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Anastasy [175]
2 years ago
5

if the principal and the amount of interest for one year are known, the rate of interest of interest can be found

Mathematics
1 answer:
Ad libitum [116K]2 years ago
7 0
For Simple Interest, I = PRT/100

Time = 1 year.

I = P*R*1/100

100*I =  PR

100I / P = R

The formula for the Rate, R = 100I / P. 
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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
I need help with this
alexira [117]

Answer:

g(x)=log(x+4)

Step-by-step explanation:

Here the parent function is f(x)=log x. The function has y intercept as 0 at x=1 .

If we observe the translated function we will observe that , the y intercept of new function is 0 at x=-3. Hence the function is moving ahead of the parent function by 4 units and reaches the y intercept being 0.

If we graph

g(X)= log X

the y intercept will be at (1,0)

X = 1 , Y =0

at X=1 , x = -3  or x = X-4

or X=x+4

Hence

new function will be g(x)=log ( x+4)

8 0
3 years ago
Write an equation for the translation of x ^ 2 + y ^ 2 = 25 by 6 units left and 3 units down.
Aliun [14]
The equation would be: (x + 6)^2 + (y + 3)^2 = 25

This equation will produce a circle. If you add the numbers inside the parenthesis to be squared, you can center of the circle. Thus, translating the shape.
3 0
3 years ago
Read 2 more answers
I know it small but can someone help me. It says The table below shows customers' favorite ice cream flavors at a popular ice cr
IgorLugansk [536]

Answer:

<h2><u>Graph A</u></h2>

Step-by-step explanation:

We know it must be graph A because when finding the most popularly bought item, the percentages only can go to 100%

So graphs C and D are eliminated.

Also since it never said any flavors were unknown, all the percents have to add up to 100%

So graph B is eliminated.

Only graph A follows the requirements

7 0
2 years ago
The legs of a right triangle have the following measurements: 5 and 10 inches. What is the length of the hypotenuse??
RideAnS [48]

Answer:

5\sqrt{5}

Step-by-step explanation:

1. 5^2 + 10^2 = c^2

2.125 = c^2

3. c=5\sqrt{5}

7 0
2 years ago
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