Answer:
see explanation
Step-by-step explanation:
given the 2 equations
y = x² - 2x - 19 → (1)
y + 4x = 5 → (2)
substitute y = x² - 2x - 19 into (2)
x² - 2x - 19 + 4x = 5 ( subtract 5 from both sides )
x² + 2x - 24 = 0 ← in standard form
(x + 6)(x - 4) = 0 ← in factored form
equate each factor to zero and solve for x
x + 6 = 0 ⇒ x = - 6
x - 4 = 0 ⇒ x = 4
substitute each value of x into (1) for corresponding y- coordinate
x = - 6 : y = (- 6)² - 2(- 6) - 19 = 36 + 12 - 19 = 29 ⇒ (- 6, 29)
x = 4 : y = 4² - 2(4) - 19 = 16 - 8 - 19 = - 11 ⇒ (4, - 11)
the solutions are (- 6, 29), (4, - 11)
Answer:
x=47
Step-by-step explanation:
We can use the triangle bisector theorem
TK TV
----------- = -----------
YK YV
Substituting what we know
87.5 77
----------- = -----------
x-22 22
Using cross products
87.5 * 22 = 77 *(x-22)
Distribute
1925 =77x - 1694
Add 1694 to each side
1925 + 1694 =77x - 1694+1694
3619 = 77x
Divide by 77
3619/77 = 77x/77
47=x
It is 6 units because you find the absolute value of the two different coordinates, in this case it is 4 and -2. Since they belong in different quadrants (one x or y value is positive and the other is negative) you add them. If they are both in the same quadrant, you subtract them.
Using your knowledge of place value the number is
12 6/10 which then reduces to
12 3/5
