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2 years ago

2a. Determine the equation of the line connecting the points (0, -1) and (2, 3) *

1 answer:

8 0

First create the equation y=Mx+ B

B is the y intercept so when y = 0, B = -1.

Now we have y=Mx - 1

The slope is M. We can calculate this by using the formula M = (y2 -y1) / (x2 - x1)

Use the points (0, -1) and (2,3) for these values. So y2 = 3, y1 = -1, x2 = 2, x1 = 0

Plug them into the equation and solve

M = (3 + 1) / (2 - 0)
M = 4/2 = 2

Now we have the equation y = 2x - 1

Next to figure out if the points given are on the line you take the values and plug them into your equation like so: 4 = 2(-2) - 1

2(-2) - 1 does not equal 4 so this point does not fall on this line. Follow this same procedure for the next point given.

You might be interested in

Use the method of Gauss to find the sum.1+2+3+.....+400

nikklg [1K]

Gauss' method for addition relies on the fact that you can 'pair' certain numbers together. Look at the example:

1+2+3+4+5+6+7+8+9+10

We could manually add all these together from left to right but a clever way to think about this is if we add together the ends of the sum (10+1) we get 11. If we then move one in from the ends and add these (2+9) we also get 11. This means that 1+2+...+9+10 is the same as 11+11+...+11+11.

Because each 2 numbers adds to 11 we know the total number of 11's we have to add together is the length of the sum divided by 2. In our case 5 (10 ÷ 2). We need to add 5 lots of 11 to get our answer. This is the same as 11 × 5 which is easily seen to be 55.

(If you add the 10 numbers together on a calculator you'll see 1+2+3+4+5+6+7+8+9+10 = 55) so this method really makes it a lot quicker.

Looking at your sequence, if we pair the ends together we get 401 (400+1) and we multiply this by the length of the sequence divided by 2. In your case, 200 (400 ÷ 2).

So the sum of all the numbers from 1 to 400 must be 401 × 200 = 80,200.

Remember the steps:
1. Pair the ends together and add them
2. Times this number by the length of the sequence halved

Hope this helps.

6 0

3 years ago

What is the slope of a line that is perpendicular to the line shown.

sertanlavr [38]

Answer:

3/4

Step-by-step explanation:

First of all, we need to calculate the slope of the line shown. This can be computed as:

$m=\frac{\Delta y}{\Delta x}$

where

$\Delta y = y_2-y_1$ is the increment along the y-direction

$\Delta x = x_2 - x_1$ is the increment along the x-direction

We can choose the following two points to calculate the slope of the line shown:

(-3,2) and (0,-2)

And so, the slope of the line shown is

$m=\frac{-2-(2)}{0-(-3)}=-\frac{4}{3}$

Two lines are said to be perpendicular if the slope of the first line is the negative reciprocal of the slope of the second line:

$m_2 = -\frac{1}{m_1}$

Using $m_1 = -\frac{4}{3}$ , we find that a line perpendicular to the line shown should have a slope of

$m_2 = -\frac{1}{-4/3}=3/4$

5 0

2 years ago

Scott bought a backpack for $35.99 at Walmart. He needed to pay a 10% tax. How much did the backpack cost in all?

stellarik [79]

$35.99 x .10=3.599
$35.99 + 3.60=$39.59

8 0

3 years ago

The linear function f(x) = 0.9x + 79 represents the average test score in your math class, where x is the number of the test tak

Levart [38]

Given:

The linear function for average test score in your math class is

$f(x)=0.9x+79$

where x is the number of the test taken.

The linear function g(x) in the given table represents the average test score in your science class, where x is the number of the test taken.

To find:

Part A: The test average for your math class after completing test 2.

Part B: The test average for your science class after completing test 2.

Part C: Which class had a higher average after completing test 4?

Solution:

Part A:

We have,

$f(x)=0.9x+79$

Put x=2 in the above function, to find the test average for your math class after completing test 2.

$f(2)=0.9(2)+79$

$f(2)=1.8+79$

$f(2)=80.8$

Therefore, the test average for your math class after completing test 2 is 80.8.

Part B:

From the given table it is clear that g(x) =79 at x=2.

Therefore, the test average for your science class after completing test 2 is 79.

Part C:

Put x=4 in f(x), to find the test average for your math class after completing test 4.

$f(4)=0.9(4)+79$

$f(4)=3.6+79$

$f(4)=82.6$

From the table it is clear that the value of g(x) is increased by 1 as x is increased by 1. So, the value of function g(x) at x=4 must be 1 more than 80.

$g(4)=81$

It is clear that,

$82.6>81$

Therefore, math class had a higher average after completing test 4.

3 0

3 years ago

The bar graph below shows the attendance at school dances. The ticket per price for each dance is $5 per student. Which two danc

topjm [15]

It's B because all the students that attended added together is 320 and 37.5 of 320 is 120

6 0

2 years ago