Answer:
RPQ = 239°
Step-by-step explanation:
Since SP is a straight line going through the center of a circle, it is a diameter.
We can say that m<SOR and m<ROP are supplementary and add up to 180° because they form a straight line. We can set up an equation:
m<SOR + m<ROP = 180°
We can substitute in the value of m<SOR:
31° + m<ROP = 180°
m<ROP = 149°
Next, we can also say that m<SOQ and m<QOP are supplementary because they form a straight line. Also, since QO is perpendicular to SP, we can say that both m<SOQ and m<QOP equal to 90°.
Now, we can say that m<ROQ (reflex angle) is equal to the sum of m<QOP and m<ROP from angle addition postulate. We can write the equation:
m<ROQ = m<QOP + m<ROP
m<ROQ = 90° + 149° = 239°
The reflex angle <ROQ cuts the arc RPQ, so they would have the same measure. So, arc RPQ = 239°
Answer:
The time it will take Natalie to pick the forty bushels alone is 10 hours
Step-by-step explanation:
The time it takes Kali to pick forty bushels of apples alone = 15 hours
The time it takes Kali and Natalie to pick forty bushels = 6 hours
The rate at which Kali picks bushels = 40/15 bushels per hour = 8/3 bushels per hour
Let x represents the rate at which Natalie picks bushels, we have;
8/3 × 6 + x × 6 = 40
x × 6 = 40 - 8/3 × 6 = 24
x = 24/6 = 4
Therefore;
The rate at which Natalie picks the bushels of apples = 4 bushels/hour
The time it will take Natalie to pick the forty bushels alone = (40 bushels)/(4 bushels/hour) = 10 hours.
Answer:
y = -3x
Step-by-step explanation:
Slope is -3
Answer:
5.14
Step-by-step explanation:
ones.tenths hundredths
