Answer:
The sum of all positive integers less than 100, which are not divisible by 3 is 3267.
Step-by-step explanation:
The all positive integers less than 100 has sum, given by
S₁ = 1 + 2 + 3 + 4 + ......... + 99
⇒ S₁ = 
Now, the sum of all positive integers less than 100 which are divisible by 3 is
S₂ = 3 + 6 + 9 + 12 + 15 + ........ + 99
⇒ S₂ = 3(1 + 2 + 3 + ........ + 33)
⇒ S₂ = 
Therefore, the sum of all positive integers less than 100, which are not divisible by 3 is = S₁ - S₂ = 4950 - 1683 = 3267. (Answer)
Note : The sum of n natural numbers S is given by
S = 1 + 2 + 3 + 4 + ....... + n = 
.
Answer: 35
Step-by-step explanation:
We substitute a for 1 and b for 6.
5(1+6)=5(7)=35
Since <span>x </span>does not contain the variable to solve for, move it to the right side of the equation by subtracting <span>x</span> from both sides
.−2y=−x+4
divide each term by −2 and simplify.
<span> the answer is y=<span>x/2</span>−<span>2
slope= 1/2
y-intercept = -2</span></span>
Answer:
<h2>D. division property of equality</h2>
Step-by-step explanation:
Answer:
Eudora spent 0.5 hours in running and 1.5 hours flying using her jet-pack.
Step-by-step explanation:
Let x represent time spent in running.
We have been given that the entire trip took 2 hours, so time spent in flying the jet-packs would be 
.
We know that distance is equal to speed times time.
Eudora ran from her home to a secret laboratory at an average speed of 12 km, so distance traveled by running would be 
.
Eudora took one of her jet-packs and flew to her school at an average speed of 76 km, so distance covered by jet-packs would be 
.
We are told that Eudora traveled a total distance of 120 km. We can represent this information in an equation as:
Combine like terms:
Divide both sides by 
:
Therefore, Eudora spent 0.5 hours in running.
Upon substituting in expression for time spent in flying jet-packs, we will get:
Therefore, Eudora spent 1.5 hours flying using her jet-pack.
