This is the deal:
Since the axis of symmetry is a vertical line, x = -7 and the parabola has a maximum height of 4 units above the x axis; we can safely conclude that it opens down and its vertex is at (-7, 4). Besides, it passes through the point (-6, 0), which is below
the vertex; definitively,...
Organize your polynomial in 2 groups:
(3p^3 - 21p^2) - (p - 7)
Now, factor the first group by GCF:
3p^2(p - 7) - (p - 7)
Notice that (p - 7) is a common factor, then factor again by GCF:
(p - 7)(3p^2 - 1)
Finally, rearrange your answer: (3p^2 - 1)(p - 7)
b2 + 5b + 6 = 0
This trinomial may be factored as the product of two binomials if we find two numbers such that:
- Their product is equal to 6, and
- Their sum is equal to 5
These two numbers indeed exist:
they are 3 and 2: (3)(2) = 6; and (3)+(2) = 5
Then our trinomial factors...
36y4(y + 12)3 + y5(y + 12)4
Let (y + 12) = u
Now rewrite the expression:
36y4u3 + y5u4 GCF: y4u3
y4u3(36 + yu)
Now, for the sake of simplicity, revert u=(y+12) inside the parenthesis only:
y4u3(36 + y(y + 12))
Now, expand the expression inside the parenthesis:
19-8d = d-17
I advise my students to start with the unknown (d). If you eliminate the smaller one, you will deal with positive values. So, let's eliminate -8d; how? add 8d on both sides of the equal sign:
19-8d+(8d) = d-17+(8d)
The parenthesis are not necessary, I use it as a mean...
Assuming the Transverse axis is horizontal and the center of the hyperbole is the origin, the foci are:
A(250, 0) and B(-250, 0) ; thus c = 250
Now, let's figure out how far appart is P from A and B. This is the fun part. Ready? OK. Since the speed of the signal is given in feet/microsecond...
OK. Let's try again.
8/(x-2) + 8/(x+2) = 3 On the left side, the LCD is (x-2)(x+2):
(8(x+2) + 8(x-2))/(x-2)(x+2) = 3 Also: (x-2)(x+2) = x2 - 4:
(8x + 16 + 8x - 16)/(x2 - 4) = 3 Simplify the numerator and multiply both sides by the denominator:
16x = 3(x2 - 4) or 16x...
If your inequality is: (-2/3)x < 6, then you just need to multiply both sides by the reciprocal of -2/3. Since you're multiplying by a negative number, you need to flip the inequality sign:
(-3/2)(-2/3)x > 6(-3/2)
x > -9
Finally, you may need to graph the solution...
I- Solve for y: 3y > -6x + 18
y > -2x + 6
II - Draw the boundary line: y = -2x + 6
(Since y is greater than, and not equal to, -2x + 6, this is a dotted line)
III - Test any point away of the line to determine the shaded region. For...
x = amount invested in fund 1, which earned 7% and
y = amount invested in fund 2, which earned 2%
Set up a system of 2 equations:
The total amount invested is the sum of the amounts invested in fund 1 plus the amount invested in fund 2:
I - x + y = 2,900