Answer:
see explanation
Step-by-step explanation:
All of these questions use the external angle theorem, that is
The external angle of a triangle is equal to the sum of the 2 opposite interior angles.
18
∠3 = 43° + 22° = 65°
19
∠2 + 71 = 92 ( subtract 71 from both sides )
∠2 = 21°
20
90 + ∠4 = 123 ( subtract 90 from both sides )
∠4 = 33°
21
2x - 15 + x - 5 = 148
3x - 20 = 148 ( add 20 to both sides )
3x = 168 ( divide both sides by 3 )
x = 56
Hence ∠ABC = x - 5 = 56 - 5 = 51°
22
2x + 27 + 2x - 11 = 100
4x + 16 = 100 ( subtract 16 from both sides )
4x = 84 ( divide both sides by 4 )
x = 21
Hence ∠JKL = 2x - 11 = (2 × 21) - 11 = 42 - 11 = 31°
Answer:
Step-by-step explanation:
A. Scale factor
When you dilate an object by a scale factor, you multiply its line lengths by the same number.
If EF/AB = 13/7, the scale factor is 13/7.
B. Length of EF
C. Area of EFGH
If the lengths in a shape are all multiplied by a scale factor, then the areas will be multiplied by the scale factor squared.
ABCD is dilated by a scale factor of 13/7, so its area is dilated by a scale factor of
The area of its dilated image EFGH is
Answer:
No, the two sets are not disjoint.
Step-by-step explanation:
Set of triangular numbers to 50: 1, 3, 6, 10, 15, 21, 28, 36, 45
Set of square numbers to 50: 1, 4, 9, 16, 25, 36, 49
They have 1 and 36 in common, so they are not disjoint, or in other words, they have some of the same numbers.
Answer:
Step-by-step explanation:
2.5 = 5 * .5
1 = 1
70 = 2 * 5 * 7
LCM = 2 * 5 * 7
If you include the 1/2, you will reduce the LCM to 35, but 70 will be left out of the LCM.
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