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Nat2105 [25]
3 years ago
5

Solve the equation by factoring: x2 − 7x + 12 = 0

Mathematics
1 answer:
Gnoma [55]3 years ago
7 0

Answer:

x = 3 . . . or . . . x = 4

Step-by-step explanation:

The factored form is ...

(x -3)(x -4) = 0

The zero product rule tells you the solutions are the values of x that make the factors be zero:

x = 3

x = 4

_____

Comment on factoring

When the leading coefficient is 1, the coefficient of the x-term is the sum of the constants in the binomial factors, and the constant term is their product. You can see this by multiplying out the generic case:

(x +a)(x +b) = x^2 +(a+b)x + ab

What this means is that when you're factoring, you're looking for factors of the constant that add up to give the coefficient of the x-term. Here, the x-term is negative and the constant is positive, so both factors will be negative.

12 = -1×-12 = -2×-6 = -3×-4

The sums of these factor pairs are -13, -8, -7. Clearly, the last pair of factors of 12 will be useful to us, since that sum is -7. So, the binomial factors of our equation are ...

(x -3)(x -4) = 0

___

If the leading coefficient is not zero, the method of factoring is similar, but slightly different. Numerous videos and web sites discuss the method(s).

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3 times a number is 54 less than the square of that number. Find the negative solution.
son4ous [18]

Answer:

-6

Step-by-step explanation:

3n = n² - 54

n² - 3n - 54 = 0

n² - 9n + 6n - 54 = 0

n(n - 9) + 6(n - 9) = 0

(n - 9)(n + 6) = 0

n = 9 , -6

5 0
3 years ago
if a tv has a diagonal measurement of 55 and a height of 30, what is the tvs width? round to the nearest whole number
Sati [7]

Answer:

  46

Step-by-step explanation:

The geometry can be modeled by a right triangle. The diagonal measure is the hypotenuse, and the height is one leg. The width is the other leg, and can be found using the Pythagorean theorem.

__

<h3>Pythagorean theorem</h3>

The relation between the leg lengths (a, b) and the hypotenuse (c) is ...

  c² = a² +b²

Solving for b gives ...

  b = √(c² -a²)

<h3>application</h3>

In this problem, we have c=55 and a=30. Then the width of the TV is ...

  b = √(55² -30²) = √(3025 -900) = √2125

  b ≈ 46.098

The width of the TV is about 46.

7 0
2 years ago
The residual plot for a data set is shown.
BaLLatris [955]
The correct answer is: <span>D. The regression line is not a good model because the points in the residual plot form a curve.  (i know this because i just passed the test ;) )</span>
5 0
3 years ago
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Does someone know the correct answer?
Ksenya-84 [330]

Answer:

C

Step-by-step explanation:

3 0
3 years ago
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Use trial and improvement to find the solution to this positive equation
Novay_Z [31]
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