CPhill

Mmmmm....."D" would be the closest to being correct.....because the side opposite angle A < the side opposite angle B, angle A is < 45 degrees and Angle B is > 45 degrees.......except that we would need to use the Law of Sines first and then apply the sin-1 to find A...thusly .....

sin 90/25 = sin A /7

7/25 = sin A

Sin-1(7/25) =Sin-1(.28) = A  = about 16 degrees

And to prove that this is correct....use the Law of Sines again to find angle B =

sin90/25 = sin B /24

(24/25) = sin B

Sin-1(24/25) = Sin-1(.96) = B = about 74 degrees

So A + B = 90   (as they should)

Using the Law of Sines.....

sin R/3.5 cm = sin 70º/6.2 cm

......is correct  ......

"A" is the correct procedure

-2(x+4)>3x+17      distribute the -2 across both terms in the parentheses

-2x - 8 > 3x + 17    add 2x to both sides and subtract 17 from both sides

-25 > 5x                divide both sides by 5

-5 > x    or

x < -5

R/(R+1)  + 2 =  3R / (R+2)   subtract the fraction on the left side from both sides

2 = 3R/(R + 2) - R/(R + 1)      get a common denominator on the right side

2 = [3R(R+1) - R(R + 2)]/ [(R + 2)(R + 1)]    cross- multiply

2 [(R + 2)(R + 1)] = [3R(R+1) - R(R + 2)]  simplify

2R^2 + 6R + 4 = 3R^2 + 3R - R^2 - 2R

2R^2 + 6R + 4 = 2R^2 + R        subtract 3R^2 + R from both sides

5R + 4 = 0             subtract 4 from both sides

5R = -4                  divide both sides by 5

R= -4/5

2(e)(f) = (2)*(9)*(6)  = 108

The Intermediate Value Theorem says that , in some interval [a, b], if f(a) and f(b) have opposite signs, then f(x) has at least one "root" in this interval. (As long as f(x) is continuous on the interval !!)

So

f(0) = (0)^3 + 4(0) - 4 = -4

and

f(1) = (1)^3 + 4(1) - 4 =  1

Then, at x=0 the function lies below the x axis, and at x =1, the function lies above the x axis........and since polynomials are always continuous, this function must cross the x axis on [0,1]

So...this tells us that this ploynomial has at least one"zero" (root) on the interval [0, 1]....In other words, whatever this value is, it makes f(x) = 0......(the "0" in the problem is correct !!!......)

Well...there is another way....

Note...... √5 / 2  = √(4*1.25) / 2  = (√4/2) * √1.25 = (2/2)* √1.25 = √1.25

And check for yourself that √1.25 = √5 / 2  !!!!

√5 / 2   ??????