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Marina86 [1]
2 years ago
8

Which of the following is the minimum value of the equation y = 2x2 + 5?

Mathematics
1 answer:
raketka [301]2 years ago
4 0
(0, 5) is the minimum value.

Find the axis of symmetry by plugging the respective variables into -b/2a

-5/2(0) = 0

There is no b-value in our equation, or rather, the value of b is 0. To see this, y = 2x^2 + 5 can be written as

y = 2x^2 + 0x + 5

We plug 0 into f(x), establishing every x-value as 0.

f(0) = 2(0)^2 + 5
f(0) = 0 + 5
f(0) = 5

5 is now your vertex’s y-value. Plot the two values together.

(0, 5)

We know that this is a minimum because the leading coefficient is positive, meaning the the graph’s parabola will open down.
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What are the features of the parabola modeled by the equation f(x) = x2 - 114x ?
notsponge [240]

Answer:

Answers are in bold type

Step-by-step explanation:

f(x) = x^{2} -144x

The parabola opens up, so has a minimum at the vertex.

Let (h, k) be the vertex

h = -b/2a = - (-144)/2(1) = 57

k = 57^2 - 144(57) = 3249 - 6498 = -3249

Therefore, the vertex is (57, -3249)

The minimum value is -3249

The domain is the set of real numbers.  

The  range = {y | y ≥ -3249}

The function decreases when -∞ < x < 57  and increases when 57 > x > ∞

The x - intercepts:  x^{2} -144x = 0

                                x(x - 114x) = 0

                                x = 0 or x = 114

x-intercepts are (0, 0) and (0, 114)

When x = 0, then we get the y-intercept.  So, 0^2 - 114(0) = 0

y-intercept is (0, 0)

3 0
3 years ago
Simplify the given equation.
77julia77 [94]

Answer:

2) 7x-6=2x+2

Step-by-step explanation:

It equals 8/9, and the equation, (5x + 2(x-3) = -2(x - 1)) equals 8/9 as well.

7 0
2 years ago
Read 2 more answers
You measure 25 turtles' weights, and find they have a mean weight of 31 ounces. Assume the population standard deviation is 12.8
Firlakuza [10]

Answer:

Margin of error = 4.21 ounces  

Step-by-step explanation:

According to the Question,

  • Given That, You measure 25 turtles' weights, and find they have a mean weight of 31 ounces. Assume the population standard deviation is 12.8 ounces

Therefore, Sample mean = 31 ounces  ,  Sample size(n) = 25 , Alpha(α) = 0.10 & Population standard deviation(σ) = 12.8 ounces

  • Thus, Margin of error  = Z_{critical} × σ / √n  (Z_{critical} at α=.010 is 1.645)

Putting The Values, We get

1.645 × (12.8 / √25 ) ⇒ 4.2112 ≈ 4.21

Thus, the maximum margin of error associated with a 90% confidence interval for the true population mean turtle weight is 4.21 ounces

8 0
2 years ago
Tom predicted that the Giants would score three 3-point field goals, score two 6-point touchdowns, and score 1 extra point. If T
Bingel [31]
3*3 = 9

2*6 = 12

1*1 = 1

9+12+1 = 22

The Giants would score 22 points if Tom is correct

6 0
3 years ago
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In the slope intercept equation of a line which quantity is given by the constant term
ankoles [38]
The slope intercept form is y = mx + c.

The quantity given by the constant term c, is the vertical or y intercept.

It is the point where the line cuts the y axis, and this point, x = 0.
4 0
2 years ago
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