Answer:
1. Proved down
2. proved down
3. f(10) = -20 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5
Step-by-step explanation:
Let us explain how to solve the question
∵ f(0) = -20, f(n) = f(n - 1) - 5 for n > 1
→ That means we have an arithmetic sequence with constant
difference -5 and first term -20
1. → f(1) means we need to find the second term, which equal the
term - 5
∵ f(1) means n = 1
∴ f(1) = f(1 - 1) - 5
∴ f(1) = f(0) - 5
∵ f(0) = -20
∴ f(1) = -20 - 5 → Proved
2. → f(3) means we need to find the third term, which equal the
second term - 5
∵ f(3) means n = 3
∴ f(3) = f(3 - 1) - 5
∴ f(3) = f(2) - 5
→ f(2) = f(1) - 5
∵ f(1) = -20 - 5
∴ f(2) = [-20 - 5] - 5 = -20 - 5 - 5
∴ f(3) = [-20 - 5 - 5] - 5
∴ f(3) = -20 - 5 - 5 - 5 → Proved
3. → From 1 and 2 we notice that the number of -5 is equal to n,
at n = 1 there is one (-5), when n= 3 there are three (-5)
∵ n = 10
∴ There are ten (-5)
∴ f(10) = -20 - 5(10)
∴ f(10) = -20 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5 → Proved
Question (1):
Assume that the first number is n. Since the two number are consecutive even numbers, this means that the second number is n + 2
We know that the sum of the two numbers is 70. This means that:
n + n + 2 = 70
2n + 2 = 70
2n = 68
n = 68/2
n = 34
This means that the two numbers are: 34 and 34+2 = 36 .......> last option
Question (2):
Assume dog's age is x. We know that cat's age is 5 less than twice dog's age. This means that:
cat's age = 2x - 5
We know that cat's age is 11, therefore:
11 = 2x - 5
11 + 5 = 2x
16 = 2x
x = 16/2 = 8
Dog's age is 8 .......> first option
Question (3):
The three numbers are consecutive. This means that we can assume the numbers to be n, n+1 and n+2. We know that their sum is 46. Therefore:
n + n + 1 + n + 2 = 46
3n + 3 = 46
3n = 43
n = 43/3
The three numbers are 43/3 , 46/3 and 49/3 .......> none of the given options in correct
Question (4):
The three consecutive numbers are all even. This means that we can assume the numbers to be n , n+2 and n+4
We know that their sum is 198. This means that:
n+n+2+n+4 = 198 .........> second option
Question (5):
The four consecutive numbers can be assumed as n, n+1 , n+2 and n+3. We know that their sum is 86. Therefore:
n + n+1 + n+2 + n+3 = 86 .......> third option
Question (6):
Assume the width is w. We know that the length is 15 cm greater than the width. This means that:
length = w + 15
Now, we have:
perimeter = 2(length + width)
150 = 2 (15 + w + w)
75 = 15 + 2w
60 = 2w
w = 60/2
w = 30 cm
This means that:
length = 15 _ 30 = 45 cm
Based on the above, the dimensions of the rectangle are:
length = 45 cm and width = 30 cm .......> first option
Question (7):
Assume original price before taxes is x
Total price = original price + taxes
825 = x + 0.1x = 1.1 x
x = 825/1.1
x = $750 .........> second option
Question (8):
Assume cost of helmet is x and that cost of bicycle is 5x. We know that the total is 240. This means that:
240 = x + 5x = 6x
x = 240/6
x = 40
This means that:
price of helmet = $40
price of bicycle = 5(40) = $200
..........> first option
Hope this helps :)
It would be A as your answer
Answer:
The slope is 
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to
we have the points
(-2, 7) and (4, 9)
substitute the values in the formula
Simplify
Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtract Property of Equality
Step-by-step explanation:
<u>Step 1: Define</u>
<u />
<u />
<u />
<u>Step 2: Solve for </u><em><u>v</u></em>
- Divide both sides by
:
Here we see that any value <em>v</em> greater than 
would work as a solution to the inequality.
