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galina1969 [7]
3 years ago
14

How do i factor the coefficent out of a variable, such as 2.4n+9.6 and -6z+12

Mathematics
1 answer:
ANEK [815]3 years ago
4 0
You are factoring one or more linear expressions (but are not factoring variables).

2.4n+9.6 can be divided by 2.4 and then the result mult. by 2.4:

2.4n+9.6 = 2.4 [ n + 4 ]

Also:  -6z+12= 6 [ -z + 2 ]  Here I have simplified linear functions but factoring out common constant coefficients (not variables).
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Multiply the binomial and the trinomial. <br> (x-2)(x^2+2x+4)
malfutka [58]

Answer:

Step-by-step explanation:

To solve this problem, we need to multiple x and -2 by x^{2} + 2x + 4 and add the results together:

x(x^{2} + 2x + 4)

x^{3} + 2x^{2} + 4x

-2(x^{2} + 2x + 4)

-2x^{2} - 4x - 8

Adding the two together give the following:

(x^{3} + 2x^{2} + 4x) + (-2x^{2} - 4x - 8)

x^{3} - 8

7 0
3 years ago
The function C(h)=(2h^2+5h)/(h^3+8) models the concentration of medication in the bloodstream (as a percent) h hours after its i
salantis [7]

Answer:

  1. h ≥ 0
  2. C = 0; concentration eventually decays to nothing
  3. (0, 0) is the only intercept in the domain. It means the concentration in the bloodstream is zero at the time the drug is injected.
  4. 1.95 hours

Step-by-step explanation:

1. a. The domain of the function in the context of this problem is h ≥ 0. The maximum value of h will correspond to the time at which the concentration is considered to be negligible. If that time is when the concentration decays to 1% of its peak value, then perhaps the suitable domain is 0 ≤ h ≤ 180.

b. The equation of the vertical asymptote of this function is where the denominator of C(h) is zero, that is ...

  h^3 +8 = 0

  h = ∛(-8)

  h = -2 . . . . the equation of the vertical asymptote

This is not a concern for a medical professional because it is outside the domain of the function.

__

2. As h gets large the value of the function approaches 2/h, which is to say the horizontal asymptote is C = 0. It means the concentration of medication in the blood eventually decays to zero.

__

3. C(0) = 0 is the only intercept in the domain of the function. (h, C(h)) = (0, 0)

In the context of this problem, it means the blood concentration of medication is zero at the time of the injection.

__

4. About 1.95 hours after injection, a maximum concentration of the drug occur in the bloodstream. This value is easily found using a graphing calculator.

Taking the derivative of the function gives you ...

  C'(h) = -2(h^4 +5h^3 -16h -20)/(h^3 +8)^2

This has two real zeros and two complex zeros. The positive real zero is near h = 1.94527, about 1.95.

That is, the concentration in the bloodstream reaches a maximum about 1.95 hours after injection into the muscle.

5 0
3 years ago
5. Louis has 21 coins in his pouch, how many nickels and<br> dimes does he have if he has $1.35?
PolarNik [594]
N + d = 21
0.5n + 0.10d = 1.35
5n + 10d = 135
d = 21-n
5n + 210 - 10n = 135
-5n = -75
n = 15
d = 6
3 0
3 years ago
What is the y intercept? f(x)=-2^2+4x-6
den301095 [7]

Answer:

The y intercept is -1

Step-by-step explanation:

the y-intercept is when y = 0

f(0) = -2^2 + 4(0) - 5

f(0) = 4 - 5

f(0) = -1

8 0
3 years ago
A car salesman sells cars with prices ranging from $5,000 to $45,000. The histogram shows the distribution of the numbers of car
iogann1982 [59]
It's either 20 or 25 thousand.
8 0
3 years ago
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