Answer:
8) 10°
9) X can not be determined.
10) 10°
11) 12 units.
Step-by-step explanation:
8) The three sides of the given triangle are equal. Hence, the triangle is an equilateral triangle, hence each angle will be 60°.
So, 6x = 60°
⇒ x = 10°.
9) The three angles of the given triangle are equal. Hence, the triangle is an equilateral triangle, hence each side will be equal.
So, 6x - 5 = 6x
So, x can not be determined from this equation.
10) Δ KLM is equilateral, so, KN will bisect ∠ MKL. So, ∠ NKL = 30°
Hence, 3x = 30°
⇒ x = 10°
11) In Δ XYZ, XZ = XY , so, ∠ Z = ∠ Y.
Again, ∠ X is given to be 60°.
Therefore, each angle is 60°.
So, the triangle XYZ is equilateral, and each side will be equal.
So, 3x + 8 = 4x - 4
⇒ x = 12 units. (Answer)
Answer:
Step-by-step explanation:
True
Answer:
m∠1=103°
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
An exterior angle of a triangle is equal to the sum of the opposite interior angles
so
In this problem
m∠1=m∠2+m∠3
substitute the given values
m∠1=31°+72°=103°
Answer:
x ≤ -11.25 or x > -8.75
Step-by-step explanation:
The graph here shows a disjunction compound inequality, in which either of the statements is true. That is for the compound inequality to be true, either one or the other statement is true. The word "OR" is used in stating this inequality.
On the graph, the directed line to our left has a full circle which starts at -11.25.
This means x ≤ -11.25.
The other directed line to our right has an empty circle, and starts at -8.75.
This means x > -8.75.
✅The compound inequality representing the graph will be written as:
x ≤ -11.25 or x > -8.75
Answer:
455 or 680, depending
Step-by-step explanation:
If we assume the three choices are different, then there are ...
15C3 = 15·14·13/(3·2·1) = 35·13 = 455
ways to make the pizza.
___
If two or three of the topping choices can be the same, then there are an additional ...
2(15C2) +15C1 = 2·105 +15 = 225
ways to make the pizza, for a total of ...
455 + 225 = 680
different types of pizza.
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There is a factor of 2 attached to the number of choices of 2 toppings, because you can have double anchovies and tomato, or double tomato and anchovies, for example, when your choice of two toppings is anchovies and tomato.
_____
nCk = n!/(k!(n-k)!)
