Answer:
85 messages
Step-by-step explanation:
The system of equations for this is
35 + .10x
18 + .3x
where x = the number of text messages
Usually, you would use substitution or elimination to solve this problem. However, because the answer choices were given, you can just plug in the values.
When you plug in 85, or x = 85, you get 43.5 for both equations because
35 + .10(85) = 43.5 18 + .3(85) = 43.5
Therefore, the answer would be 85 messages becuase both plans will cost the same when you send 85 text messages!
:)
Answer:
Graph A = 20miles/gallon
Graph B = 20
Step-by-step explanation:
For graph A, to find the change you will need to choose two points from the graph (the easier the better)
So for example, I've chosen 40miles-2gallons (2, 40) and point 0 (0, 0)
Now you will need to remember the slope formula which is:

so your point (x1, y1) will be (0, 0)
and point (x2, y2) will be (2, 40)
so 
which is 
and so you get that the slope will be 20 miles/gallon
For graph B, what they want you to see is that change of y/change of x means the same as change of miles/change of gallons since x is the gallons and y is the miles.
The equation of the hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0) is 
<h3>How to determine the equation of the hyperbola?</h3>
The given parameters are:
- Directrices at x = ±2
- Foci at (5, 0) and (−5, 0)
The foci of a hyperbola are represented as:
Foci = (k ± c, h)
The center is:
Center = (h,k)
And the directrix is:
Directrix, x = h ± a²/c
By comparison, we have:
k ± c = ±5
h = 0
h ± a²/c = ±2
Substitute h = 0 in h ± a²/c = ±2
0 ± a²/c = ±2
This gives
a²/c = 2
Multiply both sides by c
a² = 2c
k ± c = ±5 means that:
k ± c = 0 ± 5
By comparison, we have:
k = 0 and c = 5
Substitute c = 5 in a² = 2c
a² = 2 * 5
a² = 10
Next, we calculate b using:
b² = c² - a²
This gives
b² = 5² - 10
Evaluate
b² = 15
The hyperbola is represented as:

So, we have:

Evaluate

Hence, the equation of the hyperbola is 
Read more about hyperbola at:
brainly.com/question/3405939
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