Answer:
Eliminate redundant parentheses
(
−
5
)
=
1
−
5
=
1
Divide both sides of the equation by the same term−
5
=
1
-5x/-5 = 1/-5
Simplify
Cancel terms that are in both the numerator and denominator
-5x/-5=1/-5 x=1/-5
Divide the numbers
x=-1/5
Step-by-step explanation:
ANSWER x=-1/5
Answer:
θ = 60° or θ = 120°, which in radians is equivalent to θ = π/3 rad or θ = 2π/3 rad.
Explanation:
The given equation is sin θ = (√3)/2
Solving that equation is finding the value of the angle, θ, whose sine is (√3)/2.
The function that returns the value of the angle whose sine is (√3)/2 is the inverse function of the sine and it has a special name: arc sine or arcsin.
Hence, θ = arcsin (√3)/2.
You can use your knowledge of the notable angles to solve for that equation.
1) The function sine is positive in first and second quadrants.
2) The angles in the first quadrant go from 0° to 90°.
3) The sine of 60° (√3)/2, Hence the first value of θ is 60°
4) The angles in the second quatrant go from 90° to 120°. 60° is the reference angle in the second quadrant, and the angle searched is
- 180° - reference angle = 180° - 60° = 120°. So, 120° is the other solution of the equation.
5) You can convert both angles to radians using the equivalence
- π radians = 180° ⇒ 1 = π rad / 180°
- 60° = 60° × π rad / 180° = π/ 3 rad
- 120° = 120° × π rad / 180° = 2π/3 rad
6) You can verify that sin 60° = (√3)/2 = sin 120° .
Answer:
N → S (If national elections deteriorate into TV popularity contests, then smooth-talking morons will get elected.)
¬N → ¬S ( Therefore, if national elections do not deteriorate into TV popularity contests, then smooth-talking morons will not get elected.)
Step-by-step explanation:
¬ is a symbol of negation
→ is a symbol that represent "if... then..." scenario
Answer:
34.5 feet of material for 3 hat and scarf sets.
Step-by-step explanation:
First, we need to convert all measurements to the same unit: foot. (Because the answer is requested in foot)
1 yard is equal to 3 feet, and 1 inch is equal to 0.08333 feet.
3 yards are equal to 9 feet, and 30 inches are equal to 2.5 feet.
We need 3 sets of hat and scarf, so this means that we need 3 hats and 3 scarfs.
One scarf needs 9 feet of material, so 3 scarfs need 27 feet.
One hat needs 2.5 feet of material, so 3 hats need 7.5 feet.
In total, 3 scarfs and 3 hats need 27+7.5=34.5 feet of material.
Let x = smaller number
Let y = bigger number
y = 7x + 4
x + y = 92
x + (7x + 4) = 92
8x + 4 = 92
8x = 88
x = 11
y = 7x + 4
y = 81
