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ki77a [65]
3 years ago
14

qslant 20" align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
OlgaM077 [116]3 years ago
6 0
The answer is x = 6
Explanation:
First, you must assume that 5x-10=20. Next, you add 10 to 20, which makes the equation 5x=30. Next, divide 30 by 5, which then makes the equation x=6. When you substitute 6 in the original equation, it works, because 5(6)-10 equals 20.
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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,

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  • 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
Write an equation of the parabola that opens up whose vertex (−1, 2) is 3 units from the focus. (Vertex form or Parabola Form is
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Answer:

y2  =  4ax (opens right, a > 0)

y2  =  -4ax (opens right, a > 0)

x2  =  4ay (opens up, a > 0)

x2  =  -4ay (opens down, a > 0)

Vertex at (h, k) :  

(y - k)2  =  4a(x - h) (opens right, a > 0)

(y - k)2  =  -4a(x - h) (opens right, a > 0)

(x - h)2  =  4a(y - k) (opens up, a > 0)

(x - h)2  =  -4a(y - k) (opens down, a > 0)

Equation of a Parabola in Vertex form

Vertex at Origin :  

y  =  ax2 (opens up, a > 0)

y  =  -ax2 (opens down, a > 0)

x  =  ay2 (opens right, a > 0)

x  =  -ay2 (opens left, a > 0)

Vertex at (h, k) :  

y  =  a(x - h)2 + k (opens up, a > 0)

y  =  -a(x - h)2 + k (opens down, a > 0)

x  =  a(y - k)2 + h (opens right, a > 0)

y  =  -a(y - k)2 + h (opens left, a > 0)

Step-by-step explanation:

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Answer:

no ill tell u if i see her homedawgidawg

Step-by-step explanation:

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