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1 year ago

Vertex represents a maximum or minimum point for the function. Explain your

Mathematics

1 answer:

Eddi Din [679]1 year ago

7 0

Answer:

the vertex represents a maximum

Vertex is (4,7)

f(x)=-(x-4)^2+7

Step-by-step explanation:

Given the function $f(x)=-x^2+8x+9$

Equation is in the form of y=ax^2+bx+c

$a=-1$

When 'a' is negative, then vertex is maximum

when 'a' is positive, then vertex is minimum

$a=-1$ is negative, so the vertex represents a maximum

$f(x)=-x^2+8x+9$ , factor out negative

Take out negative sign in common

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1.) -9x+8 ≤ 80 * A. x ≥ -8 B. x ≤ -8 C. x ≥ 8 D. x ≤ 8

Firlakuza [10]

Answer:

$x\geq -8$

Step-by-step explanation:

$-9x+8\leq 80$

-8 -8

₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋

$\frac{-9x}{-9} \leq \frac{72}{-9}$

⇵

$x\geq -8$

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2 years ago

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100 points I have answer. Can someone explain this correct answer, I know its correct, but need to understand why? Do we subtrac

lapo4ka [179]

Answer:

c = -6

d = 2

Step-by-step explanation:

After reflection about the x-axis:

A --> A'

(2,3) --> (2,-3)

(4,3) --> (4,-3)

(2,6) --> (2,-6)

After translation:

(2 + c, -6 + d) --> (-4, -4)

2+c = -4

c = -6

-6+d = -4

d = 2

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2 years ago

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Noah said, “When you divide a number by a second number, the result will always be smaller than the first number.”

marshall27 [118]

Answer:

When dividing two fractions by each other, the result will be larger. Dividing two whole numbers, however, will always result in a smaller number because you're taking away a part of the number.

Step-by-step explanation:

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2 years ago

I need help with this problem if anyone can help ASAP please help !

MakcuM [25]

Answer:

Step-by-step explanation:

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3 years ago

In a previous exercise we formulated a model for learning in the form of the differential equation dp dt = k(m − p) where p(t) m

DaniilM [7]

I assume you mean

$\dfrac{dP}{dt} = k(M-P)$

ANSWER
An expression for P(t) is

$P = M - Me^{-kt}$

EXPLANATION
This is a separable differential equation. Treat M and k as constants. Then we can divide both sides by M - P to get the P term with the differential dP and multiply both sides by dt to separate dt from the P terms

$\begin{aligned} \dfrac{dP}{dt} &= k(M-P) \\ \dfrac{dP}{M-P} &= k\, dt
\end{aligned}$

Integrate both sides of the equation.

$\begin{aligned}
\int \dfrac{dP}{M-P} &= \int k\, dt \\
-\ln|M-P| &= kt + C \\
\ln|M-P| &= -kt - C\end{aligned}$

Note that for the left-hand side, u-substitution gives us

$u = M - P \implies du = -1dP \implies dP = -du$

hence why $\int \frac{dP}{M-P} \ne \ln|M - P|$

Now we use the definition of the logarithm to convert into exponential form.

The definition is

$\ln(a) = b \iff \log_e(a) = b \iff e^b = a$

so applying it here, we get

$\begin{aligned} \ln|M-P| &= -kt - C \\ |M - P| &= e^{-kt - C} \\ 
M - P &= \pm e^{-kt - C} 
 \end{aligned}$

Exponent properties can be used to address the constant C. We use $x^{a} \cdot x^{b} = x^{a+b}$ here:

$\begin{aligned}
 M - P &= \pm e^{-kt - C} \\
M - P &= \pm e^{- C - kt} \\ 
M - P &= \pm e^{- C + (- kt)} \\ 
M - P &= \pm e^{- C} \cdot e^{- kt} \\ 
M - P &= Ke^{- kt} && (\text{\footnotesize Let $K = \pm e^{-kt}$ }) \\ 
M &= Ke^{- kt} + P\\
P &= M - Ke^{- kt}
\end{aligned}$

If we assume that P(0) = 0, then set t = 0 and P = 0

$\begin{aligned} 
0 &= M - Ke^{- k\cdot 0} \\
0 &= M - K \cdot 1 \\
M &= K
 \end{aligned}
$

Substituting into our original equation, we get our final answer of

$P = M - Me^{-kt}$

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3 years ago

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