An estate is to be distributed among a wife, three children, and two grandchildren. the children will each receive three times as much as each grandchild, and the wife will receive four times as much as each child. if the estate amounts to $115,000, how much will each person receive?
choice b is correct answer.
given equation is :
-4x²+10x+6 = 0
ax²+bx+c = 0 is general quadratic equation.
comparing general equation with given quadratic equation,we get
a = -4 ,b = 10 and c = 6
we use the discriminant formula to find number of solution.
if d > 0 then there is two real solutions.
the formula to find discriminant is :
d = b²-4ac
putting above values in discriminant formula, we get
d = (10)²-4(-4)(6)
d = 100+96
d = 196 > 0
hence , equation have two real equation.
take out the common factor (3x + 7)
6x(3x + 7) + 5(3x + 7) = (3x + 7)(6x + 5) ← in factored form
for #2, another way to word this question is: for which of the following trig functions is π/2 a solution? well, go through them one by one. if you plug π/2 into sinθ, you get 1. this means that when x is π/2, y is 1. try and visualize that. when y is 1, that means you moved off the x-axis; so y = sinθ is not one of those functions that cross the x-axis at θ = π/2. go through the rest of them. for y = cos(π/2), you get 0. at θ = π/2, this function crosses the x-axis. for y = tanθ, your result is undefined, so that doesn't work. keep going through them. you should see that y = secθ is undefined, y = cscθ returns 1, and y = cotθ returns 0. if you have a calculator that can handle trig functions, just plug π/2 into every one of them and check off the ones that give you zero. graphically, if the y-value is 0, the function is touching/crossing the x-axis.
think about what y = secθ really means. it's actually y = 1/(cosθ), right? so what makes a fraction undefined? a fraction is undefined when the denominator is 0 because in mathematics, you can't divide by zero. calculators give you an error. so the real question here is, when is cosθ = 0? again, you can use a calculator here, but a unit circle would be more . cosθ = π/2, like we just saw in the previous problem, and it's zero again 180 degrees later at 3π/2. now read the answer choices.
all multiples of pi? well, our answer looked like π/2, so you can skip the first two choices and move to the last two. all multiples of π/2? imagine there's a constant next to π, say cπ/2 where c is any number. if we put an even number there, 2 will cut that number in half. imagine c = 4. then cπ/2 = 2π. our two answers were π/2 and 3π/2, so an even multiple won't work for us; we need the odd multiples only. in our answers, π/2 and 3π/2, c = 1 and c = 3. those are both odd numbers, and that's how you know you only need the "odd multiples of π/2" for question 3.
a ruler? idk