Solve for t 6(5^2t-9)=24
We start by dividing both sides by 6 to get 5^2t-9=4 Then, find the natural log of both sides ln(5^2t-9)=ln(4) ln5(2t-9)=ln4 Distribute 2tln5-9ln5=ln4 Add 9ln5 to both sides 2tln5=ln4+9ln5 Divide both sides by 2ln5 t=(ln4+9ln5)/(2ln5)
If a right triangle has an angle of 45 degrees and a hypotenuse of 4sqrt6, what are the values of the corresponding sides?
Because we know this is a 45 45 90 triangle (we find the remaining angle by subtracting 180-90-45=45) we know we can use our rules for a 45 45 90 triangle that say if the sides of the triangle are equal to x, then the hypotenuse is equal to xsqrt2. So, to verify the values of our missing sides, we simply need to set xsqrt2 equal to 4sqrt6. If we square both sides of the equation we are left with 2x^2=96 which we divide by to to get x^2=48 which we then find the sqare root of both sides to get x=4sqrt3
Find the x-intercepts of this equation by solving for x. 8x^2 + 22x + 15
Using the X box method, we multiply (8)(15) to get 120 at the top of our X box and 22 on the bottom. Through guess and check we find that 10 and 12 add to 22 and multiply to 120. Because our polynomial had an x^2 factor greater than 1, we then use our box method and place the numbers like so 8x^2 | 10x ------------------ By taking out our most common factor vertically and horizontally, we are 12x | 15 given our factored equation (4x+5)(2x+3) Each factored piece is set equal to zero like so 4x+5=0 2x+3=0 If we solve these, we are given x intercepts of x= -5/4 and x=-3/2 To verify, we can use a graphing calculator to see if these are indeed our intercepts