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monitta
2 years ago
6

Alex drives at an average speed that is

Mathematics
1 answer:
densk [106]2 years ago
5 0

Answer:

The answer is 162.5

Step-by-step explanation:

you divide 2 by 3 and then figure out how many examples where given to find the average and multiply by that much and you get the answer.

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For parties of six or more, a restaurant adds a 20% gratuity (or tip). If a
adelina 88 [10]

Answer: tThe total dinner bill with  tip = $177.90

Step-by-step explanation:

Given: Dinner bill = $148.25

Tip percent = 20%= 0.20

Total dinner bill = Dinner bill + Tip percent × (Dinner bill)

Total dinner bill = $ (148.25+0.20×148.25)

Total dinner bill = $ (148.25(1.20))

Total dinner bill = $177.90

Hence, the total dinner bill with  tip = $177.90

6 0
2 years ago
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
3 years ago
What is the factored form of this expression?<br><br> x2 + 15x + 56
AlladinOne [14]

Step-by-step explanation:

{x}^{2}  + 15x + 56

{x}^{2}  + 7x + 8x + 56

taking common

x(x + 7) + 8(x + 7)

(x + 8) (x + 7)

6 0
3 years ago
Read 2 more answers
If f (x) = StartRoot x EndRoot + 12 and g (x) = 2 StartRoot x EndRoot, what is the value of (f – g)(144)?
Lera25 [3.4K]

Answer:

hmm very diffecult.

Step-by-step explanation:

if f (x) = StartRoot

3 0
2 years ago
Y=2/3(x-5)^2
Anvisha [2.4K]

Answer:

  see below

Step-by-step explanation:

The graph opens upward if the sign of the squared term is positive. If that sign is negative, the graph opens downward. The first three equations open upward; the last opens downward.

The line of symmetry is the value of x that makes the squared term zero. Here, that is x=5 for all equations.

<u>y=2/3(x-5)^2</u>:  A, D

<u>y=1/2(x-5)^2</u>:  A, D

<u>y=3/4(x-5)^2</u>:  A, D

<u>y=-4(x-5)^2</u>:  B, D

8 0
3 years ago
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