What is the equation for the line that passes through the point (-4,-6) and has a slope of -1/2?

Two lines or equations are described in each part. Decide whether each system has one solution, no solution, or infinitely many

olga55 [171]

To get the solution of a set of equations means to get a point that satisfies both equations.

Part (1):
The first line has a rate of change of 7, this means that slope of first line is 7
The second line has a rate of change of -7, this means that slope of second line is -7
Since the slope of the first line = - slope of the second line, then these two lines are definitely perpendicular to each other.
Two perpendicular lines will meet only in one point. This means that one point only will satisfy both equations (check the image showing perpendicular lines attached below)
Therefore, only one solution exists in this case

Part (2):
The first given equation is:
2x + 3y = 5.5
The second given equation is:
4x + 6y = 11
If we simplified the second equation we will get: 2x + 3y = 5.5 which is exactly similar to the first equation.
This means that the two given equations represent the same line.
Therefore, we have infinite number of solutions

Part (3):
We are given that the two lines are parallel. This means that the two lines are moving the same path side by side. Two parallel lines can never intersect. This means that no point can satisfy both equations (check the image showing parallel lines attached below).
Therefore, we have no solutions for this case.

7 0

3 years ago

Read 2 more answers

Simplify 4x(2x3-7x2+x)

Gelneren [198K]

To simplify this all you need to do is distribute the 4x across each term in the parenthesis
$4x(2x^3 - 7x^2 + x) \\ (4x)(2x^3) - (4x)(7x^2) + (4x)(x) \\ 8x^4 - 28x^3 + 4x^2$

5 0

3 years ago

The figure for the other questions

stira [4]

I can't really measure the angles. I can tell you what they look like they'd be. There are three reasons why not.
1. The paper is slightly bulged where your hand is
2. The circle is slightly distorted by the camera. This is not that critical.
3. It is very hard to measure on a computer screen.
There is nothing you could do to make it any better. In fact, given what you had to do, this is a pretty good representation.

The Three angles -- Question 22
Using the crudest tools you could imagine, I measured the angle where you have written two 90s between the arms as 132°. That angle opens towards the bottom of the page.

The angle that you have called 95 degrees is actually pretty close. I think you read the upper set of numbers on the protractor when you should have been reading the lower set. I make it 89, but I'll bet it is intended to be 90 degrees.

The third angle on your right is the same as the first one. It comes in at about 132° using my tools again.

Question 23
I can help you with this. When you are asked to make an equation, you have to use an equal sign somewhere.

The sum of the three angles should be 360° I'm going to create an error term because I'm almost sure what I measured won't make 360. All circles when you make angles from any point inside them should make angles that add up to 360° when measured with a protractor if the rays of the angles all start from the same point. [If you don't know what a ray is, call it "the arms of the angles"].

So let's create the equation.
Angle1 + angle2 + angle3 + E = 360°
Angle1 = 89°
Angle2 = 132°
Angle3 = 132°
E is the error that represents the amount away from 360. Your teacher doesn't expect you to get this or to set it into your equation. The main thing you were supposed to do is add up the angles as you tried to do and state what your total was. This is what was expected.
Total = angle1 + angle2 + angle3
Total = 89 + 132 + 132 = 353. My error is 7° too little. So in my equation E = 7°

What to do
Somebody had to mark this with that green felt. You have a teacher. Go to the teacher and ask to be shown how to read the protractor if that person knows. You just need a bit of help. If the teacher cannot tell you, go to someone in your class who knows about that sort of thing and ask them. You're pretty close to getting it.

6 0

3 years ago

Use the confidence interval to find the estimated margin of error. Then find the sample mean. A biologist reports a confidence i

Pavlova-9 [17]

Answer:

$\bar X = \frac{Lower +Upper}{2}$

$\bar X= \frac{1.9+3.3}{2}= 2.6$

And the margin of error with this one:

$\bar X = \frac{Upper-Lower}{2}$

$ME = \frac{3.3-1.9}{2}= 0.7$

Step-by-step explanation:

Assuming that the parameter of interest is the sample mean $\mu$ . And we can estimate this parameter with a confidence interval given by this formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

For this case the confidence interval is given by (1.9, 3.3)

Since the confidence interval is symmetrical we can estimate the sample mean with this formula:

$\bar X = \frac{Lower +Upper}{2}$

$\bar X= \frac{1.9+3.3}{2}= 2.6$

And the margin of error with this one:

$\bar X = \frac{Upper-Lower}{2}$

$ME = \frac{3.3-1.9}{2}= 0.7$

7 0

3 years ago

Example: Find the circumference of the circle with a radius of 5 inches. Solution: Step 1: Write down the formula: IC = 2tr Step

GREYUIT [131]

Answer:

1. The circumference of any circle equals two times its radius multiplied by pi (π, approximately 3.14). We can also say it equals pi times its diameter.

Thank you

7 0

3 years ago