Please solve it <br><br> it's simultaneous equation involving logarithm

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

3 years ago

Answer nowwwwwwwwwwwwwwwwwwwwwwwwwwww

krok68 [10]

Answer:

7/6

Step-by-step explanation:

(7x/12)/(x/2)

=7/6

8 0

2 years ago

Read 2 more answers

Which is the best first step when solving the following system of equations? x + y = 3. 4 x minus y = 7. Multiply the first equa

Kryger [21]

Answer:

Multiply the first equation by 4.

Step-by-step explanation:

4(x+y=3) which gives

4x+4y=12

and

4x-y=7

Then subtract the two equations and the x variable will be eliminated.

6 0

3 years ago

Read 2 more answers

Determine which equations have the same solution set as StartFraction 2 Over 3 EndFraction minus x plus StartFraction 1 Over 6 E

Lina20 [59]

Answer:

A, B, F

Step-by-step explanation:

2/3 - x + 1/6 = 6x

Collect like terms

2/3 + 1/6 = 6x + x

(4+1) / 6 = 7x

5/6 = 7x

x = 5/6 ÷ 7

= 5/6 × 1/7

x = 5/42

a) 4 - 6x + 1 = 36x

4 + 1 = 36x + 6x

5 = 42x

x = 5/42

Equivalent to the last step of the simplification above

b) 5/6 - x = 6x

5/6 = 6x + x

5/6 = 7x

This is equivalent to the third step of the simplification

c) 4 - x + 1 = 6x

4 + 1 = 6x + x

5 = 7x

x = 5/7

Not equivalent to any of the steps in the simplification above

d) 5/6 + x = 6x

5/6 = 6x - x

5/6 = 5x

x = 5/6 ÷ 5

= 5/6 × 1/5

x = 5/30

Not equivalent to any of the steps in the simplification above

e) 5 = 30x

x = 5/30

Not equivalent to any of the steps in the simplification above

f) 5 = 42x

x = 5/42

Equivalent to the last step of the simplification above

4 0

3 years ago

An investor puts $2,500 into a life insurance policy that pays 10% simple annual interest. If no additional investment is made i

Novosadov [1.4K]

Answer:

$3750

Step-by-step explanation:

Amount = principal + interest

Simple interest = Principal *Rate * time/100

Simple interest = 2500*10*5/100

Simple interest = 25*50

Simple interest = $1250

Amount = $2500+$1250

Amount after 5 years is $3750

4 0

3 years ago

Please solve it it's simultaneous equation involving logarithm