Answer:
13). -2x³ + x² + 1 14). x + 10y - 10z 15). -2x³ + x² + 1
Step-by-step explanation:
13). (x³ - x² + 4) - (3x³ - 2x² + 3)
= x³ - x² + 4 - 3x³ + 2x² - 3
= x³ - 3x³ - x² + 2x² - 3 + 4
= -2x³ + x² + 1
14). (3x + 4y - 3z) - (2x - 6y + 7z)
= 3x + 4y - 3z - 2x + 6y - 7z
= 3x - 2x + 4y + 6y - 3x - 7z
= x + 10y - 10z
15). (x³ - x² + 4) - (3x³ - 2x² + 3)
= x³ - x² + 4 - 3x³ + 2x² - 3
= x³ - 3x³ - x² + 2x² + 4 - 3
= -2x³ + x² + 1
9514 1404 393
Explanation:
<h3>8.</h3>
An exterior angle is equal to the sum of the remote interior angles. Define ∠PQR = 2q, and ∠QPR = 2p. The purpose of this is to let us use a single character to represent the angle, instead of 4 characters.
The above relation tells us ...
∠PRS = ∠PQR +∠QPR = 2q +2p
Then ...
∠TRS = (1/2)∠PRS = (1/2)(2q +2p) = q +p
and
∠TRS = ∠TQR +∠QTR . . . . . exterior is sum of remote interior
q +p = (1/2)(2q) +∠QTR . . . . substitute for ∠TRS and ∠TQR
p = ∠QTR = 1/2(∠QPR) . . . . . subtract q
__
<h3>9.</h3>
For triangle ABC, draw line DE parallel to BC through point A. Put point D on the same side of point A that point B is on the side of the median from vertex A. Then we have congruent alternate interior angles DAB and ABC, as well as EAC and ACB. The angle sum theorem tells you that ...
∠DAB +∠BAC +∠CAE = ∠DAE . . . . a straight angle = 180°
Substituting the congruent angles, this gives ...
∠ABC +∠BAC +∠ACB = 180° . . . . . the desired relation
The triangles are isosceles. The following notation are for the angles. For example ABD is refer to the angle located in the B vertex, formed by the segments AB and BD.
Then
A)
10.00 - 3.55 = 6.45 back
a $5 bill and a $1 dollar bill = $6
a quarter and 2 dimes = 0.45
so 2 bills and 3 coins
B) 120 x 4 = 480 minutes
480/60 = 8 hours
Answer:
x=48
Step-by-step explanation:
4x+5x+6x=180
15x=180
x=12
4x=48
