<h3>#a</h3>
∠XBC= 55°
[ By corresponding angles]
- Corresponding angle are the angles which hold sane relative position as another angle but somewhere else on the figure.

<h3>#b</h3>
∵ XB and XC are equal, ∠XBC=∠BCX
<h3>Now, With angle sum property of triangle: </h3>

Answer:
second and fourth option
Step-by-step explanation:
the <em>discriminant </em>of a quadratic equation is the easiest way to know how many solutions there will be
(discriminant: b²- 4ac)
{a discriminant of 0 means 1 solution; discriminant < 0 means no real roots, discriminant > 0 means two real roots }
so, we can quickly run b² - 4ac for each equation provided:
(note: ax² + bx + c is the formatting we use to find a, b, and c)
8² - 4(-9)(-8)
64 - 288 = -224
4² - (4)(1)(4)
16 - 16 = 0
-1² - (4)(-10)(-9)
-1 - 360 = -361
-6² - (4)(3)(3)
36 - 36 = 0
So, because the second and fourth options listed have a discriminant of 0, they have 1 real solution
hope this helps!! have a lovely day :)
Answer:
<em>Thus, the dimensions of the metal plate are 10 dm and 8 dm.</em>
Step-by-step explanation:
For a quadratic equation:

The sum of the roots is -b and the product is c. Note the leading coefficient is 1.
We know the perimeter of the rectangular metal plate is 36 dm and its area is 80 dm^2. Being L and W its dimensions, then:
P=2(L+W)=36
A=L.W=80
Note both formulas are closely related to the roots of the quadratic equation, we only need to adjust the data for the perimeter to be exactly the sum of L+W and not double of it.
Thus we use the semi perimeter instead as P/2=L+W=18
The quadratic equation is, then:

Factoring by finding two numbers that add up to 18 and have a product of 80:

The solutions to the equation are:
x=10, x=8
Thus, the dimensions of the metal plate are 10 dm and 8 dm.
Answer:
Step-by-step explanation:
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