*see attachement for diagram
Answer:
∠P = 140°; ∠S = 40°
Step-by-step explanation:
The figure given is a parallelogram.
Consecutive angles (adjacent angles) of a parallelogram are supplementary.
Therefore:
(x + 15)° + (6x - 10)° = 180°
Solve for x
x + 15 + 6x - 10 = 180
Add like terms
7x + 5 = 180
7x = 180 - 5
7x = 175
x = 175/7
x = 25
✔️m<P = m<R = 6x - 10 (opposite angles of a parallelogram are congruent)
m<P = 6x - 10
Plug in the value of x
m<P = 6(25) - 10 = 140°
✔️m<S = m<Q = x + 15 (opposite angles of a parallelogram are congruent)
m<S = x + 15 = 25 + 15 = 40°
Answer:
Sin (E) = √74/(2√23)
Step-by-step explanation:
Reference Angle = E
Hypotenuse = 2√23
Adjacent = 3√2
Opposite = DC = √(2√23)² - (3√2)²) = √(4*23 - 9*2) = √(92 - 18) = √74 (pythagorean theorem)
Recall SOHCAHTOA.
Thus,
Sin (E) = opp/hyp
Sin (E) = √74/(2√23)
Answer:

Step-by-step explanation:
Given:

Required
Rewrite in vertex form
The vertex form of an equation is in form of: 
Solving: 
Subtract 2 from both sides


Factorize expression on the right hand side by dividing through by the coefficient of x²


Get a perfect square of coefficient of x; then add to both sides
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<em>Rough work</em>
The coefficient of x is 
It's square is 
Adding inside the bracket of
to give: 
To balance the equation, the same expression must be added to the other side of the equation;
Equivalent expression is: 
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The expression becomes



Factorize the expression on the right hand side





Make y the subject of formula

<em>Solved</em>
Answer:
1
Step-by-step explanation:
Because each is just being multiplied by the same number.