Answer:
Yes, the shapes are similar. Note, the angles are equivalent and the sides are scales of each other satisfying the requirements for similarly.
Step-by-step explanation:
For a shape to be similar there are two conditions that must be met. (1) Must have equivalent angles (2) Sides must be related by a scalar.
In the two triangles presented, the first condition is met since each triangle has three angles, 90-53-37.
To test if the sides are scalar, each side must be related to a corresponding side of the other triangle with the same scalar.
9/6 = 3/2
12/8 = 3/2
15/10 = 3/2
Alternatively:
6/9 = 2/3
8/12 = 2/3
10/15 = 2/3
Since the relationship of the sides is the scalar 3/2 (Alternatively 2/3), then we can say the triangles meet the second condition.
Given that both conditions are satisfied, then we can say these triangles are similar.
Note, this is a "special case" right triangle commonly referred to as a 3-4-5 right triangle.
Cheers.
Nearest 100: 543,800
Nearest 1,000: 544,800
Nearest 10,000: 540,800
Answer:
Length=12 inches Width=6 inches
Step-by-step explanation:
X can stand for the width. 2x can stand for the length since it is twice the width. The perimeter would then equal 6x. 6x is equal to 36. Divide by 6 to isolate x. X equals 6 inches. So twice the width would be 12 inches.
Answer:
x=1
Step-by-step explanation:
5x-4=9
5x=9-4
5x=5
x=1
Answer:
Sum of the first 15 terms = -405
Step-by-step explanation:
a + 3d = -15 (1)
a + 8d = -30 (2)
Where,
a = first term
d = common difference
n = number of terms
Subtract (1) from (1)
8d - 3d = -30 - (-15)
5d = -30 + 15
5d = -15
d = -15/5
= -3
d = -3
Substitute d = -3 into (1)
a + 3d = -15
a + 3(-3) = -15
a - 9 = -15
a = -15 + 9
a = -6
Sum of the first 15 terms
S = n/2[2a + (n − 1) × d]
= 15/2 {2×-6 + (15-1)-3}
= 7.5{-12 + (14)-3}
= 7.5{ -12 - 42}
= 7.5{-54}
= -405
Sum of the first 15 terms = -405
