Let Cameron be x years old now.
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<u>Now:</u>
Cameron = x
Uncle =3x
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<u>4 years ago:</u>
Cameron = x - 4
Uncle = 3x - 4
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<u>4 years ago, Uncle is 4 times older:</u>
3x - 4 = 4(x - 4)
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<u>Find x:</u>
3x - 4 = 4(x - 4)
3x - 4 = 4x - 16
4x - 3x = 16 - 4
x = 12
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<u>Find the age:</u>
Cameron = x = 12
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Answer: Cameron is 12 years old now.
We can use x to represent the total vacation budget.
x times .19 = 285
(a percentage is really just a decimal)
x = 285/.19
x = 1500
Final Answer: the total vacation budget is $1500
Remark
It's a right triangle so the Pythagorean Theorem applies. All you have to do is put the right things in the right places of the formula.
Givens
a = x
b = x + 4
c = 20
Formula and Substitution.
a^2 + b^2 = c^2
x^2 + (x + 4)^2 = 20^2
Solution
x^2 + x^2 + 8x + 16 = 20 Collect the like terms on the left.
2x^2 + 8x + 16 = 20 Subtract 20 from both sides.
2x^2 + 8x + 16 - 20 = 0
2x^2 + 8x - 4 = 0 Divide through by 2
x^2 + 4x - 2 = 0
Use the quadratic formula
a = 1
b = 4
c = - 2

From which x = (-4 +/- sqrt(24) ) / 2
x1 = (- 4 +/- sqrt(4*6) ) / 2
x1 = (- 4 +/- 2 sqrt(6) ) / 2
x1 = -2 + sqrt(6)
x2 = -2 - sqrt(6) This is an extraneous root. No line can be minus.
x1 = + 0.4495
x2 = x + 4 = 4.4495
1- not a function; 3 in the domain is repeated
2- a function
3- a function
4- a function
- A function that models the data is given by this quadratic equation, y = -0.4908x² + 5.8845x + 1.3572.
- The number of students that are absent 10 days after the outbreak is equal to 11 students.
<h3>What is a scatter plot?</h3>
A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting points showing any association (correlation) between the data set.
<h3>What is a quadratic function?</h3>
A quadratic function can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph.
In Mathematics, the standard form of a quadratic equation is given by;
ax² + bx + c = 0
By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that the quadratic function is given by:
y = -0.4908x² + 5.8845x + 1.3572
For the number of students that are absent 10 days after the outbreak, we have:
y = -0.4908(10)² + 5.8845(10) + 1.3572
y = -0.4908(100) + 58.845 + 1.3572
y = -49.08 + 58.845 + 1.3572
Number of students, y = 11.12 ≈ 11 students.
Read more on scatterplot here: brainly.com/question/6592115
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