Answer:
x = 12
Step-by-step explanation:
- (10x - 20)° and (6x + 8)° are on the straight angle and they are both equal 180°
to find the value of x:
10x - 20 + 6x + 8 = 180
10x + 6x = 180 + 20 - 8
16x = 192
x = 192/16
x = 12
Answer:
16.5mm to. 1 decimal place
Step-by-step explanation:
Please check attachment for diagrammatic representation of the triangle.
Since one of the angles of the triangle is 90, this means that we are dealing with a right angled triangle
To find the length of AC, we make use of pythagoras’ theorem which states that the square of the hypotenuse equals the sum of the square of the other two sides. The hypotenuse is the longest side of the triangle which we have as 17.88 mm
Mathematically therefore
17.8^2 = 6.6^2 + AC^2
AC^2 = 17.8^2 - 6.6^2
AC^2 = 283.28
AC = √(273.28)
AC = 16.53 mm
This is 16.5 to 1 decimal place
Answer:
e) z (max) = 24
x₁ = x₂ = 0 x₃ = 4
Step-by-step explanation:
a) The problem requires maximizing the total value from sandwich fruits and drink, therefore the objective function is associated to the sum of the values of each value.
We have three variables xi ( x₁, x₂, x₃ ) the values of sandwich, fruits and drink, and we have to maximize such quantities subject to the constraint of size (the capacity of the basket)
b) z = 6*x₁ + 4*x₂ + 6*x₃ Objective Function
Constraint :
basket capacity 17
9*x₁ + 3*x₂ + 4*x₃ ≤ 17
General constraints:
x₁ ≥ 0 x₂ ≥ 0 x₃ ≥ 0 all integers
e) z (max) = 24
x₁ = x₂ = 0 x₃ = 4
NOTE: Without the information about fractional or decimal feasible solution we decided to use integers solution
5x+7y=25
5x-2y=-65
subtract both of the equations
5x-5x=0
7y--2y= 7y+2y=9y
25--65=25+65=90
0+9y=90
9y=90
divide both sides by 9 to get y by itself
9y/9=90/9
cross out 9 and 9 which becomes 1*1*y=y
90/9=10
y=10
find x by using the substitution method
5x+7y=25
5x+7(10)=25
5x+70=25
move +70 to the other side
sign changes from +70 to -70
5x+70-70=25-70
5x=-45
divide both sides by 5 to get x by itself
5x/5=-45/5
cross out 5 and 5 then becomes 1*1*x=x
-45/5=-9
x=-9
answer:
(-9,10)
Answer:56
Step-by-step explanation:add all the sides together
