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2 years ago

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"Rebecca walks 100 feet in a straight line. She then turns 20 degrees to her left and walks another 100 feet, and then turns 20

degrees to her left again. She continues this pattern until she reaches the point where she started. How far did she walk

1 answer:

iragen [17]2 years ago

5 0

Answer:

1,800 ft

Step-by-step explanation:

Rebecca will walk in the pattern of a regular polygon with 'n' sides and internal angles of 160 degrees (180 at a straight line - 20 degrees from each turn).

The equation that describes the internal angle of a regular polygon is:

$A = \frac{(n-2)*180}{n}$

For A = 160 degrees:

$160n=(n-2)*180\\(180-160)n=360\\n=18\ sides$

If each side is 100 ft long, the total distance that Rebecca has walked is:

$d = 18*100\\d=1,800\ ft$

She walked 1,800 ft.

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Y=-1/3x^2-4x-5 in vertex form

grigory [225]

Answer:

$Y=-\frac{1}{3}(x+6)^2+7$ [Vertex form]

Step-by-step explanation:

Given function:

$Y=-\frac{1}{3}x^2-4x-5$

We need to find the vertex form which is.,

$y=a(x-h)^2+k$

where $(h,k)$ represents the co-ordinates of vertex.

We apply completing square method to do so.

We have

$Y=-\frac{1}{3}x^2-4x-5$

First of all we make sure that the leading co-efficient is =1.

In order to make the leading co-efficient is =1, we multiply each term with -3.

$-3\times Y=-3\times\frac{1}{3}x^2-(-3)\times4x-(-3)\times 5$

$-3Y=x^2+12x+15$

Isolating $x^2$ and $x$ terms on one side.

Subtracting both sides by 15.

$-3Y-15=x^2+12x-15-15$

$-3Y-15=x^2+12x$

In order to make the right side a perfect square trinomial, we will take half of the co-efficient of $x$ term, square it and add it both sides side.

square of half of the co-efficient of $x$ term = $(\frac{1}{2}\times 12)^2=(6)^2=36$

Adding 36 to both sides.

$-3Y-15+36=x^2+12x+36$

$-3Y+21=x^2+12x+36$

Since $x^2+12x+36$ is a perfect square of $(x+6)$ , so, we can write as:

$-3Y+21=(x+6)^2$

Subtracting 21 to both sides:

$-3Y+21-21=(x+6)^2-21$

$-3Y=(x+6)^2-21$

Dividing both sides by -3.

$\frac{-3Y}{-3}=\frac{(x+6)^2}{-3}-\frac{21}{-3}$

$Y=-\frac{1}{3}(x+6)^2+7$ [Vertex form]

8 0

3 years ago

Hope researches the impact of one variable on another. She graphs the data from her research and sees that the data forms a shap

zaharov [31]

Answer:

She can determine that while there is an association between the variables, there is no correlation, and she cannot determine causation.

Step-by-step explanation:

Since there is an arch shape to her graph, we know that as one variable changes, the other changes in the same manner. This means there is an association between the variables.

However, since the graph is not linear, there is no correlation between the variables. Since there is no correlation, we cannot determine causation.

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6 0

2 years ago

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Find the value of x, if f(x)=3x-15 when f(x)=30

musickatia [10]

Answer:

f(30)= 75

Step-by-step explanation:

3(30)-15

90-15

75

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1 year ago

Can you help me please?

PilotLPTM [1.2K]

Answer:

Your answer should be 0.125

Step-by-step explanation:

Divide the numerator by the denominator

1 divided by 8 = 0.125

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2 years ago

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Liono4ka [1.6K]

Answer:

C) 36

Step-by-step explanation:

Because 6^2=6*6=36.

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2 years ago

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