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3 years ago

Find the vertex of the function given below. y = x2 - 4x + 1

2 answers:

5 0

The vertex is (2, -3).
Use the formula x= -b/2a to find the x value., which is 2.Then, substitute it into the function, wherever you see an x. Follow order operations and you get y, which is -3.

olga55 [171]3 years ago

4 0

Answer: The vertex of the given function is (2, -3).

Step-by-step explanation: We are given to find the vertex of the following function :

$y=x^2-4x+1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We know that

the vertex form of a function with vertex at the point (h, k) is given by

$y=a(x-h)^2+k.$

From equation (i), we have

$y=x^2-4x+1\\\\\Rightarrow y=(x^2-4x+4)+1-4\\\\\Rightarrow y=(x-2)^2-3\\\\\Rightarrow y=(x-2)^2+(-3).$

Comparing the above equation with the vertex form, we get that the vertex of the given function is (2, -3).

Thus, the vertex of the given function is (2, -3).

You might be interested in

??????????????helpppp

zimovet [89]

answer is 25

Step-by-step explanation:

for something like this you need to use the law of sins. First identify all the angles. There is a 90 degree angle and a 59 degree angle and those are clear. the missing angle is = 59 + 90 = 149

since a triangle has 180 degrees in total you say 180 - 149 = 31. the missing angle is 31 degrees. so we give the angles names. angle with 59 degrees will be angle A, 90 will be B and 31 will be C. So now we just give the sides names. let's replace that x with an a since it's across angle A. the side along angle B will be named b and the side along angle C will be named c. so you say:

Sin A/ a (sin A over a) = Sin B/b = Sin C/c

Sin A is what we are looking for so we say

59 degrees over/ x = sin 31 degrees/ 13 (we leave out the 90 degrees since we don't know the side and also we are not interested in it)

now we do cross multiplying.

say x ×sin 31 degrees = 13× sin 59

now divide these by sin 31

x = 13 × sin 59 ÷ 31 = 25

6 0

2 years ago

An electronics hobbyist has three electronic parts cabinets with two drawers each.

Andrews [41]

Answer:

a) 0.5 = 50% probability that an NPN transistor will be selected.

b) 0.3333 = 33.33% probability that it came from the cabinet that contains both types

c) 66.67% probability that it comes from the cabinet that contains only NPN transistors

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

a) What is the probability that an NPN transistor will be selected?

1/3 probability that the first cabinet is chosen. This cabinet has two transistors, both of which are NPN, so 100% probability of selecting a NPN transistor.

1/3 probability that the second cabinet is chosen. This cabinet has two transistors, both of which are PNP, so 0% probability of selecting a NPN transistor.

1/3 probability that the second cabinet is chosen. This cabinet has two transistors, one of which is NPN, so 50% probability of selecting a NPN transistor.

$p = \frac{1}{3}*1 + \frac{1}{3}*0 + \frac{1}{3}*0.5 = \frac{1}{3} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = 0.5$

0.5 = 50% probability that an NPN transistor will be selected.

b) Given that the hobbyist selects an NPN transistor, what is the probability that it came from the cabinet that contains both types?

Here we use the conditional probability formula.

Event A: NPN transistor

Event B: From the third cabinet.

50% probability that an NPN transistor will be selected, so $P(A) = 0.5$ .

1/6 probability that it is from the third cabinet and NPN, so $P(A \cap B) = \frac{1}{6}$

The desired probability is:

$P(B|A) = \frac{\frac{1}{6}}{0.5} = 0.3333$

0.3333 = 33.33% probability that it came from the cabinet that contains both types.

c) Given that an NPN transistor is selected what is the probability that it comes from the cabinet that contains only NPN transistors?

Either it comes from the cabinet with only NPN transistors, or it comes from the cabinet with both types of transistors. The sum of the probabilities of these outcomes is 100%. So

x + 33.33 = 100

x = 66.67

66.67% probability that it comes from the cabinet that contains only NPN transistors

6 0

3 years ago

the rain caused the river to rise a total of 6 2/3 inches. the river was was rising a an average of 2/3 of an inch each hour. ho

Tasya [4]

2 1/2 you divide 6 2/3 by 2/3

8 0

3 years ago

There are twenty classes at Northwestern Middle School and twenty classes at Southeastern Middle School. The number of students

Contact [7]