Answer:
J - Janeta's age M - mother's age
A) (J-5) = .2 * (M-5)
B) J = (1/3) * M
Subtracting 5 from both sides of B:
B) J -5 = (1/3)M -5
then we substitute the right side of this into the left side of A and we get
(1/3)M -5 = .2 M -1
.333333333333M -5 = .2M -1
.1111111111111111111M = 4
Mother's Age = 36
Janeta's Age = 12
Step-by-step explanation:
Answer:
Approximately 
.
Step-by-step explanation:
The velocity of an object is the rate at which its position changes. In other words, the velocity of an object is equal to the first derivative of its position, with respect to time.
Note that the arrow here is launched upwards. (Assume that the effect of wind on Mars is negligible.) There would be motion in the horizontal direction. The horizontal position of this arrow will stays the same. On the other hand, the vertical position of this arrow is the same as its height: 
.
Apply the power rule to find the first derivative of this 
with respect to time 
.
By the power rule:
- the first derivative of (same as
- the first derivative of
(same as to the second power) with respect to
Therefore:
![\begin{aligned}\frac{dy}{d t} &= \frac{d}{d t}\left[62 \, t - 1.86\, t^2\right] \\ &= 62\,\left(\frac{d}{d t}\left[t\right]\right) - 1.86\, \left(\frac{d}{d t}\left[t^2\right]\right) \\ &= 62 \times 1 - 1.86\times\left(2\, t) = 62 - 3.72\, t\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cfrac%7Bdy%7D%7Bd%20t%7D%20%26%3D%20%5Cfrac%7Bd%7D%7Bd%20t%7D%5Cleft%5B62%20%5C%2C%20t%20-%201.86%5C%2C%20t%5E2%5Cright%5D%20%5C%5C%20%26%3D%2062%5C%2C%5Cleft%28%5Cfrac%7Bd%7D%7Bd%20t%7D%5Cleft%5Bt%5Cright%5D%5Cright%29%20-%201.86%5C%2C%20%5Cleft%28%5Cfrac%7Bd%7D%7Bd%20t%7D%5Cleft%5Bt%5E2%5Cright%5D%5Cright%29%20%5C%5C%20%26%3D%2062%20%5Ctimes%201%20-%201.86%5Ctimes%5Cleft%282%5C%2C%20t%29%20%3D%2062%20-%203.72%5C%2C%20t%5Cend%7Baligned%7D)
.
In other words, the (vertical) velocity of this arrow at time would be 
meters per second.
Evaluate this expression for 
to find the (vertical) velocity of this arrow at that moment: 
.
Answer:
The lateral surface area of a prism is the sum of the areas of its lateral faces. The total surface area of a prism is the sum of the areas of its lateral faces and its two bases.
Answer:
ABC - AAS
DEF - not enough information
GHI - not enough information
JKL - SAS
Step-by-step explanation:
SAS postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.
AAS postulate states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent.
HL postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.
ASA postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
SSS postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
1. In triangles MNO and ABC, there are two congruent sides and non-included angle - AAS
2. In triangles MNO and DEF, there are two congruent sides - there is not enough information
3. In triangles MNO and GHI, there are three congruent angles - there is not enough information
4. In triangles MNO and JKL, there are two congruent sides and included angle - SAS
