Where is the shape? Where’s the image?
Answer:
D
Step-by-step explanation:
Given the 2 equations
4x - 5y = 18 → (1)
3x - 2y = 10 → (2)
Multiplying (1) by 3 and (2) by - 4, then adding will eliminate the x- term
12x - 15y = 54 → (3)
- 12x + 8y = - 40 → (4)
Add (3) and (4) term by term to eliminate x, that is
- 7y = 14 ( divide both sides by - 7 )
y = - 2
Substitute y = - 2 into either of the 2 equations and solve for x
Substituting into (1)
4x - 5(- 2) = 18
4x + 10 = 18 ( subtract 10 from both sides )
4x = 8 ( divide both sides by 4 )
x = 2
solution is (2, - 2 ) → D
Answer:
x = -2, x = 3 − i√8, and x = 3 + i√8
Step-by-step explanation:
g(x) = x³ − 4x² − x + 22
This is a cubic equation, so it must have either 1 or 3 real roots.
Using rational root theorem, we can check if any of those real roots are rational. Possible rational roots are ±1, ±2, ±11, and ±22.
g(-1) = 18
g(1) = 18
g(-2) = 0
g(2) = 12
g(-11) = 1782
g(11) = 858
g(-22) = -12540
g(22) = 8712
We know -2 is a root. The other two roots are irrational. To find them, we must find the other factor of g(x). We can do this using long division, or we can factor using grouping.
g(x) = x³ − 4x² − 12x + 11x + 22
g(x) = x (x² − 4x − 12) + 11 (x + 2)
g(x) = x (x − 6) (x + 2) + 11 (x + 2)
g(x) = (x (x − 6) + 11) (x + 2)
g(x) = (x² − 6x + 11) (x + 2)
x² − 6x + 11 = 0
Quadratic formula:
x = [ 6 ± √(36 − 4(1)(11)) ] / 2
x = (6 ± 2i√8) / 2
x = 3 ± i√8
The three roots are x = -2, x = 3 − i√8, and x = 3 + i√8.
Answer:
27.4
Step-by-step explanation:
First multiply the numerator and denominator by 10
Then write the problem in long division format
Then divide 52 by 19 and get 2
Then multiply the quotient digit (2) by the divisor 19
Then subtract 38 from 52
Then bring down the next number of the dividend
Then divide 140 by 19 to get 7
Then multiply the quotient digit (7) by the divisor 19
Then subtract 133 from 140
Then add a decimal point to the solution
Then bring down the next number of the dividend
Then divide 76 by 19 to get 4
Then multiply the quotient digit (4) by the divisor 19
Then subtract 76 from 76
The solution for long division for 52.06./1.9 is 27.4
27.4
