Answer:
15
Step-by-step explanation:
Distance between two points is = √(x2 - x1)² + (y2 - y1)²
x1 = -5, y1 = 4; x2 = 7, y2 = -5
|PQ| = √(7 - (-5))² + (-5 - 4)²
|PQ| = √(7 + 5)² + (-9)²
|PQ| = √(12)² + 81
|PQ| = √144 + 81
|PQ| = √225
|PQ| = 15
Answer:
B.) 54π units²
Step-by-step explanation:
First, we need to find the height of the cone. We can do this using the Pythagreom Theorem.
a² + b² = c² <----- Pythagreom Theorem
3² + b² = 15² <----- Insert side lengths
9 + b² = 225 <----- Solve 3² and 15²
b² = 216 <----- Subtract 9 from both sides
b = 14.7 units <---- Take square root of 216
Now, we can use the surface area of a right cone equation to find the final answer.
r = 3 units
h = 14.7 units
SA = πr(r + √(h² + r²)) <----- Surface Area equation
SA = π(3)(3 + √(14.7² + 3²)) <----- Insert values
SA = π(3)(3 + √(216 + 9)) <----- Solve 14.7² and 3²
SA = π(3)(3 + √225) <----- Add 216 and 9
SA = π(3)(3 + 15) <----- Take square root of 225
SA = π(3)(18) <----- Add 3 and 15
SA = 54π units² <----- Multiply 3 and 18
Answer:
See proof below
Step-by-step explanation:
Two triangles are said to be congruent if one of the 4 following rules is valid
- The three sides are equal
- The three angles are equal
- Two angles are the same and a corresponding side is the same
- Two sides are equal and the angle between the two sides is equal
Let's consider the two triangles ΔABC and ΔAED.
ΔABC sides are AB, BC and AC
ΔAED sides are AD, AE and ED
We have AE = AC and EB = CD
So AE + EB = AC + CD
But AE + EB = AB and AC+CD = AD
We have
AB of ΔABC = AD of ΔAED
AC of ΔABC = AE of ΔAED
Thus two sides the these two triangles. In order to prove that the triangles are congruent by rule 4, we have to prove that the angle between the sides is also equal. We see that the common angle is ∡BAC = ∡EAC
So triangles ΔABC and ΔAED are congruent
That means all 3 sides of these triangles are equal as well as all the angles
Since BC is the third side of ΔABC and ED the third side of ΔAED, it follows that
BC = ED Proved
2y+3x-5x^2-g contains 4 terms that cannot be further simplified without know the values for the variables y, x, and g. Although 3x and -5x^2 contain the same variable x, since they have have different exponents, we can not directly add them together without knowing the value of x.
The answer is 4.
