The ordered pair is (-2, -3)
Step-by-step explanation:
- Step 1: To find whether an ordered pair is a solution, substitute values of x and y and see whether it satisfies the equation.
(-3, -2) ⇒ 7 × -3 - 5 × -2 = -21 + 10 = -11 ≠ 1
(-2, -3) ⇒ 7 × -2 - 5 × -3 = -14 + 15 = 1
(0, 4) ⇒ 0 - 5 × 4 = 20 ≠ 1
(4, 0) ⇒ 7 × 4 - 0 = 28 ≠ 1
So the ordered pair is (-2, -3)
Answer:
See below.
Step-by-step explanation:
I will assume that 3n is the last term.
First let n = k, then:
Sum ( k terms) = 7k^2 + 3k
Now, the sum of k+1 terms = 7k^2 + 3k + (k+1) th term
= 7k^2 + 3k + 14(k + 1) - 4
= 7k^2 + 17k + 10
Now 7(k + 1)^2 = 7k^2 +14 k + 7 so
7k^2 + 17k + 10
= 7(k + 1)^2 + 3k + 3
= 7(k + 1)^2 + 3(k + 1)
Which is the formula for the Sum of k terms with the k replaced by k + 1.
Therefore we can say if the sum formula is true for k terms then it is also true for (k + 1) terms.
But the formula is true for 1 term because 7(1)^2 + 3(1) = 10 .
So it must also be true for all subsequent( 2,3 etc) terms.
This completes the proof.
Answer:
The factors of given polynomial x =-1 , -2 and x =3
Step-by-step explanation:
<u><em>Step(i):</em></u>-
Given the polynomial
f(x) = x³ - 7x -6
put x =-1
f(-1) = (-1 )³- 7(-1) - 6 = -1+7-6=0
(x+1) is a one factor
By using synthetic division
x³ x² x constant
x=-1 ↓ 1 0 -7 -6
<u>↓ 0 -1 1 6</u>
<u> 1 -1 -6 0 </u>
<u />
<em>The polynomial x² - x - 6 </em>
<u><em>Step(ii):-</em></u>
The factors ( x+1)(x² - x - 6 ) = 0
x = -1 and x² - x - 6 =0
x =-1 and x² - 3x + 2 x - 6 =0
x =-1 and x (x -3) + 2( x-3) =0
x =-1 and (x+2)(x-3) =0
<u><em>Final answer:-</em></u>
The factors of given polynomial x =-1 , -2 and x =3
try using the steps in my question i have one just like you
Step-by-step explanation:
