Answer:
First term a = 41
Step-by-step explanation:
Arithmetic Progression:
Common differences d = -2
![S_{n}=\frac{n}{2}(2a+[n-1]d)\\\\S_{20}=\frac{20}{2}(2a+19*[-2])\\\\](https://tex.z-dn.net/?f=S_%7Bn%7D%3D%5Cfrac%7Bn%7D%7B2%7D%282a%2B%5Bn-1%5Dd%29%5C%5C%5C%5CS_%7B20%7D%3D%5Cfrac%7B20%7D%7B2%7D%282a%2B19%2A%5B-2%5D%29%5C%5C%5C%5C)
= 10*(2a - 38)
= 10*2a - 10*38
=20a - 380
![S_{22}=\frac{22}{2}(2a+21*[-2])\\\\](https://tex.z-dn.net/?f=S_%7B22%7D%3D%5Cfrac%7B22%7D%7B2%7D%282a%2B21%2A%5B-2%5D%29%5C%5C%5C%5C)
= 11 (2a -42)
=11*2a - 11*42
= 22a - 462
22a - 462 = 20a - 380
22a = 20a - 380 + 462
22a = 20a + 82
22a - 20a = 82
2a = 82
a = 82/2
a = 41
First term a = 41
Answer:
d. 3/2r+2c ≤ 10
Step-by-step explanation:
The amount of flour Molly needs for r batches of oatmeal raisin cookies is ...
3/2r
The amount of flour Molly needs for c batches of chocolate chip cookies is ...
2c
The total amount of flour Molly can use for cookies cannot exceed the amount available, so ...
3/2r + 2c ≤ 10
_____
<em>Comment on the question</em>
The wording is a bit odd. It asks for the amount of flour available—after it tells you the amount available is 10 cups. (I might write that as <em>f ≤ 10</em>.) The answer choices clearly suggest that what is wanted is a representation of the possible mix of batches of cookies for which Molly could use the available flour. IMO, this is another instance of poor editing of math problem wording.
Answer:
C(n)=1.25n
Where n= number of cans
Step-by-step explanation:
C=cost
n=number of cans
Quantity Total cost
1 $1.25
2 $2.50
3 $3.75
4 $5.00
Total cost, c(n) =1.25n
Check
Total cost when n=4
Total cost c(4)=1.25×4
Total cost c(4)=5.00
Answer:
The area of the circle is 56.25π cm²
Step-by-step explanation:
- The formula of the circumference of a circle is C = 2πr, where r is the radius of the circle
- The formula of the area of a circle with radius r is A = πr²
<em>To find the area of the circle use the formula of the circumference to find its radius and then use the formula of the area to find its area</em>
∵ The circumference of a circle is 15π centimeters
∵ C = 2πr
- Equate 2πr by 15π
∴ 2πr = 15π
- Divide both sides by π
∴ 2 r = 15
- Divide both sides by 2
∴ r = 7.5 centimeters
Now let us use the rule of the area to find it
∵ A = πr²
∴ A = π(7.5)²
∴ A = 56.25π centimeters²
The area of the circle is 56.25π cm²
Answer:
it will be -.
Step-by-step explanation:
