There are 15 oranges
<em><u>Solution:</u></em>
Let "x" be the number of oranges
Let "y" be the number of pears
Let "c" be the number of children
<em><u>There are 3 times as many pears are oranges</u></em>
Number of pears = 3 times the number of oranges
y = 3x -------- eqn 1
<u><em>If a group of children receive 5 oranges each, there will be no left over</em></u>
So, "c" children receives 5 oranges each, there will be no left over
number of oranges = 5(number of children)
x = 5c ------- eqn 2
<em><u>If the same group of children receive 8 oranges each, there will be 21 pears left over</u></em>
number of pears = 8 oranges(number of children) + 21
y = 8c + 21
<em><u>Substitute eqn 1</u></em>
3x = 8c + 21 ---- eqn 3
<em><u>Substitute eqn 2</u></em>
3(5c) = 8c + 21
15c - 8c = 21
7c = 21
c = 3
<em><u>Substitute c = 3 in eqn 2</u></em>
x = 5(3)
x = 15
Thus there are 15 oranges
Answer:
either a or b but maybe b is the most likely answer.
Step-by-step explanation:
Answer: Area of Δ DUO = 12.0 square units.
Step-by-step explanation:
From the diagram, Δ DPA is a right angled triangle and right angled at P.
Therefore ∠D will be
Tan ∅° = PA/DP ie, opposite side all over the adjacent.
= 4.5/3.75
Tan∅° = 1.2
to calculate ∅°, we know find the inverse of Tan 1.2
∅ = Tan^-1 1 .2 from your log tables or calculator
∅° = 50.20°.
= 50°
Since line DR is ⊥ to line OP
∠ADR = 90° - 50°
= 40°.
From the diagram,
∠ADR = ∠UDR = 40°
Therefore,
∠ODU = 180 - ( 40 + 40 + 90 ) { Angle on a straight line }
= 180 - 170
= 10°
From Δ UDM , line MU is he height of the required Δ DUO whose area is to be determined.
Now find the height MU
Tan10.0° = MU/10, where MU is the opposite side and 10.0 is the adjacent from the diagram given.
MU = Tan10.0 x 10.0
= 0.1763 x 10.0
= 1.763
Therefore to calculate the area of Δ DUO
= 1/2 x base x height
= 1/2 x line OD x line MU
= 1/2 x 14.0 x 1.763
= 7 x 1.763
= 12.341
= 12.0 square units.
=
Answer:
x=-5/11, y=-9/11. (-5/11, -9/11).
Step-by-step explanation:
3x+2y=-3
y=4x+1
---------------
3x+2(4x+1)=-3
3x+8x+2=-3
11x=-3-2
11x=-5
x=-5/11
y=4(-5/11)+1
y=-20/11+11/11
y=-9/11
