Answer:
Step-by-step explanation:
x - first
x + 12 - second
x + (x + 12) = 44
2x=44-12
x=16
first number is 16
second number is 16+12=28
two numbers are 16 and 28
As long as they have the same number of sides, no. The outcome of the first roll does not affect the outcome of the second roll in any way for this situation.
Answer:
x=4
Step-by-step explanation:
The coordinates of a point is the location of the point in a plane.
<em>The coordinates of the centers of holes are: (48.5, 28) and (28, 48.5)</em>
Given
![\theta_1 = \theta_2 = \theta_3 = 30^o](https://tex.z-dn.net/?f=%5Ctheta_1%20%3D%20%5Ctheta_2%20%3D%20%5Ctheta_3%20%3D%2030%5Eo)
![R = 60](https://tex.z-dn.net/?f=R%20%3D%2060)
![r = 56](https://tex.z-dn.net/?f=r%20%3D%2056)
I've added an attachment as an illustration
<u />
<u>Considering </u>
<u />
To solve for x1, we make use of cosine ratio.
So, we have:
![\cos(\theta_1) =\frac{x}{r}](https://tex.z-dn.net/?f=%5Ccos%28%5Ctheta_1%29%20%3D%5Cfrac%7Bx%7D%7Br%7D)
Make x the subject
![x_1 = r \times \cos(\theta_1)](https://tex.z-dn.net/?f=x_1%20%3D%20r%20%5Ctimes%20%5Ccos%28%5Ctheta_1%29)
![x_1 = 56 \times \cos(30^o)](https://tex.z-dn.net/?f=x_1%20%3D%2056%20%5Ctimes%20%5Ccos%2830%5Eo%29)
![x_1 = 48.5](https://tex.z-dn.net/?f=x_1%20%3D%2048.5)
To solve for y1, we make use of sine ratio.
So, we have:
![\sin(\theta_1) =\frac{y_1}{r}](https://tex.z-dn.net/?f=%5Csin%28%5Ctheta_1%29%20%3D%5Cfrac%7By_1%7D%7Br%7D)
Make y the subject
![y_1 = r \times \sin(\theta_1)](https://tex.z-dn.net/?f=y_1%20%3D%20r%20%5Ctimes%20%5Csin%28%5Ctheta_1%29)
![y_1 = 56 \times \sin(30^o)](https://tex.z-dn.net/?f=y_1%20%3D%2056%20%5Ctimes%20%5Csin%2830%5Eo%29)
![y_1 = 28](https://tex.z-dn.net/?f=y_1%20%3D%2028)
So, we have:
![(x_1,y_1) = (48.5,28)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%2848.5%2C28%29)
<u>Considering </u>
<u />
To solve for x2, we make use of cosine ratio.
So, we have:
![\cos(\theta_1+\theta_2) =\frac{x_2}{r}](https://tex.z-dn.net/?f=%5Ccos%28%5Ctheta_1%2B%5Ctheta_2%29%20%3D%5Cfrac%7Bx_2%7D%7Br%7D)
Make x the subject
![x_2 = r \times \cos(\theta_1+\theta_2)](https://tex.z-dn.net/?f=x_2%20%3D%20r%20%5Ctimes%20%5Ccos%28%5Ctheta_1%2B%5Ctheta_2%29)
![x_2 = 56 \times \cos(30+30)](https://tex.z-dn.net/?f=x_2%20%3D%2056%20%5Ctimes%20%5Ccos%2830%2B30%29)
![x_2 = 56 \times \cos(60^o)](https://tex.z-dn.net/?f=x_2%20%3D%2056%20%5Ctimes%20%5Ccos%2860%5Eo%29)
![x_2 = 28](https://tex.z-dn.net/?f=x_2%20%3D%2028)
To solve for y1, we make use of sine ratio.
So, we have:
![\sin(\theta_1+\theta_2) =\frac{y_2}{r}](https://tex.z-dn.net/?f=%5Csin%28%5Ctheta_1%2B%5Ctheta_2%29%20%3D%5Cfrac%7By_2%7D%7Br%7D)
Make y the subject
![y_2 = r \times \sin(\theta_1+\theta_2)](https://tex.z-dn.net/?f=y_2%20%3D%20r%20%5Ctimes%20%5Csin%28%5Ctheta_1%2B%5Ctheta_2%29)
![y_2 = 56 \times \sin(30+30)](https://tex.z-dn.net/?f=y_2%20%3D%2056%20%5Ctimes%20%5Csin%2830%2B30%29)
![y_2 = 56 \times \sin(60)](https://tex.z-dn.net/?f=y_2%20%3D%2056%20%5Ctimes%20%5Csin%2860%29)
![y_2 = 48.5](https://tex.z-dn.net/?f=y_2%20%3D%2048.5)
So, we have:
![(x_2,y_2) = (28,48.5)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%2828%2C48.5%29)
<em>Hence, the coordinates of the centers of the holes are: (48.5, 28) and (28, 48.5)</em>
Read more about coordinate geometry at:
brainly.com/question/8121530
Answer:
![y = - \frac{1}{4}x + 2](https://tex.z-dn.net/?f=y%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B4%7Dx%20%2B%202)
Step-by-step explanation:
The given line has equation
![y = \frac{1}{2}x - 5](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B1%7D%7B2%7Dx%20-%205)
The steepness is the absolute value of the slope.
The larger the absolute value of the slope, the greater the steepness.
The steepness of
![y = \frac{1}{2}x - 5](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B1%7D%7B2%7Dx%20-%205)
is
![| \frac{1}{2} | = \frac{1}{2} = 0.5](https://tex.z-dn.net/?f=%20%7C%20%5Cfrac%7B1%7D%7B2%7D%20%7C%20%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%20%3D%200.5)
The steepness of
![y = - \frac{1}{4}x + 2](https://tex.z-dn.net/?f=y%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B4%7Dx%20%2B%202)
is
![| - \frac{1}{4} | = \frac{1}{4} =0 .25](https://tex.z-dn.net/?f=%20%7C%20%20-%20%5Cfrac%7B1%7D%7B4%7D%20%7C%20%20%3D%20%20%20%5Cfrac%7B1%7D%7B4%7D%20%20%3D0%20.25)
Therefore the second line is less steep than the first line.