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2 years ago

What is an equation of the line that passes through the points (1,4) and (-2,-8)?

Mathematics

1 answer:

natita [175]2 years ago

8 0

Answer: I know it 4 but I don’t know the equation for it, I can only help you this far.(hope it help)

Step-by-step explanation:

(1,4) and (-2,-8)

(x is the first number of the point which is 1 and -2, y is the second number of the point which is 4 and -8.)

(x1 is 1, it alway the first point they tell you on the problem like (1,-4) is on the problem first so it gonna be x1 and y1, for x2 it -2, it alway the second point in the problem like (-2,-8) is the second point they tell you so it gonna be y1 and y2.)

Do x2 - x1 and y2 - y1(y/x)

-8 - 4/-2 - 1 = -12/-3

-12/-3 divide top and bottom by -3, that would equal to 4

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The height above the surface of the Earth (in meters) of a rock thrown into the air at 10 m/s after x seconds is given by f(x)

Sonbull [250]

Answer:

Rock travels about 8.2x²meters higher on the moon than on the Earth.

Step-by-step explanation:

Expression showing the height of a rock thrown into the air at Earth is,

f(x) = -9.8x² + 10x + 1.5

Similarly, expression showing the height of rock thrown on the moon is,

g(x) = -1.6x² + 10x + 1.5

Difference in the height of the rock thrown on moon = g(x) - f(x)

= (-1.6x² + 10x + 1.5) - ( -9.8x² + 10x + 1.5)

= -1.6x² + 9.8x² + 10x - 10x + 1.5 - 1.5

= 8.2x²

Therefore, rock travels about 8.2x²meters higher on the moon than on the Earth.

8 0

3 years ago

What’s the value of x?

GaryK [48]

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7 0

3 years ago

Locate the point in the complex plane and express the number in polar form.

EleoNora [17]

Answer:

We kindly invite you to see the result in the image attached below.

The number in polar form is $z = 3\sqrt{5}\cdot e^{i\cdot 0.352\pi}$ .

Step-by-step explanation:

A complex number is represented by elements of the form $a + i\,b$ , for all $a$ , $b$ $\in \mathbb{R}$ . The first part of the sum is the real component of the complex number, whereas the second part of the sum is the imaginary component of the complex number. The real component is located on the horizontal axis and the imaginary component on the vertical axis.

Now we proceed to present the point on the graph: ( $a = 6$ , $b = 3$ ) We kindly invite you to see the result in the image attached below.

The polar form of the complex number is defined by:

$z = r\cdot e^{i\cdot \theta}$ (1)

Where:

$r$ - Magnitude of the complex number, dimensionless.

$\theta$ - Direction of the complex number, measured in radians.

The magnitude and the direction of the complex number are defined by the following formulas:

Magnitude

$r =\sqrt{a^{2}+b^{2}}$ (2)

Direction

$\theta = \tan^{-1} \frac{b}{a}$ (3)

If we know that $a = 6$ and $b = 3$ , then the polar form of the number is:

$r =\sqrt{6^{2}+3^{2}}$

$r = 3\sqrt{5}$

$\theta = \tan^{-1} \frac{6}{3}$

$\theta \approx 0.352\pi \, rad$

$z = 3\sqrt{5}\cdot e^{i\cdot 0.352\pi}$

The number in polar form is $z = 3\sqrt{5}\cdot e^{i\cdot 0.352\pi}$ .

4 0

3 years ago

I need help y’all s.o.s

Firdavs [7]

Please, do not present a long list of questions like this without either explanation of what kind of help you need or what you have already done. One or two problems per post is the informal limit.

I will do just the first problem for you, to get you started, and ask you to share your efforts on the next one.

x-3y≥6

-5x-3y≥-6

We are to find values of both x and y such that points (x,y) satisfy both constraints

x-3y≥6

-5x-3y≥-6.

For simplicity's sake, replace the " ≥ " sign with " = " as follows:

x-3y = 6

-5x-3y= -6

Let's solve this system thru elimination. Mult. the 2nd eqn by -1 to change the sign of all its terms:

5x + 3y = 6

and then add this result to the 1st equation:

5x + 3y = 6

x-3y = 6

-------------------

6x = 12, so x = 6. Now subst. 6 for x in x-3y = 6: 6-3y = 6. Thus, y=0.

The point at which the 2 lines cross is (6,0).

Graph both lines, using solid (not broken) lines, due to the " = " in " ≥ .

Because of the " ≥ " signs in each of the original inequalities, shade the graph ABOVE each of these solid lines. Note that you will have TWO shaded areas, which partially overlap. The solution set here is represented by the area that has been shaded twice.

To help you with the graphing:

x-3y = 6 can be rewritten as 3y = -x + 6, or y = (-1/3)x + 2. This line has a y-intercept of 2 and a slope of -1/3.

-5x-3y≥-6 can be rewritten as - 3y = 5x - 6, or y = (-5/3)x + 2. This line has a y-intercept of 2 (same as the other line) and a slope of -1/3 (different from the other one).

If you do this graphing correctly, you will find that the 2 lines intersect at (6,0).

The most efficient way to show the "solution" of this system of inequalities is to graph the two lines and shade the areas above them. Draw lines around the area that has been shaded twice.

4 0

3 years ago

Write the set of real numbers from -10 through 10 in interval notation.

alexdok [17]

Answer:

$Interval: [-10.10]$

Step-by-step explanation:

Given

Set: -10 to 10

Required

Write as interval notation

We start by writing the given parameter as an inequality

$Inequality: -10 \leq x \leq 10$

The direct representation of $\leq$ and $\geq$ in interval representation of sets is $[$ and $]$ , which shows that the beginning and end of the interval are inclusive;

So, the above inequality in interval notation is:

$Interval: [-10.10]$

3 0

3 years ago