CPhill

Simplifying what Anonymous said, we have

y+5=(-7/2)(x+1)

y + 5 = (-7/2)x - (7/2)   subtract 5 from both sides

y = (-7/2)x - (17/2)

And that's in slope-intercept form

DS gave an approximate answer, which, in most cases, is good enough.....!!!!!

We can also give an "exact" answer....

√180 = √ (36*5) = 6√5

4x³ + 4x² = x + 1;   [−2, 2]

4x³ + 4x² = x + 1          rearranging, we have

4x³ + 4x² - x - 1 = 0       factor  this

4x² (x + 1) -1(x+1) = 0      take out the common factor

(x + 1) (4x² - 1) = 0        factor again

(x+1) (2x + 1)(2x - 1) = 0

And setting each factor to 0, we have that .....  x = -1  ....  x= -1/2 (= -.50)  and  x = 1/2 (= .50)

And all of the solutions are within the given interval.....!!!

mgh=mv^2/2   divide both sides by m

gh = v²/ 2       multiply both sides by 2

2gh = v²         take the square root of both sides

±√(2gh)  = v

If 2 divides p², then p² must be even. But, if p² is even, then p must be even, and 2 divides any even number. Thus, 2 divides p......!!!!!

3x^3 - 21x^2 - 50x + 220 = 0

13pi/6 is the same rotational angle as pi/6 = 30°

And cos 30° = (√3) / 2

And sec 30° = 1/ cos 30° = 1 / [(√3) / 2] =  2/√3 = (2/3)√3

I assume by "line," you are referring to the length of the diagonals. If so, we have

A_k = (1/2)d₁d₂     where A_k is the area, and d₁ and d₂ are the lengths of the diagonals  

A_k = (1/2)(3.16)(2)  = 3.16 sq units

(1/3)^3/2  = [(1/3)³ ]^1/2 = (1/27)^1/2 = [ (1/9)(1/3) ] ^1/2   = √(1/9)*√(1/3) = (1/3)√(1/3) = (1/3)√(1/3)√(3/3) = (√3)/9

I = Prt    where I is the interest earned, P is the amount invested, and r is the interest rate.

Call the amount he invested at 10%, "x.'  And call the amount that he invested at 12%, "4000-x."  ...so we have

460 = .10x + .12(4000-x)      simplify this

460 = .10x + 480 - .12x        subtract 480 from both sides

-20 = -.02x        

x  =  .(20)/(-.02)  = 1000   and that's the amount invested at 10%

So, 4000-x = 4000-1000 = 3000...... and that's the amount invested at 12%