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Thepotemich [5.8K]
3 years ago
15

12. The table of values below describes a quadratic relation. Find the missing value and include calculations that demonstrate t

hat this is the correct value.

Mathematics
1 answer:
True [87]3 years ago
3 0

Answer:

The quadratic equation is;

y = 3x^2-7x + 5

when x = 4, y = 25

Step-by-step explanation:

Mathematically, the general form of a quadratic equation is;

y = ax^2 + bx + c

From the first point, we have that x = 0

Thus;

5 = a(0)^2 + b(0) +c

c = 5

Now, in a case when x is 2

3 = a(2)^2 + b(2) + 5

3 = 4a + 2b + 5

4a + 2b = -2 ••••••(i)

when x = 6

71 = a(6)^2 + b(6) + 5

66 = 36a + 6b ••••••(ii)

From equation i,

2b = -2-4a ••••(iii)

we can rewrite equation ii as

66 = 36a + 3(2b)

Substitute iii into ii

66 = 36a + 3(-2-4a)

66 = 36a - 6 - 12a

66 + 6 = 36a -12a

24a = 72

a = 72/24

a = 3

Recall;

2b = -2-4a

2b = -2-4(3)

2b = -2-12

2b = -14

b = -14/2

b = -7

So the quadratic equation would be;

y = 3x^2 -7x + 5

Now let us test;

when x = 10, y = 235

That would be:

y = 3(10)^2 -7(10) + 5

y = 300 - 70 + 5

y = 235

This shows that the derived quadratic equation is correct

Now, when x = 4; we have it that;

y = 3(4)^2 -7(4) + 5

y = 48 -28 + 5

y = 20 + 5 = 25

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Most everyday situations involving chance and likelihood are examples of ______. simple probability permutations conditional pro
Fynjy0 [20]

Answer:

Most everyday situations involving chance and likelihood are examples of simple probability.

Explanation:

The probability is the chance or likelihood of any event happening. In our everyday life, we unintentionally use the probability. For example, we say there is 70% chance that tomorrow will be rain, there is 50% chance that Brazil will win the world cup, there is less likelihood of he arriving today and soon. In all these concepts we are dealing with uncertainty and there is chance factor involved in all these examples. So in most everyday situations which involve chance and likelihood are actually examples of simple probability.

6 0
3 years ago
Suppose a system of two linear equations has one solution. What must be true about the graphs of the two equations?
malfutka [58]
They should both have the same solution?
8 0
2 years ago
Read 2 more answers
Lin rode her bike 2 miles in 8 minutes. She rode at a constant speed. How
hodyreva [135]

Answer: 4

Step-by-step explanation:

For this question, we have to divide the number 8 by 2.

8 ÷ 2 = 4

Now, we have to take the quotient, 4, and multiply it by 1.

1 x 4 = 4

The answer is 4.

6 0
2 years ago
the second term of a geometric sequence is 18 and the fourth term is 8 find the common ratio . And find the sum of the first 6 t
777dan777 [17]

Answer:

  • ratio: 2/3
  • sum: 73 8/9

Step-by-step explanation:

The general term of a geometric sequence is ...

  an = a1·r^(n-1)

You have the 2nd and 4th terms, so ...

  a2 = a1·r^(2-1) = a1·r

  a4 = a1·r^(4-1) = a1·r^3

We can find r from the ratio ...

  a4/a2 = (a1·r^3)/(a1·r) = r^2 = 8/18 = 4/9

Then r is ...

  r = √(4/9) = 2/3 . . . . the common ratio

The first term is ...

  a2 = 18 = a1·(2/3)

  a1 = (3/2)·18 = 27

__

The sum of the first 6 terms is ...

  Sn = a1·(r^n -1)/(r -1)

  S6 = 27·((2/3)^6 -1)/(2/3 -1)

  S6 = 27·(64/729-1)/(2/3-1) = (27)(665)/243 = 73 8/9

The sum of the first 6 terms is 73 8/9.

_____

<em>Check on the sum</em>

The first 6 terms are ...

  27, 18, 12, 8, 5 1/3, 3 5/9

Their sum is 73 8/9, as above.

8 0
3 years ago
PLEASE<br> Need Help<br> Show Work
BartSMP [9]

This set notation really seems the hard way to exclude a single value. Anyway...

The domain doesn't include where the denominator is zero, 4x + 7 = 0,

x = -7/4

The range doesn't include the asymptotic value, which is

y=2x/4x = 1/2

So we need domain x ≠ -7/4 and range y ≠ 1/2

Answer: First choice

7 0
3 years ago
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