Answer:
<u>44 cows and 36 ducks.</u>
Step-by-step explanation:
x is ducks and y is cows.
Assuming both have 1 head each, we can write:
x + y = 80.
Let's assume each x(cow) has 4 legs and each y(duck) has two legs.
Then we can add the numbers of legs:
2x + 4y = 248 legs
Now rearrange x + y = 80 to:
x = 80-y
and substitute:
2x + 4y = 248 legs
2(80-y) + 4y = 248 legs
160 - 2y + 4y = 248 legs
2y = 88 legs
<u>y = 44 [There are 44 cows]</u>
Use this value to find the number of ducks:
x + y = 80
44 + y = 80
<u>y = 36 [There are 36 ducks]</u>
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Check:
Do 44 cows and 36 ducks have a total of 248 legs?
4*44 + 2*36 = 248 ?
176 + 72 = 248?
<u>YES</u>
Answer:
The measure of a = b = 116 degrees
Step-by-step explanation:
Here, we have value of angles to calculate.
If a and b are both supplementary to c, what this means is that when we add either a or b to c, we get 180
Hence; Mathematically;
a + c = 180 and b + c = 180
What we have here is that a and b must be equal since they are both supplementary to the same angle value
Now, we are told further in the question that the measure of angle a is 12 less than 2 times the measure of c;
Mathematically, this means that;
a = 2c - 12
So we now want to find the measure of b
Let’s substitute for a
2c -12 + c = 180
3c -12 = 180
3c = 180 + 12
3c =192
c = 192/3
c = 64
Thus; a = 2c - 12 = 2(64) -12 = 128 -12 = 116
Answer:
height = 2.5 ft , base = 8 ft
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = 
bh ( b is the base and h the height )
height = h then base = 2h + 3 and A = 10 , then
h(h + 3) = 10 ( multiply both sides by 2 to clear the fraction )
h(h + 3) = 20 , that is
h² + 3h = 20 ( subtract 20 from both sides )
h² + 3h - 20 = 0 ← in standard form
(h + 4)(2h - 5) = 0 ← in factored form
equate each factor to zero and solve for h
h + 4 = 0 ⇒ h = - 4
2h - 5 = 0 ⇒ 2h = 5 ⇒ h = 2.5
but h > 0 , then h = 2.5
and 2h + 3 = 2(2.5) + 3 = 5 + 3 = 8
that is height = 2.5 ft and base = 8 ft
Answer:
111
Step-by-step explanation:
if angle 8 and angle 4 are equal, then angle 8 and angle 5 are equal
so... angle 5= angle 4
5x10^-2 I believe is your answer
