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Y = x² - 4x convert from standard to vertex form

Pepsi [2]

Answer:

$y = (x-2)^{2} -4$

Step-by-step explanation:

To complete the square: add 4 to both sides because the product of 4 as 2 as the factor which 2 * 2 so $2^{2}$

$y + ? = x^{2} - 4x + ?$

$y + 2^{2} = x^{2} - 4x + 2^{2}$

$y + 4 = x^{2} - 4x + 4$

Now we can factor the expression

$y + 4 = (x-2)^{2}$

Move the 4 to the other side to isolate y which changes the sign

$y = (x-2)^{2} - 4$

6 0

2 years ago

Using the formula C=2pi r find the circumference of a circle with diameter of 28 inches. Round your answer to the nearest inch.

Ivenika [448]

Answer: 88 inches

Step-by-step explanation:

We know that the formula to find the circumference of circle is given by :-

$C=2\pi r$ , where r is the radius of the circle.

Given : Diameter of circle = 28 inches

Also, diameter is twice of radius.

i.e. 2r=28

Therefore, the circumference of circle will be :-

$C=2\pi r=(2r)\pi=28\times(3.14)=87.92text{ inches}\approx88\text{ inches}$

Hence, the circumference of circle is 88 inches.

5 0

3 years ago

What is 235 divided by 5?

Alex Ar [27]

The answer to this question is: 47

4 0

3 years ago

Read 2 more answers

The number sentence 4x7=(4x3)+(4x4) is an example of what property

Otrada [13]

The number sentence 4x7=(4x3)+(4x4) is an example of distributive property.
The distributive property states the following:
a × (b + c) = a × b + a × c
Multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. 
In our case, a=4 b+c=7, b=3, c=4

8 0

4 years ago

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The weight of an adult swan is normally distributed with a mean of 26 pounds and a standard deviation of 7.2 pounds. A farmer ra

Snezhnost [94]

Let $X$ denote the random variable for the weight of a swan. Then each swan in the sample of 36 selected by the farmer can be assigned a weight denoted by $X_1,\ldots,X_{36}$ , each independently and identically distributed with distribution $X_i\sim\mathcal N(26,7.2)$ .

You want to find

$\mathbb P(X_1+\cdots+X_{36}>1000)=\mathbb P\left(\displaystyle\sum_{i=1}^{36}X_i>1000\right)$

Note that the left side is 36 times the average of the weights of the swans in the sample, i.e. the probability above is equivalent to

$\mathbb P\left(36\displaystyle\sum_{i=1}^{36}\frac{X_i}{36}>1000\right)=\mathbb P\left(\overline X>\dfrac{1000}{36}\right)$

Recall that if $X\sim\mathcal N(\mu,\sigma)$ , then the sampling distribution $\overline X=\displaystyle\sum_{i=1}^n\frac{X_i}n\sim\mathcal N\left(\mu,\dfrac\sigma{\sqrt n}\right)$ with $n$ being the size of the sample.

Transforming to the standard normal distribution, you have

$Z=\dfrac{\overline X-\mu_{\overline X}}{\sigma_{\overline X}}=\sqrt n\dfrac{\overline X-\mu}{\sigma}$

so that in this case,

$Z=6\dfrac{\overline X-26}{7.2}$

and the probability is equivalent to

$\mathbb P\left(\overline X>\dfrac{1000}{36}\right)=\mathbb P\left(6\dfrac{\overline X-26}{7.2}>6\dfrac{\frac{1000}{36}-26}{7.2}\right)$
$=\mathbb P(Z>1.481)\approx0.0693$

5 0

3 years ago

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