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o-na [289]
3 years ago
6

10 study groups at the library are chosen one person is selected at random from each group

Mathematics
1 answer:
andriy [413]3 years ago
8 0

Looking at another post with the same question, the answer is B, random.

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The minimum/maximum value of the function y = a(x − 2)(x − 1) occurs at x = d, what is the value of d?
daser333 [38]

Answer:

d=\frac{3}{2}=1.5

Step-by-step explanation:

We have the function:

y=a(x-2)(x-1)

And we want to find x=d for which the minimum/maximum value will occur.

Notice that our function is a quadratic in factored form.

Remember that the minimum/maximum value always occurs at the vertex point.

And remember that the x-coordinate of the vertex is the axis of symmetry.

Since a quadratic is always symmetrical on both sides of its axis of symmetry, a quadratic’s axis of symmetry is the average of the two roots/zeros of the quadratic.

Therefore, the value x=d such that it produces the minimum/maximum value is the average of the two roots.

Our factors are <em>(x-2) </em>and <em>(x-1)</em>.

Therefore, our roots/zeros are <em>x=1, 2</em>.

So, the average of them are:

d=\frac{1+2}{2}=3/2=1.5

Therefore, regardless of the value of <em>a</em>, the minimum/maximum value will occur at <em>x=d=1.5</em>.

Alternative Method:

Of course, we can also expand to confirm our answer. So:

y=a(x^2-2x-x+2)\\y=a(x^2-3x+2)\\y=ax^2-3ax+2a

The x-coordinate of the vertex is still going to be the place where the minimum/maximum is going to occur.

And the formula for the vertex is:

x=-\frac{b}{2a}

So, we will substitute <em>-3a</em> for <em>b</em> and <em>a</em> for <em>a</em>. This yields:

x=-\frac{-3a}{2a}=\frac{3}{2}=1.5

Confirming our answer.

4 0
3 years ago
5. Consider the following equations.
WITCHER [35]

Answer:

Step-by-step explanation:

In y = mx + b form, the slope can be found in the m position and the y intercept can be found in the b position.

4x - 2y = -6

-2y = -4x- 6

y = (-4/-2)x -(6/-2)

y = 2x + 3....slope here is 2, and y int is 3

3x + y = 3

y = -3x + 3.....slope here is -3, and y int is 3

B. slopes are different, y intercepts are the same

3 0
3 years ago
If h(x) = (f o g)(x) and h(x) = sqrt(x+5), find g(x) if f(x) = sqrt(x+2)
agasfer [191]

Answer:

  • g(x) = x + 3

Step-by-step explanation:

<h3>Given</h3>
  • h(x) = (f ο g)(x)
  • h(x) = \sqrt{x+5}
  • f(x) = \sqrt{x+2}
<h3>To find</h3>
  • g(x)
<h3>Solution</h3>

<u>We know that:</u>

  • (f ο g)(x) = f(g(x))

<u>Substitute x with g(x) and solve for g(x):</u>

  • \sqrt{x+5} = \sqrt{g(x)+2}
  • x + 5 = g(x) + 2
  • x + 3 = g(x)
  • g(x) = x + 3
7 0
3 years ago
How do you show less than or equal too on a number line?
NISA [10]
It is like if you have two number lines. Then one has a pointer at 0, and the other one has the pointer facing at 2 then it will be lesser because the first one has 0 or if it turned around it would be greater. If it is equal then it would have the same number, but watch out if it is a negative number.
8 0
3 years ago
Is this relation a function? explain
Anton [14]

Answer:

A function is a relation in which no two ordered pairs have the same first element. A function associates each element in its domain with one and only one element in its range. Solution: a) A = {(1, 2), (2, 3), (3, 4), (4, 5)} is a function because all the first elements are different.

Step-by-step explanation:

4 0
3 years ago
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