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Luden [163]
3 years ago
13

If there are 1/2 cup of almonds how many more would you need for a third

Mathematics
1 answer:
irga5000 [103]3 years ago
5 0
1/6 of almonds. you multiply the two numbers together.
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Graph each of the equations and then determine which one represents the rank catcher that is elevated
Tanya [424]
We have two functions that are Parabolas. A parabola is a type of quadratic function which is a special type of “U”-shaped curve called. So let's solve this problem for the first parabola and then for the second one.

1. Graph of the first equation

We have that:

y=x^2-2x+3

So if we graph this equation, the parabola that matches it is shown in Figure 1.

1.1 Direction of Parabola

In general, a parabola or quadratic function is given by the following way:

y=ax^2+bx+c \\ \\ where \ "a" \ is \ called \ the \ leading \ coefficient

Given that our leading coefficient is positive, then the direction of the parabola is upward, that is, it opens upward.

1.2 Location of vertex with respect to the x-axis

The vertex a parabola can be found as follows:

(-\frac{b}{2a},f(-\frac{b}{2a}))

But: \\ \\ a=1 \\ b=-2 \\ c=3 \\ \\ Accordingly: \\ \\ -\frac{b}{2a}=-\frac{(-2)}{2(1)}=1 \\ \\ f(1)=1^2-2(1)+3=2 \\ \\ So \ the \ vertex \ is: \\ \\ V(1,2)

So the vertex is located two units above the x-axis.

<span>1.3 Determine if the graph depicts the rain gauge
</span>
A rain gauge is an instrument used by meteorologists and hydrologists to gather and measure the amount of liquid precipitation<span> over a set period of time.
</span>
From Figure 4 we can affirm that this is the parabola that resembles a rain gauge elevated from the ground. 

1.4 Why or why not?

It basically the question asks for the parabola that has a vertex well above the x-axis. From Figure 4, you can see that the elevated parabola is in fact:

y=x^2-2x+3

2. Graph of the second equation

We have that:

y=x^2+4x+4

So if we graph this equation, the parabola that matches it is shown in Figure 2.

2.1 Direction of Parabola

As in the previous problem, given that our leading coefficient is positive, then the direction of the parabola is also upward, that is, it opens upward.

2.2 Location of vertex with respect to the x-axis

The vertex of a parabola can be found as follows:

(-\frac{b}{2a},f(-\frac{b}{2a}))

In \ this \ case: \\ \\ a=1 \\ b=4 \\ c=3 \\ \\ Accordingly: \\ \\ -\frac{b}{2a}=-\frac{4}{2(1)}=-2 \\ \\ f(-2)=(-2)^2+4(-2)+4=0 \\ \\ So \ the \ vertex \ is: \\ \\ V(-2,0)

So the vertex lies on the x-axis.

2.3 Determine if the graph depicts the rain gauge

This parabola does not resembles a rain gauge elevated from the ground.

2.4 Why or why not?

As you can see the parabola touches the x-axis. If the x-axis represents the ground, then the rain gauge is touching it, that is, it is not elevated.

3. Graph of the third equation

We have that:

y=3x^2+21x+30

So if we graph this equation, the parabola that matches it is shown in Figure 5.

3.1 Direction of Parabola

As in the previous parabolas, given that our leading coefficient is positive, then the direction of the parabola is also upward, that is, it opens upward.

3.2 Location of vertex with respect to the x-axis

In \ this \ case: \\ \\ a=3 \\ b=21 \\ c=30 \\ \\ Accordingly: \\ \\ -\frac{b}{2a}=-\frac{21}{2(3)}=-\frac{7}{2} \\ \\ f(-\frac{7}{2})=3(-\frac{7}{2})^2+21(-\frac{7}{2})+30=-\frac{27}{4} \\ \\ So \ the \ vertex \ is: \\ \\ V(-\frac{7}{2},-\frac{27}{4})

So the vertex is shifted \frac{27}{4} units downward the x-axis.

3.3 Determine if the graph depicts the rain gauge

This parabola does not resembles a rain gauge elevated from the ground.

3.4 Why or why not?

The vertex of this parabola lies on the negative y-axis. So it is not elevated from the ground.

5 0
2 years ago
Calculate the distance between the points L = (1, -1) and J=(4,-9) in the coordinate plane.
Blizzard [7]

Answer:

8.54

Step-by-step explanation:

distance formula is d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}

plug in the coordinates the answer is 8.54

7 0
3 years ago
75 people to 25 people. What is the percent in change
igomit [66]
So it was 75 to 25 people. that would be decrease by 66.66666666 (forever) percent
5 0
3 years ago
Read 2 more answers
I am confusion. help me
timofeeve [1]
Multiple the two Collins
6 0
3 years ago
Which property is illustrated by the following statement? . Angle X = Angle Y and Angle Z = Angle Y, so Angle X = Angle Z. A.Sym
matrenka [14]
"Transitive" is the property among the following choices given in the question that <span>is illustrated by the following statement. The correct option among all the options that are given in the question is the second option or option "B". I hope that this is the answer that you were looking for and the answer has come to your help.</span>
4 0
3 years ago
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