Answer:
first one conditional
second absolute value
third identity
pretty sure last one is conditional
Step-by-step explanation:
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:
n = 16
Step-by-step explanation:
Step 1: Cross multiply
6(n - 7) = 2(2n - 5)
Step 2: Distribute
6n - 42 = 4n - 10
Step 3: Subtract 4n on both sides
2n - 42 = -10
Step 4: Add 42 to both sides
2n = 32
Step 5: Divide both sides by 2
n = 16
Answer:
$1950
Step-by-step explanation:
Simple interest amount payable is given by
A=P(1+rt) where p is principal amount, A is final amount paid, t is time and r is rate of interest. For the first case
A=15000(1+0.03*4)=$16800
For second case
A=15000(1+0.05*5)=$18750
Difference will be 18750-16800=$1950
Answer: Michael has 87 comic books while David has 41 comic books.
Step-by-step explanation:
Let x represent the number comic books that Michael has.
Let y represent the number of comic books that David has.
Michael has 5 more comic books than double David's collection. The expression would be
x = 2y + 5
If together they have a total of 128 comics, it means that
x + y = 128- - - - - - - - - -1
Substituting x = 2y + 5 into equation 1, it becomes
2y + 5 + y = 128
3y + 5 = 128
3y = 128 - 5
3y = 123
y = 123/3
y = 41
Substituting y = 41 into x = 2y + 5, it becomes
x = 2 × 41 + 5
x = 87
