The distance between the two points P (15,x)and Q(x,-5)is 20.
1 answer:
Answer:
x = - 5, x = 15
Step-by-step explanation:
Assuming you require to find the values of x
Calculate the distance PQ using the distance formula and equate to 20
d =
with (x₁, y₁ ) = P (15, x ) and (x₂, y₂ ) = Q (x, - 5 )
PQ = = 20 ( square both sides )
(- 5 - x)² + (x - 15)² = 20² ← expand factors on left side using FOIL
25 + 10x + x² + x² - 30x + 225 = 400
2x² - 20x + 250 = 400 ( subtract 400 from both sides )
2x² - 20x - 150 = 0 ( divide through by 2 )
x² - 10x - 75 = 0
consider the factors of the constant term (- 75) which sum to give the coefficient of the x- term (- 10)
the factors are - 15 and + 5 , since
- 15 × 5 = - 75 and - 15 + 5 = - 10 , then
(x - 15)(x + 5) = 0
equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5
x - 15 = 0 ⇒ x = 15
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Answer:
We have 4 solutions:
- No 10-foot truck, 10 14-foot trucks, and 15 24-foot trucks
- 2 10-foot trucks, 7 14-foot trucks, and 16 24-foot trucks
- 4 10-foot trucks, 4 14-foot trucks, and 17 24-foot trucks
- 6 10-foot trucks, 1 14-foot trucks, and 18 24-foot trucks
Step-by-step explanation:
Let the number of 10-foot truck with a capacity of 350 cubic feet purchased=a
Let the number of 14-foot truck with a capacity of 700 cubic feet purchased=b
Let the number of 24-foot truck with a capacity of 1,400 cubic feet purchased=c
The company wants to purchase 25 trucks, therefore.
- a+b+c=25
Furthermore, the combined capacity of the trucks is 28,000 cubic feet.
- 350a+700b+1400c=28000
Since the number of equations is less than the number of variables, you can not use a matrix equation to solve this problem. The solution is most easily found using an augmented matrix.
The augmented matrix is presented below:
Using the calculator, the reduced row echelon form is:
where
a- 2c=-30 means a =2c-30
b+3c=55 means b= 55-3c
We alter the value of c as long as neither a nor b becomes negative. Suitable values for c are 15, 16, 17, and 18:
We can easily verify that, for each solution, the number of trucks adds up to 25 and the fleet capacity is 28,000 cubic feet.
We therefore have 4 solutions:
- No 10-foot truck, 10 14-foot trucks, and 15 24-foot trucks
- 2 10-foot trucks, 7 14-foot trucks, and 16 24-foot trucks
- 4 10-foot trucks, 4 14-foot trucks, and 17 24-foot trucks
- 6 10-foot trucks, 1 14-foot trucks, and 18 24-foot trucks