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OverLord2011 [107]
3 years ago
12

Q) The distance between points A(2,1) and B(2,4) is ___ units.

Mathematics
1 answer:
madreJ [45]3 years ago
8 0

Answer:

3 or (0,3)

Step-by-step explanation:

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The equation of function h is h... PLEASE HELP MATH
Flura [38]

Answer:

Part A: the value of h(4) - m(16) is -4

Part B: The y-intercepts are 4 units apart

Part C: m(x) can not exceed h(x) for any value of x

Step-by-step explanation:

Let us use the table to find the function m(x)

There is a constant difference between each two consecutive values of x and also in y, then the table represents a linear function

The form of the linear function is m(x) = a x + b, where

  • a is the slope of the function
  • b is the y-intercept

The slope = Δm(x)/Δx

∵ At x = 8, m(x) = 2

∵ At x = 10, m(x) = 3

∴ The slope = \frac{3-2}{10-8}=\frac{1}{2}

∴ a = \frac{1}{2}

- Substitute it in the form of the function

∴ m(x) = \frac{1}{2} x + b

- To find b substitute x and m(x) in the function by (8 , 2)

∵ 2 = \frac{1}{2} (8) + b

∴ 2 = 4 + b

- Subtract 4 from both sides

∴ -2 = b

∴ m(x) = \frac{1}{2} x - 2

Now let us answer the questions

Part A:

∵ h(x) = \frac{1}{2} (x - 2)²

∴ h(4) = \frac{1}{2} (4 - 2)²

∴ h(4) = \frac{1}{2} (2)²

∴ h(4) =  \frac{1}{2}(4)

∴ h(4) = 2

∵ m(x) = \frac{1}{2} x - 2

∴ m(16) =  \frac{1}{2} (16) - 2

∴ m(16) = 8 - 2

∴ m(16) = 6

- Find now h(4) - m(16)

∵ h(4) - m(16) = 2 - 6

∴ h(4) - m(16) = -4

Part B:

The y-intercept is the value of h(x) at x = 0

∵ h(x) = \frac{1}{2} (x - 2)²

∵ x = 0

∴ h(0) = \frac{1}{2} (0 - 2)²

∴ h(0) =  \frac{1}{2} (-2)² =  

∴ h(0) = 2

∴ The y-intercept of h(x) is 2

∵ m(x) = \frac{1}{2} x - 2

∵ x = 0

∴ m(0) = \frac{1}{2} (0) - 2 = 0 - 2

∴ m(0) = -2

∴ The y-intercept of m(x) is -2

- Find the distance between y = 2 and y = -2

∴ The difference between the y-intercepts of the graphs = 2 - (-2)

∴ The difference between the y-intercepts of the graphs = 4

∴ The y-intercepts are 4 units apart

Part C:

The minimum/maximum point of a quadratic function f(x) = a(x - h) + k is point (h , k)

Compare this form with the form of h(x)

∵ h = 2 and k = 0

∴ The minimum point of the graph of h(x) is (2 , 0)

∵ k is the minimum value of f(x)

∴ 0 is the minimum value of h(x)

∴ The domain of h(x) is all real numbers

∴ The range of h(x) is h(x) ≥ 2

∵ m(8) = 2

∵ m(14) = 5

∵ h(8) = \frac{1}{2} (8 - 2)² = 18

∵ h(14) = \frac{1}{2} (14 - 2)² = 72

∴ h(x) is always > m(x)

∴ m(x) can not exceed h(x) for any value of x

<em>Look to the attached graph for more understand</em>

The blue graph represents h(x)

The green graph represents m(x)

The blue graph is above the green graph for all values of x, then there is no value of x make m(x) exceeds h(x)

7 0
3 years ago
An observer took a time-exposure photograph of polaris and five nearby stars. how many hours were required to show their star pa
olga55 [171]
Photographing stars requires you to keep your exposure open for a long time. Taking pictures of star trails would take about 30 minutes to three hours. If you multiply that for the 6 stars stated above in the problem then you would be needing that much time if the stars were close and approximately 3 to 18 hours capture their star trails if they were far apart from each other.
5 0
3 years ago
For what value of x will the function f(x) = -3(x - 10)(x - 4) have a maximum value? Find the maximum value.
gayaneshka [121]

Hello!

To find the maximum value of the function f(x) = -3(x - 10)(x - 4), the easiest way is to find the vertex using the formula: x = -b/2a.

Firstly, we need to simplify f(x).

f(x) = -3(x - 10)(x - 4)

f(x) = -3(x² - 14x + 40)

f(x) = -3x² + 42x + -120

Since the equation f(x) is now simplified to standard form, we can find the vertex.

a = -3, b = 42, and c = -120

x = -(42)/2(-3) = -42/-6 = 7

Then, we substitute 7 into the the function f(x) = -3(x - 10)(x - 4), or

f(x) = -3x² + 42x + -120, to find the y-value of the vertex.

f(x) = -3(7 - 10)(7 - 4)

f(x) = -3(-3)(4)

f(x) = 27

The vertex of f(x) is (7, 27).

Therefore, the maximum x-value for the function f(x) is 7.

4 0
3 years ago
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So nobody is smart enough to answer my question?
Paha777 [63]

That is ver very sad

3 0
3 years ago
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Which expression is equivalent to 3(4x+10÷2+3)?<br> a 12x+2<br> b 12x+6<br> c 12x+8<br> d 12x+24
elena-14-01-66 [18.8K]

Answer:

12x+2

Step-by-step explanation:

7 0
3 years ago
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