9514 1404 393
Answer:
- Translate P to E; rotate ∆PQR about E until Q is coincident with F; reflect ∆PQR across EF
- Reflect ∆PQR across line PR; translate R to G; rotate ∆PQR about G until P is coincident with E
Step-by-step explanation:
The orientations of the triangles are opposite, so a reflection is involved. The various segments are not at right angles to each other, so a rotation other than some multiple of 90° is involved. A translation is needed in order to align the vertices on top of one another.
The rotation is more easily defined if one of the ∆PQR vertices is already on top of its corresponding ∆EFG vertex, so that translation should precede the rotation. The reflection can come anywhere in the sequence.
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<em>Additional comment</em>
The mapping can be done in two transformations: translate a ∆PQR vertex to its corresponding ∆EFG point; reflect across the line that bisects the angle made at that vertex by corresponding sides.
Answer:
3 : 5, 4: 5
Step-by-step explanation:
Let the common multiplier of the given ratios be x.
Therefore, lengths of the legs of right triangle would be 3x and 4x
By Pythagoras Theorem:
Answer:
x=2
Step-by-step explanation:
4x−7(2−x)=3x+2
4x+(−7)(2)+(−7)(−x)=3x+2(Distribute)
4x+−14+7x=3x+2
(4x+7x)+(−14)=3x+2(Combine Like Terms)
11x+−14=3x+2
11x−14=3x+2
Step 2: Subtract 3x from both sides.
11x−14−3x=3x+2−3x
8x−14=2
Step 3: Add 14 to both sides.
8x−14+14=2+14
8x=16
Step 4: Divide both sides by 8.
x=2
Answer:
0
Step-by-step explanation:
It is not permissible for the denominator to be zero, so the "nonpermissible replacement" for x is 0.
Answer:
Okay, so a bit of math is involved, along with steps.
Step-by-step explanation:
Kyra invested $400 at 3% for 3 years. meaning 3% of $400 is 12. 400+12=
Year 1: $412
3% of 412=12.23+412=
Year 2: $424.23
3% of 424.23=12.7+423.23=
Year 3: $435.93
Kyra made $35.93 in investments.
Lishsawn invested $500 at 4% for 2 years. Meaning, 4% of $500 is 20. 500+20
Year 1: $520
4% of 520=20.8+520
Year 2: $540.8
Lishawn made $40.8 dollars in investments. Meaning that Lishawn made $4.87 more dollars
