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3 years ago

Describe the transformation from the parent function y=(x+4)^2-1

Mathematics

1 answer:

Degger [83]3 years ago

3 0

Answer:

Translation 4 units to the left., followed by

a translation 1 unit down.

Step-by-step explanation:

The parent function is y = x^2 which is a parabola that opens upwards and has a vertex at the point (0,0).

Y = (x + 4)^2 is the graph of x^2 translated 4 units to the left.

The - 1 translates the graph down 1 unit.

So the vertex of the new graph is at (-4, 1).

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7x – 8y = 112 in slope intercept form

Digiron [165]

Answer:

y = 7/8x-14

Step-by-step explanation:

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7 0

2 years ago

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Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it.

grandymaker [24]

$(2x+1)^{\cot x}=\exp\left(\ln(2x+1)^{\cot x}\right)=\exp\left(\cot x\ln(2x+1)\right)=\exp\left(\dfrac{\ln(2x+1)}{\tan x}\right)$

where $\exp(x)\equiv e^x$ .

By continuity of $e^x$ , you have

$\displaystyle\lim_{x\to0^+}\exp\left(\dfrac{\ln(2x+1)}{\tan x}\right)=\exp\left(\lim_{x\to0^+}\dfrac{\ln(2x+1)}{\tan x}\right)$

As $x\to0^+$ in the numerator, you approach $\ln1=0$ ; in the denominator, you approach $\tan0=0$ . So you have an indeterminate form $\dfrac00$ . Provided the limit indeed exists, L'Hopital's rule can be used.

$\displaystyle\exp\left(\lim_{x\to0^+}\dfrac{\ln(2x+1)}{\tan x}\right)=\exp\left(\lim_{x\to0^+}\dfrac{\frac2{2x+1}}{\sec^2x}\right)$

Now the numerator approaches $\dfrac21=2$ , while the denominator approaches $\sec^20=1$ , suggesting the limit above is 2. This means

$\displaystyle\lim_{x\to0^+}(2x+1)^{\cot x}=\exp(2)=e^2$

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3 years ago

Over the next 3 days Mrs. Messer would like to write 27 thank you cards. How many cards will she need to write each day in order

shutvik [7]

Answer:

9 Cards

Step-by-step explanation:

9 Cards a day equals 27 cards in 3 days

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1 year ago

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A cyclist managed to ride 5 miles against the wind in the same time that it took him to ride 10 miles with the wind. If the wind

bearhunter [10]

Given that the cyclist rides distances of 5 miles and 10 miles due to the wind, the equation that can be used to calculate the speed is therefore;

$\frac{10}{v + 4} = \frac{5}{v - 4}$

<h3>How can the correct equation be found?</h3>

The distance the cyclist rides against the wind = 5 miles

The distance the cyclist rides with the wind = 10 miLes

Let <em>t </em>represent the time it took the cyclist in both directions, we have;

$t = \frac{10}{v + 4} = \frac{5}{v - 4}$

Where;

v = The cyclist's average rate of speed

Which gives;

10 × (v - 4) = 5 × (v - 4)

10v - 40 = 5v - 20

5v = 20

v = 20 ÷ 5 = 5

The equation that can be used to calculate the cyclist's average rate of speed is therefore;

$t = \frac{10}{v + 4} = \frac{5}{v - 4}$

Learn more about average speed here:

brainly.com/question/6504879

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2 years ago

Using the dot plots provided, what is the mean absolute deviation of the height of basketball players, rounded to the nearest te

Kazeer [188]

Answer:

$MAD= \frac{1}{14} 27.286 = 1.949 \approx 2.0$

Step-by-step explanation:

Previous concepts

The mean absolute deviation or MAD "is the average of the absolute deviations or the positive difference of the given data and that certain value (generally central values)". And is given by this formula:

$MAD= \frac{1}{n} \sum_{i=1}^n |x_i -\bar X|$