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pav-90 [236]
2 years ago
14

Find the slope of the line that goes through the two points below.

Mathematics
1 answer:
timama [110]2 years ago
6 0

Answer:

-4

Step-by-step explanation:

The slope of the line is found by

m = (y2-y1)/(x2-x1)

    = (-7 - -19)/(-2 -1)

    = (-7+19)/(-2-1)

    = 12/-3

    = -4

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Find the roots of h(t) = (139kt)^2 − 69t + 80
Sonbull [250]

Answer:

The positive value of k will result in exactly one real root is approximately 0.028.

Step-by-step explanation:

Let h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80, roots are those values of t so that h(t) = 0. That is:

19321\cdot k^{2}\cdot t^{2}-69\cdot t + 80=0 (1)

Roots are determined analytically by the Quadratic Formula:

t = \frac{69\pm \sqrt{4761-6182720\cdot k^{2} }}{38642}

t = \frac{69}{38642} \pm \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321}  }

The smaller root is t = \frac{69}{38642} - \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321}  }, and the larger root is t = \frac{69}{38642} + \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321}  }.

h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80 has one real root when \frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} = 0. Then, we solve the discriminant for k:

\frac{80\cdot k^{2}}{19321} = \frac{4761}{1493204164}

k \approx \pm 0.028

The positive value of k will result in exactly one real root is approximately 0.028.

7 0
2 years ago
A rectangle has a length of x+2, a width of 7, and a perimeter of 32. The value of x is ?
beks73 [17]
Perimeter = sum of all sides

32 = 2(x+2) + 2(7)
32 = 2x+4 + 14
32 = 2x+18
14 = 2x
 /2     /2

7 = x
4 0
3 years ago
Read 2 more answers
What is the perimeter of a 5cm cube. help i`m stuck.
belka [17]

A cube is a solid box whose every surface is a square of same area.

Take an empty box with open top in the shape of a cube whose each edge is 2 cm. Now fit cubes of edges 1 cm in it. From the figure it is clear that 8 such cubes will fit in it. So the volume of the box will be equal to the volume of 8 unit cubes together.

7 0
3 years ago
Graph the circle (x+6)^2 + (y+5)^2 =9
Andrei [34K]

Answer:

This a circle centered at the point (-6,-5), and of radius "3" as it is shown in the attached image.

Step-by-step explanation:

Recall that the standard formula for a circle of radius "R", and centered at the point (x_0,y_0) is given by:

(x-x_0)^2+(y-y_0)^2=R^2

Therefore, in our case, by looking at the standard equation they give us, we extract the following info:

1)  R^2 = 9\,\,\,then\,\,\,R=3  since the radius must be a positive number and (R=-3) is not a viable answer.

2) x_0=-6    for ( x-x_0) to equal   (x+6)

3) y_0=-5    for ( y-y_0) to equal   (y+5)

Therefore, we are in the presence of a circle centered at the point (-6,-5), and of radius "3". That is what we draw as seen in the attached image.

5 0
3 years ago
Two number differ by 3 The sum of their reciporcal is 7/10 find tge numbers
motikmotik
The numbers are 5 and 2.

Reciprocals: 5- 5/10
                     2- 2/10
(2/10)+(5/10)= 7/10
5-2= 3
 
Answer: 5 and 2
6 0
2 years ago
Read 2 more answers
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