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3 years ago

A parabola has vertex (2, 3) and contains the point (0, 0). find an equation that represents this parabola.

1 answer:

7 0

First write it in vertex form :-

y= a(x - 2)^2 + 3 where a is some constant.

We can find the value of a by substituting the point (0.0) into the equation:-

0 = a((-2)^2 + 3

4a = -3

a = -3/4

so our equation becomes y = (-3/4)(x - 2)^2 + 3

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Solve the following quadratic equations by completing the square. y^2-14y+48=0

NISA [10]

Answer:

y = 6 or 8

Step-by-step explanation:

1. Subtract the constant:

y^2 -14y = -48

2. Add the square of half the y-coefficient:

y^2 -14y +49 = -48 +49

Write as a square, if you like:

(y -7)^2 = 1

3. Take the square root:

y -7 = ±√1 = ±1

4. Add the opposite of the constant on the left:

y = 7 ±1 = 6 or 8

The solution is y = 6 or y = 8.

5 0

3 years ago

In a 30-60-90 right triangle, the shorter leg has a length of 4. What is the length of the longer leg? How would I figure this o

iVinArrow [24]

Answer:

use a^2 +b^2=c^2

Step-by-step explanation:

5 0

3 years ago

A newspaper article states that 90% of drivers in Iowa wear their seatbelt. Suppose we are interested in estimating the proporti

konstantin123 [22]

Answer:

The sample size is $n = 3457$

Step-by-step explanation:

From the we are told that

The population proportion is p = 0.90

The margin of error is E = 0.01

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally the sample size is mathematically represented as

$n =[ \frac{ Z_{\frac{\alpha }{2} } }{E} ]^2 * p(1-p)$

=> $n =[ \frac{ 1.96 }{0.01} ]^2 * 0.90(1-0.90)$

=> $n = 3457$

8 0

3 years ago

Anybody can help me

Lyrx [107]

Answer:

y = 3x + 1

The ? is 3

Enter the numbers into the equation:

Enter (0,1) --> 1 = 0 + 1 --> 1 = 1

Enter (3,10) --> 10 = 3 · 3 + 1 --> 10 = 9 + 1 --> 10 = 10

8 0

3 years ago

The following data are direct solar intensity measurements (watts/m2 ) on different days at a location in southern Spain: 562, 8

lbvjy [14]

Answer:

Mean: 810.51

Standard deviation: 128.32

Step-by-step explanation:

First, we calculate the sample mean. We have 35 data samples, so we compute it as $\displaystyle \frac{562 + .... + 753}{35}$ .

In general, given a set of n samples $\{ X_1,...,X_n\}$ , we calculate the sample mean as

$\displaystyle \bar{X} = \sum_{i=1}^n \frac{X_i}{n}$ .

For the standard deviation $\sigma$ , we first begin by calculating it's square. It can be obtained from the formula

$\displaystyle \sigma ^2 = \sum_{i=1}^{n} \frac{(X_i - \bar{X})^2}{n-1}$

By taking square root after computing the right hand side, we attain the desired value.

The attached image shows the dot diagram of this sample. The bottom pink vertical line shows the mean, and the two horizontal pink lines have a lenght of $\sigma$ .

The standard deviation means "The average expected distance a new sample will be from the mean". That's why usually, data samples which are denser around the mean have smaller standard deviations (as opposed to distributions who have a lot of values far away from the mean, which will make the standard deviation grow bigger).

6 0

3 years ago