What are the two solutions of x2 – 2x – 4 = –3x + 9?

  x = -0.5 ± √13.25 ≈ {-4.14005, 3.14005}

Step-by-step explanation:

If the only requirement is for a solution, I like to let a graphing calculator help out. Solving by hand or with a calculator, it is convenient to write the equation in standard form. The right side can be subtracted to give ...

  x² +x -13 = 0

The vertex can be found by adding and subtracting the square of half the x-coefficient:

  (x² +x +0.25) -13 -0.25 = 0

  (x +0.5)² -13.25 = 0

The vertex is (-0.5, -13.25). The coefficient of the x² term is 1, so the vertex form of the equation can lead directly to the solutions. Adding 13.25 to the equation and taking the square root gives ...

  (x +0.5)² = 13.25

  x = -0.5 ± √13.25

option c) graph of line going through 1, 4 and 3, 10

step-by-step explanation:

let y equal to margo's coin collection

let x equal to number of years

at the begining x=0, y=1 → point=(x,y)→point=(0,1)

she adds 3 coins per year, then y=1+3x

at x=1, y=1+3(1)=1+3→y=4→point=(x,y)→point=(1,4)

at x=3, y=1+3(3)=1+9→y=10→point=(x,y)→point=(3,10)

the graph of line going through (1, 4) and (3, 10), then the option c is the correct.

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).