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aalyn [17]
3 years ago
12

Which statement illustrates the distributive property?

Mathematics
1 answer:
puteri [66]3 years ago
5 0

Answer:

3(4+5)= 3(4)+3(5)

Step-by-step explanation:

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How to factor a quadratic equation and find the vertex?
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zzz [600]

Question 11

The directrix is a horizontal line, which means the parabola opens either upward or downward. In this case, it opens downward. This is because all answer choices have a negative leading coefficient. Also, it's because the focus is below the directrix.

For vertically opening parabolas, we use this form

4p(y-k) = (x-h)^2

where (h,k) is the vertex and p is the focal distance, aka the distance from the vertex the focus. To find (h,k), we start at the focus (0,-4) and move directly up until we reach the directrix y = 4. We'll arrive at (0,4). The midpoint of (0,-4) and (0,4) is (0,0) which is the vertex's location. So (h,k) = (0,0).

Note that in moving from (0,-4) to (0,4) is a span of 4 units. So this is the value of p.

Plug h = 0, k = 0, p = 4 into the equation mentioned and solve for y

4p(y-k) = (x-h)^2

4*4(y-0) = (x-0)^2

16y = x^2

y = (1/16)x^2

The only adjustment we need to make is to change the 1/16 to -1/16 so that the parabola opens downward.

<h3>Answer:  Choice D.  y = -(1/16)x^2</h3>

===============================================

Question 3

The given equation is in the form y = ax^2+bx+c

In this case,

  • a = 2
  • b = 4
  • c = 3

Let's compute the x coordinate of the vertex h

h = -b/(2a)

h = -4/(2*2)

h = -1

This h value is plugged into the original function to find k

f(x) = 2x^2+4x+3

f(-1) = 2(-1)^2+4(-1)+3

f(-1) = 1

We find that h = -1 and k = 1 pair up together. In short, (h,k) = (-1,1) is the vertex.

<h3>Answer: Choice B.  (-1,1)</h3>
8 0
2 years ago
Read the following description of a
Annette [7]

Answer:

\sf a = \boxed{\bf 1}  \ n+ \boxed{\bf 3}

Explanation:

\sf \underline{rate} \ = \ \sf \dfrac{y_2-y_1}{x_2-x_1} \   = \  \dfrac{rise}{run}  \ = \  \dfrac{11-10}{8-7}   \ = \  \underline{1}

<u>Equation</u>:

\Rightarrow \sf a - a1 = m(n - n1)

\Rightarrow \sf a - 10 = 1(n -7)

\Rightarrow  \sf a = n - 7 + 10

\Rightarrow \sf a = n + 3

3 0
2 years ago
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