the difference of squares of 2 numbers is 112. the square of the smaller number is 9 times the larger number. find the numbers

16 and 12

Step-by-step explanation:

let the 2 numbers be x and y ( x > y ), then

x² - y² = 112 → (1)

y² = 9x → (2)

Substitute y² = 9x into (1)

x² - 9x = 112 ( subtract 112 from both sides )

x² - 9x - 112 = 0 ← in standard form

(x - 16)(x + 7) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 16 = 0 ⇒ x = 16

x + 7 = 0 ⇒ x = - 7

x > 0 , thus x = 16

Substitute x = 16 into (2)

y² = 9(16) = 144 ( take square root of both sides )

y = = 12

Thus the 2 numbers are 16 and 12

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180

f(x)=2/3x-8, which give g(x) the greatest value.

step-by-step explanation: