Solve for y. show work. 4(y+3)−2y+7

Mathematics

2 answers:

Inga [223]3 years ago

6 0

Answer: 2y + 19

Explanation: (4 • (y + 3) - 2y) + 7
4y + 19 -2y
2y + 19
Hope this helps :)

olga_2 [115]3 years ago

5 0

Dude I don’t feel like working

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The hypotenuse of a right triangle is 6 cm and one side is 2 cm longer than the other side. Find the length of each side to one

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Answer:

The two legs of the right triangle are approximately 3.1 cm and 5.1 cm and the hypotenuse is 6 cm.

Step-by-step explanation:

Let x be one leg of the right triangle.

Since the other leg is two centimeters longer, it can be represented by the expression:

$x + 2 \text{ cm}$

According to the Pythagorean Theorem, for a right triangle:

$a^2 + b^2 = c^2$

Where c is the hypotenuse and a and b are the two legs.

The hypotenuse is given to be 6 cm and the two legs are x and (x + 2). Hence:

$(x)^2 + (x+2)^2 = 6^2$

Solve for x. Simplify:

$x^2 + (x^2 + 4x + 4) = 36$

Simplify:

$2x^2 + 4x + 4 = 36$

Subtract:

$2x^2 + 4x - 32 =0$

Divide:

$x^2 + 2x - 16 = 0$

The equation is not factorable, so we can consider using the quadratic formula:

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

In this case, a = 1, b = 2, and c = -16. Substitute:

$\displaystyle x= \frac{-(2)\pm\sqrt{(2)^2-4(1)(-16)}}{2(1)}$

And evaluate:

$\displaystyle \begin{aligned}x &= \frac{-2\pm\sqrt{68}}{2} \\ \\ &= \frac{-2\pm\sqrt{4\cdot 17}}{2} \\ \\ &= \frac{-2\pm2\sqrt{17}}{2} \\ \\ &= -1 \pm \sqrt{17} \end{aligned}$