Step-by-step explanation:
in the given figure ,
the two sides of the triangle are equal , so their opposite angles are equal .
so , we get
=》Angle RPQ = Angle PRQ = 65°
and some of interior angels of the triangle measures 180°
so,
=》RPQ + PRQ + RQP = 180°
=》65° + 65° + RQP = 180°
(Because RPQ = PRQ = 65°)
=》130° + RQP = 180°
=》RQP = 50°
Answer:
C, D, E
Step-by-step explanation:
The numbers of marbles are:
- Janae - m;
- Jerome - m;
- Gwen - 4(m+2);
- John - 8m+4.
Janae, Jerome, and Gwen combined have
m + m + 4(m+2) = m + m +4m + 8 =6m + 8 marbles.
If John has more marbles than Janae, Jerome, and Gwen combined, then
![8m+4>6m+8,\\ \\8m-6m>8-4,\\ \\2m>4,\\ \\m>2.](https://tex.z-dn.net/?f=8m%2B4%3E6m%2B8%2C%5C%5C%20%5C%5C8m-6m%3E8-4%2C%5C%5C%20%5C%5C2m%3E4%2C%5C%5C%20%5C%5Cm%3E2.)
So, possible answers are
- Janae and Jerome each have 3 marbles;
- Janae and Jerome each have 4 marbles;
- Janae and Jerome each have 5 marbles.
First find the new coordinates for P and Q after the translations:
P'(2 + 3, 4 - 4) = P'(5, 0)
Q'(-3 + 3, 2 - 4) = Q'(0, -2)
Now, find the slope from this:
(0 - (-2))/(5 - 0) = 2/5
The slope has remained the same. It is important to note that after any translation, the slope will always remain the same. However, this is not always so for rotations and reflections.
Y = 3x + b
Now plug in points
-7 = 3(-1) + b
-7 = -3 + b
b = -4
The y intercept is -4