Answer:The number of yards of Chris's ribbon are neither purple nor green is 1.625 yards
Step-by-step explanation:
Chris has a total of 3 2/3 yards of ribbon. Converting 3 2/3 yards to improper fraction, it becomes 11/3 yards. Chris has 7/8 yards of purple ribbon. He also has 1 1/6 yards of green ribbon. Converting to improper fraction, it becomes 7/6 yards of green ribbon.
The total length of purple and green ribbon that Chris has would be 7/8 + 7/6 = (21+28)/24 = 49/24
The number of yards of Chris's ribbon are neither purple nor green is 11/3 - 49/24 = (88 - 49)/24
= 39/24 = 1.625 yards
Answer:
y=27.75
x=13.5
Step-by-step explanation:
(5x-17)+(3x-11)=180 (supplementary angle rule)
8x-28=180
8x=180+28
x=108/8
x=13.5
(3x-11)+90+(2y+5)=180 (supplementary angle rule)
29.5+90+2y+5=180 (replace x by 13.5)
2y=55.5
y=55.5/2
y=27.75
Answer:
12. ∠2 ≅ ∠3
The parallel Lines for these angles are q and p.
The theorem that justifies this is Corresponding Angles, because both are in the same position (the upper right-hand corner) in their group of 4 angles. These angles are also Congruent, because the transversal intersects two parallel lines and two corresponding angles are congruent. Q and P would be the parallel lines and R would be the transversal.
13. ∠6 ≅ ∠7
The parallel lines for these angles would be Q and P.
The theorem that justifies this is Alternate Interior Angles, because this pair of angles are on opposite sides of the Transversal line and on the inside of the parallel lines. This also makes them Congruent angles, because the transversal intersects two parallel lines and two Alternate Interior Angles are Congruent. The two parallel lines are Q and P are parallel because line S intersect them, making line S the Transversal.
14. ∠1 ≅ ∠4
The parallel lines for these angles are R and S.
The theorem that justifies this is Alternate Exterior Angles, because angles 1 and 4 are on opposite sides of the transversal as well as the outside of the parallel lines. This also makes these two angles Vertical Angles, because when a transversal intersects two parallel lines, and the angles are across from each other on opposite sides of the transversal, they are vertical angles. Vertical Angles are always Congruent. So R and S are the parallel lines and line Q is the Transversal because it intersects R and S.
15. m∠5 + m∠8 = 180°
The parallel lines for angles 5 and 8 are R and S.
The theorem that justifies this is Same-Side Interior Angles, because they are on the same side of the Transversal and on the inside of the parallel lines. This also makes angles 5 and 8 Supplementary, because a transversal intersects two parallel lines and Same-side Interior Angles are Supplementary. The parallel lines are R and S because Transversal line P intersects them.
Step-by-step explanation:
Explanations are within the answers for each question above.
Hope this helps!! :)
Very easy:
Since there is no involvement of y so simply draw a vertical line at x=1.And shade the part which is describing the x values.
Hence,
You will shade all the part which is on the left of the vertical line.As there is an equal sign too,so the vertical line will be a solid line instead of dotted line.
See the attachment for graph.