Answer:
15°
Step-by-step explanation:
Since P is on the median of ΔABC, it is equidistant from points B and C as well as from C and Q. Thus, points B, C, and Q all lie on a circle centered at P. (See the attached diagram.)
The base angles (B and C) of triangle ABC are (180° -30°)/2 = 75°. This means arc QC of the circle centered at P has measure 150°. The diameter of circle P that includes point Q is defined to intersect circle P at R.
Central angle RPC is the difference between arcs QR and QC, so is 180° -150° = 30°. Inscribed angle RQC has half that measure, so is 15°. Angle PQC has the same measure as angle RQC, so is 15°.
Angle PQC is 15°.
Answer:
The expression for the total cost is x = 19.99 + 0.99n .
Step-by-step explanation:
Let us assume that the total cost be x.
As given
Sophia pays $19.99 membership fee for an online music store.
If sophia purchases n songs for $0.99 each .
Than the expression becomes
Total cost = Membership fee + Cost of n songs
x = 19.99 + 0.99n
Here n represented the number of songs.
12x - 8y = -12
6x + 4y = -30
Multiply the 2nd equation by 2, to make the Y coefficients opposite:
6x + 4y = -30 x 2 = 12x + 8y = -60
Now add the two equations:
12x -8y = -12 + 12x +8y = -60
= 24x = -72
Divide bothe sides by 24 to solve for x:
x = -72/24
x = -3
Now replace x with -3 in the first equation to solve for y:
12(-3) - 8y = -12
-36 - 8y = -12
Add 36 to each side:
-8y = 24
Divide both sides by -8 to solve for y:
y = 24 / -8
y = -3
X = -3 and y = -3
(-3,-3)
Answer:
5x3 + 3x2
Step-by-step explanation:
The volume formula for a cylinder is :
V= (pi)(r^2)(h)
So r= d/2 where d = 16mm so r= 8mm h is given as equaling 5.7mm
Now just plug it into the formula.
V=(pi)(8^2)(5.7) = 364.8 pi mm = 1146.053mm
