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Alenkinab [10]
3 years ago
11

Make a table of ordered pairs for the equation. y= 1/2x − 3 Then plot two points to graph the equation.

Mathematics
2 answers:
inysia [295]3 years ago
6 0

Answer:

Check the image

Step-by-step explanation:

To create the table we just have to give values to X and evaluate the equation with those values, we will use from -3 to 3:

X       Y

-3       -4,5

-2       -4

-1        -3,-5

0        -3

1        -2,5

2        -2

3         -1,5

Now that we have this we just use two points and unite them in the graph with a straigh line, I´d recomment using the first and last points. Checjk the image.

MrMuchimi3 years ago
5 0
All you gotta do is pick a random point on the x-axis, lets say, x=2 in this case, and plug it into the equation.

If x=2, y = (1/2)2 - 3 = 2 - 3 = -1
When x = 2, y = -1

Now pick another point, x = 1

x = 1, y = (1/2)1 - 3 = 0.5 - 3 = - 2.5
When x = 1, y = - 2.5

Draw a cross on those 2 points, on the 2d plane
(1, -2.5) and (2, -1)
and draw a line between them, and make the line continue past the points, having no boundaries but the paper you hold, keeping it straight the entire time. With not turns.

If you want to draw out a table, make it have 2 rows, and 6 columns.
Write x in the first column of the first row, and write y in the first column of the second row.

Now, write down a different, random x value, in each column in the first row.
In the second row, in each column, write the y value, that corresponds to the x value given above each individual column, based on the equation
y = 1/2x - 3.
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Find the value of c so that (x-5) is a factor of the polynomial p(x)
liubo4ka [24]

I think the question is

Find the value of c so that (x-5) is a factor of the polynomial

p(x) = x^3 + 2x^2 + cx + 10

The other factor is going to be some quadratic.  We can say a few things about its coefficients but let's start by saying in general it's

q(x)= ax^2 + bx + k

p(x) = (x-5)q(x)

x^3 + 2x^2 + cx + 10 = (x-5)(ax^2 + bx+k) = ax^3 + (b-5a)x^2 + (k-5b)x - 5k

Equating respective coefficients,

a=1

b-5a = 2

k - 5b = c

-5k = 10

so we get

b = 2 + 5 = 7

k = 10/-5 = -2

c = k - 5b = 2 - 5(7)= -37

Answer: -37

Check:

(x^2 + 7x - 2)(x - 5) = x^3 + 2 x^2 - 37 x + 10\quad\checkmark




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3 years ago
What is the 100 nearest 513
ololo11 [35]

Answer: 500

Step-by-step explanation:

it is closest and is under 550. if it were 551 through 599 it would be 600

6 0
3 years ago
NEED ASAP 50 PTS FOR ANSWER
vladimir2022 [97]

Answer:

This says that the product of 3 numbers (x, x-6 and x+2) is greater than zero. In other words the product of three numbers is positive. The key to the solution is the answer to the question: "How can is it possible to get a positive result when you multiply 3 numbers?" I hope the answer is obvious to you. You get a positive result when multiplying 3 numbers when a) all 3 numbers are positive, or b) two of the numbers are negative and the third one is positive. Any other combination of 3 numbers will have a negative or zero result. So the solution to this inequality will be all the x values that make

all 3 factors positive, or

make two of the factors negative and the third one positive

Now we just have to figure out how to translate this idea into number sentences. Making this translation is easier if we take time to figure out the order of the factors, if possible. Which one is the largest? Which one is the smallest? And which one is the middle factor? Even though we do not know what value x may be, it is possible, with these 3 factors, to know the order of them. After thinking about this for a while I hope you can see that (x+2) will always be greater than the other two factors, no matter what x happens to be. Similarly (x-6) will always be less than the other two no matter what x happens to be. And that makes x the in between factor. If you have trouble seeing this:

Picture a number line.

Picture any random point on this number line. (This is our "x").

x+2 will be two units to the right of x. Being to the right makes x+2 greater than x.

x-6 will be 6 units to the left of x. Being to the left makes x-6 less than x.

With x-6 to the left and x+2 on the right, x is the in-between number.

Knowing the order of the factors, combined with some logic, will make expressing the ideas "the three factors are positive" and "two factors are negative and one is positive" easier.

"The three factors are positive"

Without using the order or any logic we could say:

x+%3E+0 and x-6+%3E+0 and x+%2B+2+%3E+0

This is not terribly difficult to solve. But if we use the order and some logic we can come up with something much easier. Think about this: If the lowest of three numbers is positive, wouldn't the other two have to be positive, too? In other words, if the lowest of three numbers is to the right of zero on the number line, wouldn't the other two numbers, which are to the right of the lowest, also be to the right of zero? I hope you can see the logic of this. So to make all three factors positive we just have to make sure the lowest one is positive:

x-6+%3E+0

"Two factors are negative and one is positive"

Without using the order or any logic we would have to describe every possible combination of two negative factors and one positive factor:

((x+%3C+0) and x+-+6+%3C+0 and x+%2B+2+%3E+0) or (x+%3C+0) and x+-+6+%3E+0 and x+%2B+2+%3C+0) or (x+%3E+0) and x+-+6+%3C+0 and x+%2B+2+%3C+0))

Yikes!! This is solvable but it will take a lot of work. But if we use the order sand some logic we can get something much simpler to solve. When we know the order of the factors, in order to have 2 of three factors negative and one of them positive we only have to make sure that the in between factor is negative and the largest factor is positive. This is so because if the in-between factor is negative then the smallest of the three would have to be negative, too. So to make two factors negative and one positive all we have to say is:

(x+%3C+0 and x+%2B+2+%3E+0)

I hope you agree that using the order and some logic makes this problem much easier to solve. When you know the order of the factors this way is much easier. (Note: if it is not possible to figure out the order of the factors, then you must use the much longer, more complicated compound inequalities.)

Remember that our solution is the set of x values that make "all three factors positive or make two factors negative and one positive". Using what we figured out above this is:

(x+-6+%3E+0) or (x+%3C+0 and x+%2B+2+%3E+0)

Now we solve this compound inequality:

(x+%3E+6) or (x+%3C+0 and x+%3E+-2)

In interval notation (x+%3E+6) is (6, infinity)

In interval notation (x+%3C+0 and x+%3E+-2) is (-2, 0)

As for "My teacher is also asking me to find the vertex, axis and symmetry.": I agree, WHAT??. Even though I think it was phrased "axis of symmetry" not "axis and symmetry" it still doesn't make sense. The words "vertex", "axis of symmetry" apply to graphs of two variable sentences (usually parabolas). But we do not have a y. And if the inequality was x%28x-6%29%28x%2B2%29+%3E+y it would simplify to x%5E3+-4x%5E2+-12x+%3C+y. This is a cubic inequality not a quadratic inequality. Its graph would not be a parabola, would not have a vertex and would not have an axis of symmetry.

Step-by-step explanation:

3 0
3 years ago
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Lorico [155]

A3.5x+1008y

Step-by-step explanation:

8 0
3 years ago
If the points (-3,2),(4,-4) are joined to form a straight line, at what point does the line intersect the y-axis
Mashcka [7]
Construct the line using the two points:
slope: m = (-4 - 2) / (4 + 3) = -6/7;
then, y = mx + b => 2 = (-6/7)(-3) + b => 14/7 - 18/7 = b => b = -4/7.
And your y-intersect is -4/7.
7 0
3 years ago
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