Answer:
X is 3
Step-by-step explanation:
15-x=12
X=15-12
X=3
Answer:
226.2 feet
Step-by-step explanation:
The fence around the dog's house is a circle, with a radius of 12 meters.
To calculate the distance the dog runs, we need to find the circumference of that circle, which is given by the formula:
C = 2 π r, since we know r, the calculation is easy:
C = 2 π 12 = 24 π = 75.4 feet.
The dog makes three laps around the circle before calming down... so he runs 3 times 75.4 feet.
Dogs run = 3 x 75.4 ft = 226.2 feet
Answer: After matching each set of conditions with the corresponding relationship between ∆ABC and ∆XYZ and the criterion that proves the relationship the matched pairs are as follows:
1 . AB = XY ,BC = YZ and ∠B ≅ ∠Y ⇒ ΔABC ≅ ΔXYZ by SAS criterion.
2 . AB = XY and ∠A ≅ ∠X and ∠B ≅ ∠Y⇒ ΔABC ≅ ΔXYZ by ASA criterion.
3 . ∠A=∠X,∠B=∠Y and ∠C=∠Z⇒ ΔABC and ΔXYZ are not necessarily congruent.[by AAA similarity criteria both triangles are similar but may not congruent ∵ every congruent triangles have equal sides and equal angles]
4 . AB = XY, BC = YZ and CA = ZX ⇒ ΔABC ≅ ΔXYZ by the SSS criterion.
Answer:
17
Step-by-step explanation:
The short answer is that algebra doesn't work that way. You wouldn't divide *everything* by 2, but every term that contains a factor of 2.
In the expression
2 (6<em>x</em> - 1) + 2 (2<em>x</em> + 5)
both terms have a factor of 2 (the 2 out in front of them). They're the ones that get canceled when dividing by 2:
(2 (6<em>x</em> - 1) + 2 (2<em>x</em> + 5)) / 2 = 2/2 (6<em>x</em> - 1) + 2/2 (2<em>x</em> - 5)
… = 1 (6<em>x</em> - 1) + 1 (2<em>x</em> - 5)
… = (6<em>x</em> - 1) + (2<em>x</em> - 5)
and so on.
Looking ahead, it turns out that the equation is solved by <em>x</em> = 7. This makes 6<em>x</em> - 1 = 41 and 2<em>x</em> + 5 = 19. So the equation is saying that, if you make these replacements,
2×41 + 2×19 = 120
If you divide *everything* on the left by 2, you end up with fractions:
(2/2)×(41/2) + (2/2)×(19/2) = 41/2 + 19/2
but 41 + 19 = 60, so the end result would be 30, but that's not the same as 120/2 = 60.
