What are the x–coordinates of the three points where the graphs of the equations intersect? x3 – 10x = x2 – 6

(- 3, 0), (2 + , 0), (2 - , 0)

Step-by-step explanation:

rearrange the equation equating to zero

x³ - x² - 10x + 6 = 0

note that when x = - 3

(- 3)³ - (- 3)² - 10(- 3) + 6 = - 27 - 9 + 30 + 6 = 0, hence

x = - 3 is a root and (x + 3) is a factor of the polynomial

dividing x³ - x² - 10x + 6 ÷ (x + 3) gives

(x + 3)(x² - 4x + 2) = 0

solve x² - 4x + 2 = 0 using the quadratic formula

with a = 1, b= - 4 and c = 2

x = (4 ± )/ 2

  = (4 ± ) / 2

  = (4 ± 2) / 2

  = 2 ±, hence

x = 2 + , x = 2 -

intersect at (- 3, 0), (2 +, 0), (2 - , 0)

Step-by-step explanation:

First, move all terms to one side with zero on the other side so the Zero Product Property can be applied:

x³ - x² - 10x + 6 = 0    Possible rational roots are: ±{1, 2, 3, 6}

Use synthetic division to find one of the roots.  Let's try x = -3

-3 |  1    -1    -10    6

   |  ↓   -3    12    -6

      1    -4     2     0  ← remainder is zero, so x = -3 is a root/intercept

Next, evaluate the reduced polynomial x² - 4x + 2 = 0

This can not be factored so use the quadratic formula to find the remaining roots/intercepts:

a = 1, b = -4, c = 2

Intercepts are

36 girls

step-by-step explanation:

the 48 boys is 4 parts of the ratio

divide 48 by 4 to obtain one part of the ratio

= 12 ← 1 part of the ratio

3 parts = 3 × 12 = 36 ← number of girls

total amount to be paid = $19.5

step-by-step explanation:

given ,

original price = $25.99

discount = 25%

discount amount = 25% of original price

discount amount = 25/100   * 25.99

discount amount = $6.49

hence , the total amount to be paid = original price - discount amount

                                                            = $25.99 - $6.49

                                                            =$19.5

total amount to be paid = $19.5