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3 years ago

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

Mathematics

2 answers:

snow_tiger [21]3 years ago

8 0

vertex = ( - $\frac{1}{3}$ , $\frac{2}{3}$ )

given a parabola in standard form : ax² + bx + c (a ≠ 0 )

then the x-coordinate of the vertex = - $\frac{b}{2a}$

y = 3x² + 2x + 1 is in standard form

with a = 3, b = 2 and c = 1

$x_{vertex}$ = - $\frac{2}{6}$ = - $\frac{1}{3}$

substitute this value into the equation for y- coordinate of vertex

$y_{vertex}$ = 3( - $\frac{1}{3}$ )² + 2(- $\frac{1}{3}$ ) + 1

= $\frac{1}{3}$ - $\frac{2}{3}$ + $\frac{3}{3}$ = $\frac{2}{3}$

vertex = ( - $\frac{1}{3}$ , $\frac{2}{3}$ )

Eduardwww [97]3 years ago

7 0

Answer:

B on edge

Step-by-step explanation:

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Plz help. 3 yd+ 10 ft+ 17 in=

Phoenix [80]

The easiest thing to do is to convert it all to the smallest units.
3 yard = 108 inches
10 ft = 120 inches
17 inch
108 +120 + 17 = 245 inches

8 0

3 years ago

how do the graphs of f(x) = sin x and g(x) = sin2x+3 compare. Must make two selections of the following that apply.

Elena L [17]

Answer:

The correct options are:

g(x) is shifted three units higher than f(x).

g(x) has a period that is half the period of f(x).

Step-by-step explanation:

We have to compare the graphs of the function:

$f(x)=\sin x$

and $g(x)=\sin 2x+3$

We have to select the correct options among the following:

As we know that the period of sine function is 2π.

i.e. Period of function f(x) is: 2π.

The period of sin(2 x) is π.

Hence, the period of the function g(x) function is π.

Hence, the period of g(x) is half the period of f(x).

Also we could observe that g(x) is shifted 3 units upward.

3 0

3 years ago

Read 2 more answers

8 minus some number divided by 3 equals 6. Find the number

san4es73 [151]

Answer:

my answer is negative 14/3.

Step-by-step explanation:

choice A hope that helps you if I'm wrong please tell me the right answer right away I can try another method.

6 0

3 years ago

Which is true about the expression 3 square root x 2 square root

dexar [7]

Answer:

Step-by-step explanation:

Neither one of the two given numbers are rational. sqrt(3)*sqrt(2) equals the square root of 6. All three numbers are irrational.

You can try it for yourself.

sqrt(2) = 1.4142

sqrt(3) = 1.732

1.4142 * 1.732 = 2.4493

sqrt(6) = 2.4493

The difference is a rounding error.

So the answer is B. sqrt(6) is totally irrational.

8 0

3 years ago

The local supermarket buys lettuce each day to ensure really fresh produce. Each morning any lettuce that is left from the previ

jekas [21]

Given Information:

Cost price = $4

Selling price = $10

Salvage value = $1.50

Average demand = μ = 250 boxes

Standard deviation = σ = 34 boxes

Required Information:

Number of lettuce boxes = ?

Answer:

The supermarket should purchase 268 boxes of lettuce

Step-by-step explanation:

The required number of lettuce boxes that supermarket should purchase is given by

Number of lettuce boxes = μ + (z*σ)

Where μ is the average demand of lettuce boxes, σ is the standard deviation, and z is the z-score which is given by

p = C_us/(C_us + C_os)

The z-score corresponding to probability p will be obtained.

The cost of under stocking is given by

C_us = Selling price - Cost price

C_us = $10 - $4

C_us = $6

The cost of over stocking is given by

C_os = Cost price - Salvage value

C_os = $4 - $1.50

C_os = $2.50

p = C_us/(C_us + C_os)

p = 6/(6 + 2.50)

p = 0.7058

p = 70.58%

The z-score corresponding to 70.58% probability is approximately 0.54

Number of lettuce boxes = μ + (z*σ)

Number of lettuce boxes = 250 + (0.54*34)

Number of lettuce boxes = 250 + (18.36)

Number of lettuce boxes = 268.36

Number of lettuce boxes ≈ 268

Therefore, the supermarket should purchase 268 boxes of lettuce.

How to use z-table?

Step 1:

In the z-table, find the probability you are looking for and note down the two-digit number of the given row. (e.g 0.5, 2.2, 0.5 etc.)

Step 2:

Then look up at the top of z-table and note down the value in the column for the remaining decimal point in the range of 0.00 to 0.09.

Step 3:

Finally, add the numbers obtained from step 1 and step 2.

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4 years ago