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2 years ago

X= algebraic expression 3=18 4=32 5=50 7=98

Mathematics

1 answer:

pogonyaev2 years ago

6 0

$3=2\cdot3^2=2\cdot9=18\\4=2\cdot4^2=2\cdot16=32\\5=2\cdot5^2=2\cdot25=50\\7=2\cdot7^2=2\cdot49=98\\\\\boxed{x=2x^2}$

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guajiro [1.7K]

Answer and Step-by-step explanation: Standard form of a quadratic equation is expressed as: y=ax²+bx+c, while vertex form is written as:

y=a(x-h)²+k.

The similarities between standard and vertex forms is that they show if the graph of the equation has a minimum (when a>0) or maximum (a<0) and it's easier to determine the y-intercept: for standard, the value of c is the intercept; for vertex, the value k is the intercept.

The advantage of standard form is that you can determine the product and sum of the equation's roots, which is a method to determine them.

The advantages of vertex form are: easier to find the vertex of the graph, which is the pair (h,k) and the axis of symmetry, which is the value of h.

8 0

3 years ago

A research study investigated differences between male and female students. Based on the study results, we can assume the popula

garri49 [273]

Using the normal distribution and the central limit theorem, it is found that the interval that contains 99.44% of the sample means for male students is (3.4, 3.6).

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

It measures how many standard deviations the measure is from the mean.

After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

In this problem:

The mean is of $\mu = 3.5$ .

The standard deviation is of $\sigma = 0.5$ .

Sample of 100, hence $n = 100, s = \frac{0.5}{\sqrt{100}} = 0.05$

The interval that contains 95.44% of the sample means for male students is between Z = -2 and Z = 2, as the subtraction of their p-values is 0.9544, hence:

Z = -2:

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$-2 = \frac{X - 3.5}{0.05}$

$X - 3.5 = -0.1$

$X = 3.4$

Z = 2:

$Z = \frac{X - \mu}{s}$

$2 = \frac{X - 3.5}{0.05}$

$X - 3.5 = 0.1$

$X = 3.6$

The interval that contains 99.44% of the sample means for male students is (3.4, 3.6).

You can learn more about the normal distribution and the central limit theorem at brainly.com/question/24663213

7 0

2 years ago

Can someone plz help me with this and i need the drawing to show work

Burka [1]

Answer:

20.833 feet

Step-by-step explanation:

The light reflects off the mirror at the same angle that it hits it at. So the triangle formed by the beam and mirror is similar to the triangle formed by Kevin and the mirror.

Therefore, we can write and solve a proportion.

h / 10 = 6.25 / 3

h = 20.833

The beam is 20.833 feet tall.