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malfutka [58]
4 years ago
5

If f = {(4, 2), (6, 1), (8, 4), (10, 2), (12, 5)}, what is the range?

Mathematics
1 answer:
Mkey [24]4 years ago
3 0
Given the function:
<span>f = {(4, 2), (6, 1), (8, 4), (10, 2), (12, 5)}
the range is all the y-values, it's not to be confuse with the domain which is all the x-values, thus the range of our function will therefore be the following set.
{2,1,4,2,5}
Answer:
</span>{2,1,4,2,5}
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A swimming pool is being drained so it can be cleaned. The amount of water in the pool is changing according to the función f(t)
TiliK225 [7]

Answer:

0 ≤ t ≤ 5.

Step-by-step explanation:

In the function f(t), t is the independent variable. The domain of f is the set of all values of t that this function can accept.

In this case, f(t) is defined in a real-life context. Hence, consider the real-life constraints on the two variables. Both time and volume should be non-negative. In other words,

  • t \ge 0.
  • f(t) \ge 0.

The first condition is an inequality about t, which is indeed the independent variable.

However, the second condition is about f, the dependent variable of this function. It has to be rewritten as a condition about t.

\begin{aligned} f(t) &\ge 0 &&\text{Assumption} \cr 80000 - 16000\, t& \ge 0 && \text{Definition of} ~ f \cr 80000 & \ge 16000\, t && \begin{aligned}&\text{Add $16000\, t$} \\[-0.5em] & \text{to both sides of the inequality}\end{aligned} \cr 5 &\ge t &&\begin{aligned}&\text{Divide both sides of} \\[-0.5em] & \text{the inequality by $16000$}\end{aligned} \cr t &\le 5 && \text{Flip the inequality}\end{aligned}.

Hence, t ≤ 5.

Combine the two inequalities to obtain the domain:

0 ≤ t ≤ 5.

6 0
3 years ago
How many and what type of solutions does 7x^2−4x+3 have? 1 rational solution 2 rational solutions 2 irrational solutions 2 nonre
Gre4nikov [31]

Answer:

2 non real solutions.

Step-by-step explanation:

We need to use discriminant,

for ax²+bx+c=0

The discriminat is b²-4ac

If the discriminant is,

→ less than 0, then 0 real solutions

→ equal to 0, then 1 real solutions

→ more than 0, then 2 real solutions

Given that,

7x²−4x+3=0

a=7, b=-4, and c=3

→ (-4)²-4(7)(3)

→ 16-84

→ -68

You can see this is less than 0, then non real solutions. [2 nonreal solutions]

7 0
3 years ago
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What’s an equation that passes through the ordered pair (3,7)and has a slope of -4
natita [175]

For this case we have that by definition, the equation of the line of the slope-intersection form is given by:

y = mx + b

Where:

m: It is the slope of the line

b: It is the cut-off point with the y axis

According to the statement data we have:

m = -4\\(x, y) :( 3,7)

Then, the equation is of the form:

y = -4x + b

We substitute the given point and find "b":

7 = -4 (3) + b\\7 = -12 + b\\7 + 12 = b\\b = 19

Finally, the equation is of the form:

y = -4x + 19

Answer:

y = -4x + 19

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Answer:

A

Step-by-step explanation:

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