Lets x to be number of students.
1) If each students get 3 ml, then all students get 3x ml.
There was n ml.
(n-3x) ml leftover
n - 3x = 5
2) If each students get 4 ml.
then all students get 4x ml.
n+21 = 4x
3)
n - 3x = 5
- (n+21 = 4x) -------> -n -21=-4x
n - 3x = 5
<span>-n -21= - 4x
</span>-3x-21=5 - 4x
x=5+21
x=26
Answer : 26 students
Check:
x=26, n-3x = 5, n-3*26=5, n=83
n+21 = 4x
83+21=4*26
104 = 104 true
Answer:
(x,y)→(y,-x)
Step-by-step explanation:
Parallelogram ABCD:
A(2,5)
B(5,4)
C(5,2)
D(2,3)
Parallelogram A'B'C'D':
A'(5,-4)
B'(4,-5)
C'(2,-5)
D'(3,-2)
Rule:
A(2,5)→A'(5,-2)
B(5,4)→B'(4,-5)
C(5,2)→C'(2,-5)
D(2,3)→D'(3,-2)
so the rule is
(x,y)→(y,-x)
Answer: the area of the shaded region is 72.96 ft²
Step-by-step explanation:
The formula for determining the area of a circle is expressed as
Area = πr²
Where
r represents the radius of the circle.
π is a constant whose value is 3.14
From the information given,
Diameter of circle = 16 feet
Radius = diameter/2 = 16/2 = 8 feet
Area of circle = 3.14 × 8² = 200.96ft²
The sides of the square are equal. To determine the length of each side of the square, L, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
Therefore,
16² = L² + L²
256 = 2L²
L² = 256/2 = 128
L = √128 ft
Area of the square is
L² = (√128)²
Area = 128 ft²
Area of shaded region is
200.96 - 128 = 72.96 ft²
Answer:
- translate down 3
- reflect across the horizontal line through A
Step-by-step explanation:
1. There are many transformations that will map a line to a parallel line. Translation either horizontally or vertically will do it. Reflection across a line halfway between them will do it, as will rotation 180° about any point on that midline.
In the first attachment, we have elected to translate the line down 3 units.
__
2. Again, there are many transformations that could be used. Easiest is one that has point A as an invariant point, such as rotation CW or CCW about A, or reflection horizontally or vertically across a line through A.
Any center of rotation on a horizontal or vertical line through A can also be used for a rotation that maps one line to the other.
In the second attachment, we have elected to reflect the line across a horizontal line through A.
Answer:
The simplified form of
is 
Step-by-step explanation:
Given : 
We have to write the simplified form of 
Consider the given expression 
We know 
and 
Thus,

Simplify, we have,

Thus, The simplified form of
is 