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tatuchka [14]
3 years ago
15

9. What is the slope of the line through the points (-2, -1) and (4, 3)?

Mathematics
1 answer:
Fofino [41]3 years ago
4 0

Step-by-step explanation:

given points,

(-2, -1) and (4,3)

we know,

slope of line = y_2 - y_1/ x_2 - x_1

x_1 and y_1 = -2 , -1

x_2 and y_2 = 4 , 3

according to the formula

3 - (-1)/4 - (-2)

→ 3 + 1/4 + 2

→ 4/6

→ 2/3

or (2,3)

therefore, slope of the given line is (2,3).

Hope this answer helps you dear!

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The polynomial $f(x)$ has degree 3. If $f(-1) = 15$, $f(0)= 0$, $f(1) = -5$, and $f(2) = 12$, then what are the $x$-intercepts o
Alex_Xolod [135]

Your calculator's cubic regression function can tell you the equation is

... f(x) = 2x³ + 5x² -12x = x(x +4)(2x-3)

The x-intercepts are -4, 0, +1.5.

_____

If you want to solve this "by hand", you can first of all recognize that since there is an x-intercept at 0, the cubic will only have three coefficients. That is, you can write the equation as

... f(x) = ax³ + bx² + cx

Substituting the given points (except (0, 0)) gives three linear equations in a, b, c.

... -a +b -c = 15 . . . . . for x=-1

... a + b + c = -5 . . . . for x=1

... 8a +4b +2c = 12 . . for x=2

adding the first two equations gives 2b=10, or b=5. Now, you can reduce the system to

... a + c = -10

... 4a +c = -4

Subtracting the first of these equations from the second gives 3a=6, or a=2. That tells you c=-12 (from a+c=10).

Then your equation is

... f(x) = x(2x² +5x -12)

Factoring by any of the usual techniques, or graphing, or using the quadratic formula will tell you the zeros (x-intercepts) are as above.

_____

Since the input values are sequential, you can also develop the function from differences of the output values. Those are 15, 0, -5, 12. First differences are -15, -5, +17. Second differences are +10, +22. The third difference is 12. Using the first of these differences in appropriate places in the interpolating polynomial formula, we have

... f(x) = 15 + (x+1)(-15 + (x)/2·(10 + (x-1)/3·(12))) = 2x³ +5x² -12x . . . . as above

4 0
3 years ago
The angles in a triangle are represented by 5x, 8x, and 2x+9. What is the value of x?
Ahat [919]

Answer:

x = 11.4

Step-by-step explanation:

The sum of the angles of any triangle must add up to 180°.  Since we have the expressions for each angle:  5x, 8x, and (2x +9), we can solve for the variable of 'x' by adding the expressions together and setting them equal to 180:

5x + 8x + (2x +9) = 180

Combine like terms:  15x + 9 = 180

Use inverse operations: 15x + 9 - 9 = 180 - 9

                                                     15x = 171  or x = 11.4

Check:  5(11.4) + 8(11.4) + 2(11.4) + 9 = 57 + 91.2 + 22.8 + 9 = 180

8 0
3 years ago
It takes leon 13 hours to seal his driveway working by hinself. If michael helps leon, they can seal the driveway in 7 hours. Ho
Monica [59]

Answer:

15.1667 hours (15 hours and 10 minutes)

Step-by-step explanation:

Using the concept of "distance = speed * time", we can formulate equations to solve this problem.

Let's call Leon's speed X, Michael's speed Y and the length of the driveway D.

If leon takes 13 hours alone, we can write the equation:

D = X * 13

If Michael helps Leon, we have this equation:

D = (X+Y) * 7

(The total speed is the sum of their speed, as they are working together)

Making the first equation equate the second, we have:

13*X = 7*X + 7*Y

7*Y = 6*X

X = (7/6)*Y

If we use this value of X in the first equation, we have:

D = 13*X = 13*(7/6)*Y = 15.1667*Y

So we have that Michael would take 15.1667 hours (15 hours and 10 minutes) to seal the driveway alone.

4 0
3 years ago
Jeff is at the local casino. As long as he has a single dollar or more, he repeatedly plays a game where the probability of gain
nekit [7.7K]

Answer:

685686

Step-by-step explanation:

miya is correct

7 0
3 years ago
Select the points that lie on function h (x) = 3x^2
Mariulka [41]
The points that lie on function h (x) = 3x² is, " (1, 3) and (-1, 3)".


You can put the values in to the equation of the abscissas of the ordered pair and solve for h(x)
A. (1, 3)   ;    h(x) = 3(1²) = 3     Equal B. (-1, 3)  ;    h(x) = 3(-1)² = 3   EqualThus, these are the points that lie on function h(x ) = 3x²
6 0
3 years ago
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