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kykrilka [37]
2 years ago
11

3. Which of the following points satisfies the inequality y > 5x – 2?

Mathematics
2 answers:
lions [1.4K]2 years ago
5 0

Answer:

b

Step-by-step explanation:

GREYUIT [131]2 years ago
5 0

Answer:

Step-by-step explanation:

to satisfy the inequality then the point needs to make the inequality true

y > 5x -2

for (x=3, y=11) we have, 11 >5*3 -2 ; 11 > 13 false

for (x=2, y=10) we have, 10 >5*2 -2; 10 > 8 true

for (x=1, y= -1) we have -1 > 5*1 -2 ; -1 > 3 false

for (x= -3, y= -17) we have , -17 > 5* -3 -2 ; -17 > -17 false

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4*8*4/8*1/2
128/4
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The answer is 32.

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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.

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Find the volume of the cone to the nearest whole number. Radius is 2 and height is 4
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Volume of the cone is 17 cm³

Step-by-step explanation:

  • Step 1: Volume of a cone = 1/3 πr²h. Find volume of the cone where r = 2 inches and h = 4 cm.

Volume = 1/3 × 3.14 × 2² × 4

             = 16.75 cm³ ≈ 17 cm³ (rounding off to nearest whole number)

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To make 6 apples pie, you need 2 pounds of apples. How many pounds of apples do you need to make 10 apple pies?
Bezzdna [24]
For every 6 apple pie, you need 2 pounds of apples.
So, how many pounds of apples do you need for 10 apple pies?
Well, first to figure out this question we first need to make a conversion factor.
I see in the fraction 6/3 we can simplify that to 2/1. Now we got our conversion factor.
We need to invert the fraction in order for the pie unit to cancel out.
1/2 * 10 = 5

You will need 5 pounds of apples to make 10 apple pies.

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What is the gradient of a line with an equation of 3x-2y-6=0​
Genrish500 [490]

Answer:

Slope <em>m</em> = 3/2

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Equality Properties

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Step-by-step explanation:

<u>Step 1: Define Equation</u>

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<u>Step 2: Rewrite</u>

<em>Find slope-intercept form</em>

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  2. Add 6 on both sides:                             -2y = -3x + 6
  3. Divide -2 on both sides:                         y = 3/2x - 3

<u>Step 3: Break Function</u>

<em>Identify Parts.</em>

Slope <em>m</em> = 3/2

y-intercept <em>b</em> = -3

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2 years ago
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