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sergiy2304 [10]
3 years ago
7

In the diagram below, the perimeter of the triangle is equal to the perimeter of the square. What is the length of a side of the

square?

Mathematics
1 answer:
kondaur [170]3 years ago
3 0

The perimeter of each is the sum of the lengths of its sides.

Triangle Perimeter = 16 + 4x-3 +3x = 7x+13

Square Perimeter = 2x +2x +2x +2x = 8x

If these are equal, you have

7x+13=8x\\\\13=x\qquad \mbox{subtract 7x}\\\\26=2x\qquad \mbox{multiply by 2}

The length of a side of the square is 26 units.

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2.<br>√3x + 7 + √x + 1 =2​
taurus [48]

Answer:

  x = -1

Step-by-step explanation:

The usual approach to these is to square the radicals until they are gone.

  \displaystyle\sqrt{3x+7}+\sqrt{x+1}=2\\\\(3x+7) +2\sqrt{(3x+7)(x+1)}+(x+1) = 4\qquad\text{square both sides}\\\\2\sqrt{(3x+7)(x+1)}=-4x-4\qquad\text{subtract $4x+8$}\\\\(3x+7)(x+1)=(-2x-2)^2\qquad\text{divide by 2, square again}\\\\3x^2+10x +7=4x^2+8x+4\qquad\text{simplify}\\\\x^2-2x-3=0\qquad\text{subtract the left expression}\\\\(x-3)(x+1)=0\qquad\text{factor}\\\\x=3,\ x=-1\qquad\text{solutions to the quadratic}

Each time the equation is squared, the possibility of an extraneous root is introduced. Here, x=3 is extraneous: it does not satisfy the original equation.

The solution is x = -1.

_____

Using a graphing calculator to solve the original equation can avoid extraneous solutions. The attachment shows only the solution x = -1. Rather than use f(x) = 2, we have rewritten the equation to f(x)-2 = 0. The graphing calculator is really good at showing the function values at the x-intercepts.

5 0
3 years ago
Write an equation of the line through the given points<br><br><br>(0, 4), (3, 3)​
andre [41]

Hello! :)

Step-by-step explanation:

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\frac{3-4}{3-0}=\frac{-1}{3}=-\frac{1}{3}

<u><em>Therefore, the slope is -1/3.</em></u>

<u><em>-1/3 is the final answer.</em></u>

Hope this helps!

Have a nice day! :)

:D

-Charlie

Thank you!

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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