Given:
C is the circumcenter of ΔPQR
PC = 3x + 7
RC = 5x - 15
QC = 51 - x
To find:
QC
Solution:
All vertices or a triangle are equidistant from its circumcenter.
Let us take .
Add 15 on both sides.
Add x on both sides.
Divide by 6 on both sides, we get
x = 11
Substitute x = 11 in QC.
QC = 51 - 11
= 40
Therefore QC = 40.
For this case we must indicate the inequality represented in the graph.
It is noted that we have a closed point at -1, so the inequality at that point contains equality and is represented by "[". On the other hand, we observe an open point at +3, so inequality does not include equality (does not include +3) and is represented as ")".
So, the interval of the graph is:
This is equivalent to:
Answer:
Option B
Answer:
Step-by-step explanation:
6). Surface area of a triangular prism = Area of the triangular bases + (Perimeter of the triangular base)×height
Area of one triangular base =
=
= 6 km²
Perimeter of the triangular base = (4 + 3 + 5)
= 12 km
Height of the triangular prism = 7 km
Surface area of the given triangular prism = 2(6) + (12)(7)
= 12 + 84
= 96 km²
7). Surface area of a rectangular prism = 2(lb + bh + hl)
Here, l = Length, b = Width and h = Height
By substituting the values from the given question,
l = 9 in, b = 9 in, h = 4 in
Surface area of the rectangular prism = 2(9×9 + 9×4 + 4×9)
= 2(81 + 36 + 36)
= 2(153)
= 306 in²
Answer:
Ginny made a mistake in step 1 when she identified b = 31. It should be b=-31
Step-by-step explanation:
Ginny factored as shown:
ac = –180 and
b = 31
36(–5) = –180 and 36 + (–5) = 31
+ 36x – 5x – 30
6x(x + 6) – 5(x + 6)
(x + 6)(6x – 5)
b is the coefficient of x and from the trinomial , b=-31.
Therefore Ginny made a mistake in step 1 when she identified b = 31. It should be b = –31.
The correct steps are: :
ac = –180 and
b = -31
36(–5) = –180 and -36+5 = -31