Enny’s mother is 5 years older than twice Jenny's age. The sum of their ages is 62 years. This is represented by the equation x
2 answers:
Answer:
Jenny´s age is 19 and her mother is 43.
Step-by-step explanation:
1. Plug in the first value of the set:
41 is different from 62, so Jenny isn´t 12 years old.
2. Plug in the second value of the set:
50 is different from 62, so Jenny isn´t 15 years old.
3. Plug in the third value of the set:
59 is different from 62, so Jenny isn´t 18 years old.
4. Plug in the fourth value of the set:
Therefore Jenny´s 19 years old.
5. Calculate Jenny´s mother age:
As the sum of their ages is 62 ages, we have the following equation:
where
x=Jenny´s age
y=Jenny´s mother age
Replacing the Jenny´s age we have:
Solving for y:
Therefore Jenny's mother age is 43 years old.
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Check the picture below.
now, we know that the slanted legs are congruent, since it's an isosceles trapezoid, we also know that the bases are the parallel sides, so, the "altitude" or distance from those bases are the same length, for each of those triangles in the picture.
now, the bases are parallel, that means the altitude segment is perpendicular to the base, the longest side at the bottom, so, we end up with a right-triangle that has a Hypotenuse and a Leg, equal to the other triangle's.
thus, by the HL theorem for right triangles, both of those triangles are congruent, and if the triangles are congruent, all their sides are also, including the ones on the base.
now, we know that the slanted legs are congruent, since it's an isosceles trapezoid, we also know that the bases are the parallel sides, so, the "altitude" or distance from those bases are the same length, for each of those triangles in the picture.
now, the bases are parallel, that means the altitude segment is perpendicular to the base, the longest side at the bottom, so, we end up with a right-triangle that has a Hypotenuse and a Leg, equal to the other triangle's.
thus, by the HL theorem for right triangles, both of those triangles are congruent, and if the triangles are congruent, all their sides are also, including the ones on the base.
The cat will take 0.8 seconds to catch up with the mouse
Step-by-step explanation:
Given:
The distance between the cat and the mouse = 4 feet
cat's speed = 17 feet per second.
mouse's speed = 12 feet per second
To Find:
how long will it take the cat to catch up with the mouse = ?
Solution:
We know that
distance = speed x time
Rewriting the equation for time we get
time =
now we know that distance is 4 feet
and the speed is 17 -12 = 5 feet per second
Thus the time is
=
= 0.8 seconds