Answer:
See Below
Step-by-step explanation
1) subtract 4 from both sides
You have the answer
Answer:

Step-by-step explanation:
To answer this problem, we must bear in mind that the express train travels 3 times faster than the freight train.
If we call F the distance that the freight train travels and we call E at the distance that the express train travels, we must have the distance between them after 15 minutes it must be 30 miles.
So

We also know that:
Since the express train travels 3 times faster than the freight train.
So, like both equations, we have to:

Then
miles in the opposite direction.
This is the distance you traveled in 15 minutes.
Therefore, the speed of the express train (
) is the distance traveled between the time it did

Answer:
a
Step-by-step explanation:
Answer:
y=kx
subst y=10 and x=20 into the above
<em>1</em><em>0</em><em>=</em><em>k20</em>
<em>k</em><em>=</em><em>1</em><em>0</em><em>/</em><em>2</em><em>0</em>
<em>k</em><em>=</em><em>1</em><em>/</em><em>2</em>
<em>therefore</em><em> </em><em>relationship</em><em>:</em><em> </em><em>y</em><em>=</em><em>1</em><em>/</em><em>2</em><em>x</em>
<em>subst</em><em> </em><em>x</em><em>=</em><em>1</em><em>5</em><em> </em><em>into</em><em> </em><em>the</em><em> </em><em>relationship</em>
<em> </em><em>y</em><em>=</em><em>1</em><em>/</em><em>2</em><em>(</em><em>1</em><em>5</em><em>)</em>
<em>y</em><em>=</em><em>7</em><em>,</em><em>5</em>
Step by step explanation:
- Step 1: when they say y varies directly with x they mean<em> y is proportional to x</em>
- step 2: so y=kx where <em>k is the constant</em>
- step 3: is to substitute <em>y=10</em> and <em>x=20</em> into the above equation y=kx
- step 4: you will end up with <em>10=k20</em> then divide both sides by 20 so that <em>k becomes the subject of the formula </em>
- step 5: your answer from the above will be <em>k=10/20 </em>so the relationship is <em>y is directly proportional to 1/2 x </em>what you did here is that you substituted k for 1/2 in the equation in step 3
- step 6: is to finally substitute x=15 into the equation <em>y=1/2x</em> to finally get your answer <em>y</em><em>=</em><em>7</em><em>,</em><em>5</em><em>.</em>
Answer:
a₂₁ = 638
Step-by-step explanation:
substitute n = 21 into the explicit formula
a₂₁ = - 2 + 32(21 - 1) = - 2 + 32(20) = - 2 + 640 = 638