Find the x-intercepts (solve for x) for the following and show your work! y=−2x^2−9x+5

see explanation

Step-by-step explanation:

To find the x- intercepts set y = 0, that is

- 2x² - 9x + 5 = 0

To factorise the quadratic consider the factors of the product of the coefficient of the x² term and the constant term that sum to give the coefficient of the x- term.

product = - 2 × 5 = - 10 and sum = - 9

The factors are - 10 and + 1

Use these factors to split the middle term

- 2x² - 10x + x + 5 = 0 ( factor the first/second and third/fourth terms )

- 2x(x + 5) + 1(x + 5) ( factor out (x + 5) )

(x + 5)(- 2x + 1) = 0

equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

- 2x + 1 = 0 ⇒ x =

x-intercepts are x = - 5 and x =

susie has 7 apples

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places