Y=-x^2+2x+10
y=x+2

substitution
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The solutions of the system of equations are the points

Step-by-step explanation:

we have

----> equation A

----> equation B

Solve the system by substitution

substitute equation B in equation A

solve for x

The formula to solve a quadratic equation of the form

is equal to

in this problem we have

so

substitute in the formula

 ----->  

 ----->  

Find the values of y

For  

 ---->  

For  

 ---->  

therefore

The solutions of the system of equations are the points

investment b is an ordinary annuity with $3,909.64 in the account after one year.

step-by-step explanation:

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form