Answer:
I'm going to use the Pythagoras theorem
1. hypotenus²= base²+height²
h²=80²+18²
h²=6400+324
√h²=√6724
hypotenuse= 82
2. 53²=45²+h²
2809=2025+h²
2809-2025=h²
784=h²
√784=√h²
h=28
3. 40²=b²+24²
1600=b²+576
1600-576=b²
√1024=√b²
b= 32
Answer:
No, Elias doesn't have enough quantity of each ingredient to make 45 mince pies.
Step-by-step explanation:
For making 18 Mince Pies Elias needs
200g Butter
225g flour
150g sugar
250g Mincemeat
1 egg
Inorder to make 45 mince pie's he's gonna need 45/18=2.5 times the ingredients he needs to make 18 Mince Pies.
As he doesn't have enough Mincemeat (has only 600g but needs 250*2.5=625g of mincemeat)
As he is short of 25g of Mincemeat, he is unable to make 45 Mincepies.
factors of
are
and
.
<u>Step-by-step explanation:</u>
Here we have , to identify all factors of this expression . let's find out :
Expression : ![f(x) = 18x^2-9x-5](https://tex.z-dn.net/?f=f%28x%29%20%3D%2018x%5E2-9x-5)
⇒ ![f(x) = 18x^2-9x-5](https://tex.z-dn.net/?f=f%28x%29%20%3D%2018x%5E2-9x-5)
Now , -9x can be written as :
⇒ ![-9x=-15x+6x](https://tex.z-dn.net/?f=-9x%3D-15x%2B6x)
Putting this value
⇒ ![f(x) = 18x^2-15x+6x-5](https://tex.z-dn.net/?f=f%28x%29%20%3D%2018x%5E2-15x%2B6x-5)
Taking out common terms we get
⇒ ![f(x) = 3x(6x-5)+6x-5](https://tex.z-dn.net/?f=f%28x%29%20%3D%203x%286x-5%29%2B6x-5)
⇒ ![f(x) = 3x(6x-5)+1(6x-5)](https://tex.z-dn.net/?f=f%28x%29%20%3D%203x%286x-5%29%2B1%286x-5%29)
⇒ ![f(x) = (3x+1)(6x-5)](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%283x%2B1%29%286x-5%29)
Therefore , factors of
are
and
.
.5 despite that .485 is longer .5 is larger