A ratio is used to describe how two or more quantities are related.
For example, we might say that a fruit drink calls for sugar crystals to be mixed with water in a ratio of 2:6. This means that for every 2 scoops sugar crystals, there will need to be 6 ounces of water. If there were 200 scoops of sugar crystals, there would need to be 600 ounces of water.
Answer:
Yes, she got a better deal.
Step-by-step explanation:
.85 x 99 = 84.15
$89 is greater than $84.15.
Using linear functions, it is found that the two plans cost the same for 5000 minutes of calling.
<h3>What is a linear function?</h3>
A linear function is modeled by:
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0.
For Plan A, the cost is of $25 plus an additional $0.09 for each minute of calls, hence the y-intercept is
, the slope is of
, and the function is:
![A(x) = 0.09x + 25](https://tex.z-dn.net/?f=A%28x%29%20%3D%200.09x%20%2B%2025)
For Plan B, the cost is of $0.14 for each minute of calls, hence the y-intercept is
, the slope is of
, and the function is:
![B(x) = 0.14x](https://tex.z-dn.net/?f=B%28x%29%20%3D%200.14x)
The plans cost the same for x minutes of calling, considering that:
![B(x) = A(x)](https://tex.z-dn.net/?f=B%28x%29%20%3D%20A%28x%29)
![0.14x = 0.09x + 25](https://tex.z-dn.net/?f=0.14x%20%3D%200.09x%20%2B%2025)
![0.05x = 250](https://tex.z-dn.net/?f=0.05x%20%3D%20250)
![x = \frac{250}{0.05}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B250%7D%7B0.05%7D)
![x = 5000](https://tex.z-dn.net/?f=x%20%3D%205000)
The two plans cost the same for 5000 minutes of calling.
To learn more about linear functions, you can take a look at brainly.com/question/24808124
Answer:
C, E, and F
Explanation:
There are two ways to answer this question. First, you could simply input each answer into both equations to see which one works but that would take quite a long time.
A better way is to simply solve each equation for x.
You could rewrite
2x + 7 < -3
as
2x + 7 = -3
and solve:
Subtract 7 from both sides
![(2x + 7) -7 = (-3) - 7\\2x = -10](https://tex.z-dn.net/?f=%282x%20%2B%207%29%20-7%20%3D%20%28-3%29%20-%207%5C%5C2x%20%3D%20-10)
Now divide both sides by 2
![\frac{2x}{2} = \frac{-10}{2}\\x = -5](https://tex.z-dn.net/?f=%5Cfrac%7B2x%7D%7B2%7D%20%20%3D%20%5Cfrac%7B-10%7D%7B2%7D%5C%5Cx%20%3D%20-5)
Now we can simply replace the equals sign with the inequality
x < -5
Where you can run into trouble is if you have to multiply or divide by a negative number across the equation, you must flip the inequality sign. It's best to leave it there to remind you, but I switched it out just to show that it's no different than a typical algebraic equation.
Now, we know that x can be any value less than -5. Let's find out the same thing for the second equation:
![x - 8 + 3x < -4\\(x + 3x) -8 < -4\\4x - 8 < -4\\(4x - 8) + 8 < (-4) + 8\\4x < 4\\\frac{4x}{4} < \frac{4}{4}\\x < 1](https://tex.z-dn.net/?f=x%20-%208%20%2B%203x%20%3C%20-4%5C%5C%28x%20%2B%203x%29%20-8%20%3C%20-4%5C%5C4x%20-%208%20%3C%20-4%5C%5C%284x%20-%208%29%20%2B%208%20%3C%20%28-4%29%20%2B%208%5C%5C4x%20%3C%204%5C%5C%5Cfrac%7B4x%7D%7B4%7D%20%3C%20%5Cfrac%7B4%7D%7B4%7D%5C%5Cx%20%3C%201)
Now we know that x must be less than 1 for the second equation. So, now we can choose the answers that are both less than -5 and less than 1.
These answers are:
C. -10
E. -8.24
and
F. -15/2 which is -7.5
NOTE: -5 is equal to but not less than -5 so G is not included.