Two pairs of numbers comply with the given condition, as it is to expect, since every quadratic equation has two solutions (except when the vertex of its graph is on the x-axis).
Let the numbers be x and (x+1) - They could be x and (x-1) as...
Let's say that m represents the amount of money members pay for aerobic classes at the fitness center.
The cost of the aerobic classes for members is defined by this simple equation: m = 6 + 3x
That is, members will pay a $6 fee to the fitness center, plus $3 every time they...
The monthly cost of at least $89 and at most $137, may be defined as:
89 ≤ C ≤ 137
Since C = 25 + 0.80(x - 60), we get this compound inequality to solve:
89 ≤ 25 + 0.80(x - 60) ≤ 137
A key ingredient of success at working with word problems is defining units correctly. In this case, note that the cost corresponds to 2 years of service. Also, the problem asks for the one-month fee. Then, a good start would be saying: OK, the cost...
When factoring trinomials of the form ax2 + bx + c, the first test you run is common factors. Since there is none in this case, you should try factoring it by product of 2 binomials, or by the quadratic formula.
I wrote a simple program in...
Distance = rate * time or (rate)(time) or "rate multiplied by time"
Define these values for each of the buses. Let's call them bus 1 and bus 2:
Bus 1: distance traveled: x miles
If the pitch is 8, it means the roof raises 8 ft. per each horizontal 12 ft.
Since slope, m, is defined as the rise/run; then m = 8/12.
Simplifying, we obtain a slope m = 2/3
In order to write the line of the roof as an equation, let's assume that the roof line starts at...
There is a correlation between the measurement of the angles of a triangle and the length of their opposite sides:
If the triangle is equiangular, then it is also equilateral
If the triangle is isosceles, then at least two sides are congruent
If the triangle does not have congruent...
I retract my opinion. Byron, you're right. Please accept my apology.
OK Joana, let's say that the amount Nico invested at 6% is x; and the amount at 5% is y. Remember, % means percent, or "out of one hundred". So 6% means 6/100; or $6 per every $100 invested.
If the two investments combined produced $214, then we can set up an...
To figure out if Marietta sold more cheese on Monday than on Tuesday, we need to compare the amount of cheese she sold on both days. However, comparing 7/9 with 0.85 is like comparing cheese with butter: they both come from milk, but are different stuff. In order...
1 - Assign a variable to the number of books each person has. Let Brian = b; Ericka = e and Jasmine = j
2 - Set up equations that reflect each situation:
A) Brian has 3 more books than Ericka: b = e + 3
B) Jasmine has triple books than Brian:...
Christy, a segment that goes from a vertex of a triangle and is perpendicular to its opposite side is called...?
Yes! The height.
So, if segment CD is the height of ΔABC, and D lies on line AB, then Line CD is perpendicular to side AB.
Then the fence that you intend...
Perhaps this function should be written: p(x)=(-4x-1)/(x-5)
If this is the case, then, what is the vertical asymptote (VA)?
Remember... the denominator can not be equal to 0. So...
what value of x will make x-5=0?
That vertical line will be your VA: x=?
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
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:
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...
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...
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...