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3 years ago

Fine the measure of the angle formed by the radius and the side of a regular dodecagon.

Mathematics

1 answer:

Elden [556K]3 years ago

3 0

Answer:

Option D.75°

Step-by-step explanation:

we know that

The sum of the interior angles of a regular dodecagon is equal to

$S=(n-2)*180$

where

n is the number of sides

In this problem

n=12 sides

substitute

$S=(12-2)*180$

$S=1,800\°$

Find the measure of each interior angle

Divide the sum of the interior angles by the number of sides

$1,800\°/12=150\°$

The measure of the angle formed by the radius and the side of a regular dodecagon is half the measure of the interior angle

therefore

$150\°/2=75\°$

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Minimum point of the quadratic x^2+6x-2

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Answer:

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Step-by-step explanation:

Compare the given quadratic equation with the general quadratic equation.

a=1, b=6 and c=-2

$x=-\dfrac{(6)}{2(1)}\\=-3$

Subsitute $-3$ for $x$ in given quadratic equation.

$y=(-3)^2+6(-3)-2\\=9-18-2\\=-11$

The minimum point is (-3,-11).

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2 years ago

Tony and Ricky spend a certain amount of money from their accounts each week at a pet shelter. The table shows the relationship

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Function 1:

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As you see the rate of change is constant: - 6 dollars per week.

The equation shows the relationship between the amount of money, y, remaining in Ricky's account and the number of weeks, x:

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The rate of change is the slope of the linear function, and this is the coefficient of the independent variable, x. Then the rate of change is - 7 dollar per week. Now you know that the two rates are constant and that the second function shows a steeper decreasing.

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3 years ago

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Is 8/11 greater, less than or equal to 0.7

jeka94

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Step-by-step explanation:

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2 years ago

Change the subject of the formula L = v 4kt - p to k.

Romashka [77]

Answer:

$\boxed{k = \frac{L^2 + p}{4t}}$

General Formulas and Concepts:

Algebra I

Basic Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Step-by-step explanation:

Step 1: Define

Identify given.

$\displaystyle L = \sqrt{4kt - p}$

Step 2: Solve for k
We can use equality properties to help us rewrite the equation to get k as our subject:

Let's first square both sides:

$\displaystyle\begin{aligned}L = \sqrt{4kt - p} & \rightarrow L^2 = \big( \sqrt{4kt - p} \big) ^2 \\& \rightarrow L^2 = 4kt - p \\\end{aligned}$

Next, add p to both sides:

$\displaystyle\begin{aligned}L = \sqrt{4kt - p} & \rightarrow L^2 = \big( \sqrt{4kt - p} \big) ^2 \\& \rightarrow L^2 = 4kt - p \\& \rightarrow L^2 + p = 4kt \\\end{aligned}$

Next, divide 4t by both sides:

$\displaystyle\begin{aligned}L = \sqrt{4kt - p} & \rightarrow L^2 = \big( \sqrt{4kt - p} \big) ^2 \\& \rightarrow L^2 = 4kt - p \\& \rightarrow L^2 + p = 4kt \\& \rightarrow \frac{L^2 + p}{4t} = k \\\end{aligned}$

We can rewrite the new equation by swapping sides to obtain our final expression:

$\displaystyle\begin{aligned}L = \sqrt{4kt - p} & \rightarrow \boxed{k = \frac{L^2 + p}{4t}}\end{aligned}$

∴ we have changed the subject of the formula.

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Learn more about Algebra I: brainly.com/question/27698547

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Topic: Algebra I

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1 year ago