Ending balance $599.43
outstanding deposit $235.14 +
total $834.57
outstanding check $117.54 -
total balance $717.03
hope this help
Given:
Quadrilateral PQRS
P(o, o), Q(a+c, o), R(2a+c, b), S(a, b)
Find:
whether the diagonals are perpendicular using coordinate geometry
Solution:
If the diagonals are perpendicular, their slopes multiply to give -1.
The slope of PR is
(b-o)/(2a+c-o)
The slope of QS is
(b-o)/(a-(a+c)) = (b-o)/(-c)
The product of these slopes is
(b-o)·(b-o)/((2a+c-o)(-c))
This value will not be -1 except for very specific values of a, b, c, and o.
It cannot be concluded that the diagonals of PQRS are perpendicular based on the given coordinates.
Answer:
c and d
Step-by-step explanation:
rise/run
for every 2 that c and d progress positive on the x-axis, it only rises 1 on the y-axis
The solution is 
and 
Step-by-step explanation:
The expression is 
and 
Using substitution method we can solve the expression.
Let us substitute 
in
Expanding and simplifying the expression, we get,
Let us use the quadratic equation formula to solve this equation,
Thus, 
and 
Substituting y-values in the equation , we get the value of x.
For ⇒ 
For ⇒ 
Thus, the solution set is and
Answer:
- <u>First choice, 984 cm²</u>
Explanation:
The plastic pencil case has form of a triangular prism.
This triangular prism has five faces:
- Top and bottom faces: two congruent triangles with a 10 cm base and 12 cm height.
- Lateral faces: two congruent rectangles with a 24 cm length and 13 cm widht, and one rectangle with 24 cm length and 10 cm widht.
<u>Surface area:</u>
- <u>Top and bottom triangles</u>:
area = (1/2) base × height
area of one triangle = 10 cm × 12 cm × (1/2) = 60 cm²
area of the two triangles = 2 × 60 cm² = 120 cm²
- <u>Lateral rectangles:</u>
area of a rectangle = length × width
area of the trhee triangles = 24 cm × 10 cm + 2 × 24 cm × 13 cm = 240 cm² + 624 cm² = 864 cm².
- <u>Total area: </u>120 cm² + 864 cm² = 984 cm²
Answer: first choice, 984 cm²
