Which triangle must be a right triangle and why?

Which table shows y as DIRECTLY PROPORTIONAL to x?

klemol [59]

Answer:

Option B gives the directly proportional relation.

Step-by-step explanation:

If a function can be written as in the form y = kx ........... (1), where x is the independent variable, y is the dependent variable and k is the proportionality constant.

Now, from the given four tables in options, the table in option B only satisfies this relation between x and y.

The ordered pairs in the option B are (1,0.5), (2,1), (3,1.5) and (4,2).

Now, take any two pairs of coordinates and find the equation of the function that satisfies all four points.

Taking (1,0.5) and (2,1) points, the equation of the straight line will be

$\frac{y - 1}{1 - 0.5} = \frac{x - 2}{2 - 1}$

⇒ 2(y - 1) = x - 2

⇒ 2y = x

⇒ $y = \frac{1}{2} x$ ............. (2)

Therefore, this equation (2) is similar to equation (1) and hence this table is directly proportional relationship. (Answer)

7 0

3 years ago

Tại 1 Doanh nghiệp sản xuất, trong tháng có số liệu về tình hình sản xuất và sản lượng hoàn thành của 2 phân xưởng sản xuất phụ

ella [17]

50000 people live in California sike I lied not really there’s more but I’m one of them

8 0

3 years ago

A set of data with a mean of 53, and a standard deviation of 6.2 is normally distributed. Find the value of a data point that is

Evgesh-ka [11]

The value of a data point that is -2 standard deviations from the mean

so, 40.6 to 65.4.

<h3>What is the empirical rule?</h3>

According to the empirical rule, also known as the 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95%, and 99.7% of the values lies within one, two, or three standard deviations of the mean of the distribution.

$P(\mu - \sigma < X < \mu + \sigma) \approx 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) \approx 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) \approx 99.7\%$

From the empirical rule, we know that for 95% we are in 2 standard deviations of the mean. so:

= 53- 6.2- 6.2

= 40.6

The value of a data point that is -2 standard deviations from the mean

53 + 6.2 + 6.2

= 65.4

Learn more about the empirical rule here:

brainly.com/question/13676793

#SPJ2

7 0

2 years ago

What statement best fills in the last blank of the proof and completes the sentence: " By the substitution property of equality,

tia_tia [17]

Since, it is given that angle A is a right angle and angle B is a right angle.

We have to prove that $m \angle A = m \angle B$

Now, we have to complete the given statement.

It is given that $\angle A$ and $\angle B$ are right angles. This means that $m \angle A = 90^\circ$ and $m \angle B = 90^\circ$ because of the definition of the right angles. By the substitution property of equality $m \angle A = m \angle B$ .