Use the distributive properly to remove the parentheses. -(4w-y-3)

The graph shown represents the number of bacteria in a dish after a certain number of minutes. It is a function in the form f(x)

SSSSS [86.1K]

Answer:

The number of bacteria in the dish after 9.9 minutes is 478

Step-by-step explanation:

The form of the function is $f(x)=a.b^{x}$ , where a is the initial amount (value f(x) at x = 0)

To find a and b let us use two points from the graph and substitute their coordinates in the equation

∵ The graph passes through point (1 , 1)

∴ x = 1 and y = 1

- Substitute them in the equation

∵ $1=a.b^{1}$

∴ a.b = 1 ⇒ (1)

∵ The graph passes through point (1 , 1)

∴ x = 3 and y = 4

- Substitute them in the equation

∵ $4=a.b^{3}$

∴ a.b³ = 4 ⇒ (2)

Use equation (1) to find a in terms of b

∵ a.b = 1

- Divide both sides by b

∴ $a=\frac{1}{b}$ ⇒ (3)

- Substitute a in equation (2) by equation (3)

∴ $\frac{1}{b}$ . b³ = 4

- Remember the rule $\frac{a^{m}}{a^{n}}=a^{m-n}$

∵ $\frac{1}{b}$ . b³ = $b^{3-1}$ = b²

∴ b² = 4

- Take √ for both sides

∴ b = 2

Substitute the value of b in equation (3) to find a

∵ a = $\frac{1}{2}$

∴ a = 0.5

∴ $f(x)=0.5(2)^{x}$

∵ f(x) represents the number of bacteria after x minutes

∵ x = 9.9 minutes

- Substitute x by 9.9 to find the number of bacteria

∵ $f(9.9)=0.5(2)^{9.9}$

∴ f(9.9) = 477.7128917

- Round it to the nearest whole number

∴ f(9.9) = 478

∴ The number of bacteria in the dish after 9.9 minutes is 478

4 0

3 years ago

a plane flying with the wind travels 630 mi in 1.5hrs. Flying against the wind , the plane travels 1120 mi in 4hrs. Find the rat

Flauer [41]

$\bf \begin{cases}
r=\textit{rate of the plane}\\
w=\textit{rate of the wind}\\
\end{cases}
\\\\

\begin{array}{ccccllll}
&distance&rate&time(hrs)\\
&\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\\
\textit{with wind}&630&r+w&1\frac{1}{2}\\
\textit{against wind}&1120&r-w&4
\end{array}
$

$\bf thus \begin{cases}
630=(r+w)1\frac{1}{2}\to 630=(r+w)\frac{3}{2}
\\\\
1120=(r-w)4\\
--------------\\
630=(r+w)\frac{3}{2}\implies 630\cdot \frac{2}{3}=r+w\\
420=r+w\implies \boxed{420-w}=r\\
--------------\\
thus\\
--------------\\
1120=(r-w)4\implies 1120=4r-4w
\\\\
1120=4(\boxed{420-w})-4w
\end{cases}
$

solve for "w", to find the wind's speed rate,

so hmmm what's the plane's rate? well 420 - w = r :)

5 0

3 years ago

Simplest form of 36/104

konstantin123 [22]

9/26 is the correct answer

6 0

3 years ago

Read 2 more answers

What seven divided by 4

Naddik [55]

Answer:

1.75

Step-by-step explanation:

$\frac{7}{4} = 1 \frac{3}{4} = 1.75$

7 0

3 years ago

Read 2 more answers

The income tax policy for residents of a tiny island nation that uses U.S. Dollars as its currency is as follows: The first $20,

Stells [14]

Answer:

C.

0.10(20,000) + 0.18(30,000) + 0.27(x − 50,000)

Step-by-step explanation:

Let's take this one step at a time. First, the $20000 dollars is taxed by 10% = .10 as a decimal. So the first term is

.10(20000)

Next, we have to add on the second term, wherein the next $30000 is taxed by .18. So the second term is

.10(20000) + .18(30000)

Then, we have to take whatever's left, whatever we haven't yet taxed, and tax it at a 27% rate. This means x-50000, not x, because we're taking whatever's over the initial 50000 that we've already taxed.

0.10(20,000) + 0.18(30,000) + 0.27(x − 50,000)

5 0

3 years ago