Answer: $450
Step-by-step explanation:
We can form an equation representing the problem. The question is essentially asking 60% of what is equal to $270. If we define that what as a variable 'x', we get the following:
![\frac{60}{100} *x=270](https://tex.z-dn.net/?f=%5Cfrac%7B60%7D%7B100%7D%20%2Ax%3D270)
![\frac{60x}{100} =270](https://tex.z-dn.net/?f=%5Cfrac%7B60x%7D%7B100%7D%20%3D270)
Multiply both sides by 100:
![\frac{60x}{100} *100=270*100](https://tex.z-dn.net/?f=%5Cfrac%7B60x%7D%7B100%7D%20%2A100%3D270%2A100)
![60x=27,000](https://tex.z-dn.net/?f=60x%3D27%2C000)
Divide both sides by 60 to solve for the value of 'x':
![x=\frac{27,000}{60} =450](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B27%2C000%7D%7B60%7D%20%3D450)
Answer is 450 bucks
We can check this answer by taking 60% of $450. In principal, this should return the discount of $270.
![\frac{60}{100} *450=270](https://tex.z-dn.net/?f=%5Cfrac%7B60%7D%7B100%7D%20%2A450%3D270)
Yup, it checks out
Given:
In an arithmetic sequence,
![a_1=2](https://tex.z-dn.net/?f=a_1%3D2)
![a_i=a_{i-1}-3](https://tex.z-dn.net/?f=a_i%3Da_%7Bi-1%7D-3)
To find:
The sum of the first 335 terms in the given sequence.
Solution:
The recursive formula of an arithmetic sequence is:
...(i)
Where, d is the common difference.
We have,
...(ii)
On comparing (i) and (ii), we get
![d=-3](https://tex.z-dn.net/?f=d%3D-3)
The sum of first i terms of an arithmetic sequence is:
![S_i=\dfrac{i}{2}[2a+(i-1)d]](https://tex.z-dn.net/?f=S_i%3D%5Cdfrac%7Bi%7D%7B2%7D%5B2a%2B%28i-1%29d%5D)
Putting
, we get
![S_{335}=\dfrac{335}{2}[2(2)+(335-1)(-3)]](https://tex.z-dn.net/?f=S_%7B335%7D%3D%5Cdfrac%7B335%7D%7B2%7D%5B2%282%29%2B%28335-1%29%28-3%29%5D)
![S_{335}=\dfrac{335}{2}[4+(334)(-3)]](https://tex.z-dn.net/?f=S_%7B335%7D%3D%5Cdfrac%7B335%7D%7B2%7D%5B4%2B%28334%29%28-3%29%5D)
![S_{335}=\dfrac{335}{2}[4-1002]](https://tex.z-dn.net/?f=S_%7B335%7D%3D%5Cdfrac%7B335%7D%7B2%7D%5B4-1002%5D)
![S_{335}=\dfrac{335}{2}(-998)](https://tex.z-dn.net/?f=S_%7B335%7D%3D%5Cdfrac%7B335%7D%7B2%7D%28-998%29)
On further simplification, we get
![S_{335}=335\times (-499)](https://tex.z-dn.net/?f=S_%7B335%7D%3D335%5Ctimes%20%28-499%29)
![S_{335}=-167165](https://tex.z-dn.net/?f=S_%7B335%7D%3D-167165)
Therefore, the sum of the first 335 terms in the given sequence is -167165.
Answer:
f(x)=(x-9/2)²-25/4
Step-by-step explanation:
f(x)=x²-9x+14
f(x)=x²-9x+(-9/2)²-(-9/2)²+14
f(x)=(x-9/2)²-81/4+14
f(x)=(x-9/2)²+(-81+56)/4
f(x)=(x-9/2)²-25/4
Answer: She should charge $10.50 for each box
Step-by-step explanation:
Total cookies = 960
Each box has 16 cookies
Her goal is $630
First, you want to find out how many boxes she made
960÷ 16 = 60
She made 60 boxes
Now you want to find the price for each box
630 ÷ 60 = 10.5
She should charge $10.50 for each box
I hope this helps!!!
Answer:
not sure but i think its 425 cm
Step-by-step explanation:
for the square i dont know
how its called in english the surface is 25×10= 250cm
and for the triangle its (25×14):2 = 175cm
so 175 + 250= 425cm