Fill in the blanks to write an equation in slope-intercept form representing the function shown in the table.

(a) For E based on d, the equation is E = 6500 - 50d (b) After 30 days, the remaining excess will be 5000.

Answer:

£700,000

Detailed explanation:

Let x represent the original price of the house. Keeping in mind that

Upon a 7% increase in the house value, it is now set at £749,000. We can express this as

We can solve for x now:

Thus, the initial valuation of the house was

£700,000

Answer:

The union of sets A and B is represented as A U B = {1,2,3,4,5,6,8}

Detailed explanation:

We begin by defining our sets.

Let ¢ signify the universal set (which includes every element in the given sets)

¢ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A= {2, 4, 6, 8}

B= {1,2,3,4,5,6}

Consequently: A U B (the union of A and B):

A U B = {1, 2, 3, 4, 5, 6, 8}

To minimize the amount of paper used, the dimensions should be perfectly matched such that the diameter equals the height. Therefore, if we denote the diameter as x, then the height equals x and the radius is x/2.
Consequently, the cone's volume is expressed as:
V=1/3πr^2h
=1/3*π*(x/2)^2*x
=0.262x^3
From this, we can derive that:
33=0.262x^3
thus, we find x^3=125.95
solving gives x=(125.95)^(1/3)
resulting in x=5.0126=5.01 cm
thus, the diameter and height are both 5.01cm.