<span>Total number of problems Nicole will have completed: y
</span><span>Number of nights she studies: x
</span><span>
She has already completed 20 practice problems:
When x=0, y=20
</span>She plans on completing 6 more problems each night:
y=20+6x
y=6x+20
Please, see the attached graph.
Thanks.
The solution of the equation is x = -4/3.
<h3>What does it mean to solve an equation?</h3>
An equation represents equality of two or more mathematical expression.
Solutions to an equation are those values of the variables involved in that equation for which the equation is true.
WE have been given an equation as;
|x - 4| = 5x + 12
In an absolute value equation, we solve the original expression as our first equation. Our second one is that we multiply the right side by -1.
Case 1: original equation
|x - 4| = 5x + 12
x - 4 = 5x + 12
x - 5x = 12 + 4
-4x = 16
x = -4
Case 2: Opposite equation
|x - 4| = 5x + 12
x - 4 = - (5x + 12)
x - 4 = - 5x - 12
x + 5x = -12 + 4
6x = -8
x = -4/3
Now we have two solutions. We need to check for extraneous solutions because of all the manipulations;
Check:
|x - 4| = 5x + 12
use x = -4
|-4 - 4| = 5(-4) + 12
| -8 | = -20 + 12
8 = -8
Thus, it is Not a solution
Now, |x - 4| = 5x + 12
use x = -4/3
| -4/3 - 4| = 5( -4/3) + 12
|-16/3 | = -20/3 + 12
|-16/3 | = 16/3
16/3 = 16/3
Thus, it is the Solution.
Learn more about solving equations here:
brainly.com/question/18015090
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a. The inequality 15x+300≤750 represents the situation.
b. It means that the band can spend at most $30 on each uniform without exceeding the budget.
Step-by-step explanation:
Given,
Budget = $750
Competition fee = $300
Uniforms to make = 15
Let,
x be the amount for each uniform.
a. Write an inequality to represent this situation.
Uniforms to make * Cost per uniform + Competition ≤ Budget
15x+300 ≤ 750
The inequality 15x+300≤750 represents the situation.
b. Solve the inequality and describe what it means in the situation.
Dividing both sides by 15
It means that the band can spend at most $30 on each uniform without exceeding the budget.
Keywords: inequality, division
Learn more about inequality at:
#LearnwithBrainly
Answer:
Step-by-step explanation:
