Translate to an inequality. Use the variable x for next year's salary.

Mathematics

1 answer:

enot [183]2 years ago

7 0

x has to be greater or equal to 16,000

x ≥ 16,000

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Trevor is analyzing a circle, y2 + x2 = 100, and a linear function g(x). Will they intersect?

lakkis [162]

Given a circle described by the equation:
$y^2+x^2=100$
and a function g(x) given by the table
$\begin{center}
\begin{tabular}{ |c |c |c }
 x & g(x) \\
 -1 & -22 \\
 0 & -20 \\
1 & -18 
\end{tabular}
\end{center}$

The function g(x) describes a straight line with the equation:
$\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1} \\ \\ \frac{y-(-22)}{x-(-1)} = \frac{-20-(-22)}{0-(-1)} \\ \\ \frac{y+22}{x+1} = \frac{-20+22}{0+1} = \frac{2}{1} \\ \\ y+22=2(x+1)=2x+2 \\ \\ y=2x-20$

To check if the circle and the line intersects, we substitute the equation of the line into the equation of the circle to see if we have a real solution.
i.e.
$y^2+x^2=100 \\ \\ (2x-20)^2+x^2=100 \\ \\ 4x^2-80x+400+x^2=100 \\ \\ 5x^2-80x+300=0 \\ \\ x^2-16x+60=0 \\ \\ (x-6)(x-10)=0 \\ \\ x-6=0 \ or \ x-10=0 \\ \\ x=6 \ or \ x=10$

When x = 6, y = 2(6) - 20 = 12 - 20 = -8 and when x = 10, y = 2(10) - 20 = 20 - 20 = 0

Therefore, the circle and the line intersect at the points (6, -8) and (10, 0).

8 0

2 years ago

Read 2 more answers

Danielle sells beauty supplies and earns a base salary of $450 per week plus a 9% commission on sales. During one particular wee

lora16 [44]

Answer:

হ্যালো অ্যাঞ্জেলা এবং তারপরে আমরা চেকটিতে অর্থ প্রদান করতে সক্ষম হব এবং অন্যটি হ'ল

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2 years ago

Explain how to use the combine place value strategy to find 223 -119.

SashulF [63]

Combine place value strategy is useful if you try to subtract a number with bigger digits from a number with a smaller digit in the same place... such as now, where 3 is smaller than 9 in the ones place.

Then we can combine two place values: 23 and 19 and subtruct those. 23-19 is 4 (you can just count up from 19 to 23), so you know that the two will give the result of 04, and then you can proceed to the left: 2-1=1.

so the final result will 104.

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2 years ago

Matteo is adjusting a satellite because he finds it is not focusing the incoming radio waves perfectly. The shape of his satelli

natka813 [3]

Answer: (1.5, 0)

Step-by-step explanation:

Given : The shape of his satellite can be modeled by $y^2=6x$ where x and y are modeled in inches.