BuilderBoi

It can also be found here: https://web2.0calc.com/questions/math-problem_35879

There are 400 numbers that are divisible by 5 within the range. Of these, 133 of them are divisible by 15, so your answer is 400-133 = 267.

Use the quadratic formula \( {-b \pm \sqrt{b^2-4ac} \over 2a}\)

You will get two imaginary solutions: 31/12 + (sqrt143i)/12

                                                  and: 31/12 - (sqrt143i)/12

Treat \(a^2\)as \(b \)

Now, when you factor \({b^2-3b+2}\)....

You get \((b-1)(b-2)\)

Remember, this equals \((a^2-1)(a^2-2)\)

Brandon has 28 pennies, 18 dimes, and 108 nickels. 

Let's start by writing equations:

pennies = 10 + dimes,

nickels = 6 x dimes.

You know Brandon used a number of pennies ending in either 3 or 8, since he has a total of $7.48.

I didn't know how to proceed from here, so I had to guess and check lol. 

174.

Consider the 3 possible choices of equivalent side lengths: 3x+62=5x+60, 7x+30=5x+60, and 3x+62=7x+30.

By solving for all three, we get the following results:

3x+62 = 5x+60, x= 1

3x+62 = 7x+30, x = 8

5x+60 = 7x + 30, x = 15. 

These show that the least possible perimeter sees x = 1, so we can solve (3x1 +62) + (5x1+60) + (7x1+30) = 174.

3.5 sq units

Split the quadrilateral into two triangles using the y-axis as a line. You now have two triangles one with 2x3x1/2 = 3 sq units and 1 with 1 x 1 x1/2 = 0.5 units. Adding these up gives you your area of 3.5 square units

Formula for the volume of a sphere: 4/3(pi)(r)³

= 4/3(pi)2³ + 4/3(pi)3³ + 4/3(pi)6³ = 10 2/3(pi) + 36(pi) + 288(pi) = 334 2/3(pi)

y = (slope)x + (y-intercept)

Slope = y₂ - y₁ / x₂ - x₁

          = 11- (-17) / -5 - (-2)

          = 28/-3 or -9.3333333 or -9 1/3

Y-intercept = 2(-9 1/3) + -17 = -35 2/3

So...

The equation is y = -28/3x - 35 2/3