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PolarNik [594]
3 years ago
11

What is the vertex of the graph of y = 3x2 + 2x + 1?

Mathematics
2 answers:
Effectus [21]3 years ago
8 0
We have that
y = 3x²<span>+ 2x + 1

step 1
</span>

Group terms that contain the same variable, and move the constant to the opposite side of the equation

y -1= (3x²+ 2x)

step 2

Factor the leading coefficient

y -1= 3*(x²+ 2/3x)

step 3

Complete the square. Remember to balance the equation by adding the same constants to each side

y -1+(1/3)= 3*(x²+ (2/3)x+(4/36))

y-2/3=3*(x+2/6)²

the vertex is the point (-2/6, 2/3)------> (-0.33,0.67)

the answer is

(-0.33,0.67)

Drupady [299]3 years ago
4 0

Answer:

B (-1/3,2/3)

Step-by-step explanation:

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How many 10-digit ternary strings are there that contain exactly two 0s, three 1s, and five 2s?
Svet_ta [14]

There are \dbinom{10}2 ways of picking 2 of the 10 available positions for a 0. 8 positions remain.

There are \dbinom83 ways of picking 3 of the 8 available positions for a 1. 5 positions remain, but we're filling all of them with 2s, and there's \dbinom55=1 way of doing that.

So we have

\dbinom{10}2\dbinom83\dbinom55=\dfrac{10!}{2!(10-2)!}\dfrac{8!}{3!(8-3)!}\dfrac{5!}{5!(5-5)!}=2520

The last expression has a more compact form in terms of the so-called multinomial coefficient,

\dbinom{10}{2,3,5}=\dfrac{10!}{2!3!5!}=2520

5 0
3 years ago
Abby and zach made cookies. They put 3 chips on each 5 cookies.
snow_lady [41]
If your asking how many chips there are in total... it would be 15
4 0
3 years ago
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Describe some data that when graphed would represent a proportional relationship. Explain your reasoning
OLga [1]
The lines would go up and over at the same rate. They would have the same slope, like parallel lines.

Hope this helps!! :)
7 0
3 years ago
Read 2 more answers
Please help with question below!
Charra [1.4K]

Answer:

45

Step-by-step explanation:

45 is constant, because no mater how many miles you drive, you will always be charged $45. It stays the same

6 0
3 years ago
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On a class trip, there were 45 more girls than boys. the total number of students on the trip was 215. write and solve an equati
Evgesh-ka [11]
(b)+(b+45)=215
b = # of boys
there are 45 more girls than boys and 215 students total.
minus 45 on both sides leaving you with
(b)+(b)=170
combine like terms leaving you with
2b=170
divide both sides by 2
b=85
there were 85 boys
85+45=130
(the 45 for the # of girls more than boys)
there were 130 girls.
3 0
3 years ago
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