12) 8 liters in total. each glass holds 1/5 of a liter. 8 x 5 = 40 glasses.
13) 3bars/4people = 3/4 of a bar.
14) same concept as 13. .5quart/3people = (1/6) of a quart of milk.
15) 3 yards in total. divides it into pieces that are 1/4 yard long. so each 1 yard makes 4 pieces. that means 3 yards makes 12 pieces in total.
Answer: y = 1.73*x - 0.46
Step-by-step explanation:
For a linear equation of the form:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we have an angle of A degrees with respect to the x-axis, the slope of the function can be calculated as:
Tan(A) = a.
in this case, we have we have an inclination of 30° to the positive x-axis (measured from the positive y-axis) and we know that the angle between the positive x-axis and the positive y-axis is 90°, then the angle measured from the positive axis will be such that:
A + 30° = 90
A = 90° - 30° = 60°
Then the slope is:
a = Tan(60°) = 1.73
Then we have the equation:
y = 1.73*x + b
And we know that this line passes through the point (2, 3) then we can replace x by 2 and y by 3 in the equation, and find the value of b.
3 = 1.73*2 + b
3 - 1.73*2 = b = -0.46
Then the equation is:
y = 1.73*x - 0.46
Answer:
6
Step-by-step explanation:
Because they are the same
The similarity ratio of ΔABC to ΔDEF = 2 : 1.
Solution:
The image attached below.
Given ΔABC to ΔDEF are similar.
To find the ratio of similarity triangle ABC and triangle DEF.
In ΔABC: AC = 4 and CB = 5
In ΔDEF: DF = 2, EF = ?
Let us first find the length of EF.
We know that, If two triangles are similar, then the corresponding sides are proportional.
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
Ratio of ΔABC to ΔDEF = 
Similarly, ratio of ΔABC to ΔDEF = 
Hence, the similarity ratio of ΔABC to ΔDEF = 2 : 1.