The cost price of the table is $40.
<h3>What is Gain ?</h3>
Gain is the amount gain by selling the product at a higher price than its cost.
Let the cost of the table is $ x
The percentage gain is x% (as given in the question)
Cost price = ?
It is known that
Step 1 : Gain = ( selling Price - Cost Price) * 100 / Cost Price
Selling price = 56
Cost Price = $ x
Therefore substituting the value
x = (56 - x) * 100 / x
x² = 5600 - 100x
x² +100x -5600 = 0
Step 2 : Factorizing
x² + 140x - 40 x -5600 = 0
x( x+14 ) -40( x +14) = 0
( x - 40)(x +14) = 0
x = $40
Therefore the cost price of the table is $40.
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Answer:
B
Step-by-step explanation:
1/2x - 2 > 0
collect like terms
1/2x > 0 + 2
1/2x > 2
Divide both sides by 1/2
x > 2 divided by 1/2
inverse of 1/2 is 2/1
x > 2 times 2/1
x > 4
-1(7+4b) - distribute the -1 to the expression
(-1 * 7) + (-1 * 4b) — ( + and - = - )when it is multiplied
= -7 - 4b — there is no like term to added to subtracted so it will stay as like
x(x^2 - 2xy+y^2) distribute x to all
= x(x^2) - x(2xy) + x(y^2)
= x^3 - 2x^2y + xy^2 in multiplication exponent add to similar variable
No like term to connect
-5x(-3+x)
= -5x(-3) -5x(+x). (- and - is +)
= 15x -5x. similar variable x so connect the like connect like term by subtracting them
= 10x
Answer:
Verified below
Step-by-step explanation:
We want to show that (Cos2θ)/(1 + sin2θ) = (cot θ - 1)/(cot θ + 1)
In trigonometric identities;
Cot θ = cos θ/sin θ
Thus;
(cot θ - 1)/(cot θ + 1) gives;
((cos θ/sin θ) - 1)/((cos θ/sin θ) + 1)
Simplifying numerator and denominator gives;
((cos θ - sin θ)/sin θ)/((cos θ + sin θ)/sin θ)
This reduces to;
>> (cos θ - sin θ)/(cos θ + sin θ)
Multiply top and bottom by ((cos θ + sin θ) to get;
>> (cos² θ - sin²θ)/(cos²θ + sin²θ + 2sinθcosθ)
In trigonometric identities, we know that;
cos 2θ = (cos² θ - sin²θ)
cos²θ + sin²θ = 1
sin 2θ = 2sinθcosθ
Thus;
(cos² θ - sin²θ)/(cos²θ + sin²θ + 2sinθcosθ) gives us:
>> cos 2θ/(1 + sin 2θ)
This is equal to the left hand side.
Thus, it is verified.
A.

B.

Megan's solution isn't correct.
The first mistake: she subtracted 5x from the right-hand side of the equation, but added 5x to the left-hand side.
The second mistake: she divided the right-hand side of the equation by 11, but didn't divide the left-hand side.
The correct solution: