Answer:
-2(-2) + (12-9) = 2 + 9 + -2(-2)
Step-by-step explanation:
Hi there!
The following trapezoidal theorem states that:
Middle segment = average of top and bottom side
Thus:
M = 1/2(b1 + b2)
21 - x = 1/2(17 + 11)
Solve:
21 - x = 1/2(28)
21 - x = 14
Subtract 21 from both sides:
-x = 14 - 21
-x = -7
Multiply both sides by -1:
x = 7
Given:
<span>tan(B/2) = sec(B) / (sec(B) * csc(B) + csc(B)) </span>
<span>Apply the half angle formula to convert tan(B/2) to terms of B: </span>
<span>sin(B) / (1+cos(B)) = sec(B) / (sec(B) * csc(B) + csc(B)) </span>
<span>Convert everything else to be in terms of sin and cos: </span>
<span>sin(B) / (1+cos(B) = (1/cos(B)) / ((1/cos(B)) * (1/sin(B)) + (1/sin(B))) </span>
<span>Multiply right side by "sin(B)/sin(B)" to simplify the fractions: </span>
<span>sin(B) / (1+cos(B) = (sin(B)/cos(B)) / ((1/cos(B)) + 1) </span>
<span>Change "1" to cos(B)/cos(B) and then combine over </span>
<span>common denominator: </span>
<span>sin(B) / (1+cos(B) = (sin(B)/cos(B)) / ((1/cos(B)) + cos(B)/cos(B)) </span>
<span>sin(B) / (1+cos(B) = (sin(B)/cos(B)) / ((1+cos(B))/cos(B)) </span>
<span>Dividing by a fraction equals multiplying by its reciprocal: </span>
<span>sin(B) / (1+cos(B) = (sin(B)/cos(B)) * (cos(B) / (1+cos(B))) </span>
<span>Multiply terms on the right side (canceling cos(B) terms): </span>
<span>sin(B) / (1+cos(B) = sin(B) / (1+cos(B)) </span>
Answer:the price for one shirt is $7.5
the price for one pair of pants is $18.5
Step-by-step explanation:
Let x represent the price for one shirt.
Let y represent the price for one pair of pants.
Lisa goes to the mall one day and buys four shirts and three pairs of pants for $85.50. This means that
4x + 3y = 85.5 - - - - - - - - - -1
She returns the next day and buys three shirts and five pairs of pants for $115.00. This means that
3x + 5y = 115 - - - - - - - - - - - 2
Multiplying equation 1 by b3 and equation 2 by 4, it becomes
12x + 9y = 256.5
12x + 20y = 460
Subtracting, it becomes
- 11y = - 203.5
y = - 203.5/ -11 = 18.5
Substituting y = 18.5 into equation 1, it becomes
4x + 3×18.5 = 85.5
4x + 55.5 = 85.5
4x = 85.5 - 55.5 = 30
x = 30/4 = 7.5
Answer:
x < -15
Step-by-step explanation:
Here is the solution:
-3x-42 > 3
Add the numbers
-3x > 45
Divide both sides of the inequation by -3 and flip the inequality sign.
x < -15
