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Nat2105 [25]
2 years ago
5

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

Mathematics
1 answer:
Gnoma [55]2 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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Brandi's new balance on her credit card statement was $256.38.
Amiraneli [1.4K]

Answer:

$38.46

Step-by-step explanation:

Minimum payment = 15% of balance

Balance = $256.38

Therefore

15% of $256.38

Change 15% to decimal

15% /100% x $256.38

0.15 x $256.38

$38.46

Her minimum payment is $38.46

6 0
2 years ago
Find the common difference of the arithmetic sequence 13, 16, 19,...13,16,19,...
VLD [36.1K]

Answer:

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4 0
2 years ago
What is 5(y-2)-2=2(y+1)-5? Solve for y and show your work please.
Inessa [10]

Answer:

y = 3

Step-by-step explanation:

Let's start with the left side of the equation.

5(y-2)-2= 2(y+1)-5

5y-10-2= 2(y+1)-5

Now let's solve the right side

5y-10-2= 2y+2-5

5y-12= 2y-3

-2y     -2y

3y-12=-3

   +12 +12

3y = 9

3y/3 = 9/3

y = 3

hope this helps!

4 0
3 years ago
Point B has coordinates ​(2​,1​). The​ x-coordinate of point A is −3. The distance between point A and point B is 13 units. What
leva [86]

Answer:

A = (-5,y)    B = (4,1)  

6 0
3 years ago
What two-dimensional figure will result from slicing this rectangular pyramid parallel to the base?
andreev551 [17]

Answer: The answer is D. Trapezoid.    


Step-by-step explanation:  As shown in the attached figure, a rectangular pyramid  ABCDE is drawn. We are slicing this rectangular pyramid parallel to the base BCDE at the points F, G, H and I.

We can clearly see from the figure that upper half of the sliced figure will be similar to the pyramid BCDE and the lower sliced figure will be a trapezoid. These are the three-dimensional figures.

Also, the sliced two-dimensional figure FGHI will be a rectangle, because

the pyramid is a rectangular one and so,  FI=GH, FG=HI and all the angles are right angles.

Thus, the resulting two-dimensional figure will be a rectagle.


7 0
3 years ago
Read 2 more answers
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