Answer: plan A lasts for 0.5 hour. Plan B lasts for 0.75 hour.
Step-by-step explanation:
Let x represent the duration of plan A.
Let y represent the duration of plan B.
On Friday there were 3 clients who did plan A and 2 who did Plan B.
Joe trained his Friday clients for a total of 3. It means that
3x + 2y = 3- - - - - - - - - -1
On Saturday there were 5 clients who did plan A and 6 who did plan B. Joe trained his Saturday clients for a total of 7 hours. It means that
5x + 6y = 7- - - - - - - - - 2
Multiplying equation 1 by 5 and equation 2 by 3, it becomes
15x + 10y = 15
15x + 18y = 21
Subtracting, it becomes
- 8y = - 6
y = - 6/-8
y = 0.75
Substituting y = 0.75 into equation 1, it becomes
3x + 2 × 0.75 = 3
3x + 1.5 = 3
3x = 3 - 1.5 = 1.5
x = 1.5/3
x = 0.5
Divide given eq. by -2, we get, x^2-4x+0.5=0. Here a=1, b=-4 and c=0.5. As disccriminant is given by sqrt(b^2-4*a*c).so sqrt((-4)^2-4*1*0.5)=3.7417.
Real roots are x1,2=-b+-discriminant
x1=-4+3.7417=-0.2583 and x2=-4-3.7417=-7.7417
Answer: first box: 1/8
second box: 4
Step-by-step explanation:
Answer:
10.6666666667 as a fraction equals 106666666667/10000000000
Answer: Angle x equals 19 degrees
Step-by-step explanation: We have two polygons, one with five sides and the other with eight sides. The question states that the pentagon has exactly one line of symmetry which means the line that runs down from point D to line AB divides the shape into exactly two equal sides. Hence angle A measures the same size as angle B (in the pentagon).
First step is to calculate the angles in the pentagon. The sum of angles in a polygon is given as
(n - 2) x 180 {where n is the number of sides}
= 3 x 180
= 540
This means the total angles in the pentagon can be expressed as
A + B + 84 + 112 + 112 = 540
A + B + 308 = 540
Subtract 308 from both sides of the equation
A + B = 232
Since we have earlier determined that angle A measures the same size as angle B, we simply divide 232 into two equal sides, so 232/2 = 116
Having determined angle A as 116 degrees, we can now compute the value of angle A in the octagon ABFGHIJK. Since the figure is a regular octagon, that means all the angles are of equal measurement. So, the sum of interior angles is given as
(n - 2) x 180 {where n is the number of sides}
= 6 x 180
= 1080
If the total sum of the interior angles equals 1080, then each angle becomes
1080/8
= 135 degrees.
That means angle A in the octagon measures 135, while in the pentagon it measures 116. The size of angle x is simply the difference between both values which is
x = 135 - 116
x = 19 degrees
