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4 years ago

What is the area of a 7 and 9 side length triangle

Mathematics

2 answers:

katovenus [111]4 years ago

7 0

The formula is A = 1/2bh
So, plug in
A = 1/2 7(9)
A = 1/2(63)
A = 31.5

coldgirl [10]4 years ago

5 0

The aria of your triangle is (7*9)/2 = 31.5;

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A culture of bacteria has an initial population of 9300 bacteria and doubles every 3

sp2606 [1]

Answer:

The approximate population of bacteria in the culture after 10 hours is 93,738.

Step-by-step explanation:

<h3>General Concepts:</h3>

Exponential Functions.
Exponential Growth.
Doubling Time Model.
Logarithmic Form.

BPEMDAS Order of Operations:

Brackets.
Parenthesis.
Exponents.
Multiplication.
Division.
Addition.
Subtraction.

<h2>Definitions:</h2>

We are given the following Exponential Growth Function (Doubling Time Model), $\displaystyle\mathsf{P_{(t)}\:=\:P_0\cdot2^{(t/d)}}$ where:

$\displaystyle\sf{P_t\:\:\rightarrow}$ The population of bacteria after “<em>t </em>” number of hours.
$\displaystyle\sf{P_0 \:\:\rightarrow}$ The initial population of bacteria.
$\displaystyle{t \:\:\rightarrow}$ Time unit (in hours).
$\displaystyle{\textit d \:\:\rightarrow}$ Doubling time, which represents the amount of time it takes for the population of bacteria to grow exponentially to become twice its initial quantity.

<h2>Solution:</h2>

<u>Step 1: Identify the given values.</u>

$\displaystyle\sf{P_0\:=}$ 9,300.
<em>t</em> = 10 hours.
<em>d</em> = 3.

<u>Step 2: Find value.</u>

1. Substitute the values into the given exponential function.

$\displaystyle\mathsf{P_{(t)} = P_0\cdot2^{(t/d)}}$

$\displaystyle\mathsf{\longrightarrow P_{(10)} = 9300\cdot2^{(10/3)}}$

2. Evaluate using the BPEMDAS order of operations.

$\displaystyle\mathsf{P_{(10)} = 9300\cdot2^{(10/3)}\quad \Longrightarrow BPEMDAS:\:(Parenthesis\:\:and\:\:Division).}$

$\displaystyle\sf P_{(10)} = 9300\cdot2^{(3.333333)}\quad\Longrightarrow BPEMDAS:\:(Exponent).}$

$\displaystyle\sf P_{(10)} = 9300\cdot(10.079368399)\quad \Longrightarrow BPEMDAS:(Multiplication).}$

$\boxed{\displaystyle\mathsf{P_{(10)} \approx 93,738.13\:\:\:or\:\:93,738}}$

Hence, the population of bacteria in the culture after 10 hours is approximately 93,738.

<h2>Double-check:</h2>

We can solve for the amount of <u>time</u> <u>(</u><em>t</em> ) it takes for the population of bacteria to increase to 93,738.

1. Identify given:

$\displaystyle\mathsf{P_{(t)} = 93,738 }$ .
$\displaystyle\mathsf{P_0 = 9,300}$ .
<em>d </em>= 3.

2. Substitute the values into the given exponential function.

$\displaystyle\mathsf{P_{(t)} = P_0\cdot2^{(t/d)}}$

$\displaystyle\mathsf{\longrightarrow 93,378 = 9,300\cdot2^{(t/3)}}$

3. Divide both sides by 9,300:

$\displaystyle\mathsf{\longrightarrow \frac{93,378}{9,300} = \frac{9,300\cdot2^{(t/3)}}{9,300}}$

$\displaystyle\mathsf{\longrightarrow 10.07936840 = 2^{(t/3)}}$

4. Transform the right-hand side of the equation into logarithmic form.

$\boxed{\displaystyle\mathsf{\underbrace{ x = a^y}_{Exponential\:Form} \longrightarrow \underbrace{y = log_a x}_{Logarithmic\:Form}}}$

$\displaystyle\mathsf{\longrightarrow 10.07936840 = \bigg[\:\frac{t}{3}\:\bigg]log(2)}$

5. Take the <em>log</em> of both sides of the equation (without rounding off any digits).

$\displaystyle\mathsf{log(10.07936840) = \bigg[\:\frac{t}{3}\:\bigg]log(2)}$

$\displaystyle\mathsf{\longrightarrow 1.003433319 = \bigg[\:\frac{t}{3}\:\bigg]\cdot(0.301029996)}$

6. Divide both sides by (0.301029996).

$\displaystyle\mathsf{\frac{1.003433319}{0.301029996} = \frac{\bigg[\:\frac{t}{3}\:\bigg]\cdot(0.301029996) }{0.301029996}}$

$\displaystyle\mathsf{\longrightarrow 3.3333333 = \frac{t}{3}}$

7. Multiply both sides of the equation by 3 to isolate "<em>t</em>."

$\displaystyle\mathsf{(3)\cdot(3.3333333) = \bigg[\:\frac{t}{3}\:\bigg]\cdot(3)}$

$\boxed{\displaystyle\mathsf{t\approx10}}$

Hence, it will take about 10 hours for the population of bacteria to increase to 93,378.

__________________________________

Learn more about Exponential Functions on:

brainly.com/question/18522519

7 0

2 years ago

Find the slope and the y-intercept in this equation: 3y+6=-2x

Dmitry [639]

Hello,

To solve this problem, you should first put in it slope intercept form.

Here are the steps:

3y + 6 = -2x Add 6 to both sides
3y = -2x - 6 Divide both sides by 3
y = (-2/3)x - 2

The you can see that the slope is (-2/3) and the y-intercept is (0, -2).

I hope this helps,
MrEQ

7 0

4 years ago

Read 2 more answers

Copy the problems onto your paper, mark the givens and prove the statements asked.

natulia [17]

The statements and reasons for the proof are:

CN ≅ WN [given]
∠C ≅ ∠W [given]
m∠CNR ≅ ∠WNO [vertical angles theorem]
ΔCNR ≅ ΔWNO [ASA theorem]
RN = ON [CPCTC]

<h3>What is the CPCTC and ASA Congruence Theorem?</h3>

When two triangles have two corresponding congruent angles and one corresponding included sides that are congruent, both triangles are congruent by ASA. By implication, the CPCTC states that since they are congruent triangles, all its corresponding parts are congruent to each other.

The statement for the proof along with the reasons in bracket are:

CN ≅ WN [given]
∠C ≅ ∠W [given]
m∠CNR ≅ ∠WNO [vertical angles theorem]
ΔCNR ≅ ΔWNO [ASA theorem]
RN = ON [CPCTC]

Learn more about the CPCTC theorem on:

brainly.com/question/14706064

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2 years ago

The product of a number (n) and 12 is 64. Which equation shows this relationship

skelet666 [1.2K]

The answer would be 12n=64 because the definition of product is, "the number received when multiplying two numbers together." Hope this helps!

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3 years ago

How can I find the area of a 5 sided shape with a simple formula

Slav-nsk [51]

1. Break into triangles, then add. In the figure<span> on the right, the </span>polygon<span> can be broken up into triangles by drawing all the diagonals from one of the vertices. If you know enough sides and angles to </span>find the area<span> of each, then you can simply add them up to </span>find<span> the total.</span>

4 0

3 years ago