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3 years ago

Use the quadratic formula to solve x^2+8x+9=0

1 answer:

4 0

None of your options, not via complete the square nor quadratic the formula.

Solve for x over the real numbers:
x^2 + 8 x + 9 = 0

x = (-8 ± sqrt(8^2 - 4×9))/2 = (-8 ± sqrt(64 - 36))/2 = (-8 ± sqrt(28))/2:
x = (-8 + sqrt(28))/2 or x = (-8 - sqrt(28))/2

sqrt(28) = sqrt(4×7) = sqrt(2^2×7) = 2sqrt(7):
x = (2 sqrt(7) - 8)/2 or x = (-2 sqrt(7) - 8)/2

Factor 2 from -8 + 2 sqrt(7) giving 2 (sqrt(7) - 4):
x = 1/22 (sqrt(7) - 4) or x = (-2 sqrt(7) - 8)/2

(2 (sqrt(7) - 4))/2 = sqrt(7) - 4:
x = sqrt(7) - 4 or x = (-2 sqrt(7) - 8)/2

Factor 2 from -8 - 2 sqrt(7) giving 2 (-sqrt(7) - 4):
x = sqrt(7) - 4 or x = 1/22 (-sqrt(7) - 4)

(2 (-sqrt(7) - 4))/2 = -sqrt(7) - 4:

Answer: x = sqrt(7) - 4 or x = -sqrt(7) - 4_____________________________________________________

Solve for x:
x^2 + 8 x + 9 = 0

Subtract 9 from both sides:
x^2 + 8 x = -9

Add 16 to both sides:
x^2 + 8 x + 16 = 7

Write the left hand side as a square:
(x + 4)^2 = 7

Take the square root of both sides:
x + 4 = sqrt(7) or x + 4 = -sqrt(7)

Subtract 4 from both sides:
x = sqrt(7) - 4 or x + 4 = -sqrt(7)

Subtract 4 from both sides:
Answer: x = sqrt(7) - 4 or x = -4 - sqrt(7)

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(a) A photography student borrows RM2 500 to buy a camera. The bank loans this money at a rate of 9 % capitalized monthly. What

Monica [59]

Answer:

The student will have to reimburse 2,991.03 two years later.

Step-by-step explanation:

This is a compound interest problem:

The compound interest formula is given by:

$A = P(1 + \frac{r}{n})^{nt}$

In which A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

In this problem, we have that:

A is the amount the student will have to reimburse two years later.

P is his loan. so $P = 2,500$

The bank loans this money at a rate of 9 % capitalized monthly. This means that $r = 0.09$ and $n = 12$ , since the money is compounded monthly, this means, 12 times in a year.

He will have to reimburse two years later, so $t = 2$

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3 years ago

Consider the table below.

Licemer1 [7]

Answer:

y = 0.5x² +3x +5

Step-by-step explanation:

There are several ways to do this. The most straightforward may be to fill three table values into the equation and solve for a, b, c. Using the first three values, the equations would be ...

y = ax² + bx + c

0.5 = 9a -3b +c . . . . first point
1.0 = 4a -2b +c . . . . second point
2.5 = a -b +c . . . . . . third point

Solving this system of equations by your favorite method gives ...

a = 0.5, b = 3, c = 5

so the quadratic is ...

y = 0.5x² +3x +5

Since you are given the y-intercept (0, 5), you know the constant in the equation is 5. The given table values are equally-spaced, so finding differences can be informative.

first differences: 1 -0.5 = 0.5; 2.5 -1 = 1.5; 5 -2.5 = 2.5; 8.5 -5 = 3.5

second differences: 1.5 -0.5 = 1; 2.5 -1.5 = 1; 3.5 -2.5 = 1

That is, second differences are 1, which value is double the "a" coefficient of the equation. So, we know the equation is ...

y = 0.5x² +bx +5

Filling in x=1, we get

8.5 = 0.5 +b +5

3 = b

and the equation is ...

y = 0.5x² +3x +5

You can also let your graphing calculator or spreadsheet program show you a quadratic regression equation through these points. It gives the same result.

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3 years ago