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Likurg_2 [28]
3 years ago
8

A farmer builds a fence to enclose a rectangular pasture. He uses 160 feet of fence. Find the total area of the pasture if it is

50 feet long
Mathematics
1 answer:
Feliz [49]3 years ago
6 0

Answer:

  1500 ft²

Step-by-step explanation:

The sum of two adjacent sides of the pasture is half the perimeter (160 ft/2 = 80 ft), so the side adjacent to the 50 ft side will be 80 ft - 50 ft = 30 ft.

The product of adjacent sides of a rectangle gives the area of the rectangle. That area will be ...

  area = (50 ft)(30 ft) = 1500 ft²

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when 6 is subtracted from the square of a number, the result is 5 times the number. Find the negative solution.
sveta [45]

When 6 is subtracted from the square of a number, the result is 5 times the number, then the negative solution is -1

<h3><u>Solution:</u></h3>

Given that when 6 is subtracted from the square of a number, the result is 5 times the number

To find: negative solution

Let "a" be the unknown number

Let us analyse the given sentence

square of a number = a^2

6 is subtracted from the square of a number = a^2 - 6

5 times the number = 5 \times a

<em><u>So we can frame a equation as:</u></em>

6 is subtracted from the square of a number = 5 times the number

a^2 - 6 = 5 \times a\\\\a^2 -6 -5a = 0\\\\a^2 -5a -6 = 0

<em><u>Let us solve the above quadratic equation</u></em>

For a quadratic equation ax^2 + bx + c = 0 where a \neq 0

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

Here in this problem,

a^2-5 a-6=0 \text { we have } a=1 \text { and } b=-5 \text { and } c=-6

Substituting the values in above quadratic formula, we get

\begin{array}{l}{a=\frac{-(-5) \pm \sqrt{(-5)^{2}-4(1)(-6)}}{2 \times 1}} \\\\ {a=\frac{5 \pm \sqrt{25+16}}{2}=\frac{5 \pm \sqrt{49}}{2}} \\\\ {a=\frac{5 \pm 7}{2}}\end{array}

We have two solutions for "a"

\begin{array}{l}{a=\frac{5+7}{2} \text { and } a=\frac{5-7}{2}} \\\\ {a=\frac{12}{2} \text { and } a=\frac{-2}{2}}\end{array}

<h3>a = 6 or a = -1</h3>

We have asked negative solution. So a = -1

Thus the negative solution is -1

6 0
3 years ago
Which of the following are valid names for the given triangle? Check all that apply:
natka813 [3]

Answer:

A, C, E

Step-by-step explanation:

Only letters T, A, and X on the triangle can be used to describe it, regardless of the order they are in.

4 0
2 years ago
Write the ratio as a fraction in simplest form 35 girls: 15 boys
nika2105 [10]

Answer:

7:3

Step-by-step explanation:

think of it as a fraction

6 0
2 years ago
Graph and solve the system <br><br> Y=-3x+3<br> Y=2x-7
guajiro [1.7K]
An equation of the form y=ax+b, where a and b are constants; y and x are variable, is called a linear equation.

They are called "linear" because if we draw all the solutions of such an equation, they form a line. 

This also means that it is enough to:
 
1. find to solutions 
2. plot them on the coordinate axis
3.join those 2 points

and all the solutions of the equation y=ax+b will be on that line.


Thus, to draw line y=-3x+3

let x=0, then y=3, so one solution is (0, 3)

let y=0, then x=1 so a second solution is (1, 0)

(remark we can pick x or y to be any value, then solve for the other)


to draw the second line y=2x-7

let x=0, then y=-7
let x=3, then y=-1


plot these points and join them as shown in the picture.


The solution of the system is the point where the lines intersect, which is
 (2, -3)


8 0
3 years ago
Read 2 more answers
PLEASE HELP!!!!!<br> will mark brainliest!!!!!
PSYCHO15rus [73]

Answer:

x      y

4     7

5     -1

6     -9

5 0
2 years ago
Read 2 more answers
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