Answer:
A 180 degree counterclockwise rotation about the origin followed by a translation 5 units to the right
Step-by-step explanation:
The directed line segment AB points west (B is west of A). The directed line segment A'B' points east. A rotation of 180° is required to reverse the direction like that.
The two answer choices involving rotation of 180° give you the option of selecting ...
- a vertical translation up before rotation, or
- a horizontal translation right after rotation.
Translation of the figure 5 units upward will put it in the first quadrant, and the rotation will put the final figure in the 3rd quadrant.
__
Rotation 180° will put the figure in the 2nd quadrant (A"B"C" in the attachment) and translation to the right will move it to the 1st quadrant. Of course, rotation 180° in either direction (CW or CCW) about the origin is the same as reflection across the origin. (It negates all of the coordinate values.)
Hence the appropriate description of transformations is ...
A 180° rotation about the origin followed by a translation right 5 units
Answer:
D
Step-by-step explanation:
The first equation will have to do with the the quantities sold.
We know that 97 total items were sold so
w + p = 97
The second equation has to do with prices.
Our final profit was 96.25 so we tag on each individual price to the different items sold. This amounts to the final profit.
0.75w + 1.25p = 96.25
----------------------------------------------------
w + p = 97
0.75w + 1.25p = 96.25
Answer:
log₁.₅3 or 2.70951
Step-by-step explanation:
- 3^(2x) - 2^(x + 1) * 3^x - 3*2^(2x) = 0
- 3^(2x)- 2*2^x*3^x + 2^(2x)- 4*2^(2x)=0
- (3^x-2^x)^2 - (2*2^x)^2=0
- (3^x-2^x+2*2^x)(3^x - 2^x - 2*2^x)=0
- (3^x+2^x)(3^x- 3*2^x)=0
- 3^x+2^x>0 for any value of x
- 3^x- 3*2^x=0
- 3^x= 3*2^x
- 3^x/2^x=3
- 1.5^x=3
- x= log₁.₅ 3 = 2.70951
Answer/Step-by-step explanation:
5. ✔️Exterior angle = angle outside the triangle = W
✔️Remote interior angle of the triangle to the exterior angle W = opposite angles to angle W which are X and Y
✔️m<X + m<Y = m<W (exterior angle theorem of a triangle)
✔️m<W + m<Z = 180° (linear pair/angles on a straight line)
6. m<6 = 115°
m<5 = 120°
✔️m<2 = 180° - m<5° (linear pair/angles on a straight line)
m<2 = 180° - 120°
m<2 = 60°
✔️m<3 = 180° - m<6° (linear pair/angles on a straight line)
m<3 = 180° - 115°
m<3 = 65°
✔️m<1 = 180° - (m<2 + m<3) (sum of triangle theorem)
m<1 = 180° - (60° + 65°)
m<1 = 55°
✔️m<4 = 180° - m<1 (linear pair/angles on a straight line)
m<4 = 180° - 55°
m<4 = 125°