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Dvinal [7]
3 years ago
12

How would you find the quadratic that goes through the point (4,0), the axis of symmetry is x=7, and it also goes through the po

int (1,5)?

Mathematics
1 answer:
nasty-shy [4]3 years ago
4 0

9514 1404 393

Answer:

  y = (5/27)(x -7)^2 -5/3

Step-by-step explanation:

Use the given points to find the unknowns in the equation.

If the axis of symmetry is x=7, then the equation can be written in the form ...

  y = a(x -7)^2 +b

Filling in the two point values, we have two equations:

  0 = a(4 -7)^2 +b   ⇒   9a +b = 0

  5 = a(1 -7)^2 +b   ⇒   36a +b = 5

__

Subtracting the first equation from the second, we have ...

  (36a +b) -(9a +b) = (5) -(0)

  27a = 5

  a = 5/27

Substituting that value into the first equation gives ...

  9(5/27) +b = 0

  5/3 +b = 0

  b = -5/3

So, the quadratic can be written in vertex form as ...

  y = (5/27)(x -7)^2 -5/3

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Answer:

Table 1 is the only table which represents PROBABILITY DISTRIBUTION table.

Step-by-step explanation:

In any given probability distribution:

1) The probability of each event should be strictly POSITIVE.

2) Sum of all events in a a distribution should be 1.

Now, here

A) All of the values of probability (0.11, 0..5, 0.49,0.35)  are positive.

Also, 0.11 +  0.5 +  0.49 + 0.35  = 1

So, the given table is a PROBABILITY DISTRIBUTION.

B)The table is NOT a PROBABILITY DISTRIBUTION as here

P(Blue) =  -1, which is negative.

C)The table is NOT a PROBABILITY DISTRIBUTION as here

P(Green) =  -0.49, which is negative.

D)The table is NOT a PROBABILITY DISTRIBUTION as here

P(Purple) =  -0.1, which is negative.

Hence, table 1 is the only table which represents  PROBABILITY DISTRIBUTION table.

3 0
3 years ago
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Answer:

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Step-by-step explanation:

4 0
3 years ago
Which equation represents a circle with a center at (2, -7) and a radius of<br> 4 units?
Bezzdna [24]

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Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
a surveyor measures the distance to the two landmarks as shown in the diagram what is the distance d. between the landmarks​
Inessa [10]
<h3>The distance between two landmarks is 123 meters</h3>

<em><u>Solution:</u></em>

We have to find the distance between two landmarks

<em><u>Use the law of cosines</u></em>

The third side of a triangle can be found when we know two sides and the angle between them

c^2 = a^2 + b^2 - 2ab\ cos c

Here, angle between 90 meters and 130 meters is 65 degrees

From figure,

a = 90

b = 130

c = d

Therefore,

d^2 = 90^2 + 130^2 - 2(90)(130)\ cos 65\\\\d^2 = 8100 + 16900 - 23400\ cos\ 65\\\\d^2 = 25000 - 23400 \times 0.4226\\\\d^2 = 25000 - 9889.267\\\\d^2 = 15110.73\\\\d = 122.92\\\\d \approx 123

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8 0
3 years ago
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Svetach [21]

They will be 15 miles apart after one hour if they left the same point at the same time.

<h3>How do we measure and calculate the distance in Geometry?</h3>

The distance between two points in geometry can be calculated by using the Pythagoras theorem.

Mathematically, the Pythagoras theorem can be expressed as:

\mathbf{d = \sqrt{x^2 +y^2}}

where;

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\mathbf{d = \sqrt{(9)^2 +(12)^2}}

\mathbf{d = \sqrt{81+144}}

\mathbf{d = \sqrt{225}}

d = 15 miles  

Therefore, we can conclude that they will be 15 miles apart after one hour if they left the same point at the same time.

Learn more about calculating the distance between two points here:

brainly.com/question/7243416

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5 0
1 year ago
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