the corral.

Solution: Let the width of the rectangular garden be <em>x</em> yards.

So, the length of the diagonal is $x+5$

width of the rectangular corral is $3x$

We know that the square of the diagonal is sum of the squares of the length and width.

So,

$(3x)^{2} +x^{2} =(x+5)^{2}$

$9x^{2} +x^{2} =x^{2}+10x+25$

$9x^{2}-10x-25=0$

$x=\frac{-b\pm\sqrt{b^{2} -4ac} }{2a}$

$x=\frac{10\pm\sqrt{(-10)^{2} -4(9)(-25)} }{2(9)}$

$x=\frac{10\pm\sqrt{100}}{18}$

Since, side can't be negative.

$x=\frac{5}{9}+\frac{5}{9}\sqrt{10}$

Now, length of the diagonal is

$5+\frac{5}{9}+\frac{5}{9}\sqrt{10}$

Hence, length of diagonal is 7.3 yards.

4 0

2 years ago

Joe's Painting charges $100 plus $20 per hour to paint the exterior of your home. Steve's Painting charges $120 plus $15 per hou

Tanzania [10]

Joe's Painting: 20x + 100 = y

Steve's Painting: 15x + 120 = y

x = hours worked

y = total income

We can find when the two equations intersect by making them equal to each other. That means we put an equal sign in the middle. So, it would look something like this:

20x + 100 = 15x + 120

First, we have to move the 100 by subtracting it from both sides.

20x = 15x + 120 - (100)

20x = 15x + 20

Then, we need to move the 15x by subtracting it from both sides.

20 - (15x) = 20

5x = 20

Lastly, we need to divide 5 from both sides.

5x = 20/5

x = 4

Therefore, Joe and Steve would have to work for 4 hours in order for their models to be equal to each other.

5 0