Multiply corresponding components, then add the products:
Length AC is 12 .
<u>Step-by-step explanation:</u>
We have , △ABC is inscribed in a circle such that vertices A and B lie on a diameter of the circle. If the length of the diameter of the circle is 13 and the length of chord BC is 5 . According to the data given in question we can visualize that triangle must be a right angled triangle where:
AB = hypotenuse = 13
BC = base = 5
Ac = Perpendicular
Now, By Pythagoras Theorem:
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
∴ Length AC is 12 .
Answer:
2 tickets left
Step-by-step explanation:
12✖️29=348
350-348=2
Answer:
- 12x +15y = 4140; x + y = 300
- x = 120; y = 180
Step-by-step explanation:
The first equation is for receipts. Each x ticket generated $12 in receipts, so the first term needs to be 12x. Each y ticket generated $15 in receipts, so the second term needs to be 15y. U in this set of equations is the total number of tickets, said to be 300.
The equations are ...
12x +15y = 4140; x +y = 300
__
Using the second equation to write an expression for x, we have ...
x = 300 -y
Substituting this into the first equation gives ...
12(300 -y) +15y = 4140
3600 +3y = 4140
y = (4140 -3600)/3 = 180
x = 300 -180 = 120
The number of tickets sold is ...
$12 tickets -- 120
$15 tickets -- 180
_____
You might want to notice that the equation we ended up with:
4140 -12(300) = 3y
is equivalent to this "word solution." This can be done in your head; no equations required.
If all the tickets sold were $12 tickets, the revenue would be $3600. The revenue is $540 more than that. Each $15 ticket generates $3 more revenue than a $12 ticket, so to have $540 more revenue, we must have 540/3 = 180 $15 tickets.
Answer:
t = 204
Step-by-step explanation:
Let t = initial number of trees
"remove 5 trees at the start of the season" means
(t - 5) remain
"each remaining tree made 210 oranges for a total of 41,790 oranges" means
( t - 5) * 210 = 41790
Now, you can solve for t:
(t-5)(210) = 41790 [just re-writing]
210t - 1050 = 41790 [distribute]
210t = 42840 [add 1050 to each side]
t = 204 [divide each side by 210]
There were initially 204 trees. After 5 were removed, the remaining 199 produced 210 oranges each for a total of 199*210 = 41790 oranges.
