solve the equation (Please answer step by step the problems so I can make sure I know how to do them correctly). Please TYPE or write very clear. Thanks!

x² + 4x - 21 = 0

x² - x = 30

x² - 81 = 80x

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surekha.asurekhaLv1

10 Jun 2022

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Related questions

Studying to my math exam. Know the answers but would like toknow how to solve these

problems step by step, so later would be able to solve them bymyself :)))

1) Find an equation of the line that satisfies the givenconditions.

Through (1,-2), parallel to the line x+2y=6

2) Find the equation of the line that satisfies thegiven conditions.

Through (1/2,-2/9), perpendicular to the line 4x - 8y =1

3) Find the slope and y-intercept of the line and drawits graph.

3x - 5y +15 = 0

I need help with these as soon as possible Please. Thank You!!

Q15. In 1990, the population of a country was estimated at 4 million. For any subsequent year the population, P(t) (in millions), can be modeled by the equation P(t) = 240/(5 + 54.99e^-0.0208t), where t is the number of years since 1990. Estimate the year when the population will be 21 million.
a. approximately the year 2093
b. approximately the year 2041
c. approximately the year 2088
d. approximately the year 2016

Q18. A size 6 dress in Country C is size 52 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x) = 2(x + 20). Find a formula for the inverse of the function described.
a. f ^-1(x) = (x - 20)/2
b. f ^-1(x) = x - 20
c. f ^-1(x) = (x/2) - 20
d. f ^-1(x) = (x/2) + 20

Q19. If f(x) = 4^x and g(x) = 12, find the point of intersection of the graphs of f and g by solving f(x) = g(x). Give an exact answer.
a. (log ₄ 12, 12)
b. (log ₄ 12, 4)
c. (log ₄ 12, 0)
d. (12, 12)

Q20. Find functions f and g so that f â g = H(x) = (5 - 2x³)².
a. f(x) = 5 - 2x³ ; g(x) = x²
b. f(x) = (5 - 2x)³ ; g(x) = x²
c. f(x) = x² ; g(x) = 5 - 2x³
d. f(x) = x³ ; g(x) = (5 - 2x)²

Q29. Solve the system of equations using Cramer's Rule if it is applicable.

a. x = 9, y = 2, z = 5; (9, 2, 5)
b. x = 8, y = 4, z = 5; (8, 4, 5)
c. x = 4, y = 5, z = 4; (4, 5, 4)
d. x = 8, y = -4, z = -5; (8, -4, -5)

Q30. Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.

a. x = 2, y = 3, z = -7; (2, 3, -7)
b. x = 1, y = 3, z = -4; (1, 3, -4)
c. x = 5, y = 13/2, z = -3; (5, 13/2, -3)
d. x = 1, y = -3, z = -16; (1, -3, -16)

Q33. Write the partial fraction decomposition of the rational expression (4x³ + 4x²)/(x² + 5)².
a. (4x - 4)/(x² + 5) + (-20x + 20)/(x² + 5)²
b. (4x + 4)/(x² + 5) + (-20x - 20)/(x² + 5)²
c. (4x + 4)/(x² + 5) + (20x - 20)/(x² + 5)²
d. (4x + 4)/(x² + 5) + (20x + 20)/(x² + 5)²

Q34. Solve the linear programming problem. Minimize z = 11x + 6y + 7 subject to: x = 0, y = 0, x + y = 1.
a. minimum: 7
b. minimum: 18
c. minimum: 24
d. minimum: 13

Q35. Solve the system of equations by elimination.

a. x = 10, y = 0; (10, 0)
b. x = 10, y = 10; (10, 10)
c. x = 0, y = 10; (0, 10)
d. x = 0, y = 0; (0, 0)

Q36. Perform the row operations on the given augmented matrix.

a.
b.
c.
d.

Q37. Solve the system of equations using Cramer's Rule if it is applicable.

a. x = -4, y = 3; (-4, 3)
b. x = -3, y = -4; (-3, -4)
c. x = 4, y = 3; (4, 3)
d. x = 3, y = 4; (3, 4)

Q38. Write the partial fraction decomposition of the rational expression x/(x² - 9x + 20).
a. -4/(x - 4) + 5/(x - 5)
b. -5/(x - 4) + 4/(x - 5)
c. 4/(x - 4) + -5/(x - 5)
d. -4/(x - 4) + -5/(x - 5)

Q39. Solve the system of equations.

a. x = -4, y = 4, z = -3; (-4, 4, -3)
b. x = -3, y = 4, z = -4; (-3, 4, -4)
c. x = -4, y = -3, z = 4; (-4, -3, 4)
d. inconsistent

Q40. Find the value of the determinant.

a. 224
b. 24
c. -72
d. 72