Find the coefficient of x2 in (3x2 – 5) (4 + 4x2), expand using algebraic expressions and answer

Answer:

Detailed solution:

Given:

The problem to solve is:

Convert the equation into the standard quadratic form , where represent constants.

So, by adding to both sides, we get:

Note that .

The roots of this quadratic are found by applying the quadratic formula given as:

Substitute into the formula and calculate for .

Hence, the roots are:

Answer:

link:

Step-by-step explanation:

Answer:

1.4×10⁻⁵=0.000014

Step-by-step explanation:

Since the exponent of the 10 term is negative, shift the decimal point to the left by 5 positions;

1.4×10⁻⁵=0.000014

Answer: Ana should produce more fudge, and Leo should produce more toffee.

Step-by-step explanation:

Comparative advantage defined: A person or country has a comparative advantage producing a good if their opportunity cost for it is lower than someone else's.

In this case, Ana and Leo will both benefit if they focus on the product for which they have the lower opportunity cost.

(a) Ana’s production possibilities:

If she spends all her time making fudge: 3 pounds; or toffee: 2 pounds.

Opportunity cost of 1 pound fudge = 2/3 = 0.66 pounds toffee

Opportunity cost of 1 pound toffee = 3/2 = 1.5 pounds fudge

(b) Leo’s production opportunities:

All time making fudge: 4 pounds; or toffee: 5 pounds.

Opportunity cost of 1 pound fudge = 5/4 = 1.25 pounds toffee

Opportunity cost of 1 pound toffee = 4/5 = 0.8 pounds fudge

Since Ana’s opportunity cost for fudge is lower than Leo’s, she should specialize in fudge production.

Conversely, Leo has a lower opportunity cost for toffee, so he should focus on producing toffee.

Response:

5.8%

Detailed reasoning:

For the business,

retail space rental = $2400

wages = $1800

utilities = $480

Total operating cost = $4680

However,

retail space rent decreased by 5%, which results in;

5% of $2400 = 0.05 x $2400 = $125

The new rental amount for retail space = $2400 - $125

                                             = $2275

wages were lowered by 6%, calculated as;

6% of $1800 = 0.06 x $1800 = $108

The revised wages = $1800 - $108

                           = $1620

Utilities experienced a 7% increase, calculated as;

7% of $480 = 0.07 x $480 = $33.6

The adjusted utilities cost = $480 + $33.6

                                               = $513.6

New total operating costs = $2275 + $1620 + $513.6

                             = $4408.6

The percentage change in monthly expenses = x 100%

x 100%                                    = 5.8%