For lines to be parallel, the slopes have to be the SAME.
To find the value of k, you can first find the slope of line 1 using the slope(m) formula, and plug in the points:
Now that you know the slope, you can use the slope formula to find k by plugging in what you know:
Multiply (5 - k) on both sides
Multiply -2 on both sides
5 - k = -2(7 + 1)
5 - k = -2(8)
5 - k = -16 Subtract 5 on both sides
-k = -21 Divide -1 on both sides
k = 21
Answer:-2/3
Step-by-step explanation:the problem is asking for the slope of (0,2) and(3,0). The formula for this problem is y2-y1 over x2-x1. And if your writing this formula down write it like a fraction with y on top and x on bottom. (x,y) (x2,y2). You take the 0 from the second set and the 2 from the first set and subtract them to get -2. Then you take the 3 from the sea d set and the 0 from the first set and you subtract them to get 3. That’s how you get the answer of -2/3.
Answer:
7.) 7
10.) 0
Step-by-step explanation:
When it means "evaluate the function", it's in essence asking us to see what the function spits out when we feed it a certain input. Our inputs are our x values, which spit out a y value.
Evaluating the function when x = 1:
Let's look at where the function has an x value of 1. We see it near the bottom of the table and see the y value associated with the input is 7. So when the function is fed 1 as an input, it spits out 7.
Evaluating the function when f(x) = - 2:
This one is a weird because of the new notation. Just think of it as some value of f, which we don't know (so we represent it as an x-variable) must equal -2. So let's look at our table to find out where our output is -2. We find that when f(x) = -2 the input is 0. So the input which gives -2 is 0.
Answer:
a) 6 gigabytes
b) $100
Step-by-step explanation:
Let c represent the total cost in dollars and d represent the amount of data used in gigabytes.
For the first smartphone
One smartphone plan costs $52 per month for talk and messaging and $8 per gigabyte of data used each month.
Equation =
c = 52 + 8d
For the Second smartphone
A second smartphone plan costs $82 per month for talk and messaging and $3 per gigabyte of data used each month.
Equation =>
c = 82 + 3d
How many gigabytes would have to be used for the plans to cost the same?
We would equate both cost to each other
52 + 8d = 82 + 3d
Collect like terms
8d - 3d = 82 - 52
5d = 30
d = 30/5
d = 6
Therefore,
a) The number of gigabytes for the cost of both Smartphone data plans to be the same = 6 gigabytes.
b) The cost of both plans if 6 gigabytes is used =>
c = 52 + 8d
c = 52 + 8 × 6
c = $100
First method: by the rule of three:
126 miles---------------------3 hours
x---------------------------------7 hours
x=(126 miles * 7 hours) / 3 hours=294 miles.
Answer: 294 miles.
Second method:
Speed=distance/ time ⇒distance=speed x time
We calculate the speed of the car:
Speed=126 miles/3 hours= 42 miles/hour.
Data:
Speed=42 miles/hour
time=7 hours
Distance=speed x time
Distance=(42 miles/hour)(7 hours)=294 miles
answer: 294 miles.
