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3 years ago

What is the area of this triangle? Between the coordinates (5,4) (8,2) (5,2

Mathematics

1 answer:

Snezhnost [94]3 years ago

6 0

Answer:

Step-by-step explanation:

Step 1:

The triangle undergoes a translation and then a rotation.

The translation is that the units are translated 5 units to the right.

So the rule for the translation is (x+5, y).

The coordinate (4, 2) becomes (9, 2).

The coordinate (0, -3) becomes (5, -3).

The coordinate (-5, 3) becomes (0, 3).

Step 2:

When the points are rotated the x and y values are not interchanged and the symbol depends on the quadrant in which the shape is reflected on to.

The points (9, 2) and (0, 3) are in the first quadrant. After translation, they will be in the third quadrant where the x and y values are both negative.

The point (5, -3) is in the fourth quadrant. After translation, it will be in the second quadrant where the x value is negative and the y value is positive.

The coordinate (9, 2) becomes (-9, -2).

The coordinate (0, 3) becomes (0, -3).

The coordinate (5, -3) becomes (-5, 3).

So the points are (-9, -2), (-5, 3), and (0, -3) which is option C.

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3 years ago

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2 years ago

If p stays constant and u is doubled what happens to e? given U=EP

Stolb23 [73]

We are given the expression:

U = E * P

The equality symbol “ = “ means that for all cases, the value of U and E * P must always be equal. This means that whatever happens on the left side, must equally happen on the right side.

So what this actually means is that, if we double U so we must also double the expression E * P, that is:

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4 years ago

Find the probability that in five tosses of a fair die, a 3 will appear (a) twice, (b) at most once, (c) at least two times.

Jobisdone [24]

Answer:

A) 0.1612

B) 0.8031

C) 0.1969

Step-by-step explanation:

For each toss of the die, there are only two possible outcomes. Either it is a 3, or it is not. The probability of getting a 3 on each toss is independent from other tosses. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

Five tosses, so $n = 5$

The die has 6 values, from 1 to 6. The die is fair, so each outcome is equally as likely. The probability of a 3 appearing in a single throw is $p = \frac{1}{6} = 0.167$