Alan

A sequence is defined by a_{n + 1} = a_n + 2n, and a_1 = 4. 

This recursion can be written as:  a_n = a₁ + (n-1)*n

You can easily obtain a₇ + a₈ from this.

Nine points are evenly spaced on a standard number line. They are labeled A through I, from left to right. The coordinates of points A and I are 1 and 10, respectively. What is the coordinate of point B?...

Nine points have eight gaps.   Hence A to B is a distance of (10 - 1)/8  = 9/8.

Coordinate of B  = coordinate of A + 9/8

I'll let you finish.

A bag contains five white balls and four black balls. Your goal is to draw two black balls....

If the two coefficients of the highest order terms of both polynomials have the same sign, then the sum is also a 7th degree polynomial.

If the highest order terms have coefficients that are of equal magnitude but opposite sign, then the sum would be a polynomial of lower degree.

If the two polynomials are, say, f(x) = ax⁷, and g(x) = -ax⁷, then the sum is zero, so the product of the degrees would be zero.

Assuming this is not the case and we have, say, f(x) = ax⁷ + bx + c, and g(x) = -ax7 + dx + e, then the sum is of first degree and the product is 7.

(The above assumes I've interpreted the question correctly!).

Replace P in the second equation by 3K - 10 (from the first equation) then rearrange to get K.

Find an equation of the tangent to the circle x2 + y2  = 36 at the point (5, √ 11)

See:  https://web2.0calc.com/questions/please-help_18922#r2 

If P and K represent the current ages of Paula and Kaye, respectively, then:

P = 3K - 10

and

P + 2 = 2K

Can you take it from here?

"Three circles, two with radius R and one with radius r, are drawn on the same side of a straight line in such a way that each circle is tangent to the line and both other circles.  What is the relationship between R and r?"

"The average age of the 10 females in a choir is 30 years. The average age of the 15 males in the same choir is 35 years. What is the average age, in years, of the 25 people in the choir?"

Average age of total = (10*30 + 15*35)/25