Find the value of x in each case. Give reasons to justify your solutions! answer ASAP

Mathematics

1 answer:

schepotkina [342]3 years ago

5 0

Answer:

x = 19

Step-by-step explanation:

YZ || XW, so ∠Y = ∠W

if ∠Y = ∠W, then ∠W = 2x

since the sum of the angles of a triangle is 180 degrees:

(3x-5) + 2x + 90 = 180

x = 19

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Select the procedure that can be used to show the converse of the Pythagorean theorem using side lengths chosen from 6 feet, 8 f

zhannawk [14.2K]

<h3>Answer: Choice A</h3>

========================================================

Explanation:

The left side $6^2+8^2$ simplifies to $100$ since $6^2+8^2 = 36+64 = 100$

The right side is also 100 because $10^2 = 100$

So $6^2+8^2 = 10^2$ is a true equation because both sides are the same number.

Therefore, a triangle with sides 6,8,10 is a right triangle. The hypotenuse 10 is the longest side opposite the 90 degree angle. In other words, the 90 degree angle is between the sides 6 ft and 8 ft.

So this is why choice A is the final answer.

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Choice B is false because the inequality $8^2+10^2 < 11^2$ becomes $164 < 121$ which is also false. Even if that inequality was true, we can't use it to form a right triangle. We need both sides to be equal.

Choice C is false because we need to have both sides equal to the same number. We need to have $a^2+b^2 = c^2$ to be true if we want a right triangle with sides a,b,c.

Choice D is false because of the phrasing "Draw any two of the sides with a right angle between them". The 90 degree angle must go between the 6 and the 8, and nowhere else.

5 0

2 years ago

What are the roots of the quadratic equation x2+2x=-5

stiks02 [169]

Answer:

x = -1 +/-2i

Step-by-step explanation:

Write the equation in standard form to find the roots, also known as the solutions, zeros, or x-intercepts, of the quadratic.

x² + 2x + 5 = 0

Use the quadratic formula by substituting a= 1, b = 2 and c = 5.

$x = \frac{-2 +/- \sqrt{(-2)^2 - 4(1)(5)} }{2(1)} = \frac{-2 +/-\sqrt{4 -20 } }{2} = \frac{-2 +/-\sqrt{-16 } }{2} = \frac{-2 +/-4i }{2} = -1 +/-2i$