From the figure, we can conclude that the little triangle is an isosceles triangle, the greatest angle is 90 because ∠A = 90 and they are supplementary, therefore, using the triangle sum theorem:
Original coordinates of the points:
A (8,15) ; B (12,13) ; C (8,10)
Dilated scale factor of 3.
A ⇒ 3x = 3(8) = 24 ; 3y = 3(15) = 45 ⇒ A' (24,45)
B ⇒ 3x = 3(12) = 36 ; 3y = 3(13) = 39 ⇒ B' (36, 39)
C ⇒ 3x = 3(8) = 24 ; 3y = 3(10) = 30 ⇒ C' (24, 30)
The given image forms a right triangle. So, I'll get the short leg and long leg of the right triangle to solve for the hypotenuse, length of CB.
Short leg: y value of B and C
39 - 30 = 9
Long leg: x value of B and C
36 - 24 = 12
a² + b² = c²
9² + 12² = c²
81 + 144 = c²
225 = c²
√225 = √c²
15 = c
The length of CB is 15 units.
Answer:
x≈ 3.2056
Step-by-step explanation:
Set both sides by log. Then, solve for x.
1. 14^(x + 1) = 36
(x + 1)log(14) = log(36)
x + 1 = log(36)/log(14) . . . Divide both sides by log(14)
x = log(36)/log(14) - 1 . . . . Subtract both sides by 1.
x ≈ 0.3579 . . . . . . . . . . . .Use calculator to simplify the expression.
Note that the second problem is similar to the first.
2. 12^(y - 2) = 20
(y - 2)log(12) = log(20)
y - 2 = log(20)/log(12)
y = log(20)/log(12) + 2
y ≈ 3.2056
<h3>Answer: 10</h3>
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Work Shown:
First add up all the ages
9+13+9+10+10+9+10+10+11+9 = 100
Then divide that sum by 10, since there are 10 values we added up
100/10 = 10
The average age is 10 years old.
Answer:
15 I just stared so I am bad but I think I am correct
